environmental technologies for sonic boom mitigation in

Environmental Technologies for Sonic Boom Mitigation in

Eco-Efficient Supersonic Transport Design

(環境性・経済性を両立した超音速旅客機設計におけるソニックブーム低減の環境技術)

by Hiroshi Yamashita

A dissertation submitted to the Department of System Information Science of Tohoku University

DEPARTMENT OF SYSTEM INFORMATION SCIENCE TOHOKU UNIVERSITY

JAPAN

December 2008

i

Abstract

Three environmental technologies for sonic boom problem have been

developed in this dissertation: First, an elemental technology, applied to the supersonic

biplane MISORA to improve the aerodynamic performance under the off-design

conditions. Second, an estimation technology for the variation of sonic boom

propagation due to atmospheric fluctuations of wind and temperature. Third, the

evaluation technology for the variation of sonic boom impact under the actual

environmental condition.

In recent years, when we design a new aircraft, it is important to reduce the

effects of the aircraft on the environment. A supersonic aircraft design has no exception

in that it needs to achieve performances of higher fuel efficiency, lower emissions in the

atmosphere, and lower noise than the conventional design of supersonic aircraft. That is,

we need to develop an “eco-efficient” supersonic aircraft. Especially, sonic boom

problem is the major issue to make a supersonic aircraft feasible: For one thing, the

sonic boom is strongly associated with these performances; and for another, it could

produce undesirable effects (startling sound) on people, animals, and structures. In fact,

a commercial supersonic flight is currently prohibited over the United States and most

other nations. The environmental technologies for sonic boom proposed in this

dissertation are probably useful to create an eco-efficient supersonic aircraft.

Recently, in forging ahead with the design of the supersonic biplane MISORA,

it is expected to overcome the severe drag penalty of the Busemann biplane due to the

phenomena of choked-flow and flow-hysteresis at off-design conditions. For this issue,

ii

we proposed a practical solution to reduce the drag penalty by using the plain flaps. To

examine the effects of the leading and trailing edge flaps, four different biplanes were

investigated. It was confirmed that the leading-edge flaps can alleviate the drag increase

due to the choked-flow, and reduce the area of flow-hysteresis; while the trailing-edge

flaps can reduce the wave drag near to the speed of sound, and also shift the

drag-divergence Mach number to a higher one. In addition, by the use of both flaps, we

can smoothly achieve the design point from subsonic regime without the severe drag

penalty due to the choked-flow and flow-hysteresis.

Additionally, a sonic boom evaluation method considering atmospheric

fluctuations of wind and temperature was also developed. This method was applied to

the near-field pressure wave for the Sears-Haack body, which was calculated by using

the Computational Fluid Dynamics (CFD) in Euler mode. The sonic boom signature

was calculated by the modified Waveform Parameter Method, considering each

fluctuation, respectively. Our investigation showed the various influences of the

atmospheric fluctuations acting on sonic boom intensity, propagation path and reaching

points on the ground. And then, it was found that there was a high possibility that sonic

boom intensity would decrease due to the fluctuations of wind and temperature,

respectively.

Finally, the effect of real atmospheric gradients on sonic boom intensity was

investigated, since it is well known that real atmosphere has significant influence on

sonic boom propagation. The global distribution of sonic boom intensity is examined,

especially, focusing on the variation in boom intensity due to the seasons and regions.

Form the results, it became clear that that the boom intensity varies according to the

seasons and regions of the world. Also, under the real environmental conditions, the

mountainous regions had a relatively small value on boom intensity. By using the

present results, we will be able to improve the scientific understanding of the influences

of a real atmosphere on sonic boom phenomenon.

iii

Acknowledgments

The author would like to thank Prof. Shigeru Obayashi for his helpful advices

and guidance. He gave me a lot of chances from various aspects, and under his support,

I could enjoy and concentrate on my research for the past three years. I sincerely thank

Prof. Keisuke Asai for his kind support and his helpful advices; He gave me many

opportunities to perform the experiments. I also would like to thank Prof. Satoru

Yamamoto for his helpful suggestions about this research and dissertation. I am also

grateful to Prof. Kisa Matsushima for her helpful suggestions, invaluable teachings, and

discussions about this research and dissertation. I would like to thank Prof. Kazuhiro

Nakahashi and Prof. Shinkyu Jeoung for his helpful advices about my researches.

The author wishes to thank Dr. Kazuhiro Kusunose of Ministry of Defense for

his invaluable teachings and comments for this research. I would like to thank Prof.

Akihiro Sasoh, Prof. Hiromitsu Kawazoe, Dr. Hiroki Nagai and Dr. Takashi Matsuno

for their invaluable teachings for my researches on supersonic biplane project.

I would like to thank Dr. Daisuke Sasaki of Tohoku University and Dr.

Kazuhisa Chiba of Mitsubishi Aircraft Corporation. I believe that their precepts and

advices formed a preliminary part of my research skills.

I would like to thank you Dr. Kenji Yoshida, Dr. Yoshikazu Makino of Japan

Aerospace Extrapolation Agency (JAXA) for their suggestions and support on my sonic

boom researches and Dr. Masahiro Kanazaki of Tokyo Metropolitan University for his

iv

teachings and comments for this research.

Numerical part of this research was performed using the supercomputer

system at the Advanced Fluid Information Research Center of Institute of Fluid Science,

Tohoku University. I would like to thank all the staff for their support. Without their

support, my research would not make and progress.

I am also grateful all the colleagues, senior members, post doctors and

secretaries of Obayashi-Jeong Laboratory and Nakahashi-Sasaki Laboratory. In addition,

I also thank senior members of Asai Laboratory.

The author also wishes to gratefully acknowledge my colleagues, especially

Ms. J. N. Lim and Mr. F. K. Nakabayashi, in publishing this thesis.

This research was supported by a grant from the Research Fellowships of the

Japan Society for the Promotion of Science for young Scientists. Also, early part of my

doctoral research was supported by the International Center of Excellence (COE) of

Flow Dynamics in Institute of Fluid Science, Tohoku University. I sincerely thank the

people related to the COE program.

Finally, I would like to thank my family for their support throughout the long

years.

Hiroshi Yamashita

v

Table of Contents Abstract i

Acknowledgments iii

Table of Contents v

List of Figures viii

List of Tables xvi

Chapter 1 Introduction 1

1.1 Overview of Sonic Boom Problem 1

1.1.1 Development of Technology for Sonic Boom Reduction 3

1.1.2 Development of Technology for Evaluation of Sonic Boom Influence

6

1.2 Sonic Boom and Environmental Problem 8

1.3 Aircraft Design for Environment 9

1.4 Objective and Outline of Dissertation 12

References 15

Chapter 2 Reduction of Drag Penalty by means of Plain Flaps in the Boomless

Busemann Biplane 29

2.1 Introduction 30

vi

2.2 Major Issues 33

2.2.1 Off-design Performance of the Busemann Biplane 33

2.2.2 Physics Considerations 38

2.3 Numerical Models and Methods 39

2.3.1 Definition of the Four Biplanes 41

2.3.2 CFD Calculation of the Biplanes 42

2.4 Results and Discussion 44

2.4.1 Diamond Airfoil Separated into Two Elements 44

2.4.2 Busemann Biplane with Deflected Leading-Edge Flaps 46

2.4.3 Busemann Biplane with Deflected Trailing-Edge Flaps 50

2.4.4 HLD-1 55

2.5 Conclusion 59

Appendices 60

References 62

Chapter 3 Variability of Sonic Boom Intensity and Propagation Path Due to

Atmospheric Fluctuations of Wind and Temperature 67

3.1 Introduction 69


3.2.1 CFD Calculation of the Near-Field 71

3.2.2 Generation of the Atmospheric Fluctuation Fields 73

3.2.3 Sonic Boom Calculation 76


3.3.1 Determination of the Near-field Pressure Wave for Sonic Boom

Calculation 78

3.3.2 Variability of Sonic Boom Intensity 80

3.3.3 Variability of Propagation Path and Reaching Point on the Ground 92

3.4 Conclusion 98

vii

References 99

Chapter 4 Effect of Atmospheric Gradients on Sonic Boom Intensity by the Four

Seasons 103

4.1 Introduction 104


4.2.1 Processing of Observational Data of Radiosonde 106

4.2.2 Sonic Boom Calculation 110

4.2.3 Mapping of Global Distribution of Sonic Boom Intensity 112


4.3.1 Variation of Sonic Boom Waveform 112

4.3.2 Seasonal Change of Sonic Boom Intensity 115

4.3.3 Effect of Atmospheric Gradients on Sonic Boom Intensity 120

4.3.4 Effect of Altitude on Sonic Boom Intensity 126

4.4 Conclusion 127

References 129

Chapter 5 Conclusions 131

viii

List of Figures

Fig. 1.1 Sketch of the sonic boom pressure field. 2

Fig. 1.2 Wave front of sonic boom and the ground pressure patterns. 2

Fig. 1.3 Several Projects to develop the sonic boom reduction technology: a)

SSBD (Shaped Sonic Boom Demonstration); b) Quiet SpikeTM; c)

MISORA (MItigated SOnic-boom Research Airplane); and d) Oblique

Flying Wing.

5

Fig. 1.4 Indoor sonic boom simulators to investigate the human response to sonic

booms : a) NASA Langley; b) Lockheed-Martin; c) Gulfstream

Aerospace Corporation; and d) JAXA. 7

Fig. 1.5 Percentage of emission of global CO2 in the atmosphere: The air

transport is one of the important factors which contribute to the global

CO2 emissions. 9

Fig. 1.6 Transitional changes of the airline fuel consumption per one hundred

passenger-km, and also the emission of CO2 per passenger-km in the

atmosphere. 11

Fig. 1.7 ICAO noise certification standards. The new Chapter 4 standard is

officially applied to the all new aircraft created as from 2006: The figure

shows the cumulative margin relative to the Chapter 3. 11

Fig. 1.8 The historical progress in noise reduction: Cases with a) the jet-powered

aircraft and b) the propeller-driven regional aircraft. 12

Fig. 2.1 Conceptual drawing of a boomless supersonic biplane. Cruise Mach

ix

number is assumed as M∞ = 1.7 for supersonic level flight.1.1

Overview of Sonic Boom Problem 32

Fig. 2.2 Configurations of both the baseline diamond airfoil (t/c = 0.1) and the

Busemann biplane (t/c = 0.05). The wedge angles of the diamond airfoil

and the Busemann biplane are 2ε = 11.4 deg. and ε = 5.7 deg.,

respectively. 34

Fig. 2.3 Comparison of the drag characteristics: The solid line represents the

Busemann biplane. In this case, when accelerating, Cd follows curve A.

When decelerating, Cd follows curve B. The dashed line shows the

baseline diamond airfoil. Also, the diamond symbol is the design point at

Mach number M∞ = 1.7. 35

Fig. 2.4 Cp-contours of the Busemann biplane with zero-lift in decelerating

condition (1.5 ≤ M∞ ≤ 1.7). 36

Fig. 2.5 Cp-contours of the Busemann biplane with zero-lift in accelerating

condition (1.7 ≤ M∞ ≤ 2.18). 37

Fig. 2.6 Start/Un-start characteristics of a supersonic inlet diffuser: The solid line

(curve A) shows the Kantrowitz limit; the dashed line (curve B) shows

the isentropic contraction limit. Here, the ratio of throat-to-inlet-area of

the Busemann biplane is At/Ai = 0.8, as shown by the dotted line. The

diamond symbol represents the design point of the Busemann biplane at

Mach number 1.7. 39

Fig. 2.7 Comparison of biplane configurations utilized in this research: a)

Diamond airfoil separated into two elements; b) Busemann biplane with

deflected leading-edge flaps; c) Busemann biplane with deflected

trailing-edge flaps; d) HLD-1. 42

Fig. 2.8 Structured grid of the HLD-1 used for CFD (UPACS-code) analyses. 43

Fig. 2.9 Comparison of drag characteristics: The solid line represents the

diamond airfoil separated into two elements; the dotted line shows the

x

Busemann biplane. In the case of the Busemann biplane, when

accelerating, Cd follows curve A. When decelerating, Cd follows curve B.

Also, the dashed line shows the baseline diamond airfoil. The diamond

symbol is the design point at Mach number M∞ = 1.7. 45

Fig. 2.10 Comparison of the Cp-contours with zero-lift at Mach number M∞ = 1.5:

a) diamond airfoil separated into two elements; b) Busemann biplane. 45


Busemann biplane with deflected leading-edge flaps; the dotted line

shows the Busemann biplane. In both cases, when accelerating, Cd

follows curves A and C. When decelerating, Cd follows curves B and D.



Fig. 2.12 Cp-contours of the Busemann biplane with deflected leading-edge flaps

with zero-lift in decelerating condition (1.3 ≤ M∞ ≤ 1.7). 48


with zero-lift in accelerating condition (1.3 ≤ M∞ ≤ 1.61). 49


Busemann biplane with deflected trailing-edge flaps; the dotted line

shows the Busemann biplane. In both cases, when accelerating, Cd

follows curves A and C. When decelerating, Cd follows curves B and D.



Fig. 2.15 Cp-contours of the Busemann biplane with deflected trailing-edge flaps

with zero-lift in decelerating condition (1.5 ≤ M∞ ≤1.7). 52


with zero-lift in accelerating condition (1.7 ≤ M∞ ≤ 2.18). 53

Fig. 2.17 Comparison of the Mach number distributions in subsonic flow

conditions: The baseline Busemann biplane is shown in the left row and

xi

the Busemann biplane with deflected trailing-edge flaps is shown in the

right row. Mach contours in those figures are represented only for

supersonic areas. Free-stream Mach numbers are: a) M∞ = 0.66; b) M∞ =

0.82; and c) M∞ = 0.9. 54

Fig.2.18 Comparison of the drag characteristics: The solid line represents the

HLD-1; the dotted line shows the Busemann biplane. In both cases,

when accelerating, Cd follows curves A and C. When decelerating, Cd

follows curves B and D. Also, the dashed line shows the baseline

diamond airfoil. The diamond symbol is the design point at Mach

number M∞ = 1.7. 56

Fig. 2.19 Cp-contours of the HLD-1 with zero-lift in decelerating condition (1.3 ≤

M∞ ≤ 1.7). 57

Fig. 2.20 Cp-contours of the HLD-1 with zero-lift in accelerating condition (1.3 ≤

M∞ ≤ 1.6). 58

Appendix A:Cp-contours of the diamond airfoil separated into two elements with

zero-lift condition (α = 0 deg., 0.9 ≤ M∞ ≤ 1.7). 60

Appendix B:Cp-contours of the baseline diamond airfoil with zero-lift condition

(α = 0 deg., 0.9 ≤ M∞ ≤ 1.7). 61

Fig. 3.1 Logical flow chart of sonic boom calculation program. 71

Fig. 3.2 Structured grid of the Sears-Haack body in a symmetry plane, used for

CFD (UPACS-code) analysis. The grid is aligned with the shock waves

generated at Mach number M∞ = 1.7. 72

Fig. 3.3 Vrms values of 100 different fields calculated with wind fluctuation. 75

Fig. 3.4 Trms values of 100 different fields calculated with temperature

fluctuation. 75

Fig. 3.5 Sketch of the coordinate system for the present model. The solid line

shows a ray path of sonic boom through a wind fluctuation field,

propagating from the flight path to the ground. 77

xii

Fig. 3.6 Trilinear interpolation of random atmospheric fluctuations of wind and

temperature for the ray path calculation. 78

Fig. 3.7 Comparison of near-field pressure signatures propagating from the

Sears-Haack body at h/l = 1.0 − 5.0. 79

Fig. 3.8 Comparison of sonic boom signatures on the ground calculated from

five different near-field pressure waves without atmospheric fluctuations

of wind and temperature: flight Mach number M∞ = 1.7, flight altitude H

= 60,000 ft, model reference length ML = 1.0 and body reference length

AL = 202 ft. 80

Fig. 3.9 Calculated sonic boom signatures for all cases: a) no fluctuation case; b)

wind fluctuation cases including the 100 different signatures; and c)

temperature fluctuation cases including the 100 different signatures. 84

Fig. 3.10 Correlation between initial and tail overpressures for both fluctuation

cases: a) wind fluctuation; and b) temperature fluctuation. 85

Fig. 3.11 Distribution of initial and tail overpressures for the 100 cases calculated

with wind fluctuation. The bin size is 0.25, respectively: (a) initial

overpressure; (b) tail overpressure. 86

Fig. 3.12 Distribution of initial and tail overpressures for the 100 cases calculated

with temperature fluctuation. The bin size is 0.25, respectively: (a) initial

overpressure; (b) tail overpressure. 87

Fig. 3.13 Cumulative probability distributions for the overpressure: a)

experimental data for the XB-70 aircraft, as obtained in June 1966 (Ref.

11); b) simulation data from 100 cases of initial overpressures calculated

with wind fluctuation; and c) simulation data from 100 cases of initial

overpressures calculated with temperature fluctuation. 89

Fig. 3.14 Variation of the ray tube area relative to the altitude for the wind

fluctuation cases: a) increased and b) decreased initial overpressure of

sonic boom, as compared to the no fluctuation case. 90

xiii

Fig. 3.15 Variation of the ray tube area relative to the altitude for the temperature

fluctuation cases: a) increased and b) decreased initial overpressure of

sonic boom, as compared to the no fluctuation case. 91

Fig. 3.16 Comparison of propagation paths of sonic boom from flight path to the

ground: a) wind fluctuation case; and b) temperature fluctuation case.

Both figures include the following three cases: no fluctuation case,

northmost path and southmost path on ray tracing among all cases

calculated with atmospheric fluctuations, respectively (SST flies in the

north-south direction). 94

Fig. 3.17 Distribution of sonic boom reaching points on the ground for all 100

cases: a) wind fluctuation case; and b) temperature fluctuation case.

Flight is in the north-south direction, and ground track (line x = 0) lies

just under the flight path at 60,000 ft. 95

Fig. 3.18 Distribution of sonic boom reaching points on the ground for the wind

fluctuation cases, including the no fluctuation case. These figures

suggest there is no considerable correlation between the reaching point

on the ground and the initial overpressure of sonic boom: a) increased

and b) decreased boom intensity as compared to the no fluctuation case.

96

Fig. 3.19 Distribution of sonic boom reaching points on the ground for the

temperature fluctuation cases, including the no fluctuation case. These

figures suggest there is no considerable correlation between the reaching

point on the ground and the initial overpressure of sonic boom: a)

increased and b) decreased boom intensity as compared to the no

fluctuation case. 97

Fig. 4.1 Logical flow chart of the creation of a distribution map of sonic boom

intensity. 106

Fig. 4.2 The 491 observation points (closed circles) of the radiosonde in the

xiv

world used for the sonic boom calculation in the case of MAM: The

diamond symbols indicate the locations of the four observation points

mainly discussed in the present study. The detailed information of these

points was given in Table 1. 108

Fig. 4.3 Variation of the temperature gradients of Singapore, Madrid, Tasiilaq,

and Yushu in 2007-2008, as compared to that of the standard atmosphere

(as indicated by thin solid line). These temperature gradients were

calculated from the observational data of radiosonde: Cases with a) JJA;

and b) DJF. 109

Fig. 4.4 Near-field pressure signature for the Sears-Haack body at h/l = 5.0,

which was obtained by the use of the CFD calculation in Euler mode. 111

Fig. 4.5 Comparison of the sonic boom signatures on the ground calculated with

the five atmospheric gradients given in Fig.3, respectively: Cases with a)

JJA; and b) DJF. Both figures include the results of Singapore, Madrid,

Tasiilaq, and Yushu, and the standard atmosphere. The initial conditions

were set as flight Mach number M∞ = 1.7, flight altitude H = 60,000 ft,

model reference length ML = 1.0 and body reference length AL = 202 ft.

114

Fig. 4.6 Distribution maps of variation in sonic boom intensity in the world for

four seasons in 2007-2008 north of 60°S: a) MAM; b) JJA; c) SON; and

d) DJF. In all figures, the contour interval is 0.025, and also, the contours

represent the difference in sonic boom intensity between the value of

each point and that of the standard atmosphere. Therefore, the value of

zero shows the same result calculated with the standard atmosphere. 118

Fig. 4.7 Comparisons of a) ground temperature and b) sonic boom intensity on

the ground in the four observation points for four seasons in 2007-2008,

which also includes the results of the standard atmosphere. 119

Fig. 4.8 Comparison of vertical profiles in Tasiilaq for four seasons in

xv

2007-2008: a) (ρ∞a∞)1/2; b) A1/2; c) (ρ∞a∞/A)1/2; and d) ΔP. 123

Fig. 4.9 Comparison of vertical profiles in Singapore for four seasons in

2007-2008: a) (ρ∞a∞)1/2; b) A1/2; c) (ρ∞a∞/A)1/2; and d) ΔP. 125

Fig. 4.10 Comparison of sonic boom intensity with altitude for the cases of

Singapore, Madrid, Tasiilaq, Yushu, and the standard atmosphere: Cases

with a) JJA; and b) DJF. 127

xvi

List of Tables

Table. 2.1 Comparison between the CFD results and the analytical results of

aerodynamic performance for the four configurations. 40

Table. 2.2 Number of grid points for the four biplanes. 43

Table. 4.1 Information of the observation points discussed in this study. 108

Table. 4.2 Comparison of sonic boom intensity and the difference in boom

intensity on the ground between the value of each observation point

and the standard atmosphere. 114

1

Chapter 1. Introduction 1.1 Overview of Sonic Boom Problem

An aircraft flying in supersonic speed generates strong shock waves and

expansion waves to the ground; which is called a “sonic boom”1-4. Figure 1.1 shows the

sonic boom pressure field.2 As the waves propagate from the flight path to the ground,

in general, a waveform distortion occurs and the waves are consolidated into an N-wave

due to the non-linear effect. An N-wave has a first abrupt pressure rise at the front,

linear decrease to below the ambient pressure and a second abrupt pressure rise, as

shown in Fig. 1.1. When the waves sweep over the people, they would hear an

explosive sound, without precursor. They could also produce undesirable effects on not

only people, but also animals, and structures.2,5

Figure 1.2 shows the wave front of sonic boom and the ground pressure

patterns.6 As shown in Fig. 1.2, sonic boom spreads widely on the ground.7-13 For

example, sonic boom generated by the British-French Concorde (1969 − 2003)14

propagated about 80-100 km in lateral direction from the flight track. The sonic boom

sound is not a comfortable one for the people, therefore, a commercial supersonic flight

is currently prohibited over the United States and most other nations15 due to startling

(annoyance) sound caused by the sonic boom. In fact, the Concorde confines its

supersonic flight only to the oversea routes. Even now, the noise boom problem caused

by the sonic boom is not completely solved and this problem is the major issue to create

a new supersonic transport.16-21

2

At present, many considerable researches have been conducted22-30 in order to

overcome the sonic boom problem; they are classified into two major classes. One is

concerned with the development of technology for sonic boom reduction. The other is

concerned with the development of technology for the evaluation of sonic boom

influence.

Fig. 1.1 Sketch of the sonic boom pressure field.2

Fig. 1.2 Wave front of sonic boom and the ground pressure patterns.7

3

1.1.1 Development of Technology for Sonic Boom Reduction

As for the development of sonic boom reduction technology, Fig. 1.3 shows

several projects addressed on this matter. For example, the Defense Advanced Research

Projects Agency (DARPA)31 has initiated the Quiet Supersonic Platform (QSP) program

in 2000 to investigate the feasibility of sonic boom suppression technology no more

than 0.3 lb/ft2. In addition, by 2001, DARPA has started the Shaped Sonic Boom

Demonstration (SSBD) program.32,33 In this program, a F-5 was modified as the F-5

SSBD,34 particularly changing its nose configuration into a blunted nose-shape to create

a low boom signature on the ground.35 In 2003, the program successfully demonstrated

in flight for the first time that sonic boom can be reduced by aircraft shaping

techniques.36-39 From the pressure measurements in the air and on the ground, it

confirmed that the modified F-5 SSBD aircraft has produced a “flat-top” signature, as

expected.40,41 This accomplishment has proven the effect of the sonic boom reduction

technology by the modification of aircraft configuration.

The Gulfstream Aerospace Corporation42 has proposed an innovative concept

by use of an extendable nose spike, i.e., the Gulfstream Quiet SpikeTM,43-47 as shown in

Fig. 1.3 (b). The Quiet SpikeTM is extendable and can break up the strong front shock

wave into several weak shock waves, which propagate parallel to each other without

coalescing during its propagation to the ground.48-52 Therefore, the spike can increase a

rise time of sonic boom signature, leading to the alleviation of sound loudness on the

ground. The flight tests were conducted between 2006 and 2007, and the obtained

results represented that the concept is the feasible technology for sonic boom

suppression.53

In our research group, we have addressed the biplane concept54,55 proposed by

Kusunose, in 2004. The biplane concept is based on the effect of Busemann biplane,56

which can enable a significant reduction of shock waves, i.e., the sonic boom signature

on the ground.57 The fundamental researches have been performed by use of both

4

Computational Fluid Dynamics (CFD)58-69 and Experimental Fluid Dynamics (EFD),70

respectively.

As for the CFD researches, for example, the airfoil and wing configuration of

the supersonic biplane were investigated.71-73 Particularly, the aerodynamic performance

of the original Busemann biplane and the Busemann biplane with leading- and

trailing-edge flaps under low speed condition were examined for takeoff and landing.

An ideal supersonic biplane configuration with lift has been designed by using the

Inverse design method.74-76 Here, the designed Mach number is set as M∞ = 1.7 for ideal

supersonic steady flight. In addition, the characteristics of Busemann biplane at

off-design conditions were examined in detail, in order to fly through subsonic,

transonic, and supersonic regimes in real flight. From there researches, the fundamental

design knowledge was obtained to create a silent supersonic biplane.

Regarding the EFD researches, on the other hand, the wind tunnel tests have

been performed to investigate the aerodynamic performance in subsonic (about M∞ =

0.05), transonic (0.3 < M∞ < 1.4), and supersonic flow conditions (1.5 < M∞ < 1.9,

including the designed Mach number of M∞ = 1.7), respectively.77 Specially, the shock

wave interaction between the two biplane elements were examined in detail, by using

the Schlieren visualization method, static pressure measurement, and Pressure and

Temperature Sensitive Paint (PSP and TSP)78,79. From the results, the flow-field feature

was found out; therefore, the design knowledge obtained by the CFD calculations was

demonstrated by these EFD researches.

Now, our research group proposes a silent supersonic biplane; MISORA

(MItigated SOnic-boom Research Airplane, as shown in Fig. 1.3 (c)),80 which is likely

to fly with low boom and low drag (i.e., fuel economy) in supersonic speed. That is, the

biplane concept is thought to be effective to reduce the environmental impact of sonic

boom.

Other several projects are involved with the design of low boom configurations,

5

for example, the Oblique Flying Wing project,81-89 as shown in Fig. 1.3 (d). The flight

tests are scheduled to be performed in 2011 to demonstrate its ability for steady flight in

supersonic condition.90 Even now, as mentioned above, many considerable technologies

have been proceeded to achieve sonic boom reduction.

Fig. 1.3 Projects aiming to develop sonic boom reduction technology: a) SSBD

(Shaped Sonic Boom Demonstration);32 b) Quiet SpikeTM;43 c) MISORA

(MItigated SOnic-boom Research Airplane);80 and d) Oblique Flying Wing.90

6

1.1.2 Development of Technology for Evaluation of Sonic Boom Influence

Many technologies have been developed to evaluate the sonic boom influence

until now. The goal of these researches is to provide a technical basis to meet the criteria

of sonic boom for during overland supersonic flight. In other words, these researches

are realism studies and assess the real impacts of sonic boom under the real

environmental condition, which includes the influence on people, structures, and so on.

Initially, the prediction methods on sonic boom propagation, signature, and

intensity on the ground, were discussed and developed. Around 1970, when people

started to develop a Supersonic transport (SST), significant researches were performed

to clear up the sonic boom phenomenon. From the results, fundamental theories were

constructed to predict sonic boom generation and propagation,91-100 and considerable

experiments were performed to demonstrate the theories of sonic boom propagation.

Recently, we focused on the effects of atmospheric turbulence on sonic boom

propagation, since the sonic boom is strongly affected by the atmospheric

condition.101,102 As the representative example, Blanc-Benon, P., et.al examined the

variations in sonic boom intensity and rise time, due to atmospheric turbulence, by

numerical simulation and experiments.101 Also, Sasoh et.al investigates the effects of

turbulence flow on weak shock wave, to clarify the definitive mechanisms of variation

in signature and intensity.103

On the other hand, realistic researches have been performed in order to

investigate the human response to sonic boom sound and its impact on buildings; it is

called as the “Indoor boom”.104,105 For example, subjective tests using the indoor sonic

boom simulators and/or in the field were performed, as represented in Fig. 1.4, by

NASA Langley,106 Lockheed-Martin,107 and Gulfstream Aerospace Corporation42: these

project are the PARTNER project.108 Also, JAXA (Japan Aerospace Exploration

Agency)109 has collaborated on the research activities with NASA for the simulator

7

assessment of indoor boom since 2008.

Now, we have many progressed technologies, enough to create a small

supersonic aircraft, i.e., the supersonic business jet. It is desirable to turn these

technologies and knowledge into a development of Supersonic transport (SST) for

everyone (as a public transportation). This will pave the way to further improvement in

efficient supersonic transport design.

Fig. 1.4 Indoor sonic boom simulators to investigate the human response to sonic

booms : a) NASA Langley;106 b) Lockheed-Martin;107 c) Gulfstream Aerospace

Corporation;42 and d) JAXA.109

8

1.2 Sonic Boom and Environmental Problem

There are many environmental problems in the world, such as noise issue,

energy problems, and global warming. In General, the technologies, which are helpful

to overcome these problems and mitigate the influences on us, are called “The

environmental technology”.110

In the aviation industry, an aircraft development is strongly associated with the

environmental problems. Particularly, in the development of a new supersonic aircraft,

sonic boom is one of the biggest environmental problems for the following three

reasons: First, sonic boom is a loud sound, leading to disamenity for the people on the

ground and damage to buildings.104,105 Therefore, sonic boom is a noise issue which can

bother us.108 Second, sonic boom is generated by the strong shock waves from the

supersonic aircraft. These shock waves can increase the wave drag for the aircraft,

which results in considerable fuel consumptions during the flight. That is, the sonic

boom problem is closely associated with the energy issue. Third, fuel-inefficient flight

with high wave drags due to sonic boom can increase the emissions of carbon dioxide

(CO2), oxides of nitrogen (NOx), and other greenhouse gases. Figure 1.5 shows the

percentage of emission of global CO2 in the atmosphere. From Fig. 1.5, we can confirm

that the air transport is one of the important factors which contribute to the global CO2

emissions.111,112 In fact, the jet aircraft produce about 2-3 % of worldwide NOx

emissions and 2.5 % of worldwide CO2 emissions by burnig the fossil fuel, which

becomes a contributor to the global warming. As mentioned above, sonic boom problem

gets directly involved in the environmental issues.112

In this dissertation, an elemental technology for low boom design, and also an

evaluation technology for sonic boom influence are called “The environmental

technology for sonic boom”, which can be helpful for sonic boom reduction in

supersonic transport design.

9

Fig. 1.5 Percentage of emission of global CO2 in the atmosphere: The air transport is one of the important factors which contribute to the global CO2

emissions.112

1.3 Aircraft Design for Environment

As described in section 1.2, the development of a new aircraft is strongly

related to the environmental issues. Naturally, it is reasonable to suppose that the noise,

fuel efficient, and emission are one of the major drivers for current and future aircraft

designs.111,112 In other words, for the aviation industry, ecological and economic

development, i.e., “eco-efficient” development will continue to be the main topic for

decades. The actual examples for the matters are as follows:

Figure 1.6 shows the transitional changes of the airline fuel consumption and

the emission of CO2 in the atmosphere. We can see that the airlines have improved their

fuel efficiency and CO2 emissions, continuously. Also, the airlines have determined to

improve at least a further 25% by 2020, compared to that of 2005. Therefore, the fleet

renewal is aggressively carried out now in many airlines; in fact, the eco-efficient

aircrafts like Boeing 787 have won the order in the selection of a new aircraft.

10

In recent years, the noise reduction issue has emerged in the world of aviation,

which had been placed less significance on the aircraft development. Figure 1.7 shows

the ICAO noise certification standard (Chapter 4),111,113 which has been officially

effective since 2006. In the Chapter 4, a cumulative 10 decibels (dB) is more stringent

than the standard of the Chapter 3. Now, this Chapter 4 is applied to all new aircrafts

created as from 2006.

In accordance with this ICAO noise certification standard, the noise reduction

technology has been developed, specially, focusing on the components of jet, fan, and

airframe noise, which are the most important contributors to the aircraft noise. Figure

1.8 shows the historical progress in noise reduction; cases with (a) the jet-powered

aircraft and (b) the propeller-driven regional aircraft, respectively. From Fig. 1.8, the

total aircraft noise reduction has been addressed for the past 40 years; thereby, the

aircraft noise certainly decreases for year to year.

The most important part of these descriptions is that the several requirements in

designing the aircraft, which are based on the environmental concern, will become all

the more severe in the future. That is, the certification standards will not be alleviated in

the future, compared to the present standards.

For example, from Figs. 1.7, and 1.8, it can be seem that the ICAO noise

standard certification will become more strict. Therefore, when we design a new aircraft,

we have to take into account the predicted noise certification standard after ten or

twenty years. This is because airlines, which buys new aircrafts, would continue to use

them and perform service for long time under the changing standard. In other words, a

new aircraft will become competitive by considering and adapting its performance to

the regulations in the future. For more growth in the world aviation, we need to continue

the efforts to further mitigate the impact of an aircraft on the environment.

The supersonic aircraft design has no exception in that it needs to achieve the

performances of higher fuel efficiency, lower emissions in the atmosphere, and lower

11

noise (i.e., lower sonic boom) than the conventional design of supersonic aircraft: We

need to develop an “eco-efficient” supersonic aircraft, which can meet the

environmental criteria, by our innovations of technology.

Fig. 1.6 Transitional changes of the airline fuel consumption per one hundred

passenger-km, and also the emission of CO2 per passenger-km in the atmosphere.112

Fig. 1.7 ICAO noise certification standards. The new Chapter 4 standard is

officially applied to the all new aircraft created as from 2006: The figure shows the cumulative margin relative to the Chapter 3.111

12

Fig. 1.8 The historical progress in noise reduction: Cases with a) the jet-powered aircraft and b) the propeller-driven regional aircraft.111

1.4 Objective and Outline of Dissertation

As discussed in previous sections, the creation of an eco-efficient supersonic

aircraft, which can keep the impact on the environment minimum, is a technological

challenge. For the challenge, the development of a breakthrough technology for low

boom design needs to alleviate sonic boom intensity as much as possible. In addition, it

is desirable to develop an evaluation technology for sonic boom, in order to improve the

scientific understanding of the impact on the environment, including people, animals,

and structures. Also, this means that the accurate evaluation method needs to develop

the right reduction method of sonic boom impact.

In this dissertation, three environmental technologies for the sonic boom

problem are investigated. First, the elemental technology applied to the supersonic

biplane MISORA is developed, which can avoid the choked-flow and flow-hysteresis

phenomena of Busemann biplane. By use of the plain flaps, the aerodynamic

13

performances under the off-design conditions are improved. This proposed technology

is a highly possible solution, since not only it will overcome the problems, but also has

application of high-lift device used at takeoff and landing conditions. Second, the

evaluation technology for sonic boom impact on the environment is developed. This

technology can capture the actual phenomena, qualitatively, which results in variability

of sonic boom intensity due to atmospheric fluctuations of wind and temperature. Last,

the variation in sonic boom intensity under the real environmental condition is

investigated. The estimation method is developed as one of the evaluation technologies.

On top of that, the possibility of sonic boom reduction by utilizing the effect of real

environmental conditions is described. The outline of this dissertation is as follows:

Chapter 1 introduces the background and objectives of the present research.

In chapter 2, we present the practical solution to reduce the severe drag penalty

of Busemann biplane, under the off-design conditions, by the use of plain flaps. To

examine the effects of the leading and trailing edge flaps, four different biplanes are

investigated. Then, mechanisms of the choked-flow and the flow-hysteresis phenomena

of the four biplanes are described in detail. This research discusses the elemental

technology for low boom design of the supersonic biplane MISORA.

In chapter 3, the sonic boom evaluation method considering the atmospheric

fluctuations of wind and temperature is presented. The method is applied to the

computational near-field signature for the Sears-Haack body. We investigate the

non-deterministic effect of each fluctuation on sonic boom propagation, separately, by

using respective one hundred different fluctuation fields. Particularly, we focus on the

variability of sonic boom intensity, propagation path and sonic boom reaching point on

the ground, as compared to the no fluctuation condition.

In chapter 4, the effect of real atmospheric gradients on sonic boom intensity is

investigated, since the sonic boom propagation is affected by the real meteorological

conditions. The global distribution of sonic boom intensity is examined for four seasons.

14

We especially focus on a tendency of seasonal variations of sonic boom intensity and of

the areal difference of boom intensity, as compared to the standard atmospheric

condition. Also, the effect of an altitude on sonic boom mitigation is discussed under the

real environmental conditions.

Chapter 5 concludes the dissertation.

15

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111(1), Pt. 2, Jan. 2002, pp. 487−498.

102Lipkens, B., and Blackstock, D. T., “Model Experiment to Study Sonic Boom

Propagation through Turbulence. Part І: General Results,” J. Acoust. Soc. Am., Vol.

103(1), Jan. 1998, pp. 148−158.

103Kim, J. H., Matsuda, A., and Sasoh, A., “Effects of Turbulent Flow sheet on Weak

Shock Wave,” Proceedings of the Fifth International Conference on Flow Dynamics,

Sendai, Japan, 2008, p. OS5-5.

104Shepherd, K. P., and Sullivan, B. M., “A Loudness Calculation Procedure Applied

to Shaped Sonic Booms,” NASA TP-3134, Nov. 1991.

105Leatherwood, J. D., and Sullivan, B. M., “Laboratory Studies of Effects of Boom

Shaping on Subjective Loudness and Acceptability,” NASA TP-3269, 1992.

106“NASA Langley Research Center,” NASA,

http://www.nasa.gov/centers/langley/home/index.html (cited December 10, 2008).

107“Lockheed Martin,” Lockheed Martin Corporation,

http://www.lockheedmartin.com/ (cited December 10, 2008).

108“PARTNER Project,” MIT,

http://web.mit.edu/aeroastro/partner/index.html (cited December 10, 2008).

109“Japan Aerospace Exploration Agency,” JAXA,

27

http://www.jaxa.jp/index_e.html (cited December 10, 2008).

110“Team Minus 6%,” Team-6%committee & Ministry of the Environment,

http://www.team-6.jp/ (cited December 10, 2008).

111IATA, Environmental Review 2004, International Air Transport Association,

2004.

112IATA, Building a greener future 3rd edition, International Air Transport

Association, Oct. 2008.

113“Aircraft Noise,” International Civil Aviation Organization,

http://www.icao.int/icao/en/env/noise.htm (cited December 10, 2008).

29

Chapter 2. Reduction of Drag Penalty by means of Plain Flaps in the Boomless Busemann Biplane Nomenclature

Ai = inlet area

At = throat area

c = chord

Cd = wave drag coefficient

Cp = pressure coefficient

M∞ = free-stream Mach number

t = airfoil thickness

α = angle of attack

β = shock-wave angle

γ = ratio of specific heats

ε = wedge angle of the Busemann biplane

30

2.1 Introduction

In 2003, the first successful supersonic transport (SST), the Concorde1 (1969 −

2003), ceased its operations and flight services. This means that, without a complete

development of the next-generation SST,2,3 commercial airplanes today can only fly at

transonic speeds. It is important to note, however, that the Concorde had already flown

for over 30 years, although our aviation history comprises only about 100 years. These

30 years of flight are a truly admirable achievement and have given us great knowledge,

technologies and significant challenges.

As for the development of the next supersonic aircraft, there is an important

problem that needs to be overcome; the sonic boom problem.4-7 Sonic boom is a

phenomenon caused by the shock waves propagating from an airplane at supersonic

speed, which leads to a very loud sound resembling a thunder on the ground. Therefore,

commercial airplanes are prohibited to fly over land at supersonic speed due to the

loudness of sonic boom.8

For this issue, considerable research has been conducted to test different sonic

boom reduction technologies. In 2003, for example, the F-5 Shaped Sonic Boom

Demonstration (SSBD) program was performed to assess the shaped boom signature.9-12

Also, from 2006 to 2007, the Quiet Spike Flight Test program was conducted by

Gulfstream Aerospace Corporation in order to demonstrate the feasibility of the

extendable nose spike (i.e., the Quiet Spike) used for sonic boom suppression.13-17 Both

programs successfully demonstrated their concept of sonic boom reduction and showed

the potential of their approaches. Even now, several projects are involved with the

design of low boom configurations.18

In our research, we have addressed the biplane concept proposed by

Kusunose19,20 which enables a significant reduction, if not complete elimination, of

31

shock waves. Fundamentally, for two-dimensional airfoils, wave drag may be separated

into drag due to lift (including the camber effect of the airfoils) and drag due to

thickness in supersonic flow.21 In spite of the fact that wave drag due to lift cannot be

eliminated completely; it can be reduced significantly by using multi-airfoil

configurations. These configurations re-distribute the system’s total lift among the

individual airfoil elements, reducing the lift of each individual element and the total

wave drag of the system. We call this the “wave reduction effect”. In the same way, the

wave drag due to thickness can also be almost eliminated by using a biplane

configuration, which depends on mutual cancellation of waves between the two airfoil

elements. This will be referred to as the “wave cancellation effect” hereinafter in this

paper. For these reasons, an ideal boomless biplane configuration can be designed by

applying these two effects.22-24 At present, Kusunose and the author’s group have

addressed the design of a supersonic biplane.25-28 Figure 2.1 shows the conceptual

drawing of boomless supersonic biplane; the cross-sectional shape of the wing is a

Busemann-type biplane, and the engines are mounted between the wings.

It is, however, difficult to design an ideal boomless biplane that can fly

effectively from subsonic to supersonic speed in real flight. The reason for this is that

the desired wave cancellation effect, which is based on the Busemann biplane, can only

be achieved at the designed Mach number and at a specific flow condition.

Unfortunately, under off-design conditions, we have the phenomena of choked-flow and

flow-hysteresis, which result in a severe drag penalty.28 Therefore, it is important to

formulate how a biplane airfoil, based on the Busemann biplane, will be able to

overcome the choked-flow and flow-hysteresis problems under off-design conditions.

In this paper, we present a practical solution to these problems with the

application of plain flaps, which may be used primarily for takeoff and landing

condition, as in a high-lift device. Particularly, we investigate the four different biplanes

in order to examine the effects of the leading and trailing edge flaps: The flaps are

32

hinged to the leading and trailing edges of the Busemann biplane, and then they can

change the area of the front and rear streamlines.

The paper is organized as follows: Section 2.2 explains the major issues to be

addressed, i.e., the choked-flow and flow-hysteresis problems of the Busemann biplane

at off-design conditions. Section 2.3 brings a brief description of the numerical models

and methods for the CFD calculations. Section 2.4 presents the results and discussion

for the four different biplanes. Finally, Section 2.5 concludes the present study.

a) Supersonic level flight

b) Takeoff and landing

Fig. 2.1 Conceptual drawing of a boomless supersonic biplane. Cruise Mach number is assumed as M∞ = 1.7 for supersonic level flight.

33

2.2 Major Issues

2.2.1 Off-design performance of the Busemann biplane

Figure 2.2 shows the configurations of both the baseline diamond airfoil and the

Busemann biplane. The thickness-chord ratio of the diamond airfoil and Busemann

biplane are t/c = 0.1 and t/c = 0.05, respectively, since it is necessary for these two

airfoils to have the same total thickness to simulate an equivalent (total) airfoil thickness.

The wedge angle of the diamond airfoil is therefore 11.4 deg., and the wedge angles of

Busemann biplane are 5.7 deg., which is just half the angle of the diamond airfoil (as

shown in Fig. 2.2, where ε is the wedge angle of Busemann biplane). The distance

between the two biplane elements is 0.5 (when the chord length is 1.0), for a theoretical

minimum drag at design Mach number of 1.7.

Also, the drag characteristics of the two airfoils over a range of Mach numbers

(0.3 ≤ M∞ ≤ 3.3) are shown in Fig. 2.3, using the CFD analyses in inviscid flow (Euler)

mode with zero-lift conditions (α = 0 deg.). From the results, we can confirm that the

Busemann biplane, for a wide range of Mach numbers (1.64 ≤ M∞ ≤ 2.7), has a wave

drag lower than that of the diamond airfoil. In this low-drag range, the wave

cancellation effect is critical and we hope to use this range in real flight. In decelerating

condition, however, a high wave drag occurs when Mach number is M∞ = 1.63 because

of the appearance of a strong bow shock in front of the biplane, as shown by curve B in

Fig. 2.3. This is a choked-flow phenomenon of Busemann biplane. The Cp distributions

of the Busemann biplane (including the choked-flow at 1.5 ≤ M∞ ≤ 1.7) are illustrated in

detail in Fig. 2.4. As the Mach number is reduced from its design Mach number (M∞ =

1.7), shock waves generated by the wing elements interact with one another and a

subsonic area is formed near the throat of the biplane. Eventually, the flow is choked at

the maximum thickness sections between the two elements, and the subsonic area

34

propagates upstream, forming a bow shock (as shown in Fig. 2.4 (e)). In accelerating

conditions (as shown in Fig. 2.5), the Busemann biplane has a flow-hysteresis for a

range of Mach numbers (1.63 ≤ M∞ < 2.18). For this reason, the Cd values of the

accelerating and decelerating conditions are not the same. Thus, if we would like to

make the Busemann biplane reach the design point (M∞ = 1.7) from subsonic regime, it

needs first to exceed the Mach number M∞ = 2.18, where the bow shock is swallowed

backward between the wing elements.

Fig. 2.2 Configurations of both the baseline diamond airfoil (t/c = 0.1) and the Busemann biplane (t/c = 0.05). The wedge angles of the diamond airfoil and the

Busemann biplane are 2ε = 11.4 deg. and ε = 5.7 deg., respectively.28

35

Fig. 2.3 Comparison of the drag characteristics:28 The solid line represents the Busemann biplane. In this case, when accelerating, Cd follows curve A. When decelerating, Cd follows curve B. The dashed line shows the baseline diamond

airfoil. Also, the diamond symbol is the design point at Mach number M∞ = 1.7.

36

Fig. 2.4 Cp-contours of the Busemann biplane with zero-lift in decelerating

condition (1.5 ≤ M∞ ≤ 1.7).28

37

Fig. 2.5 Cp-contours of the Busemann biplane with zero-lift in accelerating condition (1.7 ≤ M∞ ≤ 2.18).28

38

2.2.2 Physics considerations

Before we examine how these problems can be overcome, it may be useful to

discuss the start/un-start characteristics of a supersonic inlet diffuser29 (as shown in Fig.

2.6), because these phenomena can also be verified in the Busemann biplane. In Fig. 2.6,

the solid line shows the Kantrowitz limit.30 Once the bow shock is generated in front of

the inlets, it becomes necessary to exceed the Mach number set by the Kantrowitz limit

for the inlets to go from unstart to start condition. The limit is given by Eq. (2.1):

( )( )

( )( )

( )11

2

221

2

2

112

121 −

∞

∞

∞

∞⎥⎦

⎤⎢⎣

⎡+

−−⎥⎦

⎤⎢⎣

⎡+

+−=

γγMγγγM

MγM

AA

i

t (2.1)

where Ai is the inlet area and At is the throat area. Also, the dashed line refers to the

isentropic contraction limit,29 where the Mach number is M∞ = 1.0 at the throat of

supersonic inlets. The isentropic contraction limit is calculated by Eq. (2.2):

( )

( )( )12

12

121 −

+−

∞∞ ⎥

⎦

⎤⎢⎣

⎡+

+−=

γγ

i

t

γMγM

AA

(2.2)

It is reasonable to suppose that this rule is applicable to avoid the choked-flow

and flow-hysteresis of the Busemann biplane, i.e., that the cross-section area variation

of the front streamline can be helpful in overcoming these problems. In fact, the results

from CFD analyses are in good agreement with the values which are calculated using

Eqs. (2.1) and (2.2), as shown in Figs. 2.3 and 2.6 (here the At/Ai of Busemann biplane

is 0.8, as plotted by the dotted line in Fig. 2.6). Therefore, we make an attempt to avoid

the choked-flow and flow-hysteresis problems by utilizing this rule with the plain flaps

in the Busemann biplane.

39

Fig. 2.6 Start/Un-start characteristics of a supersonic inlet diffuser: The solid line (curve A) shows the Kantrowitz limit; the dashed line (curve B) shows the

isentropic contraction limit. Here, the ratio of throat-to-inlet-area of the Busemann biplane is At/Ai = 0.8, as shown by the dotted line. The diamond symbol represents

the design point of the Busemann biplane at Mach number 1.7.

2.3 Numerical Models and Methods

In this study, the four different biplanes were investigated, as shown in Fig. 2.7.

The Euler equation is solved for all configurations by the CFD tool (UPACS-code31),

developed at the Japan Aerospace Exploration Agency (JAXA). Actually, if we

examine the detailed mechanisms of the choked-flow and flow-hysteresis phenomena,

then it becomes important to use the Navier-Stokes equation for the CFD analysis. In

our research, however, we simply focus on whether these phenomena occur under off-

design conditions or not. Therefore, the Euler code for CFD analysis is appropriate for

40

the objectives of the present study. The following sections describe the configurations

of the four biplanes and the calculation methodology in detail.

Here, it is important to note the accuracy of the CFD analysis by using the

UPACS-code. Table 2.1 shows the comparison between the CFD and the analytical

results at Mach number M∞ = 1.7 for several configurations, such as a single flat plate

airfoil, parallel flat plate airfoils, a diamond airfoil, and the Busemann biplane. In the

analyses, the single flat plate airfoil and the parallel flat plate airfoils were simulated in

Euler mode with lift conditions. On the other hand, the diamond airfoil and the

Busemann biplane were calculated in Euler mode with zero-lift condition. From Table

2.1, we can confirm that the CFD and the analytical results derived from the supersonic

thin airfoil theory21 are, generally, in good agreement for these configurations. In

addition, the results of CFD analyses show that the Busemann biplane can not

completely eliminate the wave drag coefficient due to the non-linear effect which occurs

in the actual wave interaction. References 20 and 25 have demonstrated these

validations in more detail. Therefore, we do not further discuss these validations in this

paper. Also, the detailed descriptions of the UPACS-code can be found in Ref. 31.

Table. 2.1 Comparison between the CFD results and the analytical results of aerodynamic performance for the four configurations.20,25

41

2.3.1 Definition of the four biplanes

Figure 2.7 (a) shows the configuration of the diamond airfoil separated into two

elements along the chord of the baseline diamond airfoil. We used this biplane to start

our investigation regarding the avoidance of choked-flow and flow-hysteresis. The

thickness-chord ratio (t/c) of the individual elements was 0.05 (because the ratio of the

baseline diamond airfoil is 0.1), and the distance between the two elements was set to

0.5 (relative to the chord length of 1.0), respectively.

In order to examine the effect of changing the area of the front streamline on

choked-flow and flow-hysteresis, the Busemann biplane with deflected leading-edge

flaps (as sketched in Fig. 2.7 (b)) was investigated. This biplane is actually a Busemann

biplane with its elements deflected inward from the leading-edges up to 28 % of the

chord length, so as to have a configuration which is similar to plain flaps used at takeoff

and landing conditions. The inner sides of the deflected parts are parallel to each other,

and the uniform flow is undisturbed between them. In supersonic flow, therefore, the

oblique shock waves are generated among the two elements at 28 % of the chord length,

and they meet the vertex of the triangle at the opposite elements, respectively, at M∞ =

1.3 (the shock-wave angle is about β = 63 deg. at M∞ = 1.3).

In the same way, the Busemann biplane with deflected trailing-edge flaps was

calculated to examine the effect of changing the area of the rear streamline on choked-

flow and flow-hysteresis. In this case, the Busemann biplane elements (t/c = 0.05) are

deflected inward from the trailing-edge and back 28% of the chord length, as sketched

in Fig. 2.7 (c). Then, the inner sides of the deflected parts become parallel to each other.

Finally, we have also designed an airfoil as sketched in Fig. 2.7 (d), which

consists of a Busemann biplane with flaps at both the leading and trailing edges. This

airfoil will be referred to as HLD-1 (High-Lift Device-1) in this paper, and will be

utilized to investigate the combined effects of flaps in the Busemann biplane.

42

Fig. 2.7 Comparison of biplane configurations utilized in this research: a) Diamond airfoil separated into two elements; b) Busemann biplane with deflected

leading-edge flaps; c) Busemann biplane with deflected trailing-edge flaps; d) HLD-1.

2.3.2 CFD calculation of the biplanes

The Multiblock method was applied to grid generation in all cases. Table 2.2

represents the number of grid points for all biplanes. As an example, Fig. 2.8 shows the

structured grid of the HLD-1 used for the 2-D analyses. Approximately 0.59 million

grid points were used in total. The grid numbers around each biplane element and

between these two elements were 1000 and 501×251, respectively.

The flow field for the biplane was calculated by considering flow-hysteresis.

Mach numbers ranged from 0.3 to 3.3, including its design Mach number M∞ = 1.7,

43

since an airplane has to fly through subsonic, transonic, and supersonic regimes in real

flight. Also, the angle of attack was set to zero for all configurations, i.e., zero-lift

conditions. For the calculation of the drag coefficient, we applied the same reference

chord for all biplanes as 1.0 (i.e., equal to the chord length of the baseline diamond

airfoil). Additionally, in subsonic flow conditions, the Cd values of the Busemann

biplane with deflected leading and trailing edges were calculated by the time averaging

method, since these two biplanes, as shown in Figs. 2.7 (b) and (c), produced an

oscillatory convergence in the present calculations.

Table. 2.2 Number of grid points for the four biplanes.

Fig. 2.8 Structured grid of the HLD-1 used for CFD (UPACS-code) analyses.

44

2.4 Results and Discussion

2.4.1 Diamond airfoil separated into two elements

The drag characteristics of the diamond airfoil separated into two elements are

plotted in Fig. 2.9, which also includes the drag characteristics of the Busemann biplane

and the baseline diamond airfoil (given in Fig. 2.3). It becomes clear from Fig. 2.9 that

the wave drag of the diamond airfoil separated into two elements agrees very well with

that of the baseline diamond airfoil at all Mach numbers. That is, the choked-flow and

flow-hysteresis do not exist for any Mach number. Also, in the light of the start/un-start

characteristics of a supersonic inlet diffuser as shown in Fig. 2.6, these results are

credible since the ratio of throat-to-inlet-area of the present biplane is At/Ai = 1.0, i.e.,

the flow conditions are always within a startable region in supersonic flow. For

reference purposes, the pressure coefficient contours of the present biplane and of the

baseline diamond airfoil are given in Appendix A and Appendix B, respectively, for

different values of free-stream Mach number.

In addition, Fig. 2.10 shows the comparison between the pressure coefficient

contours of the diamond airfoil separated into two elements and of the Busemann

biplane at Mach number M∞ = 1.5. From Fig. 2.10, we can confirm that there is no

choked-flow phenomenon with the present biplane, in contrast to the Busemann biplane

for which a bow shock is generated in the upstream. Therefore, these facts suggest that

it is possible to avoid the phenomena of choked-flow and flow-hysteresis in the

Busemann biplane by bringing its shape close to that of the diamond airfoil separated

into two elements.

45

Fig. 2.9 Comparison of drag characteristics: The solid line represents the diamond airfoil separated into two elements; the dotted line shows the Busemann biplane. In

the case of the Busemann biplane, when accelerating, Cd follows curve A. When decelerating, Cd follows curve B. Also, the dashed line shows the baseline diamond

airfoil. The diamond symbol is the design point at Mach number M∞ = 1.7.

Fig. 2.10 Comparison of the Cp-contours with zero-lift at Mach number M∞ = 1.5: a) diamond airfoil separated into two elements; b) Busemann biplane.

46

2.4.2 Busemann biplane with deflected leading-edge flaps

Figure 2.11 shows a comparison of drag characteristics for the Busemann

biplane with deflected leading-edge flaps, the baseline Busemann biplane, and the

baseline diamond airfoil. Also, Figs. 2.12 and 2.13 show the pressure coefficient

contours around the biplane for different values of free-stream Mach number. It is found

from Fig. 2.11 that the leading-edge flaps have the effect of downscaling the wave drag

in supersonic flow condition, and also in the range of high-subsonic flow conditions

(around 0.7 < M∞ < 1.0), as compared to the baseline Busemann biplane. Moreover, the

drag increase of the biplane due to choked-flow becomes small (as represented by curve

B), in contrast to that of the Busemann biplane (represented by curve D). In addition,

the change in the area of the front streamline enables a shift of the Mach number, at

which the flow is choked in the maximum thickness sections between the two elements,

to a lower value M∞ = 1.41 (in the case of the Busemann biplane, M∞ = 1.63), which in

turns propagates the subsonic area to upstream, forming the bow shock. From Fig. 2.12

(a) to (f), we can observe this process of change of the flow conditions in detail.

As for the area of flow-hysteresis, it is possible to observe that the area is

reduced for a range of Mach numbers (1.41 ≤ M∞ < 1.61), as compared to that of the

Busemann biplane. Then, the flow conditions of flow-hysteresis up to M∞ = 1.61 are

represented in Fig. 2.13: As the Mach number increases from M∞ = 1.3, the normal

shock wave is formed at the entrance of the biplane, and is swallowed at Mach number

M∞ = 1.61, as shown in Fig. 2.13 (f).

These results are consistent with the theoretical values of the start/un-start

limits, as indicated before in Fig. 2.6. For the Busemann biplane with deflected leading-

edge flaps, the ratio of throat-to-inlet-area is about At/Ai = 0.9, and therefore, we have

found that the leading-edge flaps can be effective in avoiding the choked-flow and flow-

hysteresis problems of the Busemann biplane.

47

Fig. 2.11 Comparison of the drag characteristics: The solid line represents the Busemann biplane with deflected leading-edge flaps; the dotted line shows the

Busemann biplane. In both cases, when accelerating, Cd follows curves A and C. When decelerating, Cd follows curves B and D. Also, the dashed line shows the

baseline diamond airfoil. The diamond symbol is the design point at Mach number M∞ = 1.7.

48


with zero-lift in decelerating condition (1.3 ≤ M∞ ≤ 1.7).

49


with zero-lift in accelerating condition (1.3 ≤ M∞ ≤ 1.61).

50

2.4.3 Busemann biplane with deflected trailing-edge flaps

In the same way, a comparison of the drag characteristics for the Busemann

biplane with deflected trailing-edge flaps, the Busemann biplane, and the baseline

diamond airfoil is shown in Fig. 2.14. In addition, the pressure coefficient contours

around the biplane are plotted in Figs. 2.15 and 2.16 for different values of free-stream

Mach number. It becomes clear from Fig. 2.14 that the trailing-edge flaps are not

effective in avoiding the choked-flow and flow-hysteresis of the Busemann biplane. In

fact, the increase in the Cd value due to the choked-flow (curve B) is a little higher with

the trailing-edge flaps than in the case of the baseline Busemann biplane (curve D).

From the results, we have a Cd value for the biplane equal to Cd = 0.1040 at M∞ = 1.63,

while the Cd value for the baseline Busemann biplane is Cd = 0.0944 at M∞ = 1.63 (both

flow conditions are shown in Fig. 2.15 (e) and Fig. 2.4 (e), respectively). Furthermore,

the area of flow-hysteresis (1.63 ≤ M∞ < 2.18) is exactly the same as compared to that of

the Busemann biplane. That is, the bow shock is swallowed at the same Mach number

M∞ = 2.18, as shown in Fig. 2.16 (f) and Fig. 2.5 (f).

Here, we would like to focus our attention on the effects of trailing-edge flaps

in subsonic flow. Fortunately, we can observe from Fig. 2.14 that the wave drags are

decreased between M∞ = 0.5 and M∞ = 0.9, as compared to those of the Busemann

biplane. Also, the aerodynamic drag at a speed near to or above the speed of sound is

reduced, i.e., the drag-divergence Mach number is shifted to a higher one. Hence, the

trailing-edge flaps proved to be actually useful in downscaling the wave drag in

subsonic flow conditions.

In order to investigate the reason for the decrease in wave drag at subsonic flow

conditions, Fig. 2.17 shows the Mach number distributions of the baseline Busemann

biplane and the Busemann biplane with deflected trailing-edge flaps, respectively,

where only the supersonic area is represented. In the case of the baseline Busemann

51

biplane, we can confirm that the flow is accelerated between the two airfoil elements.

This results in supersonic flow between the two airfoil elements, and also in the

generation of the normal shock wave. Thus, as the Mach number increases in subsonic

flow, the Cd value is also increased. In the case of the biplane with trailing-edge flaps,

on the other hand, the flow between the two elements is moderately accelerated by the

trailing-edge flaps, as compared to the Busemann biplane. This results in a slow

progression of the formation of a supersonic area between the two elements. Therefore,

the wave drags of the biplane with trailing-edge flaps are smaller than those of the

baseline Busemann biplane in subsonic flow.

Fig. 2.14 Comparison of the drag characteristics: The solid line represents the Busemann biplane with deflected trailing-edge flaps; the dotted line shows the

Busemann biplane. In both cases, when accelerating, Cd follows curves A and C. When decelerating, Cd follows curves B and D. Also, the dashed line shows the

baseline diamond airfoil. The diamond symbol is the design point at Mach number M∞ = 1.7.

52


with zero-lift in decelerating condition (1.5 ≤ M∞ ≤1.7).

53


with zero-lift in accelerating condition (1.7 ≤ M∞ ≤ 2.18).

54

Fig. 2.17 Comparison of the Mach number distributions in subsonic flow

conditions: The baseline Busemann biplane is shown in the left row and the Busemann biplane with deflected trailing-edge flaps is shown in the right row.

Mach contours in those figures are represented only for supersonic areas. Free-stream Mach numbers are: a) M∞ = 0.66; b) M∞ = 0.82; and c) M∞ = 0.9.

55

2.4.4 HLD-1

Finally, Fig. 2.18 plots the drag characteristics of the HLD-1, which includes

the previous results for the Busemann biplane and the baseline diamond airfoil. In

addition, Figs. 2.19 and 2.20 show that the pressure coefficient contours around the

HLD-1 for different values of free-stream Mach number. From Fig. 2.18, it becomes

clear that the wave drag values of the HLD-1 are close to those of the baseline diamond

airfoil at all Mach numbers. This result suggests that the HLD-1 utilizes the effects of

both the leading and trailing edge flaps in the subsonic and supersonic conditions: In

subsonic flow, the HLD-1 can smoothly overcome the sound barrier, as compared to the

Busemann biplane, by using the effect of the trailing-edge flaps. In supersonic flow, on

the other hand, the increase of Cd due to choked-flow is downscaled (curve B), and also,

the flow-hysteresis area is reduced for the range of Mach numbers 1.41 ≤ M∞ < 1.6 (as

the At/Ai of HLD-1 is about 0.9), due to the effect of the leading-edge flaps. The

processes of choked-flow and flow-hysteresis can be observed in detail in Figs. 2.19 and

20.

Furthermore, we need to pay attention to the fact that the design Mach number

is now set at M∞ = 1.7, in order to use the wave cancellation effect of the Busemann

biplane for sonic boom reduction. When the HLD-1 is in accelerating condition

(represented by curve A in Fig. 2.18), the bow shock generated in front of the leading-

edges is swallowed over at M∞ = 1.6, as shown in Fig. 2.20 (f). Therefore, if the HLD-1

can be transformed back into the Busemann biplane as the Mach number reaches above

M∞ = 1.64, we can arrive at the design point smoothly from a subsonic regime, i.e.,

move from the solid line to the dotted line (curve D including the design-point). The

reason for this is that once the bow shock has been swallowed over at Mach number M∞

= 1.64, there is no choked-flow phenomenon at the Busemann biplane, as shown in Fig.

2.4 (a) to (d).

56

Fig. 2.18 Comparison of the drag characteristics: The solid line represents the HLD-1; the dotted line shows the Busemann biplane. In both cases, when

accelerating, Cd follows curves A and C. When decelerating, Cd follows curves B and D. Also, the dashed line shows the baseline diamond airfoil. The diamond

symbol is the design point at Mach number M∞ = 1.7.

57

Fig. 2.19 Cp-contours of the HLD-1 with zero-lift in decelerating condition (1.3 ≤ M∞ ≤ 1.7).

58

Fig. 2.20 Cp-contours of the HLD-1 with zero-lift in accelerating condition (1.3 ≤ M∞ ≤ 1.6).

59

2.5 Conclusion

In this paper, four different biplanes have been analyzed, focusing on the use of

plain flaps to overcome the problems of choked-flow and flow-hysteresis of the

Busemann biplane. From the results, we observed that the leading-edge flaps, by

changing the area of the front streamline, can be effective to alleviate the increase in the

Cd value due to choked-flow, and also to reduce the area of flow-hysteresis. Also, the

flaps could downscale the wave drag in supersonic flow and high-subsonic flow

conditions, as compared to the baseline Busemann biplane. On the other hand, the

trailing-edge flaps were not effective in avoiding the choked-flow and flow-hysteresis.

However, these flaps were useful in downscaling the wave drag in subsonic flow

conditions, which resulted in a smooth transition from subsonic to supersonic flow as

compared to the baseline Busemann biplane. In addition, it was found that the biplane

equipped with both flaps could benefit from both effects; arriving at the design point

smoothly from subsonic conditions, and avoiding the severe drag penalty due to

choked-flow and flow-hysteresis. As a conclusion, we would like to note that the use of

flaps is a highly plausible solution to the problems of choked-flow and flow-hysteresis

of the Busemann biplane under off-design conditions, since it will not only overcome

these problems, but it also has applications as a high-lift device for takeoff and landing

conditions.

60

Appendices Appendix A: Cp-contours of the diamond airfoil separated into two elements with

zero-lift condition (α = 0 deg., 0.9 ≤ M∞ ≤ 1.7).

61

Appendix B: Cp-contours of the baseline diamond airfoil with zero-lift condition (α = 0 deg., 0.9 ≤ M∞ ≤ 1.7).

62

References



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Speed? A Design Anatomy of Supersonic Transportation Part1,” The Aeronautical

Journal, 2008, 112(1129), pp. 141-151.

3Chudoba, B., Oza, A., Coleman, G., and Czysz, P. A., “What Price Supersonic

Speed? An Applied Market Research Case Study Part2,” The Aeronautical Journal,

2008, 112(1130), pp. 219-231.

4Robert, J. M., “A Supersonic Business-Jet Concept Designed for Low Sonic Boom,”

NASA TM-2003-212435, 2003.


Supersonic Experimental Airplane in Japan,” Proceedings of the ECCOMAS 2004,

Finland, 2004.


Minimization,” Journal of Aircraft, 2006, 43(5), pp. 1301-1306.



Aircraft, 1999, 36(4), pp. 668-674.



63

9Pawlowski, J. W., Graham, D. H., Boccadoro, C, H., Coen, P. G., and Maglieri, D.

J., “Origins and Overview of the Shaped Sonic Boom Demonstration Program,” AIAA

2005-0005, 2005.

10Plotkin, K. J., Haering, E. A. Jr., Murray, J. E., Maglieri, D. J., Salamone, J.,

Sullivan, B. M., and Schein, D., “Ground Data Collection of Shaped Sonic Boom

Experiment Aircraft Pressure Signatures,” AIAA 2005-0010, 2005.

11Plotkin, K. J., Martin, R., Maglieri, D. J., Haering, E. A. Jr., and Murray, J. E.,

“Pushover Focus Booms from the Shaped Sonic Boom Demonstrator,” AIAA 2005-

0011, 2005.

12Morgenstern, J. M., Arslan, A., Lyman V., and Vadyak, J., “F-5 Shaped Sonic

Boom Demonstrator’s Persistence of Boom Shaping Reduction through Turbulence,”

AIAA 2005-0012, 2005.

13Henne, P. A., “Case for Small Supersonic Civil Aircraft,” Journal of Aircraft, 2005,

42(3), pp. 765-774.

14Howe, D. C., “Improved Sonic Boom Minimization with Extendable Nose Spike,”

AIAA 2005-1014, 2005.

15Cowart, R., and Grindle, T., “An Overview of the Gulfstream / NASA Quiet

SpikeTM Flight Test Program,” AIAA 2008-0123, 2008.

16Howe, D. C., Simmons, III, F., and Freund, D., “Development of the Gulfstream

Quiet SpikeTM for Sonic Boom Minimization,” AIAA 2008-0124, 2008.

17Howe, D. C., Waithe, K. A., and Haering, E. A. Jr., “Quiet SpikeTM Near Field

Flight Test Pressure Measurements with Computational Fluid Dynamics Comparisons,”

AIAA 2008-0128, 2008.

18Smith, H., “A Review of Supersonic Business Jet Design Issues,” The Aeronautical

Journal, 2007, 111(1126), pp. 761-776.

64


Transport,” Proceedings of the First International Conference on Flow Dynamics,

Sendai, Japan, 2004, pp. 46-47.

20Kusunose, K., Matsushima, K., Goto, Y., Yamashita, H., Yonezawa, M.,

Maruyama, D., and Nakano, T., “A Fundamental Study for the Development of

Boomless Supersonic Transport Aircraft,” AIAA 2006-0654, 2006.

21Liepmann, H. W., and Roshko, A., Elements of Gas Dynamics, John Wiley & Sons,

Inc., New York, 1957, pp. 107-123, 389.

22Matsushima, K., Kusunose, K., Maruyama, D., and Matsuzawa, T., “Numerical

Design and Assessment of a Biplane as Future Supersonic Transport − Revisiting

Busemann’s Biplane,” Proceedings of the 25th ICAS Congress, ICAS 2006-3.7.1, pp. 1-

10, Hamburg, Germany, 2006.


Design of Biplane Airfoils for Low Wave Drag Supersonic Flight,” AIAA 2006-3323,

2006.


Design of Three-dimensional Low Wave-drag Biplanes Using Inverse Problem

Method,” AIAA 2008-0289, 2008.

25Kusunose, K., Matsushima, K., Obayashi, S., Furukawa, T., Kuratani, N., Goto, Y.,

Maruyama, D., Yamashita, H., and Yonezawa, M., Aerodynamic Design of Supersonic

Biplane: Cutting Edge and Related Topics, The 21st Century COE Program,

International COE of Flow Dynamics Lecture Series, Vol. 5, Tohoku University Press,

Sendai, Japan, 2007.


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65



Sonic-Boom Reduction,” AIAA 2007-3674, 2007.


Busemann-type Biplane for Avoiding Choked Flow,” AIAA 2007-0688, 2007.

29Aksel, M. H., and Eralp, O. C., Gas Dynamics, Prentice Hall Inc., Englewood

Cliffs, 1994, Chap. 5, pp. 186-195.

30Van Wie, D. M., Kwok, F. T., and Walsh, R. F., “Starting Characteristics of

Supersonic Inlets,” AIAA 1996-2914, 1996.


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Symposium, ISHPC 2003, Springer, Tokyo, 2003, pp. 307-319.

67

Chapter 3. Variability of Sonic Boom Intensity and Propagation Path Due to Atmospheric Fluctuations of Wind and Temperature Nomenclature

Symbols

a = speed of sound

AL = body reference length in feet

E = von Karman and Pao energy spectrum

F = coefficient for unit normal vector calculation

h = distance taken perpendicularly from the body chord axis to the ground

direction

H = flight altitude above the ground in feet

k = wave number

kd = dissipation wave number of the energy spectrum

ke = peak wave number of the energy spectrum

kl = wave number corresponding to the largest eddy scale

kn = wave vector of the nth Fourier mode

K = turbulent kinetic energy

l = longitudinal dimension and body reference length used by computational

fluid dynamics

68

M = Mach number

ML = model reference length

N = limit of Fourier mode

Nx, Ny = horizontal components of wavefront unit normal vector

Nz = vertical component of wavefront unit normal vector

N = wavefront unit normal vector

P = pressure

∆P = overpressure

psf = pounds per square foot

r = radius distribution

R = ray path vector

t = time

T = random temperature field

ut = random wind field

tnu~ , ju~ = amplitude of the nth Fourier mode

V = total volume

Vrms = root of mean square of wind velocity

Vx, Vy = horizontal components of wind velocity vector

Vz = vertical components of wind velocity vector

V = wind velocity vector

x, y, z = Cartesian coordinates

y = given point of fluctuation field

ε = turbulent dissipation rate

σn = direction of the nth Fourier mode

Ψn = phase of the nth Fourier mode

Subscripts

0 = ambient

69

∞ = free-stream

j, n = Fourier mode

3.1 Introduction

There are several technical problems that prevent commercial transport from

going supersonic. These include, for example, engine exhaust emissions, airport noise

(especially during take-off or landing), and sonic boom.1 Particularly, sonic boom

reduction is the key technology required to make supersonic transport feasible.2,3 For

this issue, Dr. Kusunose and the author’s group have addressed the biplane concept in

order to design a low boom configuration:4-9 the concept allows a significant reduction,

if not complete elimination, of sonic boom by use of the Busemann type biplane.

In forging ahead with the design of the supersonic biplane, it is necessary to

evaluate the sonic boom influence on the ground. On the other hand, before reaching the

ground, the sonic boom propagates through real atmosphere, which is not a uniform

field. Therefore, sonic boom can be affected by atmospheric conditions such as

temperature gradient, winds distribution with height, homogeneous atmospheric

fluctuation (i.e., atmospheric turbulence), lower layer (2000-ft depth) of the atmosphere,

etc. According to previous experimental researches,10-12 it has been noted that

atmospheric variations can bring about distortions to the sonic boom propagation path

and also to its signature, leading to variations in the sonic boom intensity. In order to

replicate these real circumstances, it is necessary to develop a simulation code that

accounts for the influences of a real atmospheric field.

Here, we present a sonic boom estimation method considering atmospheric

fluctuations of wind and temperature, and then, we investigate the non-deterministic

effects of these fluctuations on sonic boom propagation, respectively. In particular, we

70

are interested in the variability of sonic boom intensity, propagation path and sonic

boom reaching point on the ground, as compared to the no fluctuation condition.

The paper is organized as follows: Section 3.2 brings a brief description of the

numerical models and methods for sonic boom calculation. Section 3.3 presents the

results and discussion for the one hundred different fluctuation fields that were

randomly generated. Finally, Section 3.4 concludes the present study.


Figure 3.1 shows the logical flow chart of the sonic boom calculation program in

this study. The computational procedure consisted of the following three components:

First, the near flow field was calculated by using CFD in Euler mode, and then the near-

field pressure was extracted from CFD results in order to estimate the sonic boom on

the ground. Secondly, random fluctuation fields of wind and temperature were

calculated by a finite sum of discrete Fourier modes, respectively. Finally, the sonic

boom signature was calculated by the modified Waveform Parameter Method,13,14 using

the near-field pressure wave and the fluctuation field as input-data.

As for the fluctuation fields, we created 100 different fluctuation fields by

different random numbers, respectively. Then, 100 different sonic boom signatures,

calculated with the respective 100 different fluctuation fields, were investigated in order

to assess the non-deterministic effects of these fluctuations on sonic boom.15 In addition,

it is assumed that the fluctuation fields are frozen, i.e., the fluctuations of wind and

temperature are constant during sonic boom propagation. This is reasonable due to the

fact that sonic boom propagation occurs in a much smaller time scale than it takes for

the fluctuating structures to evolve.16,17 The following sections describe the calculation

methodology in detail.

71

Fig. 3.1 Logical flow chart of sonic boom calculation program.

3.2.1 CFD Calculation of the Near-Field

The Sears-Haack body was calculated using CFD (UPACS-code,18 developed at

Japan Aerospace Exploration Agency: JAXA) in Euler mode, mainly focusing on shock

wave properties around the body. The angle of attack was set to zero at M∞ = 1.7 for

supersonic steady flight. The reason for investigating the Sears-Haack body is that this

configuration can create a simple N wave on the ground, thus making it easy to

understand the effect of an atmospheric fluctuation on sonic boom propagation. The

definition of a Sears-Haack body is as expressed in Eq. (3.1):19,20

⎟⎠⎞

⎜⎝⎛ ≤≤−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−=

22

21

43

2

max

lxll/x

rr (3.1)

where rmax is the maximum radius and was set as rmax = 0.052 with respect to the

dimensionless body length l = 1.0. The total volume of the body became V = 0.005.

72

Figure 3.2 shows the structured grid of the Sears-Haack body used for the near-

field calculation, where the grid is a shock aligned one for Mach number 1.7, so as to

obtain pressure distribution at near-field with high accuracy. Here, we actually

calculated only half of the body due to its symmetry. The number of grid points on the

surface of the body was 4.2 thousand points and the total of grid points was

approximately 3.0 million for the near-field calculation (from 0.0 to 8.0 body lengths).

It is important to note the accuracy of the CFD analysis by using the UPACS-

code. It has been demonstrated in Ref. 5 that the CFD results and analytical results

derived from the supersonic thin airfoil theory21 are in good agreement. Therefore, we

are not concerned here with its validation. The detailed description of the UPACS-code

can be found in Ref. 18.

Fig. 3.2 Structured grid of the Sears-Haack body in a symmetry plane, used for CFD (UPACS-code) analysis. The grid is aligned with the shock waves generated

at Mach number M∞ = 1.7.

73

3.2.2 Generation of the Atmospheric Fluctuation Fields

Random fluctuation fields of wind and temperature are created by first using the

energy spectrum of von Karman and Pao,22 which is defined by Eq. (3.2):

( )

( )[ ] ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+

⎟⎠⎞

⎜⎝⎛=

34

617

2

425

23

49exp

132)(

de

e

kk

kk/

kk/KkEε

(3.2)

where k is the wave number and ke is the peak wave number of the energy spectrum.

Also, kd is the dissipation wave number of the spectrum. In the field of meteorology,

atmospheric phenomena are classified according to the time scale and the space scale,23

such that we have micro-scale phenomena, like turbulence in an atmospheric boundary

layer, meso-scale phenomena, which include cumulonimbus clouds (thunderhead) and

hurricanes, and macro-scale phenomena, such as the monsoons. Then, the values of the

wave numbers are defined according to this meteorological classification. In the present

model, we used the micro-scale fluctuations defined by this classification in order to

generate atmospheric fluctuation fields of wind and temperature, respectively. From this,

the parameters were given as following: ke = 6.28 × 10-3 m-1 and kd = 628 m-1, and the

wave number corresponding to the largest eddy was set as kl = 3.14 × 10-3 m-1 (as

described in Ref. 28). Also, the parameters K and ε were estimated with experimental

data as shown in Refs. 24, 25, and 26: In the case of wind fluctuation, the kinetic energy

of turbulence was estimated as K = 0.4 m2s-2 and the turbulent dissipation rate as ε =

1.15 × 10-4 m2s-3 in this study; while in the case of temperature fluctuation the K and ε

were set as K = 9.5 × 10-2 m2s-2 and ε = 1.15 × 10-4 m2s-3, respectively.

After the energy spectrums were defined, the random fluctuation fields were

generated by using a finite sum of N discrete Fourier modes: the wind fluctuation field

was created by Eq. (3.3), while the temperature fluctuation field was generated by Eq.

(3.4). These methods have been used in past researches27,28 in order to create

74

atmospheric fluctuation fields. Therefore, we used the same approaches and fixed N to

200 Fourier modes28 in all calculations.

( ) ( ) nt σy2yu ∑=

+⋅=N

nnntn Ψu

1cos~ k (3.3)

( ) ( )∑=

+⋅=N

jnnj ΨuT

1cos~ y2y k (3.4)

where y is a given point of the fluctuation fields.

The grid width of each fluctuation field was 2 km × 15 km × 18.5 km in x, y, and

z directions, respectively (as shown in Fig. 3.5). The total of grid points was

approximately 6 hundred-thousands for the whole field, and the grid spacing was 100 m

in all directions. Then, random wind velocities and random temperatures with micro-

scale fluctuations were randomly assigned throughout the fluctuation fields, respectively.

It can be confirmed from Fig. 3.3 that all 100 different wind fluctuation fields have rms

wind velocity (i.e., root of mean square of the wind velocity) of Vrms = 2.5 ms-1 after the

above setting of parameters. Also, rms temperature fluctuation of Trms = 0.4 K was

obtained for each 100 different fields, as shown in Fig. 3.4.

75

Fig. 3.3 Vrms values of 100 different fields calculated with wind fluctuation.

Fig. 3.4 Trms values of 100 different fields calculated with temperature fluctuation.

76

3.2.3 Sonic Boom Calculation

Sonic boom was calculated by the modified Waveform Parameter Method:13,14

the method is based on results from geometric acoustics and isentropic wave theory, and

allows the calculation of wave amplitude, nonlinear waveform distortion, and ray

tracing. Figure 3.5 depicts a ray path (solid line) through a wind fluctuation field. In this

model, the grid points of each fluctuation field do not correspond with the calculating

points of ray tracing. Therefore, a trilinear interpolation was performed to interpolate

the random fluctuations of wind and temperature into the ray path calculation, as shown

in Fig. 3.6. The ray tracing can be determined from the following set of Eqs. (3.5) and

(3.6):

( ) ( ) ( )III RRR Δ1 +=+ (3.5)

( ) ( ) ( )III NNN Δ1 +=+ (3.6)

where R (I) is a ray path vector and N (I) is a wavefront unit normal vector. The

increment ∆R (I) and ∆N (I) are given by Eqs. (3.7), (3.8), and (3.9):

( ) ( ) ( ) ( )[ ] tIIIaI 0 ΔΔ 0VNR += (3.7)

( )( )( )( )

( )( ) ( )( ) ( )( ) ( )

tININ

ININININ

IFINININ

I

yx

zy

zx

z

y

x

ΔΔΔΔ

Δ22 ⎥

⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=N (3.8)

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )Idz

daIdz

dVINIdz

dVINI

dzdVINIF 0z0

zy0

yx0

x +++= (3.9)

where ∆t is the time increment between the calculation points. The path-integral

calculation was performed by a fourth order Runge-Kutta method. In the case of wind

fluctuation, the wind velocity in the z-direction was included for the ray tracing, that is,

we have assumed that the realization field is a quasi-stratified atmosphere,29 since the

velocity of wind fluctuation is much smaller than that of the local speed of sound in the

77

atmosphere. In fact, the rms velocity of wind fluctuation was set as Vrms = 2.5 ms-1,

while the local speed of sound is around a0 = 300 ms-1.

The initial conditions assuming real supersonic flight for the Waveform

Parameter Method were set as follows: flight Mach number M∞ = 1.7, flight altitude

above ground H = 60,000 ft (around 18.3 km), model reference length ML = 1.0 and

body reference length AL = 202 ft (AL referred to the total length of the Concorde). In

this study, by adding the rms values of wind and temperature fluctuations into the

standard atmospheric condition,30 each fluctuation effect on sonic boom was separately

investigated. Also, sonic boom signatures were calculated only at the perpendicular

plane from the flight path to the ground, as shown in Fig. 3.5. The reason is that the

strongest sonic boom intensity can be measured at this plane, for the Sears-Haack body

is a body of revolution and the propagation distance becomes the shortest at this plane.

Fig. 3.5 Sketch of the coordinate system for the present model. The solid line shows a ray path of sonic boom through a wind fluctuation field, propagating from

the flight path to the ground.

78

Fig. 3.6 Trilinear interpolation of random atmospheric fluctuations of wind and temperature for the ray path calculation.


3.3.1 Determination of the Near-field Pressure Wave for Sonic Boom Calculation

In order to determine the near-field pressure wave to be utilized as input-data for

sonic boom calculation, the comparison of near-field pressure signatures for the Sears-

Haack body at h/l = 1.0 − 5.0 are plotted in Fig. 3.7. Also, Fig. 3.8 shows the sonic

boom signatures calculated without atmospheric fluctuations by using the near-field

pressure signatures at h/l = 1.0 − 5.0, respectively. The reason is that it is important to

confirm the grid dependency and the three dimensional effect of the flow for the

accuracy of sonic boom calculation.31 It becomes clear from Fig. 3.8 that the sonic

boom waves present the same signature on the ground. That is, the grid quality is

adequate to capture a near-field pressure wave with accuracy. Therefore, in this research,

the near-field pressure signature at h/l = 5.0 was used as input-data for sonic boom

79

calculation, in order to investigate the effect of atmospheric fluctuations of wind and

temperature.

Fig. 3.7 Comparison of near-field pressure signatures propagating from the Sears-Haack body at h/l = 1.0 − 5.0.

80

Fig. 3.8 Comparison of sonic boom signatures on the ground calculated from five different near-field pressure waves without atmospheric fluctuations of wind and temperature: flight Mach number M∞ = 1.7, flight altitude H = 60,000 ft, model

reference length ML = 1.0 and body reference length AL = 202 ft.

3.3.2 Variability of Sonic Boom Intensity

Figure 3.9 (a) shows the calculated sonic boom signatures for the no fluctuation

case, whereas Figs. 3.9 (b) and (c) show the 100 different signatures calculated with the

100 different fluctuation fields of wind and temperature, respectively. From the results,

we can confirm that there are the fluctuations of sonic boom signatures due to

atmospheric fluctuations for both cases, although all sonic boom waves were calculated

by using the same near-field pressure wave extracted at h/l = 5.0 (as shown in Fig. 3.7).

In the case of the wind fluctuation, there is a large variability of waveform, which

results in a large variation of sonic boom intensity. On the other hand, the results of

81

temperature fluctuation show small variability of waveform, therefore, the variation is

small for both initial and tail overpressures.

As for the variability of sonic boom intensity, the correlations between initial

and tail overpressures for both cases are shown in Figs. 3.10 (a) and (b), respectively. In

the case of no fluctuation, the initial and tail overpressure are ∆P = 1.09 psf and ∆P = −

1.15 psf, respectively, as indicated by the diamond symbol. On the other hand, in the

wind fluctuation cases, the initial and tail overpressures are distributed over a wide

range of sonic boom intensities, as compared to that of the temperature fluctuation

cases: The initial overpressure changes between ∆P = 0.62 and ∆P = 7.17 psf. Also, the

tail overpressure changes between ∆P = − 0.65 and ∆P = − 7.55 psf. Therefore, we can

confirm that wind fluctuation has an impact on sonic boom intensity more relevant than

that of temperature fluctuation. In addition, strong correlations are confirmed between

both overpressures from Figs. 3.10 (a) and (b), i.e., a case with high initial overpressure

also has a strong value of tail overpressure.

Figures 3.11 and 3.12 show the frequency distributions of relative initial and tail

overpressures in the presence of wind and temperature fluctuations, respectively. The

bin size is 0.25 for both Figs. 3.11 and 3.12. The horizontal axis is the ratio ∆PFluctuation /

∆PNo fluctuation , where ∆PFluctuation is the overpressure for each of the 100 cases with

atmospheric fluctuation, and ∆PNo fluctuation is the value of overpressure for the no

fluctuation case as shown in Fig. 3.9 (a). From the results, it can be seen that there is a

variability of boom intensity for both cases. In the case of wind fluctuation, sonic boom

intensity may decrease to as much as half the value of the no fluctuation case, but it may

also increase to more than twice this value. Under temperature fluctuations, the result

shows the small variability of boom intensity, as shown in Fig. 3. 12.

The obtained variability of boom intensity were compared with past actual

ground-based measurements taken for an XB-70 aircraft (Jun. 1966) in Refs. 11, 32, and

33 (the aircraft length of the XB-70 is about 185 ft), as shown in Fig. 3.13. From the

82

results, we can observe that the variability for both cases calculated from the present

model are, qualitatively, in good agreement with these experimental data.

In addition, we can see from Fig. 3.11 that 59 % of the cases had a decreased

sonic boom intensity for both initial and tail overpressures, while 41 % of the cases had

an increased intensity as compared to the no fluctuation case. Also, in the temperature

case, 53 % of the cases had a decreased boom intensity for both overpressures.

Therefore, there is a high possibility that sonic boom intensity will decrease due to

atmospheric fluctuations. Then, we have confirmed that similar results are obtained

when calculating with 200 or 300 different fluctuation fields.

Also, Fig. 3.11 shows that a few cases have extremely high overpressures,

around 3.5 and 6.5 times the value for the no fluctuation case. Here, it is reasonable to

suppose that these cases are not likely to occur in the real-world. For one thing, Fig.

3.11 already indicates that the probability of having these extreme values of

overpressure is very low. For another, the present model utilized in this research is a

simplified one, which considers the homogeneous atmospheric fluctuation field. The

fact of the matter is that the intensity of fluctuations can vary with altitude in the real

atmosphere. Figures 3.11 and 3.12 also reveal that the frequency distributions have the

same shape for both the initial and tail overpressures. This is because there is a strong

correlation between initial and tail overpressures for each case, as indicated before in

Fig. 3.10. Therefore, we proceed now to the discussion of sonic boom intensity,

focusing on the results of initial overpressure only.

In order to confirm the causing factor for the variability in sonic boom intensity,

Figs. 3.14 and 3.15 bring a plot of the variation in the ray tube area with altitude for

wind and temperature fluctuation cases, respectively: In both figures, the cases of (a)

increased, and (b) decreased sonic boom intensity are represented, as compared to the

no fluctuation case. It is possible to observe that the variation of the ray tube area does

not occur as smoothly as in the no fluctuation case, where this variation is

83

approximately linear with altitude. Furthermore, we found that sonic boom intensity is

closely associated with the variation of the ray tube area. In the case of wind fluctuation,

from Fig. 3.14 (a), sonic boom intensity becomes stronger as we have a reduced ray

tube area on the ground. On the other hand, sonic boom intensity becomes weaker as we

have an enlarged ray tube area, as shown in Fig. 3.14 (b). This finding is consistent with

the theoretical results from the geometrical acoustic approach, where the wave

amplitude is inversely proportional to the square root of the ray tube area. Also, in the

case of temperature fluctuation, we can get the same results, as show Figs. 3.15 (a) and

(b). Hence, we confirm that the variation of ray tube area due to the fluctuations plays a

major role in varying sonic boom intensity.

a) No fluctuation

84

b) Wind fluctuation

c) Temperature fluctuation

Fig. 3.9 Calculated sonic boom signatures for all cases: a) no fluctuation case; b) wind fluctuation cases including the 100 different signatures; and c) temperature

fluctuation cases including the 100 different signatures.

85

a) Wind fluctuation

b) Temperature fluctuation

Fig. 3.10 Correlation between initial and tail overpressures for both fluctuation cases: a) wind fluctuation; and b) temperature fluctuation.

86

a) Initial overpressure

b) Tail overpressure

Fig. 3.11 Distribution of initial and tail overpressures for the 100 cases calculated with wind fluctuation. The bin size is 0.25, respectively: (a) initial overpressure; (b)

tail overpressure.

87

a) Initial overpressure

b) Tail overpressure

Fig. 3.12 Distribution of initial and tail overpressures for the 100 cases calculated with temperature fluctuation. The bin size is 0.25, respectively: (a) initial

overpressure; (b) tail overpressure.

88

a) Experimental data for the XB-70 aircraft11

b) Calculated data for wind fluctuation

89

c) Calculated data for temperature fluctuation

Fig. 3.13 Cumulative probability distributions for the overpressure: a) experimental data for the XB-70 aircraft, as obtained in June 1966 (Ref. 11); b)

simulation data from 100 cases of initial overpressures calculated with wind fluctuation; and c) simulation data from 100 cases of initial overpressures

calculated with temperature fluctuation.

90

a) Case with increased boom intensity

b) Case with decreased boom intensity

Fig. 3.14 Variation of the ray tube area relative to the altitude for the wind fluctuation cases: a) increased and b) decreased initial overpressure of sonic boom,

as compared to the no fluctuation case.

91



Fig. 3.15 Variation of the ray tube area relative to the altitude for the temperature fluctuation cases: a) increased and b) decreased initial overpressure of sonic boom,

as compared to the no fluctuation case.

92

3.3.3 Variability of Propagation Path and Reaching Point on the Ground

In this research, we assumed that the SST flies in the north-south direction as

shown in Fig. 3.5. Figure 3.16 shows a comparison of the propagation paths of sonic

boom in the perpendicular plane, for the following three cases: the first is the path

calculated for the no fluctuation case, while the second is the northmost path, and the

third is the southmost path among the 100 cases calculated with atmospheric

fluctuations of (a) wind and (b) temperature, respectively. It becomes clear from Fig.

3.16 that the propagation paths for the above three cases are approximately the same in

both cases (a) and (b), that is, each of the fluctuations has little effect on the propagation

path in any appreciable way. The reason for this is that the rms values of both

fluctuations are much smaller than that of the local speed of sound in the atmosphere.

For example, the rms value set for the wind fluctuation is Vrms = 2.5 ms-1, while the

local speed of sound is around a0 = 300 ms-1. Therefore, the local speed of sound is

dominant to decide the direction of the propagation path of sonic boom.

On the other hand, Fig. 3.17 shows the distribution of sonic boom reaching

points on the ground for both cases, being centered on the reaching point for the no

fluctuation case. The horizontal axis is the north-south direction (direction of flight);

and the vertical axis is the east-west direction (as shown in Fig. 3.5). Then, the ground

track (line x = 0) lies just under the flight path at 60,000 ft. We can observe that the

reaching point on the ground for the no fluctuation case occurs right over the ground

track, as expected. On the other hand, the reaching points for both fluctuation cases are

randomly distributed around the reaching point of the no fluctuation case. Thus, we

have found that the reaching point of sonic boom on the ground varies due to

atmospheric fluctuations of wind and temperature. From the results, in the cases of wind

fluctuation, it is possible to observe that the reaching points on the ground are

distributed over a range of 1820 ft in the north-south direction, and 115 ft in the east-

west direction. Also, in the cases of temperature fluctuation, the reaching points are

93

distributed over a range of 325 ft only in the north-south direction. This is because the

temperature fluctuation affects the local speed of sound and local pressure in terms of

the ray tracing. Then, the calculations were conducted in the perpendicular plane in this

study. Therefore, the propagation paths can not be affected by the temperature

fluctuations in the east-west direction.

Finally, Figs. 3.18 and 3.19 show the distribution of the reaching points on the

ground for both fluctuation cases, respectively, which have the cases with a (a) stronger,

and (b) weaker boom intensity as compared to the no fluctuation case. By comparing

these figures, it is possible to realize that there is no clear correlation between boom

intensity and the location of the reaching point on the ground. Therefore, the increase or

decrease in the propagation distance from the flight path to the ground does not

considerably affect sonic boom intensity. This result supports the variation of the ray

tube area due to the fluctuations as the main cause for the variation in sonic boom

intensity, as mentioned in section 3.2.

94

a) Wind fluctuation


Fig. 3.16 Comparison of propagation paths of sonic boom from flight path to the ground: a) wind fluctuation case; and b) temperature fluctuation case. Both

figures include the following three cases: no fluctuation case, northmost path and southmost path on ray tracing among all cases calculated with atmospheric

fluctuations, respectively (SST flies in the north-south direction).

95

a) Wind fluctuation


Fig. 3.17 Distribution of sonic boom reaching points on the ground for all 100 cases: a) wind fluctuation case; and b) temperature fluctuation case. Flight is in the north-south direction, and ground track (line x = 0) lies just under the flight path

at 60,000 ft.

96



Fig. 3.18 Distribution of sonic boom reaching points on the ground for the wind fluctuation cases, including the no fluctuation case. These figures suggest there is

no considerable correlation between the reaching point on the ground and the initial overpressure of sonic boom: a) increased and b) decreased boom intensity as

compared to the no fluctuation case.

97



Fig. 3.19 Distribution of sonic boom reaching points on the ground for the temperature fluctuation cases, including the no fluctuation case. These figures suggest there is no considerable correlation between the reaching point on the

ground and the initial overpressure of sonic boom: a) increased and b) decreased boom intensity as compared to the no fluctuation case.

98

3.4 Conclusion

This study has investigated the non-deterministic effect of atmospheric

fluctuations of wind and temperature on sonic boom propagation, focusing on the

variability of sonic boom intensity and propagation path. From the results, we verified a

variation of sonic boom intensity due to the variation in the ray tube area provoked by

the atmospheric fluctuations. In both fluctuation cases, for increased ray tube areas we

verified a decreased boom intensity, as opposed to an increased intensity for decreased

ray tube areas. The variability of sonic boom intensity for both fluctuation cases

obtained from the present model were, qualitatively, in good agreement with the

experimental results for the XB-70 aircraft (Jun. 1966). Present results showed that

59 % of the cases with wind fluctuation presented a decreased sonic boom intensity

regarding both initial and tail overpressures, as compared to the no fluctuation case;

53 % of the cases with temperature fluctuation presented a decreased boom intensity.

Thus, atmospheric fluctuations seem to favor a decrease in sonic boom intensity, rather

than increase it. In addition, atmospheric fluctuations had a considerably small influence

on the propagation path from the flight altitude to the ground. However, this influence

still resulted in a variability of the reaching point on the ground: The reaching points

distributed by the wind fluctuation over 1820 ft in the north-south direction (direction of

flight), and 115 ft in the east-west direction; the points distributed by the temperature

fluctuation over 325 ft only in the north-south direction. As a conclusion, we would like

to remark that it is desirable to alleviate sonic boom as much as possible relative to a

target criterion, since environmental conditions such as atmospheric fluctuations may

result in a considerable variation of sonic boom intensity felt on the ground.

99

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10Plotkin, K. J., and George, A. R., “Propagation of Weak Shock Waves through

Turbulence,” J. Fluid Mech., Vol. 54, pt. 3, 1972, pp. 449−467.

11Maglieri, D. J., “Sonic Boom Flight Research – Some Effects of Airplane

Operations and the Atmosphere on Sonic Boom Signatures,” NASA SP-147, Apr. 1967,

pp. 25−48.

12Kane, E. J., “Some Effects of the Atmosphere on Sonic Boom,” NASA SP-147,

Apr. 1967, pp. 49−63.





15Lipkens, B., and Blackstock, D. T., “Model Experiment to Study Sonic Boom

Propagation through Turbulence. Part І: General Results,” J. Acoust. Soc. Am., Vol.

103(1), Jan. 1998, pp. 148−158.

16Blanc-Benon, P., Lipkens, B., Dallois, L., Hamilton, M. F., and Blackstock, D. H.,

“Propagation of Finite Amplitude Sound through Turbulence: Modeling with

Geometrical Acoustics and the Parabolic Approximation,” J. Acoust. Soc. Am., Vol.

111(1), Pt. 2, Jan. 2002, pp. 487−498.

17Chernyshev, S. L., Kiselev, A. P., and Vorotnikov, P. P., “Sonic Boom

Minimization and Atmospheric Effects,” AIAA Paper 2008-0058, Jan. 2008.

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Detailed Vertical Wind Speed Profiles,” J. Atmosph. Sci., Vol. 26, Issue 5, 1969, pp.

1030−1041.

25Chkhetiani, O. G., Eidelman, A., and Golbraikh, E., “Large- and Small-scale

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29Hayes, W. D., and Runyan, H. L. Jr., “Sonic-Boom Propagation through a

Stratified Atmosphere,” J. Acoust. Soc. Am., Vol. 51(2), Pt. 3, Nov. 1972, pp. 695−701.

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103

Chapter 4. Effect of Atmospheric Gradients on Sonic Boom Intensity by the Four Seasons Nomenclature

a = speed of sound

AL = body reference length in feet

A = ray tube area

cn = speed that a wave propagates normal to itself

C1 = atmospheric quantity given by equation (4.4)

C2 = atmospheric quantity given by equation (4.5)

h = distance taken perpendicularly from the body chord axis to the ground

direction

H = flight altitude above the ground in feet

l = longitudinal dimension and body reference length used by computational

fluid dynamics

m = slope of waveform

M = Mach number

ML = model reference length

P = pressure in psf

104

ΔP = overpressure of sonic boom in psf and pressure rise across shock at the

juncture of waveform

psf = pounds per square foot

t = time

x, y, z = Cartesian coordinates

χ = wave amplitude

γ = ratio of specific heats

λ = time duration of waveform

ρ = density

Subscripts

i = segment

0 = ambient

∞ = free-stream

4.1 Introduction

A meteorological condition can significantly affect a sonic boom during its

propagation. Particularly, it is well known that a sonic boom is strongly affected by an

atmospheric gradient in a real atmosphere, which results in the variation of sonic boom

intensity felt on the ground. In the supersonic aircraft design, the standard atmospheric

condition1 is generally utilized to estimate the influence of sonic boom. However, the

atmospheric conditions widely vary by the seasons and the regions. Therefore, it is

reasonable to suppose that a variation in boom intensity is likely to occur in the

real-world.

Several studies have been conducted to evaluate the sonic boom influence,

assuming the actual flight under the real atmospheric condition.2-4 This is because,

105

naturally, it is important to improve the understanding of the precise impact of sonic

boom under the real environment condition, in order to create a supersonic aircraft in

the near future. In addition, it seems to be better to alleviate the sonic boom sound not

only by the use of low boom design, but also by utilizing the effect of meteorology.2-4

That is, there may be an area and/or a route in the world where low boom flight can be

possible due to the real atmospheric condition.

The purpose of this study is to investigate the effect of real atmospheric

gradients on sonic boom intensity, followed by an examination of the global distribution

of sonic boom intensity for four seasons. Especially, we focus on tendency of seasonal

variations and areal difference of sonic boom intensity, as compared to the standard

atmospheric condition.

The paper is organized as follows: Section 4.2 brings a brief description of the

numerical models and methods for the sonic boom calculations with the observational

data. Section 4.3 presents the results and discussions on the effect of atmospheric

gradients on sonic boom intensity. Finally, Section 4.4 concludes the present study.


Figure 4.1 shows the logical flow chart of the sonic boom calculation in the

present study. The computational procedure consisted of the following three

components: First, the meteorological data5 obtained by a radiosonde (balloon-borne

instrument)6, were processed. This process includes the data filtering, the vertical

interpolation of the observational data, and the calculation of the seasonal average

obtained by averaging the data for three months. The temperature gradient was created

at all observation points of the world (as shown in Fig. 4.3). Second, the sonic boom

was calculated by using the near-field pressure wave, which was induced by the

Sears-Haack body,7 and the seasonal temperature gradient and the ground pressure as an

106

input-data. Last, we created the distribution maps of sonic boom intensity of the world.

The detailed descriptions of the calculation methodology are discussed in the following

sections.

Fig. 4.1 Logical flow chart of the creation of a distribution map of sonic boom

intensity.

4.2.1 Processing of Observational Data of Radiosonde

The observational data were obtained by a radiosonde,6 which measures

temperature, pressure, humidity, and wind to monitor weather, climate, and the

environment of the world. This upper-air observations are performed twice a day at

0000 and 1200 UTC (Universal Time Coordinated) in many parts of the world.5 In this

study, the data of temperature and ground pressure at each observation point from

March 1, 2007 to February 29, 2008 were used. Also, the calculation of the seasonal

107

average for three months were performed for the cases of MAM (March, April, and

May), JJA (June, July, and August; northern hemisphere summer), SON (September,

October, and November), and DJF (December, January, and February; northern

hemisphere winter). In the case of DJF, the averaging was performed by using the data

from December 2007, and January and February of 2008 for three months data.

The observations are carried out at 491 (MAM), 495 (JJA), 487 (SON), and 499

(DJF) stations for each season. Figure 4.2 shows the observation points in the case of

MAM. From Fig. 4.2, we can see that many observation points are concentrated in the

northern hemisphere, while there are few points in southern hemisphere; particularly the

points in the South-America and the Africa continent are very limited. Therefore, we

proceed with our discussion focusing mainly on the northern hemisphere and around the

Southeast-Asia.

In addition, four observation points were mainly discussed to investigate the

effect of atmospheric gradients on sonic boom intensity. Table 4.1 shows the station

information of these four points, regarding the latitude, longitude, and elevation. The

locations of the points are indicated by the diamond symbols in Fig. 4.2, respectively.

The characteristics of these four points are as follows: Singapore, Madrid, and Tasiilaq

are located at low latitude (near the equator), mid-latitude, and high latitude,

respectively; Yushu is located at high-altitude near the Himalaya Mountains, as shown

in Fig. 4.2.

Figure 4.3 shows the variation of the temperature gradients in JJA and DJF for

the four points, which were obtained by the processed data of radiosonde, as compared

to that of the standard atmosphere. It becomes clear from the figures that there are the

differences in the value of temperatures between the real atmosphere and the standard

atmosphere, and then, the atmospheric gradients can change considerably by the seasons

and the regions.

108

Fig. 4.2 491 observation points of the radiosonde in the world (indicated by closed circles) used for the sonic boom calculation in the case of MAM: The

diamond symbols indicate the locations of the four observation points mainly discussed in the present study. The detailed information of these points is given in

Table 4.1.

Table. 4.1 Information of the particular observation points discussed in this

study.

109

a) Case of JJA

b) Case of DJF

Fig. 4.3 Variation of the temperature gradients of Singapore, Madrid, Tasiilaq, and Yushu in 2007-2008, as compared to that of the standard atmosphere

(indicated by thin solid line). These temperature gradients were calculated from the observational data of radiosonde: a) JJA; and b) DJF.

110

4.2.2 Sonic Boom Calculation

Figure 4.4 shows the computational near-field signature for the Sears-Haack

body7 at h/l = 5.0, which was obtained from the previous study8 by using the CFD

calculation in Euler mode9. By using this signature as an input-data, a simple N wave

was created on the ground. We used this signature in this study to make it easy to

understand the effect of atmospheric gradients on sonic boom intensity. Also, sonic

boom calculation was performed by the Waveform Parameter method10,11 in the

perpendicular plane from the flight path to the ground. The equations of the method can

be written by Eqs. (4.1), (4.2), and (4.3):

i22

i1i mCmC

dtdm

+= (4.1)

( ) i21iii1i pCmmpC

21

dtpd

ΔΔΔ

++= − (4.2)

( ) ii11ii1i mCppC

21

dtd

λΔΔλ

−+−= + (4.3)

where mi, ΔPi and λi are the waveform parameters. The atmospheric quantities C1 and

C2 are given by Eqs. (4.4) and (4.5):

n0

01 cp

a2

1Cγ

γ += (4.4)

⎟⎟⎠

⎞⎜⎜⎝

⎛−−+=

dtdA

Adtdc

cdtd

dtda

aC n

n

121321 0

0

0

02

ρρ

(4.5)

where γ is the ratio of specific heats and a0, p0, and ρ0 are the ambient properties. Also,

cn is the speed that a wave propagates normal to itself and A is the ray tube area.

As for the calculation conditions, the supersonic aircraft was assumed to be in

111

steady flight at an altitude of H = 60,000 ft with a cruise mach number of M∞ = 1.7; the

model reference length and the aircraft length were set as ML = 1.0 and AL = 202 ft,

respectively (AL referred to the total length of the Concorde12). The temperature

gradients and the ground pressure of each observation point were used as the initial

setting of the atmospheric conditions, where there is no wind. Besides, the difference of

gravity according to the latitude was considered in terms of the calculation of pressure

and atmospheric quantity, defined by Eq. (4.5).

It is important to note that the difference of altitude of each observation point

was considered in this calculation: sonic boom intensity was multiplied by the sonic

boom reflection factor of 1.9 at each ground elevation. When calculating with the

standard atmosphere, on the other hand, the boom intensity at the sea level (0 ft) was

used; the latitude and longitude were set as zero, respectively.

Fig. 4.4 Near-field pressure signature for the Sears-Haack body at h/l = 5.0,

which was obtained by the use of the CFD calculation in Euler mode.8

112

4.2.3 Mapping of Global Distribution of Sonic Boom Intensity

An initial overpressure of sonic boom was evaluated as a sonic boom intensity.

Subsequently, the differences in boom intensity between each observation point and the

standard atmosphere were interpolated by using the Generic Mapping Tools.13,14 In this

study, the values of boom intensity over the sea were masked: the values over the sea

were used for the interpolation, however, they were not visualized. This is because there

are only limited number of observation points available over the sea, as shown in Fig.

4.2., i.e., the spatial resolution over the sea is not sufficient to ensure a reliable result.

However, this treatment does not pose much problem in examining the effects of

atmospheric gradients on sonic boom intensity, since the supersonic flight is prohibited

only over the land in the United States and other nations.15

As for the sonic boom calculation, the boom propagates and moves away from

the observation point, i.e., the point where the sonic boom reaches the ground for each

case is not the same as the observation point. However, we treated the calculated boom

intensity as the value of the each observation point, since the distance between the

observation point and the reaching point is small enough when considering the entire

world.


4.3.1 Variation of Sonic Boom Waveform

Figure 4.5 shows the sonic boom signatures for the five cases calculated with

each atmospheric gradient, as shown in Figs. 4.3 (a) and (b), respectively. From the

results, we can confirm that there is a variation of sonic boom signature due to

atmospheric gradients, although all sonic boom signatures were calculated with the

same near-field pressure wave, as shown in Fig. 4.4. Table 4.2 represents the

113

comparison of boom intensity (ΔP) and the difference in boom intensity between the

value of each case and the standard atmosphere (ΔP − ΔPstandard atmosphere), respectively.

As indicated in Table 4.2, the reference boom intensity of the standard atmosphere

became ΔP = 1.109 psf (= lb/ft2). On the other hand, there are differences in boom

intensity compared to that of the standard atmosphere at each observation point. Thus,

we discussed the variation in boom intensity, focusing on these differences in the

following sections.

a) Case of JJA

114

b) Case of DJF

Fig. 4.5 Comparison of the sonic boom signatures on the ground calculated with the five atmospheric gradients given in Fig. 4.3, respectively: a) JJA; and b) DJF.

Both figures include the results of Singapore, Madrid, Tasiilaq, Yushu, and the standard atmosphere. The initial conditions were set as flight Mach number M∞ =

1.7, flight altitude H = 60,000 ft, model reference length ML = 1.0, and body reference length AL = 202 ft.

Table. 4.2 Comparison of sonic boom intensity and the difference in boom intensity on the ground, between the value of each observation point and the

standard atmosphere.

115

4.3.2 Seasonal Change of Sonic Boom Intensity

Figure 4.6 shows the distribution maps of the variation in sonic boom intensity

throughout the world in 2007−2008. These figures represent the cases of (a) MAM, (b)

JJA, (c) SON, and (d) DJF, respectively, in order to compare the sonic boom intensity

among the seasons. The contours show the difference in sonic boom intensity between

the value of each point and that of the standard atmosphere; the contour interval is 0.025

for all figures. That is, the contour value of zero is the result of the standard atmosphere.

Hence, in the case where the sonic boom intensity is positive, it means the boom

intensity increased, while the case where the value is negative, the boom was reduced

by the effect of atmospheric gradients in a real atmosphere.

From Fig. 4.6 (a) to (d), we can confirm that the boom intensity varies according

to the regions of the world. In the low latitude regions around the Southeast-Asia, it is

possible to observe that the boom intensity increases slightly throughout the year, while

the intensity decreases in the high latitude regions of the northern hemisphere. Also, the

mountainous regions, around the Himalaya Mountains and the Rocky Mountains, have a

relatively small value on sonic boom intensity (we discussed on this matter in the

following section 4.3.4).

In addition, it becomes clear from Fig. 4.6 that there is a variation in boom

intensity according to the seasons. In the northern hemisphere, similar results are

obtained in MAM (northern spring) and SON (northern autumn), while the intensity is

actually stronger in JJA (northern summer) than DJF (northern winter). These results

mean that there is a certain correlation between the meteorological condition and the

boom intensity on the ground. Furthermore, there is a possibility that the atmospheric

effect will be effective for low boom flight by choosing a right flight path.

The tendency of the seasonal variations in sonic boom intensity seems to be

similar to the change of the ground temperature. As for the correlation between them,

Fig. 4.7 shows the comparison of the seasonal variation of the ground temperature and

116

the boom intensity at the four observation points (as shown in Table 4.1), respectively.

In Madrid and Tasiilaq, where the four seasons are clear, the boom intensity increases in

JJA along with the ground temperature, whereas the intensity decreases in DJF.

However, the tendency of boom intensity does not always correspond with the

seasonal variation in ground temperature. In Singapore, for example, the intensity varies

slightly with the seasons, although the ground temperature remains constant, as shown

in Fig. 4.7 (a). Additionally, the intensity of Tasiilaq increase sharply in JJA compared

to other cases. These are because the examinations described above only consider

ground temperature, though the sonic boom is mainly affected by a state quantity in the

real atmosphere during its propagation. Therefore, it is necessary to examine a

correlation between the changes of the atmospheric gradients and the boom intensity on

the ground.

117

a) Case of MAM

b) Case of JJA

118

c) Case of SON

d) Case of DJF

Fig. 4.6 Distribution maps of variation in sonic boom intensity throughout the world for four seasons in 2007-2008 north of 60°S: a) MAM; b) JJA; c) SON; and d) DJF. In all figures, the contour interval is 0.025, and the contours represent the difference in sonic boom intensity between the value of each point and that of the

standard atmosphere.

119

a) Ground temperature

b) Sonic boom intensity on the ground

Fig. 4.7 Comparisons of a) ground temperature and b) sonic boom intensity on the ground in the four observation points for four seasons in 2007-2008, which also

includes the results of the standard atmosphere.

120

4.3.3 Effect of Atmospheric Gradients on Sonic Boom Intensity

In order to investigate a correlation between the atmospheric gradients and the

sonic boom intensity on the ground, we examined the change of an acoustic impedance

density ρ∞a∞ and the ray tube area A of an altitude, respectively, where the ρ∞ is the

local density and the a∞ is the local speed of sound in the atmosphere. The value of ρ∞a∞

determines the atmospheric condition through which sound propagates. Also, the ray

tube area is affected by the transition of the propagation path of sonic boom due to

atmospheric condition: These two physical values vary due to the effect of atmospheric

gradients. In addition, from geometric acoustics, the wave amplitude χ is proportional to

the square root of the acoustic impedance density, and also the amplitude is inversely

proportional to the square root of the ray tube area, as given in Eq. (4.6);

Aa∞∞∝

ρχ (4.6)

It is important to note that there are other factors which can affect sonic boom

intensity, for example, the nonlinear waveform distortion. However, in the present study,

we simply focus on whether the variation in boom intensity is associated with the

atmospheric gradients. Therefore, it is appropriate to examine the variations of ρ∞a∞ and

A.

For sample cases, we selected Tasiilaq and Singapore since these two observation

points have characteristic seasonal variation in boom intensity: From Fig. 4.7, Tasiilaq

has seasonal temperature variation and indicates clear seasonal variation in boom

intensity; Singapore slightly varies throughout the year in boom intensity, though it does

not have seasonal temperature variation.

Figures 4.8 and 4.9 show the comparison of the vertical profiles in Tasiilaq and

Singapore for four seasons, respectively. These figures include the results of (a)

121

(ρ∞a∞)1/2, (b) A1/2, (c) (ρ∞a∞/A)1/2, and (d) ΔP. In Fig. 4.8 (d) and Fig. 4.9 (d), the sonic

boom reflection factor was not employed, since both figures represent the value of ΔP

during the propagation. In the case of Tasiilaq, the values of (ρ∞a∞)1/2 and A1/2 vary

according to the seasons, which results in the change of (ρ∞a∞/A)1/2, as shown in Fig. 4.8

(a) to (c). Also, by comparing the result of (ρ∞a∞/A)1/2 with that of ΔP, both results

indicate similar tendency in seasonal variation, as shown in Figs. 4.8 (c) and (d). From

these results, we found that the sonic boom intensity is closely associated with the

variation of the atmospheric gradients, i.e., state quantity in the real atmosphere.

Thereby, the boom intensity turns out to be changed at the ground.

On the other hand, it is seen from Fig. 4.9 that the (ρ∞a∞)1/2 and A1/2 still slightly

change during the propagation, although in Singapore the four seasons are not distinct,

as shown in Fig. 4.7 (a). These small changes in both values probably result in the

seasonal variation of sonic boom intensity on the ground, consequently. Therefore, we

confirm that atmospheric gradients will affect the variation of boom intensity more

strongly than the ground condition of atmosphere.

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a) Square root of acoustic impedance density

b) Square root of ray tube area

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c) Square root of acoustic impedance density divided by ray tube area

d) Sonic boom intensity

Fig. 4.8 Comparison of vertical profiles in Tasiilaq for four seasons in 2007-2008: a) (ρ∞a∞)1/2; b) A1/2; c) (ρ∞a∞/A)1/2; and d) ΔP.

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a) Square root of acoustic impedance density

b) Square root of ray tube area

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c) Square root of acoustic impedance density divided by ray tube area

d) Sonic boom intensity

Fig. 4.9 Comparison of vertical profiles in Singapore for four seasons in 2007-2008: a) (ρ∞a∞)1/2; b) A1/2; c) (ρ∞a∞/A)1/2; and d) ΔP.

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4.3.4 Effect of Altitude on Sonic Boom Intensity

As mentioned in section 4.3.2, sonic boom intensity of Yushu was much

smaller than that of other regions throughout the year, as shown in Fig. 4.7 (b). For this

matter, Fig. 4.10 shows the comparison of sonic boom intensity with altitude for four

cases in (a) JJA, and (b) DJF, as compared to the case of the standard atmosphere. Here,

the sonic boom intensity is not multiplied by the sonic boom reflection factor for all

cases. From the results, it is possible to observe that the sonic boom intensity decreases

until around 35,000 ft (i.e., the tropopause). Below that height, the boom intensity stops

decreasing and increases slightly until sonic boom reaches at the ground. In the case of

Yushu, sonic boom reaches on the ground faster than that of other cases, since the

altitude of Yushu is 12,080 ft. Therefore, the sonic boom intensity decreased at Yushu.

This result supports that under real atmospheric conditions, sonic boom intensity

becomes weaker in high-altitude region (around mountainous region), as described in

section 4.3.2.

a) Case of JJA

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b) Case of DJF

Fig. 4.10 Comparison of sonic boom intensity with altitude for the cases of

Singapore, Madrid, Tasiilaq, Yushu, and the standard atmosphere: a) JJA; and b) DJF.

4.4 Conclusion

The effect of real atmospheric gradients on sonic boom intensity has been

investigated by the use of upper-air observational data of radiosonde. From the results,

we found that there was a fluctuation of sonic boom signature due to atmospheric

gradients, which resulted in a variation of sonic boom intensity, as compared to the

intensity of standard atmosphere. We verified that this variation of boom intensity was

caused by real atmospheric condition varied by the regions and seasons. Regarding the

areal difference, a high latitude region of the northern hemisphere had lower intensity,

as compared to the low latitude region around the Southeast-Asia throughout the year.

As for the seasonal variation of boom intensity, in the northern hemisphere, the boom

128

intensity decreased in winter, in contrast to an increased intensity in summer. In

addition, under the real environmental condition, the mountainous regions around the

Himalaya Mountains and the Rocky Mountains presented a decrease in sonic boom

intensity due to their characteristics of high-altitude. In conclusion, we would like to

remark that it is important to improve understanding of alteration in sonic boom under

the real environmental condition for the realization of a supersonic flight in the near

future. Actually, several factors such as atmosphere and terrains have a significant

influence on sonic boom propagation.

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References

1Anderson, J. D. Jr., Introduction to Flight: Fourth Edition, McGraw-Hill

Companies, Inc., New York, 2000, pp. 94−99, 709−720.

2Blumrich, R., Coulouvrat, F., and Heimann, D., “Variability of Focused Sonic

Booms from Accelerating Supersonic Aircraft in Consideration of Meteorological

Effects,” J. Acoust. Soc. Am., Vol. 118, No. 2, August 2005, pp. 696−706.

3Blumrich, R., Coulouvrat, F., and Heimann, D., “Meteorologically Induced

Variability of Sonic-Boom Characteristics of Supersonic Aircraft in Cruising Flight,” J.

Acoust. Soc. Am., Vol. 118, No. 2, August 2005, pp. 707−722.

4Coulouvrat, F., Blumrich, R., and Heimann, D., “Meteorologically Induced

Variability of Sonic Boom of a Supersonic Aircraft in Cruising of Acceleration Phase,”

Proceedings of the 17th International Symposium on Nonlinear Acoustics, State college,

Pennsylvania, 2005, pp. 579−586.

5“Weather Data for Wyoming,” University of Wyoming, Department of Atmospheric

Science, http://weather.uwyo.edu/wyoming/ (cited November 10, 2008).

6“Upper-air Observations,” Japan Meteorological Agency,

http://www.jma.go.jp/jma/en/Activities/ observations.html (cited December 9, 2008).

7Sears, W., “On Projectiles of Minimum Wave Drag,” Quarterly of Applied

Mathematics, Vol. IV, No. 4, Jan. 1947.

8Yamashita, H., and Obayashi, S., “Numerical Investigation on Sonic Boom

Reduction with Non-axisymmetric Body Shapes,” AIAA 2008-0059, 46th AIAA

Aerospace Sciences Meeting and Exhibit, Reno, USA, Jan. 2008.

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13“The Generic Mapping Tools,” The University of Hawai`i System,

http://hawaii.edu/ (cited November 10, 2008).

14Smith, W. H. F., and Wessel, P., “Gridding with Continuous Curvature Splines in

Tension,” Geophysics, Vol. 55, No. 3, March 1990, pp. 293−305.



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Chapter 5. Conclusions

The objective of this thesis is to develop the three environmental technologies

for sonic boom problem, which can be effective to reduce the sonic boom and also to

evaluate the sonic boom impact on the environment. The proposed method to overcome

the severe drag penalty by using the plain flaps achieved improvement in the

aerodynamic performance of Busemann biplane. Therefore, it is expected to be applied

for the supersonic biplane MISORA, as one of the design technique to realize a low

boom flight. In addition, by using the evaluation method for the variation of sonic boom

due to atmospheric fluctuations is expected to investigate the definitive mechanisms and

effects of atmospheric turbulence. Furthermore, the precise analyses on environmental

impact due to sonic boom are useful to create a precise noise regulation on sonic boom.

On top of that, there is a possibility that utilization of the effect of real environmental

conditions will be effective to reduce sonic boom. Following is the conclusions derived

from this thesis:

In chapter 2, a design technology applied for MISORA was proposed to

overcome the choked-flow and flow-hysteresis problems of the supersonic biplane at

off-design conditions, by using plain flaps at the leading and trailing edges.

Two-dimensional analyses of four different biplanes were addressed in order to examine

the effect of the flaps, using Computational Fluid Dynamics (CFD) in inviscid flow

(Euler) mode. Results show that the leading-edge flaps can alleviate the drag increase

due to the choked-flow, and reduce the area of flow-hysteresis. In contrast, the

trailing-edge flaps are not effective in overcoming these problems. However, the

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trailing-edge flaps can reduce the wave drag near to the speed of sound, and also shift

the drag-divergence Mach number to a higher one. Thus, the combined effect of both

flaps allows us to smoothly achieve the design point (M∞ = 1.7) from subsonic regime,

and to avoid the severe drag penalty due to the choked-flow and flow-hysteresis

problems.

In chapter 3, the non-deterministic effects of wind and temperature fluctuations

on sonic boom propagation were separately investigated. The Sears-Haack body was

calculated in three-dimensions by use of Computational Fluid Dynamics (CFD) in

inviscid flow (Euler) mode, in order to create the near-field pressure wave. The

fluctuation fields were represented by a finite sum of discrete Fourier modes, based on

the von Karman and Pao energy spectrum. Then, the sonic boom signature was

calculated by the modified Waveform Parameter Method, considering random

fluctuations of wind and temperature, respectively. Results show that the wind

fluctuation has a great influence on sonic boom intensity during its propagation to the

ground. As compared to the no fluctuation condition, we have observed that 59 % of the

cases had a decreased, and 41 % of the cases had an increased sonic boom. Hence, the

wind fluctuation seems to favor a decrease in boom intensity, rather than increase it. On

the other hand, the temperature fluctuation results in a small variation of the sonic boom

intensity. In addition, we observed that both fluctuations have a considerably small

effect in changing the propagation path from the flight altitude to the ground.

Nonetheless, this small change in the propagation path may result in a variability of the

sonic boom reaching point on the ground of up to 1820 ft in the north-south direction

(flight direction) and 115 ft in the east-west direction.

In chapter 4, the effect of atmospheric gradients under a real atmospheric

condition on sonic boom intensity was discussed, focusing on the variation in boom

intensity due to the seasons and regions. The atmospheric gradients observed by

radiosonde and the near-field signature for the Sears-Haack body obtained from

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Computational Fluid Dynamics (CFD) were employed. Then, sonic boom was

extrapolated through the atmospheric gradients without winds in the world, by use of

the Waveform Parameter Method. Results show that atmospheric gradients have a great

influence on sonic boom intensity under the real environmental condition. Throughout

the year, the high latitudes of northern hemisphere seem to decrease slightly the boom

intensity, as compared to the low latitudes around the Southeast-Asia. Also, in the

northern hemisphere, we observed a decreased intensity in winter, as opposed to an

increased intensity in summer. In addition, we verified that the high-altitude regions

favor a decrease in boom intensity.

In eco-efficient supersonic aircraft design, environmental technologies which

can reduce and evaluate sonic boom impact are needed, respectively, such as the

technologies proposed in this thesis. By the use of those technologies, we will be able to

improve the scientific understanding of sonic boom phenomenon, and the improved

understanding can also help us to develop a right approaching method for low boom

flight.

environmental technologies for sonic boom mitigation in

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