measurements of the pressure distribution on the horizontal-tail

Sz NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICSz

TECHNICAL NOTE

No. 1539

MEASUREMENTS OF THE PRESSURE DISTRIBUTION ON THE

HORIZONTAL-TAIL SURFACE OF A TYPICAL PROPELLER-

DRIVEN PURSUIT AIRPLANE IN FLIGHT. III - TAIL

LOADS IN ABRUPT PULL-UP PUSH-DOWN MANEUVERS

By Melvin Sadoff and Lawrence A. Clousing

S1 .. Ames Aeronautical Laboratory

Moffett Field, Calif.

iii Washington

February 1948

Reproduced FromBest Available Copy 2000080 205

Vi q unmor

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL NOTE NO. 1539

MEASUREMENTS OF TEE PRESSURE DISTRIBUTION ON THEHORIZONTAL-TAIL SURFACE OF A TYPICAL PROPELLER-

DRIVEN PURSUIT AIRPLANE IN FLIGHT. III - TAILLOADS IN ABRUPT PULL--UP PUSH-DOWN MAIEUVERS

By Melvin Sadoff and Lawrence A. Clousing

SUMMARY

The total horizontal-tail load and the root bending-momentincrements calculated by the use of existing rational proceduresare compared with experimental values obtained in pull-up push-downmaneuvers on a representative propeller-&riven pursuit-type airplanefor six different combinations of power, indicated airspeed, andpressure altitude. The computed loads were determined for theexperimental elevator motions, and for two estimated linear designmotions. There is also presented a comparison between the computedand the experimental load distributions. Briefly touched upon aretwo abbreviated static methods for predicting the maximum up-loadsin pull-up push-down maneuvers.

The results showed that where the computed load and bending-moment increments are determined from measured elevator motions,the agreement with the experimental results is fairly good, thusindicating the validity of methods currently available for calcula-ting maximum maneuvering tail loads. It was also shown that ifpossible errors in the aerodynamic parameters were accounted for,the agreement between the measured load and bending-moment incrementsand those computed from the estimated linear elevator motions, forvalues of maximum airplane load factor approximately the same asthose measured, would be practically as good as that obtained usingthe experimental elevator motions. Results are also includedshowing that the prediction of the maximum maneuvering loads by theuse of two less rigorous abbreviated procedures agreed satisfactorilywith the load increments measured. Comparison of the calculated withthe experimental load distributions showed that fairly good agreementwas obtained when the measured and computed over-all tail loads werein close agreement. However, as compared with experimental results,

2 NACA TN No. 1539

an increase in loading was computed for the inboard stabilizersections and a decrease in loading for the outboard sections, The

difference in loading would be equivalent to a root bending moment

approximately 10 percent less than the measured values when the over-all loads were the same.

INTRODUCTION

In recent years particular emphasis has been placed on providing

a simplified rational method for predicting the maneuvering horizontal-tail loads associated with abrupt motions of the elevator. The methods

available in the past for computing dynamic tail loads rationally were

too unwieldy to use in routine design analyses. Modifications of

these methods have been directed primarily toward simplifying andshortening the necessary computations, and toward selection of a

longitudinal maneuver which would be amenable to computation and

which would adequately define the critical loading condition on the

horizontal tail.

In reference 1, for example, general design charts in nondimensional

form are given by which the tail-load increment variation in abrupt

maneuvers may be determined for any arbitrary elevator motion. Simi-

larly, reference 2, which is a part of the tail-load design requirements

for the Army, presents a simple tabular integration method for comput-

ing maneuvering tail loads resulting from abrupt linear variations

of elevator motion. In this method the time histories of these motions

are represented by a series of straight lines simulating a pull-up

push-down maneuver for an unstable airplane where the maximum up-

elevator deflection is arbitrarily assumed twice the maximum downvalue.

A check of the validity of the assumptions and mathematicalsimplifications of references 1 and 2 is, of course, desirable. This

is provided in the present investigation by comparing the horizontal-

tail load increments measured in flight with values computed for

maneuvers having elevator motions identical to the experimental. The

computations of tail load for the purpose of this comparison were made

using only the method of reference 1, since it is mathematically similar

to that of reference 2, and a check of either method would establish

the validity of the other. Furthermore, the graphical method of

reference 1 is adaptable to the irregular or nonlinear elevator motions

that generally occur in flight, which is not the case for the methodof reference 2. Some results of comparisons of this type have already

been presented in reference 3.

Since designers must use estimated elevator motions in tail-loadcomputations, it is also desirable to determine how closely horizontal-

tail-load values computed in linearized pull-up push-down maneuvers

NACA TN No. 1539 3

of the type described in reference 2 compare with those measured inpull-up push-down maneuvers made by a pilot in flight. Comparisonsare therefore made of the horizontal-tail-load increments measuredin flight and those computed by the method of reference 2. In thesecomparisons the values of elevator deflection used in the computationswere taken such that the computed increments of maximum accelerationwere identical with those measured in the maneuvers for which thecomparisons were made. In setting up rates of elevator motion inthese computations, data presented in reference 4 were of consider-able value.

Although the methods of references 1 and 2 for computing dynamictail loads are less unwieldy than the unsimplified classical methodsavailable formerly, considerable computational time is still requiredin their application. Therefore, information relative to means forshortening the computations is believed of interest. Two abbreviatedmethods of tail-load computation, which result from modifications ofthe method of reference 2, are described, and comparisons are madeof tail loads computed by these shortened methods with those measured.The comparisons are made on the basis of identical increments ofacceleration.

An additional objective of this report is the investigation ofthe validity of methods currently used for predicting the maneuver-ing load distributions over the horizontal tail, and information onthis subject is presented.

The experimental tail loads and tail-load distributions presentedin this note were measured in abrupt pull-up push-down maneuvers forsix different combinations of power, indicated airspeed, and pressurealtitude. The two previous notes in this series nave dealt with tailloads in steady unaccelerated and steady accelerated flight (reference 5),and tail loads in steady sideslips (reference 6).

SYMBOLS

W airplane weight during test run, pounds

g acceleration of gravity, feet per second per second

m airplane mass (W/g), slugs

S horizontal surface area, square feet

b horizontal surface'span, feet

wing mean aerodynamic chord, feet

4 NACA TN No. 1539

c local tail chord, feet

Ky radius of gyration about Y-axis, feet

Iy moment of inertia about Y-axis, slugs-feet squared

xt tail length (distance from airplane center of gravityto one-third maximum chord point of tail), feet

Vi correct indicated airspeedo0.286 I

{17o3[(--+i) -iJ , miles per hour

H free-stream total pressure

p free-stream static pressure

P0 standard atmospheric pressure at sea level

hp pressure altitude, feet

M free-stream Mach number

V true airspeed, feet per second

p mass density of air, slugs per cubic foot

q free-stream dynamic pressure, pounds per square foot

Pu pressure on upper surface, pounds per square foot

pI pressure on lower surface, pounds per square foot

PR resultant pressure coefficient (P -Pu)/q

Tit tail efficiency factor (qt/q)

M pitching moment (stalling moment positive),foot-pounds

Mr root bending moment (positive when tail tip isdeflected upward), foot-pounds

Nt normal air load on horizontal tail (positive whenload is acting upward), pounds

NACA TN No. 1539 5

Cm pitohing-moment coefficient (M/qSw)

Cmt tail-moment coefficient due to effective camber(Mtbt/q~qtSt

2 )

CMr tail root bending-moment coefficient (Mr/qStbt)

Cn section normal-force coefficient

CNt tail normal-force coefficient (Nt/TtqBt)

AZ the ratio of the net aerodyvnamic force alongthe airplane Z-axis (positive when directedupward) to the weight of the airplane

CL airplane lift coefficient (WAz/qSw)

a horizontal surface angle of attack, radians

E downwash angle, radians

be elevator angle, radians (unless otherwise noted)

sideslip angle (positive when right wing isforward), degrees

e angle of pitch, radians

MYj pitching velocity (d/dt), radians per second

K empirical damping factor denoting ratio of dampingmoment of complete airplane to damping moment oftail alone

F elevator stick force, pounds

t time, seconds

Taerodynamic time t/(m/PSwV)

Athis symbol before any quantity other than asubscript denotes the change in value ofquantity from time T = 0

KI',K 2 ',K 3 ' nondimensional constants occurring in basicdifferential equation in reference 1

a,bV,V' functions of the aerodynamic derivatives in thebasic differential equations in reference 2

hL

6 NACA TN No. 1539

functions of de/dt and the aerodynamicderivatives in the basic differentialequations in reference 2

&W do4/dt or da/dT

4 de/dt or d0/d'r

d2aw/dt 2 or . d2aw/dT2

" d2e/dt 2 or d2 6/dr2

Subscripts

a airplane

a-t airplane minus tail

w wing

t tail

av average

exp experimental

calc calculated

max maximum value

bal for balance

man in maneuver

Abe due to change in elevator-angle increments atmaximum acceleration, such asAe = (Aebal - Abeman)AZmax

0" due to pitching acceleration at AZmax

DESCRIPTION OF AIRPLA1NE

The test airplane used was a single-engine, pursuit-type, low-wing monoplane with a tractor propeller. Figures 1 and 2 are photo-graphs of the airplane as instrumented for the flight tests; figure 3

NACA TN No. 1539 7

is a three-view drawing of the airplane. The pertinent geometric4 , and aerodynamic characteristics of the airplane are given in tables I

and II, respectively. The aerodynamic characteristics were obtainedfrom the various sources listed in table II.

INSTRUMENTATION AND PRECISION

A 6 0-cell pressure recorder was used to measure the resultantpressures over the horizontal tail at the locations given in table IIIand shown in figure 4. The precision with which the pertinent quanti-ties were believed to be measured in the tests is indicated in thefollowing table:

Item Estimated accuracy

Normal acceleration ±0.10 g

Elevator angle ±0.500

Sideslip angle ±1.00

Airspeed (to 200 mph) ±22percent(above 200 mph) .-- percent

Altitude ±300 feetTail load (steady,

unaccelerated flight) ±50 pounds

(accelerated flightin abrupt maneuvers) ±250 pounds

It should be noted that the estimated precision of the normalacceleration and the tail loads in accelerated flight during abruptmaneuvers is less than that reported in references 5 and 6. Thisreduction in the estimated accuracy of the measurements results fromthe fact that in abrupt maneuvers the manometer records were moredifficult to correlate at given time instants, and the effect ofpitching acceleration on the readings of the accelerometer, displacedslightly aft of the center of gravity, was not accounted for. Thepressure-lag characteristics of typical horizontal-tail lines wereinvestigated and it was found that the lag was negligible for therates of pressure change encountered in this investigation. Other

4instrumentation of the test airplane and the precision of the

8 NACA TN No. 1539

measurements were the same as given in reference 5o

FLIGHT PROGRAM

Six abrupt pull-up push-down maneuvers were made at the flightconditions listed in the following table:

Power

Run Viav hpav Mav Estimatedl

Power setting brakehorsepower

1 358 20250 0.68 Off, propeller in high pitch -802 257 24750 °54 On, full throttle and 3000 rpm 10303 376 10150 .59 Off, propeller in high pitch -1304 258 9500 .40 Off, propeller in high pitch -1205 311 10150 .49 On, 39 in. Hg manifold pres- 920

sure and 2600 rpm6 313 9850 o49 Off, propeller in high pitch -120

1Estimated from manufacturer's engine power charts.

The maneuver was entered from steady straight flight by pullingabruptly back on the elevator control, holding it fixed until thespecified normal acceleration was nearly reached, then pushing thecontrol abruptly forward to pitch the airplane out of the pull-up.It should be noted that the rates of elevator control motion usedwere the fastest the pilot could apply consistent with the structurallimitations of the airplane. At speeds where the limit allowableload factor could be exceeded, the rates of movement and maximum up-elevator deflection were reduced. The measured rates of motion were,in general, slightly less rapid than those indicated in reference 4.

DESCRIPTION OF THE METHODB OF TAIL-LOAD COMPUTATION

In all the methods of computation used it was assumed that:

1. The change in acceleration factor as a result of attitudechange is small as compared with that due to a change in angle ofattack.

2. The speed is constant during the maneuver.

3. The aerodynamic parameters vary linearly with angle ofattack.

NACA TN No. 1539 9

4. The effects of structural flexibility may be neglected.

Graphical Method

This method, which is described in detail in reference 1, usesa graphical integration procedure to predict the motions of theairplane following any arbitrary elevator control moment.

The differential equation of motion for a unit elevator deflec-tion can be written as

+ K1 ' w + K2 ' LMw = K3 ' Abe (i)

where KI', K2 1, and K3' are functions of the aerodynamic andgeometric characteristics of the airplane. Equation (1) is solvedfor the unit solutions and the variations of 6aw and &w aredetermined for the specified elevator motions by employing Duhamel'sintegral theorem. The increment in effective tail angle of attackat any time during a maneuver, which is related to aw and &wby the equation,

2at = mw 1 _de dCL) pSwxt _ xt (d + 1 +da Adaw d a a m j/ - V da , -/Tit d5e

The tail-load increment is determined from equation (2) by theequation

dCNtM~t : smt nt q St (3)

The load or acceleration factor increment is obtained from therelation

AZ= i s- (4)-~ \cL)a W/Sw

10 NACA TN No. 1539

Tabular Method

This method, a detailed description of which is reported inreference 2, is mathematically similar to that given in reference 1.

It is, however, more convenient to use when linear elevator motions

are assumed. The general differential equations of motion used in

this case, for an elevator deflection proportional to time are

aw- aw + b~w = (t+V) (5)

9- a + bO - '(t+v') (6)

where a, b, v, and vlare functions of simplified aerodynamicderivatives and * and *' are dependent on the rates of elevator

motion and on the derivatives. Equations ( .) and (6) are solved for

the unit functions of AZ, aw, w, 6, and e and the variationsof these quantities are determined for specified or assumed linear

elevator motions by a convenient tabular integration procedure. The

increment in equivalent tail angle of attack is obtained from theequation,

dc ~ (% N. xt + tAb'1_'6a + (L- +(;,, - (7)

It should be noted in the preceding equation that the tail lengthxt is considered positive for conventional airplanes, while in

the method of reference 1 it is considered negative. The incrementin tail load is obtained from equation (7) by the use of equation (3).

The type of linear elevator motion used in the application of

this method to compute maximum maneuvering tail loads is shown in

figure 5. It is noted that the motions, as specified In reference 2,

simulate a pull-up push-down maneuver. The rates of motion, as

indicated in the figure, were based for the most part on the data ofreference 2 and reference 4. In contrast with the computations using

the graphical method where the elevator motion used was identical to

that measured in flight, the maximum up-elevator angle was adjusted

so that the maximum experimental value of tAZ was just reached in

the design maneuver. The comparisons here then are based upon common

or identical values of LAAZmax. Motions with both a 0.2-second and

0.4-second elevator reversal were included because, upon occasion,

the designer may be undecided as to the exact rate of reversal to

use. This being the case, and since the reversal rate is probably

NACA TN No. 1539 11

the most important variable in establishing the linear motions, itwas believed to be of interest to know quantitatively the effect ofa change in the reversal rate on the calculated results.

Abbreviated Methods

In one of these methods the tabular integration method is usedto establish the elevator-angle increment 6beman corresponding tothe maximum value of AAz in the maneuver for a 0o2-second reversalof the elevator. The elevator-angle increment for balance at , Zmaxis determined from the equation

Abebal = C \dOL/a (8)(dCm/d.e)a

Assuming that the maximum maneuvering tail-load increment occurs atIAZmax, the load increment is computed from the equation

Ntman =tbal + d (AZeman -26Sebal) Zma qntSt (9)

where aitbal is computed by the use of the equation given inreference 5 for CL corresponding to A2zmax in the maneuver.

A second abbreviated procedure was used in which the value ofangular pitching acceleration is determined at LAZmax by establish-ing the elevator motion with a 0.2-second elevator reversal, as forthe previous method for the desired maximum acceleration factorincrement, and by computing the pitching accelerations associatedwith this elevator motion. The maximum maneuvering tail-load incrementis again assumed to occur at AAzmax so that

A~tmau = 6Ntbal + lye (10)It

where ANtbal is determined as before from the equation given inreference 5.

12 NACA TN No. 1539

RESULTS

Experimental Data

The experimental results including time histories of basic flightvariables, total tail-load and root bending-moment increments,acceleration-factor and elevator-angle increments, and the load

distributions are presented in figures 6 to 9. Most of the datashown in figures 6 (a) to 6(f) are used subsequently to compute thetail-load increment variations following specified elevator motions.

In figures 7(a) to 7(f) the experimental tail-load and rootbending-moment increments are shown for the several runs. Theseincrements were determined by subtracting from the measured loadsand bending moments at any instant the balancing loads and momentsat time T = 0. (See fig. 6.) The measured elevator-eangle andacceleration-factor increments (figs. 8 (a) to 8(f)) were determinedin a similar manner. The experimental resultant pressure distributionsare shown in figures 9(a) to 9(f)). For purposes of comparison withcomputed. results these distributions correspond to the time in eachrun when the calculated load increments based on the experimentalelevator motions are a maximum. In this way differences in elevatorangles which would distort the comparisons of the load distributionswere avoided.

Computed Data

From the basic flight data presented in figure 6 and from the

aerodynamic and geometric characteristics of the test airplane, thecalculated variations of tail-load and root bending-moment increments(fig. 7) were determined. The root bending-moment increments weredetermined by multiplying one-half the computed tail-load incrementsby the calculated distance to the center of pressure which was assumedat the centroid of area of one side of the tail. The computed orassumed variations of elevator-angle and acceleration-factor incrementare shown in figure 8. The computed tail-load distributions shown infigure 9 were determined by the methods of references 7 and 8.

A summary of the experimental and the computed results ispresented in tables IV and. V.

In the computations, Mach number effects on most of the aero-dynamic parameters were not included, since the load calculationsfor the one test airplane of reference 3 which attained a Machnumber of 0.61 showed no appreciable compressibility effects on thecomputed load increments. In the present investigation only run 1was made at a higher Mach number (M = 0.68).

NACA TN No. 1539 13

DISCUSSION

As previously pointed out, the measured and computed resultsare compared either upon the basis of identical elevator motionsor approximately the same values of maximum normal acceleration.In the former case, the purpose of the comparison is to provide acheck on the validity of the methods currently available forpredicting maximum maneuvering tail loads from known or prescribedelevator motions. In the latter, the reason for the comparison is todetermine the extent to which tail loads computed by use of estimatedlinear elevator motions or abbreviated methods, agree with tail loadsmeasured in abrupt pull-up push-down maneuvers as made by a pilotin flight.

Comparisons Made to Check Validity of RigorousMethods of Computation

In general, as seen in figure 7 and table IV(A), the resultsof comparisons made on the basis of identical elevator motions showthat relatively good agreement is obtained between the maximummeasured and computed tail-load increments. The comparisons alsoshow, however, that where the basic assumption of the methods ofcomputation are violated, agreement between computed and measuredvalues may not be good. For example, in run 2, where the liftcoefficient reached a value of nearly 1.2 at a Mach number of 0.54the lack of close agreement is attributed to the fact that the air-plane was stalled at this moderate Mach number; consequently, thebasic assumption that the aerodynamic parameters varied linearlywith angle of attack was not valid for this run. For the samereason lack of agreement might be expected in run 4 in which a liftcoefficient of 1.4 was reached at a Mach number of about 0.41. Inrun 5, however, in which a lift coefficient of about 1.2 was reachedat a lower Mach number than that reached in run 2, namely 0.49, theagreement between computed and measured values was good. The resultspresented in table IV(A) show that the maximum computed up-loadincrements deviate from the experimental results an average of 114percent for five of the six runs investigated. (Run 2 was notincluded in the average deviation because of the stalled condition.)

The agreement shown in figure 8 between the maximum experimentaland the maximum computed wing-load or acceleration-factor incrementsis not as satisfactory as was the case for the tail-load increments.It is believed that part of the discrepancy can be attributed topossible errors in certain aerodynamic parameters used in the calcula-tion, in particular the airplane lift-curve slope. This possibilityis indicated by the fact that, while a value of (dCL/d.)a of 4.12

14 NACA TN No. 1539

was used in the computations for the present investigation, unpublished

data (which were not available at the time most of the computations

for this report were made) from the Ames 16-foot high-speed wind

tunnel indicated a value of 4.80 at a Mach number of 0.40. Calcula-

tions showed that while this difference in (dCL/d)a had little

effect on the tail-load increments, it had an appreciable effect on

the values of the computed acceleration-factor increments. The use

of the Ames 16-foot wind-tunnel value of (dCL/d)a would have

reduced the average discrepancy between computed and actual values

of AZmax from about 20 to about 15 percent. It is important to

note that, while the change in (dCL/d.)a did not affect the tail-

load increments appreciably, it would have a large effect in cases

where the elevator motions are varied to produce specified values

of 6AZmax. This distinction is illustrated further in a later

section of this report.

These results are in general agreement with those presented in

reference 3 which showed, in a majority of the comparisons, that the

maximum computed wing- and tail-load increments for several airplanes

agreed quite well with the measured values. Where poor agreement was

obtained, the trouble was traced either to poor quantitative knowledge

of the value of certain aerodynamic parameters or to violations of the

assumptions upon which the methods of computation are based.

It appears, then, that methods currently available for predict-

ing maximum maneuvering tail loads from prescribed elevator motions

are valid and can be used with assurance, provided the aerodynamic

parameters are accurately known. It should be recognized that these

methods would not be valid for predicting tail loads in maneuvers

where the basic assumptions common to these methods were not applicable.

Comparisons Made to Check Validity of Using

Estimated Linear Elevator Motions

This type of comparison is made to permit an over-all apprecia-

tion of the accuracy with which maneuvering tail loads may be expected

to be computed for given values of load factor. Comparisons are made

between loads measured and those computed in pull-up push-down maneu-

vers in which the elevator motions are assumed to be linear (method of

reference 2).

As is shown in table IV(A), where comparisons are made on the

basis of the same values of nAZmax , the maximum tail-load increments

computed using estimated linear elevator motions with 0.2-second and

0.4-second reversal deviate from the experimental results an average

of 41.3 and 21.4 percent, respectively.

NACA TN No. 1539 15

It appears that the use of estimated linear elevator motionsconsistent with the experimental values of 6AZmax, instead ofthe actual motions produced increases in the average deviations of29.9 and 10.0 percen% respectively, for the assumed elevator motionswith 0.2-second and 0.4-second reversals. Analysis indicates, how-

ever, that most of the increased deviations are traceable to possibleerrors in some of the aerodynamic parameters.

Since, for design purposes, the fastest possible rate of reversalwould generally be used for predicting maximum maneuvering tail loads,subsequent discussion will be confined to analysis of the resultscomputed using the linear elevator motions with a 0.2-second reversal.(As was previously noted, the linear motion with 0.4I-second reversal,was included to show the effect of a change in the reversal rate onthe computed results.)

To illustrate the effects of inconsistencies or errors in theaerodynamic parameters consider, for example, the effect of apossible error in (dCL/dm)a discussed initially in the previoussection, where comparisons were based on identical elevator motions.It can be shown that for a constant value of 6AZmax, an increase in(dCL/d)a from 4.12 to 4.80 (as indicated by Ames 16-foot wind-tunnel tests) would reduce the average deviation of the computed tailloads from the measured results from 41.3 to 23.3 percent. This wasbased on computations which were repeated for one run using a valueof 4.80 for the airplane lift-curve slope. It can be further shownthat a small additional error was introduced into the tail-loadcomputations because the values of (dCm/dm)a-t and (dCm/dm)aobtained from two equally valid sources were not determined withsufficient accuracy to permit a perfect check of one value with theother. Results of a large number of studies presented in reference 2

show that, depending on whether AAZmax or the elevator motion is

held constant, the maximum maneuvering tail load will increaseeither about 2 or 5 percent, respectively, for a 2-percent (the degreeof inconsistency in (dCm/dm)a obtained from the two sources) move-

ment aft of the airplane center of gravity. Thus, it can be shownthat the use of a consistent value of (dCnr/d)a in the present

case would further reduce the difference between the average computed

load deviations using the measured and the estimated linear elevatormotions. If the value given in reference 5 is assumed correct, theaverage deviation of the computed results (using linear elevatormotions) from the measured load increments would be reduced from23.3 to 21.3 percent. Assuming that the value of (dn/d)a givenin reference 9 is correct, the average deviation from the experimentalload increments of the values computed using the experimentalelevator motions would be increased from 11.4 to 16.4 percent. Fromthe foregoing, it appears that the difference between the averagecomputed load deviations using the estimated linear and the measured

16 NACA TN No. 1539

elevator motions can be reduced from 29.9 to either 9.9 or 6.9percent by accounting for possible errors or inconsistencies in thevalues of (dCL/d)a and (dCm/d)a.

Analysis of the present results indicates, then, that theestimated linear elevator motions with a 0.2-second reversal arepractically as satisfactory as the actual elevator motions for comput-ing maximum maneuvering tail loads in abrupt pull-up push-downmaneuvers.

Comparisons Made to Check Validity of AbbreviatedMethods of Prediction

Comparison is made in table V(A) between the maximum experimentaltail-load increments and the maximum values computed by the twoabbreviated methods previously described. Although not as rigorousas the more complete graphical and tabular methods, they gave resultswhich are considered fairly satisfactory. Average deviations betweenthe measured values and those computed using 6Ntbal + NtAbe and

Attbal + Nt6" were 14.3 and 22.4 percent, respectively.

It should be noted that the computations could be further short-ened by estimation of the maneuvering elevator angle at AZmax and

and the pitching acceleration at AAZmax . As a first approximation,

L eman at AAZmax was assumed one-half the elevator-angle incrementrequired for balance. For the test airplane, this resulted in computedtail loads which predicted the actual within an average of 13 percentfor the six runs. For the special case where the center of gravityis located at the position for neutral stick-fixed stability, theaforementioned method would be invalidated, since Abebal would bezero and the maneuvering load so computed would be equal to thebalancing load. Similarly, an assumption of a common pitching accel-eration at AAZma of 4 radians per second squared for the six runsresulted in an average deviation of the computed from the measuredload increments of about 20 percent. Caution should be exercised ingeneralizing these results, however, since possible errors in the aero-dynamic parameters used (as indicated by previous discussion) wouldchange the average deviations significantly. These changes would beof the order of about.-5 percent to 20 percent for the extreme cases.

Although these results cannot be conclusively consideredrepresentative (since they were obtained on only one airplane) theymay indicate the accuracy to be expected of the methods if they areused to compute design maneuver loads for any airplane of the samegeneral configuration as that of the test airplane. The results

NACA TN No. 1539 17

obtained on the test airplane are considered sufficiently accurate

for preliminary design estimates.

Effects of Speed on Load Comparisons

A comparison between the computed and the experimental limit

maneuvering and balancing tail loads is included as figure 10 for arange of indicated airspeed to show where maximum maneuvering loads

may be encountered, and to indicate the relative magnitude of thebalancing and maneuvering loads as measured and as computed. Itshould be noted that the computed maneuvering loads were obtainedusing values of 4.12 and -0.124 for the airplane lift-curve andmoment-curve slopes, respectively. It was indicated previouslythat better agreement with the measured results would have beenobtained if a good quantitative knowledge was had of these twopertinent aerodynamic parameters. The balancing loads for the limit

load factor of 7.33 and for zero load factor were obtained from thedata of reference 5. The computed and experimental maneuvering tail-load variations for the load factor of 7.33 were obtained by fairing

through the individual load increments reduced to a common ZAZmax

of 7.33 and adding to the resulting curves the corresponding balancingloads at Az = 0. The individual data points are included to show the

relative amount of scatter, which is considerable in the case of themeasured loads and the loads computed using the measured elevatormotions. This scatter results, of course, from variations in theseverity of the experimental elevator motions used. In accord withthe data of reference 2, the maneuvering loads computed by the

several methods decrease from the neighborhood of the upper left-hand corner of the V-g diagram from about 15 to 25 percent over theairspeed range covered, The measured loads increase up to about 300miles per hour, then fall off quite rapidly at higher speeds.

Comparisons Between Measured and Computed RootBending-Moment Increments

A comparison between the maximum experimental and the maximumcalculated tail bending-moment increments based on the measured andthe computed elevator motions is made in table IV(B). It is shownthat if the experimental elevator functions are known, the averagedeviation of the computed bending-moment increments from the measuredresults if 7.1 percent compared to 11.4 percent for tail loads. Themaximum bending-moment increments, based on the linear elevatormotions with reversal occurring in 0.2 second and 0.4 second adjustedto give values of AAz identical with those measured, deviate anaverage of 28.3 and 14.2 percent, respectively, from the experimentalvalues; whereas the corresponding tail-load deviations were 41.3 and21.4 percent.

18 NACA TN No. 1539

The maximum root bending-moment increments calculated by the useof the two shortened procedures are compared with the experimentalresults in table V(B). The bending-moment increments based on thecomputed elevator-angle change at AAZmax deviate an average of 9°3percent from the measured values, while those based on the calculatedvalue of pitching acceleration at AAZmax are in error an averageof 13.2 percent.

It will be noted from the above comparisons that the computedbending-moment increments are generally less conservative than thecomputed load increments. This results from the fact that thecomputed lateral distance to the center of pressure is inboard ofthe measured values. Figure 11 presents the experimental and cal-culated distances to the center of pressure as a function of tailnormal-force coefficient CNt. As previously noted, the computedvalue was assumed to be located at the centroid of area of one sideof the tail. It should be noted from figure 11 that the experimentalvalue appears to move slightly inboard with an increase in CNt.Furthermore, the computed distance to the center of pressure isinboard of the measured values an average of about 10 percent.

Evaluation of Methods for Predicting Load Distributions

The previous sections of this report have dealt with the evalua-tion of several methods for computing the maximum horizontal-tailloads and root bending-moment increments in abrupt maneuvers. Havingascertained the accuracy with which the over-all loads and bendingmoments were determined, it seems desirable to determine how

closely

the calculated load distributions compare with the experimental dis-tributions. This was done by distributing the maximum computed over-all loads based on the experimental elevator motions over the tailspan by assuming unit span loads proportional to the tail chord.The methods of references 7 and 8 were used to distribute the unitspan loads over the tail chord, and the resulting distributions werecompared with the experimental results at the same time. This wasdone so that the elevator angles would be the same for the computedand measured distributions.

The comparisons shown in figure 9 indicate, in general, fairlygood agreement at the midspan stations. At the spanwise stationsadjacent to the fuselage and tip, however, the computed chordwiseload distributions generally show higher peaks near the stabilizerleading edge for the former, and lower peak loads for the latterstations, as compared with the experimental results. One possiblereason for this is the effect of the fuselage in causing a reductionof load at the inboard tail stations. For a given load, the resultingoutward shift of the center of pressure would cause some of thediscrepancies between the calculated and experimental distributions.The agreement shown between the computed and measured span loading

NACA TN No. 1539 19

curves is considered fairly good, although it is evident that the

computed total loads for run 2 and run 4 are considerably higher

than the actual values. Better agreement was not obtained because

present design practice incorrectly assumes that the unit span

loads are proportional to the tail chord.

CONCLUSIONS

Comparisons have been made between the horizontal-tail loadingobtained in six pull-up push-down maneuvers in flight on a repre-sentative pursuit-type airplane and the computed tail loading basedon several rational procedures. On the basis of these comparisonsit was concluded that for airplanes of the sane general configura-tion as the test airplane:

1. Methods currently available for predicting maximum maneu-vering tail loads from prescribed elevator motions are valid and canbe used with assurance, provided the aerodynamic parameters areaccurately known.

2. Computations of tail load based on linear elevator motionin a pull-up push-down maneuver with a 0.2-second elevator reversalmay be expected to give very nearly the same values of maneuveringtail load as those that would be measured in actual pull-up push-down maneuvers at identical values of AAZmax, provided aerodynamicparameters used in the computations are accurate.

3. The maximum tail-load increments computed by the use of thetwo abbreviated methods will be in fairly good agreement with actualvalues and would, in general, be sufficiently accurate for pre-liminary design studies.

4. For a given maximum maneuvering tail load, the maximumcomputed root bending moment will be approximately 10 percent lessthan the value that would be obtained in flight, as the computeddistance to the center of pressure would be about 10 percent inboardof the actual value.

5. The computed chordwise and spanwise tail-load distributionswill be in fairly good agreement with actual values, provided thecomputed values of over-all loads are in close agreement with actualvalues. Better agreement would be expected if, in distributing theload along the span, the effects of the fuselage were considered inaddition to the variation of tail chord.

Ames Aeronautical Laboratory,National Advisory Committee for Aeronautics,

Moffett Field, Calif.

20 NACA TN No. 1539

REFERENCES

1. Pearson, Henry A.: Derivation of Charts for Determining the

Horizontal Tail Load Variation with any Elevator Motion,NACA ARE, Jan. 1943.

2. Kelley, Joseph, Jr., and Missal, John W.: ManeuveringHorizontal Tail Loads. Army Air Forces Technical Rep.No. 5185, January 25, 1945. (Now available from Department ofCommerce as PB No. 49611.)

3. Matheny, Cloyce E.: Comparison Between Calculated and MeasuredLoads on Wing and Horizontal Tail in Pull-Up Maneuvers. NACAARE No. L5Hll, 1945.

4. Beeler, De E.: Maximum Rates of Control Motion Obtained FromGround Tests. NACA RB No. L4E31, 1944.

5. Sadoff, Melvin, Turner, William N., and Clousing, Lawrence A.:Measurements of the Pressure Distribution on the Horizontal-Tail Surface of a Typical Propeller-Driven Pursuit Airplanein Flight. I - Effects of Compressibility in Steady Straightand Accelerated Flight. NACA TN No. 1144, 1947.

6. Sadoff, Melvin and Clousing, Lawrence A.: Measurements of thePressure Distribution on the Horizontal Tail Surface of aTypical Propeller-Driven Pursuit Airplane in Flight. II -

The Effect of Angle of Sideslip and Propeller Operation.NACA TN No. 1202, 1947.

7. Allen, H. Julian: Calculation of the Chordwise Load DistributionOver Airfoil Sections with Plain, Split, or Serially HingedTrailing-Edge Flaps. NACA Rep. io. 634, 1938.

8. Abbot, Ira H., von Doenhoff, Albert E., and Stivers, Louis S. Jr.:Summary of Airfoil Data. NACA ACR No. L5C05, 1945.

9. Turner, William N., Steffen, Paul J., and Clousing, Lawrence A.:Compressibility Effects on the Lonritudinal Stability andControl of a Pursuit-Type Airplane as Measured in Flight.NACA ACR No. 5113, 1945.

10. Silverstein, Abe, and Katzoff, S.: Aerodynamic Characteristicsof Horizontal Tail Surfaces. NACA Rep. No. 688, 1940.

11. Gilruth, R. R., and White, M. D.: Analysis and Prediction ofLongitudinal Stability of Airplanes. NACA Rep. No. 711, 1941.

NACA TN No. 1539 21

4

12. White, Maurice D.: Estimation of Stick-Fixed Neutral Pointsof Airplanes. NACA CB No. L5C01, 1945.

13. Ames, Milton B., Jr., and Sears, Richard I.: Determination ofControl-Surface Characteristics from NACA Plain-Flap and TabData. NACA Rep. No. 721, 1941.

22 NACA TN No. 1539

TABLE I.- GEOETRIC CH1ARACTERISTICS OFTEST AIRPLANE

Item Value

Gross wing area (Sw), sq ft 213.22

Gross horizontal-tail area (St sq ft 40.99

Tail incidence, with reference to thrust axis, deg 2.25

Average airplane weight during test run (W), lb 7600

Design gross weight 7406

Wing span (bw), ft 34,0

Horizontal-tail span (bt), ft 13.0

Moment of inertia of airplane (Iy), slug-ft2 6380

Mass of airplane (m), slugs 236

Radius of gyration of airplane (Ky), ft 5o2

Tail length (xt), ft ±15*0

Mean aerodynamio chord (s), ft 6.72

Center-of-gravity location, percent 3 30.3

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