A Low-Reynolds Number UAV System Analysis Program (UAV-SA)

Instruction Manual

Prepared By Xiong Qing Yu Under the Guidance of Prof. Stephen Batill

at the University of Notre Dame

Notre Dame, Indiana July, 1998

A Low-Reynolds Number UAV System Analysis Program (UAV-SA) Instruction Manual

1. Introduction UAV-SA is an integrated computer program to be used to predict the aerodynamic charateristics, propulsion system performance, weight and center of gravity location, flight performance, longitudinal stability and control of a low Reynolds number UAV. Originally, UAV-SA program was intended to serve as System Aanalysis for the research work on an application of Concurrent Subspace Design (CSD) framework to UAV design. This program is also useful tool for students to design UAV in their design project. This UAV system analysis program was developed for electric-powered, remotely or autonomously controlled, low Reynolds number flight vehicles. The vehicles are powered by fixed-pitch propeller driven by electric motors. The airframe are fabricated using lightweight, organic, orthotropic composite (wood) and plastics. The data base used to provide the empirical models for certain parts of the system analysis contains aircraft with 6-15 ft2 wing area, weights of 5-15 lbs with maximum flight speeds of less than 100 ft/sec. The aircraft itself is restricted to a simple planform configuration with a nose mounted motor and propeller, single main wing and after mounted horizontal tail. The fuselage is divided into three segments: forward section, which contains the motor; mid-section, which contains any payload and avionics and support for the main wing; aft-section, which support the empennage. Only tricycle-gear aircraft configuration is considered in the program.. The nose landing gear is assumed to be mounted to the connection between forward and mid-section fuselage. The location of the main landing gear is determined based on the assumption that it stands 90% of total weight of aircraft. This manual briefly describes analysis methods associated with each of the disciplines ,and presents the program description and an example demonstrating the procedure of running UAV-SA program. The program itself is quite straightforward to use.

2. Discipline Analysis 2.1 Aerodynamics The lift and induced drag characteristics of UAV is modeled and analyzed using vortex lattice method. The program of this discipline analysis is an adaptation of VLM program[1] which was developed by Yu based on the Fortran program[2]. Parasite drag estimation for UAV is based on the component build-up method as presented by Jensen[3]. The output from the aerodynamic analysis is an estimate of maximum lift coefficient Clmax, drag polar CD vs. CL and pitching moment characteristics for the aircraft. 2.2 Propulsion This discipline analysis has two primary components. The first is a blade element propeller analysis for fixed-pitch propellers which includes induced velocities, tip loses, as well as Mach and Reynolds number correction[4]. The program for propeller analysis is adapted from Notre Dame Propeller Program (NDProp)[5]. The second is the analysis of power available for a permanent magnet electric motor with battery energy storage. The program of the analysis of power available is adapted from Power Available Estimation Program for Electric RPVs developed by Batill. The propeller is matched with the electric motor to determine thrust and power available as well as current draw which are output for this discipline. 2.3 Weight and C.G. Estimation Weight prediction is based on empirical models developed from a database of UAV designed and fabricated at the University of Notre Dame during the past decade. Weights are estimated for the major components: wing, fuselage empennage surfaces, landing gear and propeller. The database of these components is given in appendix A. Empirical formulae for the major component weight prediction have been developed using regression analysis method based upon the database. These formulae are stated as below. wing weight : Wwing = 0.14676·Sw0.4852·ARw0..7082·(100 t/c)-0.2210 ( lb ) fuselage weight: Wfsuelage = 0.07092·(Wm/Hm)0.04832·L1.6566 ( lb ) horizontal tail weight: Whor = 0.1570·Sh0.1939 (lb) vertical tail weight: Wvert = 0.1393·Sv0.6729 ( lb )

landing gear weight: Wlg = Wto·0.07 (lb) propeller weight: Wpropeller = 3.0346×10-6·D3.76468 ( lb ) where Sw -- wing aera ( ft ), Sh -- horizontal tail aera ( ft ), Sv -- vertical tail area( ft ), ARw -- wing aspect ratio, t/c -- wing airfoil thickness ratio Wm -- mid-section fuselage width, Hm -- mid-section fuselage height L -- fuselage length (ft), D -- propeller diameter ( in ) The accuracy of these models was illustrated as figure 1 in Appendix B. It is shown that the models are able to give reasonably approximate prediction of component weights for preliminary design of this class aircraft although more accurate models should be addressed in the future. Avionics and payload weights are fixed as user input. Motor and battery weights are determined by the selection of those individual components. Center of gravity of major components is determined using the method presented by Torenbeek[6]. The output from weight discipline analysis is total weight of aircraft and center of gravity location. 2.4 Performance Analysis The flight performance is computed based on the information, such as lift curve, polar drag, power vs velocity and weight, provided by aerodynamics, propulsion and weight disciplines. The programs associated with the analyses of maximum, minimum level flight speed and maximum steady rate of climb are adapted from the code developed by Smetana[7]. Stall speed is computed and compared to the minimum level flight speed from power available so that actually minimum level flight speed can be determined. The takeoff distance is a numerical integration ground roll prediction, and its program was adapted from the TAKEOFF program developed by Batill. Maximum range and endurance are determined by varying the throttle setting. 2.5 Stability and Control The basic longitudinal stability and control characteristics are assessed by this discipline analysis. The static margin is estimated based upon the center of gravity provided by the weight discipline and the pitch moment characteristics provided by the aerodynamics discipline. The elevator of UAV is sized by the requirement for takeoff rotation. For a tricycle-gear aircraft the elevator should be powerful enough to rotate the nose at 80% of takeoff speed. The flap angle at given elevator size is

computed based on this control requirement, where takeoff speed is equal to 1.2 stall speed. If flap angle computed is too large (large than 15 deg), it means the elevator is not powerful enough to meet this requirement. 3. Description of the Program and Data Files The UAV-SA Program consists of various Fortran program, Matlab file and data files. A Simplified flow chart of the code appears in Figure 1. The primary Fortran subroutines, Matlab file and data files are described briefly in the following sections.

Figure 1 UAV—SA flow chart

read input data

genrate a additional data

aerodynamic analysis

weight and C.G

power availiable vs

aircraft_display.m

display

flight performance

stability & control write output data

3.1 Description of primary Fortran subroutines and Matlab file 1) Primary Fortran subroutines are listed in the following table. File Name function aero.f computing lift and induced drag characteristics using vortex lattice

method cd0.f Parasite drag estimation based on the component build-up method fit.f this subroutine is designed to express the lift-drag in a functional form

suitable for use in the performance computation. The data are are fit by Least Squares Distance method in the form: CD = k1 + k2CL

2 + k3CLk4 prop.f determining thrust, power available and current draw vs. velosity weight.f estimating the major component weight, total aircraft weight and center

of gravity location velocity.f computing the maximum, minimum level flight speed and maximum

steady rate of climb vstall.f computing the stall speed takeoff.f computing takeoff distance range.f computing maximum range and endurance control.f estimating static margin and flap angle of elevator required for takeoff

rotation requirements. UAV-SA.f main program orchestrating all subroutines mentioned above and

controlling the excutive process 2) Matlab file There is only one Matlab file aircraft_display.m which is used to display the top view of the aircraft external configuration. 3.2 Data files for wing airfoils and propeller airfoils The system analysis of UAV requires wing airfoil data, data for the prediction of parasite drag, propeller geometric data and propeller airfoil data. Airfoil Data Currently five different low-Reynolds number airfoils are available for use in UAV-SA program. These airfoil data files and data files associated with parasite drag are listed in the following table.

No. Airfoil Type Airfoil Data File Drag Data File 1 FX63-137B FX63-137B.dat FX63-137B.drg 2 SD7032D-PT SD7032D.dat SD7032D.drg 3 SD7062-PT SD7062.dat SD7062.drg 4 E205B-PT E205B.dat E205B.drg 5 NACA6409-PT NACA6409.dat NACA6409.drg

Each data in the first line of airfoil data file (for example FX63-137B.dat) indicates x location in percentage of the chord, and in the second and third line is y location of upper and lower surface coordinates associated with that x location of airfoil, respectively. The information required by the parasite drag prediction for low Reynolds number aircraft is included in drag data files (for example FX63-137B.drg). The first column in drag data files indicates the Reynolds number, and the second column indicates the minimum drag coefficient, that is Cdmin as presented by Jensen[3], found from the Cd vs Cl of the airfoils[8]. The propulsion system analysis requires propeller geometric information and propeller airfoil data. The date file propeller.dat describes some propeller geometric characteristics except D and Pitch as specified in input data file, and propeller airfoil is described in the data files .d. These two file were detailed in NDProp program instruction Manual[5]. Currently five different propeller airfoils are available for the propulsion system analysis. 3.3 Input data file Input data file is used to completely describe a design and associated flight condition. It includes the description of the external dimensions on UAV configuration , the description of propulsion system, payload and its location. The complete parameters in the input data file are listed as the following. wing external definition ARw wing aspect ratio Sw wing area (ft**2) taper_w wing taper ratio sweepw wing leading edge sweep (deg) theta wing washout (deg) Incw wing incidence angle (deg) Iairfoil wing airfoil selection (integer)

horizontal tail external definition ARh horizontal tail aspect ratio Sh horizontal tail area (ft**2) taper_h horizontal tail taper ratio sweeph horizontal tail leading edge sweep (deg) Inch horizontal tail incidence angle (deg) tc_h horizontal tail airfoil thickness ratio elevator size portion elevator size in fraction of the horizontal tail fuselage Wm main section width (ft) Hm main section height (ft) Lm main section lenght (ft) La after section lenght (ft) Lf forward section lenght (ft) taper_a after fuselage section taper ratio taper_f forward fuselage section taper ratio alp_ref fuselage reference line definition (deg) vertical tail Sv vertical tail area (ft**2) tc_v vertical tail airfoil thickness ratio sweepv vertical tail leading edge sweep (deg) crv vertical tail root chord (ft) taper_v vertical tail taper ratio wing location Xwing wing location (measured from the nose of fuselage, ft) distz vertical distance of the horizontal tail planform with respect the wing root chord height (in Z direction as defined in the UAV manual[1], ft) battery Ibat battery type (integer) Numbat number of batteries (integer)

x1_battery battery location (measured from the nose of fuselage, ft) motor Imotor motor type (integer) x1_motor motor location (measured from the nose of fuselage, ft) propeller x_propeller location of propeller (measured from the nose of fuselage, ft) dia diameter of propeller (in) Iaf propeller airfoil selection (integer) pitch propeller pitch (in) payload w_avionics avionics weight (lb) w_payload payload weight (lb) x1_avionics avionics location (measured from the nose of fuselage, ft) x1_payload payload location (measured from the nose of fuselage, ft) flight condition altitude flight altitude for computation of performance (times 1000, ft) MU friction coefficient of ground Since input data file contains the selections of airfoil, battery type, battery number, motor type and propeller airfoil, these design variables are considered as discrete variables. The following description explains the meaning of these discrete variables. 1) airfoil type can be specified as 1 or 2,3,4,5. 1 - FX63-137B 2 - SD7032D-PT 3 - SD7062-PT 4 - E205B-PT 5 - NACA6409-PT 2) battery type can be specified as 1 or 2, 3, 4. 1 - P-130SCRC 2 - P-120SRCP 3 - P-130SCR

4 - P-140SCR 3) motor type can be specified as 1 or 2. 1 - Astro Cobalt 15 2 - Astro Cobalt 25 4) number of battery can be 9 or 10, 11, 12, 13, 14, 15. 5) propeller airfoil can be specified as 1 or 2,3,4,5. 1 - propeller airfoil = flatplate.d 2 - propeller airfoil = ClarkY.d 3 - propeller airfoil = RAF6.d 4 - propeller airfoil = NACA44LowRE.d 5 - propeller airfoil = Symmetrical.d 3.5 Output file The information in output file includes: 1) lift-drag curve in a functional form, maximum lift coefficient and (L/D)max. 2) each component weights, its location, total aircraft weight and center of gravity location. 3) power, thrust available vs velocity and motor current vs velocity. 4) maximum level flight speed, maximum rate of climb, minimum level flight speed, as well as maximum rate ROC, power available, power required vs velocity. 5) takeoff distance and time for run. 6) maximum range and endurance, as well as the flight speed and throttle setting associated with them. 7) static margin and elevator flap angle for takeoff rotation at the rotate speed. 4. Running UAV-SA program The purpose of this section is to demonstrate how to use UAV-SA program throught an example. 1) Setting up the input data Followed by the example of input data file 'demo.inp' which is listed in appendix C, it is quite easy to setup a input data file. 2) Invoking UAV-SA program and read in the name of input data file and output

file The program can be invoked by the command: UAV-SA then you should type the name of input data file which you have setup and the name of output file whatever you like to define. For example, read in input data file <---- message from the computer screen demo.inp <---- input data file name was typed read in output file <---- message from the computer screen demo.out <---- output file name was typed 3) Seeing Results When the program is ended, open output data file to obtain the system analysis results of the UAV which you designed in the input data file. For example, open output file demo.out using Text Editor in Unix system, the contents of demo.out are listed in Appendix D. 4) Displaying the top view of aircraft external configuration A additional data file (xy.dat) is generated during running the UAV-SA. This data file is used to display the top view of the aircraft external configuration by Matlab program aircraft_display.m. In order to display the aircraft configuration, you should first invoke Matlab software, then type 'aircraft_display'. For example, the top view of aircraft external configuration, which is specified in the input data file demo.inp, is shown in Appendix E. 5. Some comments on UAV-SA Program Since UAV-SA program is a newly developed program aimed at providing a useful tool for the designer, extensive evaluation of the program is ongoing. Maybe, some issues, such as more accurate weight estimation model, should be addressed in the future version of the program. It should be pointed out that UAV-SA program might be interrupted without final results if you provide an inconsistent design specified in input data file. If this happens, please check the aircraft configuration and propulsion system you designed. If any of the subroutines is modified for some reason, the file associated with this subroutine should be compiled first, and then all the Fortran files must be linked in way as stated below: f77 -o UAV-SA UAV-SA.o aero.o cd0.o fit.o weight.o control.o prop.o range.o takeoff.o velocity.o vstall.o

References 1. Yu,X.Q., VLM program user's manual, University of Notre Dame, Feb. 1997. 2. Margason, R.J., and Lamar, J.E., Vortex-Lattice FORTRAN Program for Estimating Subsonic Aerodynamic Characteristics of Complex Planforms, NASA TN D-6142, Feb., 1971. 3. Jensen, D.T., A drag prediction methodology for low Reynolds number flight vehicles, M.S. Thesis, University of Notre Dame, May 1990. 4. Young, B., Propeller performance analysis for small computer, M.S. Thesis, University of Notre Dame, May 1984. 5. Krummen, D.E., Notre Dame Propeller program - Instruction Manual, University of Notre Dame, May 1990. 6. Torenbeek, E., Synthesis of subsonic airplane design, Delft University Press, 1982. 7.Smetana, F.O., Computer Assisted Analysis of Aircraft Performance, Stability and Control, McGraw-Hill, New York, 1984. 8. Selig, M.S., Donovan, J.F., Fraser, D.B., Airfoils at Low Speeds, H.A. Stokely, Virginia, 1989.

Appendix A Aircraft Component Weight Data Base Summary

No. Aircraft 1 FX/90 2 Crab 3 Wormburner 4 Hintz 5 Icarus 6 Elite 7 Balsa Bullet 8 RTL-46 9 Gold Rush 10 Bunny 11 Blue Emu 12 Airplane 13 Hermes CX-7 14 Exodus 15 Arrow 227 Wing Structure Weight Data Base No. Wwing(lb) ARw t/c Sw (ft2) 1 .6250 5.8400 .1300 4.3800 2 1.1900 7.8700 .1360 9.6000 3 .6910 5.7600 .1400 8.5000 4 .8200 6.1800 .1300 7.9300 5 1.0640 7.2000 .1100 7.5000 6 .9230 9.0000 .1100 6.5000 7 .8000 7.2000 .1360 6.3300 8 1.3160 8.4600 .1400 9.9300 9 .8400 7.0000 .1360 10.9400 10 1.3300 8.5000 .1400 10.0000 11 1.2300 10.0000 .1500 10.0000 12 1.3300 9.5000 .1170 9.5000 13 1.1750 12.0000 .1200 8.0000 14 1.2800 9.6200 .1170 9.6200 15 1.2900 10.6400 .1300 9.4000

Fuselage Structure Weight Data Base No. Wfuse(lb) W/H L(ft) 1 .6250 .8750 3.3330 2 1.3300 1.0600 4.9200 3 .5200 1.0000 4.0000 4 .5900 .8000 4.5000 5 .9300 1.2700 3.7500 6 .4540 1.0000 3.1700 7 .2800 1.0000 3.3300 8 .4500 1.0000 5.5000 9 .8600 1.2000 5.0000 10 2.0000 1.2000 4.8000 11 .8700 1.7400 5.0400 12 1.4160 1.8750 5.3300 13 1.8500 .6730 4.5000 14 1.2500 1.0600 5.0000 15 .9200 .6500 4.9500 Horizontal Tail and Vertical Tail Structure Weight Data Base No. Whor (lb) Sh ( ft2 ) Wvert Sv ( ft2 ) 1 .1250 .4820 0.0940 0.3510 2 .1700 2.2900 0.2000 1.0400 3 .0820 1.2990 0.0210 0.4380 4 .2100 1.3300 0.1600 0.4700 5 .2300 1.5600 0.1100 0.5000 6 .1750 .9000 0.0820 0.3000 7 .1490 1.5000 0.0560 0.5000 8 .1300 1.9200 0.0400 0.7300 9 .2000 1.6000 0.1730 1.0000 10 .2000 2.9800 0.1300 1.1800 11 .2050 1.6100 0.1370 0.6800 12 .1600 1.2500 0.1500 0.8330 13 .2000 1.2000 0.1300 0.6700 14 .1900 1.4400 0.1200 0.5300 15 .1700 1.5600 0.1130 0.6700

Propeller Weight Data No. Wprop(lb) D( in ) 1 26.4000 14.0000 2 22.0000 13.0000 3 16.0000 12.0000 4 11.5000 11.0000 5 9.0000 10.0000

Appendix B Comparison between actual weight and estimated weight

Appendix C Input Data File : Example wing external definition 8.0 ! wing aspect ratio 9.0 ! wing area (ft**2) 1.0 ! taper ratio 0.0 ! wing leading edge sweep (deg) 0.0 ! wing washout (deg) -1.0 ! wing incidence angle (deg) 2 ! wing airfoil selection ( 1 or 2,3,4,5) horizontal tail external definition 2.00 ! horizontal tail aspect ratio 2.50 ! horizontal tail area (ft**2) 1.0 ! horizontal tail taper ratio 5.0 ! horizontal tail leading edge sweep (deg) -2.2 ! horizontal tail incidence angle (deg) 0.14 ! horizontal tail airfoil thickness ratio elevator sizing 0.3 ! elevator size in fraction of h. tail fuselage external definition 0.408 ! mid-section width (ft) 0.350 ! mid-section height (ft) 0.80 ! mid-section length (ft) 2.04 ! after section length (ft) 0.85 ! forward section length (ft) 0.3 ! after fuselage section taper ratio 0.5 ! forward fuselage section taper ratio 0.0 ! fuselage reference line definition (deg) vertical tail external definition 1.50 ! vertical tail area (ft**2) 0.13 ! Vertical tail airfoil thickness ratio 0.0 ! Vertical tail leading edge sweep 0.90 ! Vertical tail root chord (ft) 1.0 ! Vertical tail taper ratio wing location 0.92 ! wing location (measured from the nose of fuselage, ft) 0.0 ! vertical distance of the horizontal tail planform with respect the wing

! root chord height (ft) battery 4 ! battery type (1 or 2, 3, 4) 14 ! number of batteries (9 or 10, 11, 12, 13, 14, 15) 1.03 ! battery location (measured from the nose of fuselage, ft) motor 1 ! motor type (1 or 2) 0.26 ! motor location (measured from the nose of fuselage, ft) propeller 0.0 ! location of propeller (measured from the nose of fuselage, ft) 12.0 ! diameter of propeller (in) 4 ! propeller airfoil selection 7.00 ! propeller pitch (in) weight 0.53 ! avionics weight (lb) 0.40 ! payload weight (lb) 1.00 ! avionics location (measured from the nose of fuselage, ft) 1.00 ! payload location (measured from the nose of fuselage, ft) flight condition 2.0 ! reference altitude (times 1000, ft) 3.0 ! flight altitude ( times 1000, ft) 0.1 ! friction coefficient of ground

Appendix D Output File: Example Aerodynamic Analysis Results ============================== CD = 0.020808 + 0.04518*CL**2 + 0.00047*CL** 6.0 CLmax = 1.153353 (L/D)max = 16.32310 Weight and C.G. Computation Results ========================================== Components Weight (lb) C.G. (feet) Wing 1.1185 1.3231 Fuselage 0.6214 1.2177 H. tail 0.1875 3.0583 V. tail 0.1830 3.1680 L/G 0.3939 1.1515 Motor 0.6700 0.2600 Prop 0.0351 0.0000 Battery 1.4875 1.0300 Avionics 0.5300 1.0000 Payload 0.4000 1.0000 Total 5.6268 1.1515 Power and Thrust available vs velocity ====================================== BATTERY VOLTAGE = 16.8000 MAX MOTOR POWER(hp) = 0.474176 MAX MOTOR POWER(watts) = 353.599

1 POWER AVAILABLE VS. VELOCITY ELECTRIC MOTOR REFERENCE ALTITUDE = 2000.00000 FEET PA(FT-LBS/SEC) V(FT/SEC) 20.32060 7.00000 35.33820 12.00000 50.46707 17.00000 64.21593 22.00000 75.56451 27.00000 85.31043 32.00000 92.94473 37.00000 98.49387 42.00000 103.05720 47.00000 105.19215 52.00000 105.36998 57.00000 102.72104 62.00000 98.31702 67.00000 93.06873 72.00000 83.95576 77.00000 1 MOTOR CURRENT VS. VELOCITY ELECTRIC MOTOR REFERENCE ALTITUDE = 2000.00000 FEET CURRENT(AMP) V(FT/SEC) 14.73247 7.00000 14.31424 12.00000 14.10736 17.00000 14.02705 22.00000 14.10743 27.00000 14.13137 32.00000 14.01618 37.00000 13.83997 42.00000 13.63932 47.00000

13.27858 52.00000 12.83670 57.00000 12.22314 62.00000 11.45497 67.00000 10.60744 72.00000 9.68926 77.00000 1 THRUST AVAILABLE VS. VELOCITY ELECTRIC MOTOR REFERENCE ALTITUDE = 2000.00000 FEET THRUST(LBS) V(FT/SEC) 2.90294 7.00000 2.94485 12.00000 2.96865 17.00000 2.91891 22.00000 2.79869 27.00000 2.66595 32.00000 2.51202 37.00000 2.34509 42.00000 2.19271 47.00000 2.02293 52.00000 1.84860 57.00000 1.65679 62.00000 1.46742 67.00000 1.29262 72.00000 1.09033 77.00000 FLIGHT SPEED PERFORMANCE AT = 0.20000D+01 FT

===================================

MAXIMUM LEVEL FLIGHT SPEED = 0.74598D+02 FT/SEC

LIFT COEFFICIENT = 0.10027D+00 DRAG COEFFICIENT = 0.21262D-01

MAXIMUM RATE OF CLIMB = 0.14141D+02 FT/SEC

VELOCITY FOR MAXIMUM RATE OF CLIMB = 0.41898D+02 FT/SEC

POWER FOR MAXIMUM RATE OF CLIMB = 0.98390D+02 FT-LBS/SEC

LIFT COEFFICIENT = 0.31785D+00 DRAG COEFFICIENT = 0.25372D-01

MAXIMUM R/C, POWER AVAILABLE, & POWER REQUIRED VS VELOCITY

AT 0.20000D+01 FT

R/C(FT/SEC) PA(FT-LBS/SEC) PRQ(FT-LBS/SEC) V(FT/SEC)

0.37519D-05 0.35916D+02 0.35916D+02 0.12190D+02

0.88752D+01 0.58987D+02 0.90478D+01 0.20000D+02

0.12657D+02 0.81618D+02 0.10400D+02 0.30000D+02

0.14119D+02 0.96418D+02 0.16976D+02 0.40000D+02

0.13425D+02 0.10460D+03 0.29066D+02 0.50000D+02

0.10024D+02 0.10409D+03 0.47688D+02 0.60000D+02

0.38078D+01 0.95425D+02 0.73999D+02 0.70000D+02

0.22949D-05 0.89008D+02 0.89007D+02 0.74598D+02

MINIMUM LEVEL FLIGHT SPEED = 0.21994D+02 FT/SEC

Takeoff Performance ====================================== Static Thrust (lb) = 2.91471 Time for Run(sec) = 2.00000 V at Takeoff (ft/sec) = 26.8003 Distance(FT) = 26.1518 Thrust(lb) at Takeoff = 2.82090 Range and Endurance Performance ============================== Cruise speed for Max. Range = 35.781 ft/s at Vset = 8.200 V Cruise speed for Max. Endurance = 27.565 ft/s at Vset = 7.000 V

Max. Endurance = 31.681 minutes Max. Range = 10.827 miles Longitudinal Static Stability and Control ========================================= Static Margin = 15.8601 % Elevator rotation angle for takeoff rotation = 8.00000

Appendix E Aircraft External Configuration--Example