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1999 Kitfox IV Analysis

Joseph Lee & Zhengcheng GuDecember 14, 2010

Abstract – The Kitfox IV is an experimental aircraft built from separately manufactured parts assembled in a home environment. The specifications of the aircraft will be used for analysis and compared with actual values from the manufacturer. Various assumptions are made to simplify calculations. Main concepts and equations are discussed to lead into the analysis. The coefficient of lift, coefficient of drag, thrust required, power required, power available, range, and endurance were calculated and compared with the Kitfox manufacturer’s values. Additional recommendations and experiments were also noted.

I. Introduction

The Kitfox IV is an experimental single engine, two seater aircraft manufactured in parts by the Kitfox Aircraft LLC. The main functions of the aircraft are for recreation and research. All of the Kitfox planes are home-made, where all of the parts come in the mail and are assembled in a home-like setting. Since Kitfox’s inception in 1991 in Oshkosh, WI, there have been no in-flight failures of the thousands of aircraft that have been sold and assembled [2].

Figure 1: Kitfox IV Airplane.

Stability, control, performance, cost, and short take-off and landing (STOL) contribute to the popularity of the Kitfox IV airplane. Compared to earlier

models produced by the Kitfox Company, the Kitfox IV has better overall performance. The newer airfoil added speed and performance and the flaperon airfoil, area, placement and movement ratios changed significantly compared to earlier models.  Furthermore, a new flaperon design was implemented such that the flaperon moving up traveled twice as far as the flaperon moving down [2].

Since the planes are often custom built, the Kitfox planes often use different, customized powerplants to provide thrust as desired by the pilots and aircraft builders. Some common powerplants include the Rotax 503, 582, and 912 models. Horsepower for the Rotax engines range from around 45 Hp to 120 Hp [3]. The propellers are also custom made by the supply manufacturers for control and specifications as desired. The aircraft that will be analyzed in this report uses an Ivoprop propeller.

II. Specifications and Topics of Interest

The experimental aircraft that will be analyzed is a 1993 Kitfox IV with specifications listed below in Table 1 on the next page.

There are three sections of interest which will be analyzed in this report:

1) Performance of Aircraft (range, endurance, power required, etc.) with wheels

2) Stability and Control3) Verification of Parameters

The aircraft with the floats attached will not be analyzed in this report due to unknown behavior of the floats and the varying aerodynamic influence from the floats on the whole structure of the plane. All sections of interest will be compared to actual values given in Table 1 on Page 2.

2Table 1: Specifications of Analyzed Kitfox IVAircraft.

VMAX 125 MPHRange 300 milesEndurance 5.4 hoursMGTOW 1200 lbfDry Weight 769 lbf (floats)

696 lbf (wheels)Wingspan 32 ftArea of Wing 132 ft2

Aspect Ratio 7.85VSTALL 40 MPH (wheels)

51 MPH (floats)Fuel Capacity 26 gallonsCruise Velocity 75 MPH indicated airspeedPowerplant 65 Hp Rotax 582-LC with C

transmissionPropeller Ivoprop In-Flight Electrical

Adjustable Pitch (#UL366E)Service Ceiling 14,000 ftMax Rate of Climb 1000 ft/minMAC 51.1”Floats Full Lotus Inflatable FloatsTail Length 7’9”Tail Area 18.802 ft2

III. Equations and Concepts for Analysis

Fundamental physical and aerodynamic equations will be used in analyzing the performance, stability, and balance of the airplane. The dynamic pressure for a section of the wing is given as follows:

q∞=12

ρ∞V ∞2(1)

The following equations describe the lift, drag, and moment coefficients used to analyze the thrust and power required.

CL ≡L

q∞ S(2)CD=Cd , o+

CL2

πeAR(3)

Cmc/4=M c/4

q∞ Sc(4)

The plots of CL/CD and CL3/2/CD are analyzed to

show the optimal performance velocity.Assuming that the thrust required is equal to the drag force, the thrust required is defined as follows:

T R=WCL

CD

(5)

With the thrust required equation, the power required is just the thrust required times the overall velocity of the aircraft:

PR=T R∗V ∞¿( WCL /CD

)V ∞(6)

The power available to the engine is the horsepower of the engine times the efficiency such that

PA=η∗( HP )∗550 lbf

1 HP(7)

Thus, for the thrust available,

T A=PA

v∞

(8)

Excess power from the powerplant can be used to find the Rate of Climb which is defined from Equation 9.

RoC= excess powerW

=PA−PR

W (9)

This Rate of Climb is dependent on the velocity of the aircraft. By finding the maximum value of the difference between the excess power and required power at a certain altitude, a maximum Rate of Climb can be calculated. Combining the various altitudes from sea level to a desired height, the service ceiling and absolute ceiling of the aircraft can be approximated.

The range of the aircraft depends on the power of the engine, velocity of the airplane, fuel consumption, and the initial and final weight of the aircraft from start to finish. A general equation for range is shown below:

R=∫W o

W 1 V ∞

cPdW (10)

With the assumptions listed in the Assumptions Section (III) and cruise flight, Equation 10 can be simplified to become the Breguet Range Formula:

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R=ηc

CL

CD

∗ln(W o

W 1)(11)

The Endurance for the aircraft is similar to the range of the aircraft except without the velocity term:

E=∫W 1

W o

1cP

dW (12)

Simplifying Equation 12 with the report assumptions yields the Breguet Endurance Formula, which is calculated in a similar manner used to find the Breguet Range Formula:

E=ηc (CL

32

C D)(2 ρS )

12 ( 1

√W 1

− 1

√W o)(13)

IV. Assumptions

There will be some assumptions that will be made such that equations from John D. Anderson’s “Introduction to Flight” and from the FAA’s (Federal Aviation Administration) “Pilot’s Handbook of Aeronautical Knowledge” can be applied and compared with actual values. These assumptions include:

1) The airfoil analyzed is best modeled as a NACA 4412 airfoil from measurements and pictures.

2) Air acts as an ideal gas.3) Table of values for the temperature,

pressure, and density for corresponding altitudes from Appendix D in “Introduction to Flight.”

4) Neglecting friction from various bumps and anomalies along the aircraft

5) The aircraft is flying at a slow enough speed such that the Mach number will not be accounted for.

6) Given information from Table 1 on Page 17) Steady, level flight will have the lift force

equal to the weight of the aircraft8) Fuel consumption behaves as a constant9) Reynolds Number of 60000010) No flaps for the main wing

11) Span Efficiency Factor = .9012) 1 gallon of fuel = 5.62 lbf13) Parasitic Drag Coefficient ≈ 0.02814) Efficiency of Engine, η ≈.8

Figure 2 below shows a graphically produced cross section of a NACA 4412 Airfoil.

Figure 2: NACA 4412 Airfoil [6].

From the Airfoil Investigation Database, Figure 3 below shows a drag polar for the NACA-4412 airfoil. Using the data given from Table 1 on page 1, the average Reynolds number is approximately 600000. An approximate Reynolds number from the graph on Figure 3 below yields an approximate parasitic drag (CD,O) is approximately 0.015. To account for other drag possibilities due to the structure of the airplane, CD,O is rounded up to a realistic 0.03.

Figure 3: Drag Polar for NACA-4412 [6].

V. Results and Analysis

4The first step in this report analysis is to analyze the plots of CL/CD vs. V∞ and CL

3/2/CD vs. V∞ with maximum (takeoff) weight and minimum (landing) weight. These plots are shown in Figure 4 on the top right of this page. The maximum weight used in the calculations was taken from Table 1 on Page 2. Also, in order to determine whether the aerodynamics behaviors will change a lot with fuel consuming, we choose 10% fuel + 150lb pilot and dry weight of aircraft as an additional weight for analysis.

For the plots of CL/CD from Figure 4, the optimal velocity for the Kitfox IV with maximum weight is higher than when the Kitfox is at minimum weight. The same can be said for the CL

3/2/CD plot as well.

Figure 4: Graphs of CL/CD and CL3/2/CD for Minimum and

Maximum Weight

The minimum power required happens when CL

3/2/CD is at a maximum. For the takeoff (maximum) weight, the approximate velocity based on the graph as shown in Figure 4 on the previous page is 75 ft/s (~ 51.1 mph). This velocity is also the optimal velocity for maximum endurance. Additionally, this velocity is very close to the cruise velocity of the aircraft according to Table 1 on Page 2. At takeoff, the ideal velocity for maximum range is when CL/CD is maximized. The corresponding velocity for maximum range on Figure 4 is 99 ft/s (~ 67.5 mph). The maximum range velocity is also known as the cruise velocity.

The thrust required vs. velocity plot is shown in Figure 5 on the upper right. The thrust available is calculated using Equation 8 on Page 3.

Figure 5: Thrust Required vs. V∞

As seen from Figure 5 above and setting Equations 5 and 8 on Page 3 equal to each other, the maximum velocity of the aircraft is calculated using a computational tool (MATLAB). The graph shown by Figure 5 was produced by plotting the thrust available curve and the thrust required curves for the minimum and maximum weight. The intersection of the thrust required and thrust available plots correspond to the maximum velocity of the aircraft. From Figure 5 above, the maximum possible velocity with minimum weight is around 185 ft/s (~126.1 mph). The max possible velocity with maximum weight is 182 ft/s (~124.1 mph).

The results from Figure 5 show the differences when the aircraft with different fuel status are not significant. For simplification, the maximum take-off weight will be used in further calculations.

Figure 6 on the next page shows the Power Required vs. V∞ graph for the aircraft.

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Figure 6: Power Required vs. V∞

The graph shown in Figure 6 was plotted by plotting Equations 6 and 7, and finding the intersection of these equations. The maximum velocity from Figure 6 is the same as the maximum velocity found from Figure 5 using the max takeoff weight. Figure 6 also states that the minimum power required for a level accelerating flight at sea-level condition is about 7411.2 lb*ft/s, when the aircraft is operating at 75 ft/s.

Figure 7 below shows a graph of the Maximum Rate of Climb vs. Altitude.

Figure 7: Maximum Rate of Climb vs. Altitude

From Figure 7 above, the service ceiling and absolute ceiling are shown above, with a service ceiling of 24,599 ft and absolute ceiling of 27,721 ft.

Figure 8 through Figure 15 show the Range and Endurance plots for the minimally weighted aircraft with 10% fuel and a 150 lb pilot and an aircraft with just the 150 lb pilot. There were three elevations that were considered and analyzed: sea level, 7,000 ft, and 14,000 ft.

Figure 8 through Figure 11 show the Range and Endurance plots for the minimally weighted aircraft with 10% fuel and a 150 lb pilot, along with a minimally weighted aircraft with just the pilot at sea level.

Figure 8: Range vs. Cruise Speed, Sea Level, Min Weight + 10% Fuel + 150lb Pilot

Figure 9: Range vs. Cruise Speed, Sea Level, Min Weight + 150lb Pilot

From Figure 8, the maximum range of the aircraft at minimum weight plus the pilot and 10% fuel is 1425530 ft (269.98 miles), which occurs at a speed of 99 ft/s (~67.5 mph). Figure 9 shows a maximum range of the aircraft at minimum weight and just the pilot of 1498970 ft (283.90 miles).

The endurance plots with maximum and minimum weight are shown in Figure 10 and Figure 11 below and on page 6, respectively.

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Figure 10: Endurance vs. Cruise Speed, Sea Level, Min Weight + 10% Fuel + 150lb Pilot

Figure 11: Endurance vs. Cruise Speed, Sea Level, Min Weight + 150 lb Pilot

From Figure 10, the maximum endurance with an aircraft at minimum weight with the pilot and 10% fuel is 17837.8 seconds (4.95 hours) Figure 11 shows a maximum endurance with an aircraft at minimum weight and the pilot of 18839.5 seconds (5.23 hours).

The plots for the Range and Endurance at 7000 ft are shown in the Appendix at the end of this report.

Figures 11 through 14 show the Range and Endurance plots for the minimally weighted aircraft with 10% fuel and maximally weighted aircraft at 14,000 ft.

Figure 12: Range vs. Cruise Speed, 14000 ft, Min Weight + 10% Fuel + 150 lb Pilot

Figure 13: Range vs. Cruise Speed, 14000 ft, Min Weight + 150 lb Pilot

From Figure 12, the maximum range of the aircraft at minimum weight plus the pilot and 10% fuel is 1425530 ft (269.98 miles), which occurs at a speed of 99 ft/s (~67.5 mph). Figure 13 shows a maximum range of the aircraft at minimum weight and just the pilot of 1498970 ft (283.90 miles). Figure 12 and Figure 13 show that the cruise velocity for maximum range has increased compared to when the aircraft was at sea level.

Figure 14: Endurance vs. Cruise Speed, 14000 ft, Min Weight + 10% Fuel + 150 lb Pilot

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Figure 15: Endurance vs. Cruise speed, 14000 ft, Min Weight + 150 lb Pilot

From Figure 14 on the previous page, the maximum endurance with an aircraft at minimum weight with the pilot and 10% fuel is 14379 seconds (3.99 hours). Figure 15 shows a maximum endurance with an aircraft at minimum weight and the pilot of 15187.4 seconds (4.219 hours). In direct correlation to Figure 12 Figure 13, Figures Figure 14Figure 15 show that endurance is reduced when the aircraft is flying at its service ceiling. Additionally, the operating velocity of the maximum endurance increases for higher altitude.

VI. Data Comparison and Error Analysis

In this section, the percent error for certain calculated values compared to the given data is calculated and listed in Tables 2, 3, and 4. The percentage error is calculated by Equation 14 below.

ξ=|Data Calculated−Data GivenDataGiven |∗100 %

(14)

Table 2: Comparison for maximum velocity from thrust

Max velocity for Maximum weight

Max velocity for Minimum weight

Calculated Data 182.0 ft/s 185.0 ft/sGiven Data 183.3 ft/s 183.3 ft/sPercentage Error 0.71% 0.93%

In the error calculation from Table 2 above, the main sources of error are from two assumed parameters from Equation 3 on page 3; ‘e’ (Span Efficiency Factor) and CD,O (Parasitic Drag Coefficient). Table 2 indicates the percentage errors are less than 1% for this section. Therefore, the estimated values for ‘e’ and CD,O are close to the actual values.

Figure 6 on page 5 shows that the minimum power required for a level accelerating flight at sea-level condition is about 7411.2 lb*ft/s, when the aircraft is operating at 75 ft/s. By Equation 15, the ratio between the minimum power required and the power available is calculated.

Ratio= Minimum Power RequiredPower Available

∗100 %

(15)

The result of Equation 15 from the data acquired from Figure 6 is 25.9%. This means the Kitfox IV needs at least 25.9% of its available power to fly at steady level flight for sea-level conditions.

Table 3: Comparison for Maximum RoC (Rate of Climb), Service ceiling and Absolute Ceiling

Maximum RoC

Service Ceiling

Absolute Ceiling

Calculated Data

1059.44 ft/min

24599 ft 27721 ft

Given Data 1000 ft/min 14000 ft No Data

Percentage Error

5.94% 75.7% -

Percentage error for maximum Rate of Climb is 5.94%. Since the Rate of Climb is calculated by Equation 9. More estimated data are used in calculation. For instance, ‘e’ (Span Efficiency Factor), CD,O (Parasitic Drag Coefficient), efficiency of engine, and the standard atmosphere model built. Since there are more possible errors in the calculations, the resulting error will increase. The estimated error can be calculated from Equation 16

ξ total=∑ ξi (16)

The Equation 16 comes from the theorem for percentage error, it states:

The percentage uncertainty is the sum of the percentage uncertainties in each individual measurement.

From Table 3, percentage error for the service ceiling is huge, which is about 75.7%. The calculation was checked thoroughly.

8Further research was done online to analyze the service ceiling error. A computation with same method has been done in Introduction to Flight for CP-1 (Cessna 185 Skylane) [1]. The service ceiling for the CP-1 was calculated to be 24720 ft. However, the published data available online showed a maximum service ceiling of 20000 for the CP-1 [8], which is 19.09% off. Therefore, a possible explanation is:

The published service ceiling data was obtained from a more unstable atmosphere, which may or may not multiply a safety factor in order to comply with FAA standards.

Another possible explanation can be made with starting point at temperature. By checking the standard atmosphere table from Appendix D [1], the sea level temperature is 58.69 ºF. And temperature at 14000 ft and 24500 ft are 8.8 ºF and -28.58 ºF, respectively. As the altitude increases, according to Appendix D [1], the temperature will decrease. The Kitfox IV does not have any heating system for protecting crews and devices.

Table 4 Comparison for Maximum Range and Maximum Endurance at Sea-level condition

Computed data

Given data Percentage error

Max Range with W1* 269.99 mi 300 mi 10%

Max Range with W2** 283.90 mi 300 mi 5.4%

Max Range with W3*** 293.55 mi 300 mi 2.2%

Max Endurance with W1*

4.95 hours 5.4 hours 8.3%

Max Endurance with W2**

5.23 hours 5.4 hours 3.1%

Max Endurance with W3***

5.43 hours 5.4 hours 0.56%

* W1 = Dry Weight + Crew(150 lb) + 10% Fuel** W2 = Dry Weight + Crew(150 lb)***W3 = Dry Weight + Crew(140 lb)

Table 4 shows the comparison of maximum range between calculated data and given data. There are three different empty weight categories to plug in Equation 11. The main source of error for the first two cases is from choosing the data. The weight assumption is more closely related to the assumption made for given data.

The endurances also show a similar relation as the range. The endurance calculated with weight assumption #3 (Dry Weight + 140 lb pilot) is the most precise assumption comparing it with actual data from Table 1.

Error from these calculations is mainly from two sources. As mentioned before, one of the main sources of error is the weight assumption. The difference in percentage error for different weight assumptions could be more than 8%, which comes from subtracting the maximum endurance with weight assumption #1 (Dry Weight + 150 lb + 10% fuel) by that with weight assumption #3. In addition, the non-precise estimation would be another major error source.

VIII. Conclusion

For the 1993 Kitfox IV aircraft analyzed in this report, the coefficient of lift, coefficient of drag, thrust required, power required, power available, rate of climb, range, and endurance were calculated and compared with actual values. The calculated values from computer analysis yielded reasonably small error. With the analysis of major performance characteristics for the aircraft, there are many different types of experiments and improvements that can stem from this report.

IX. Recommendations

There are many possibilities for improving and extending the topics covered in this report. There were some parameters that had to be assumed when real life situations would yield some assumptions as ineffective or unrealistic. Through wind tunnel testing, many parameters will be better approximated and the behavior of such parameters can be better modeled. To better model the lift and drag coefficients, an actual model can be

9constructed and tested in a wind tunnel. From the wind tunnel tests, the drag polar will be better estimated since more forces and inconsistencies on the aircraft will be better modeled. Also, the thrust required will be more accurately calculated through wind tunnel testing. Some testing with a steadily decreasing aircraft mass will better model the performance of an aircraft as it burns through fuel as described by Equations 10 and 12 on page 3.

The engine for the Kitfox IV can be further analyzed to predict and model the maximum thrust and efficiency of the motor. To further increase the accuracy of the thrust of the engine, the propeller blades can be aerodynamically tested in a wind tunnel. Additionally, since there are sections of the propeller blades that contribute little to the thrust of the aircraft (primarily the part of the propeller nearest to the root), a more complex model dealing with the net effective area and wing can be analyzed.

Other topics not discussed in detail in this report are not limited to but include analyzing the weight and balance of the aircraft, take-off performance, the roll, pitch, and yaw moments about an aircraft, and analysis of controls and sensors. The effects of using the floats instead of the wheels can also be investigated.

X. References

[1] Anderson, John D. Introduction to Flight. 6th ed. New York: McGraw-Hill, 2005.

[2] Kitfox Aircraft. Kitfox Aircraft LLC. 2006. <http://www.kitfoxaircraft.com/>

[3] BRP-Rotax GmbH & Co. KG. Rotax – Power in Motion. 2010. <http://www.rotax.com/en/>

[4] US Department of Transportation, Federal Aviation Administration. Pilot’s Handbook of Aeronautical Knowledge. Flight Standards Service, 2003.

[5] IVOPROP CORP. Ivoprop – Ivo prop – Ivo propeller. 2010. < http://www.ivoprop.com/>

[6] AID, Airfoil Investigation Database. 2010. <http://www.worldofkrauss.com/foils/>

[7] Sport Aviation. Kitfox IV. 12 December 2010. <http://old.sportaviation.eu/products/Kitfox/KF-4.htm>

[8] Demand Media. The Cessna 182 Skylane. Airliners.net, 2010. <http://www.airliners.net/aircraft-data/stats.main?id=145>.

XI. Appendix.

A1. Plots with full resolutionA2. MATLAB code