Homebuilt Aircraft Design

Response
to
Request for Proposal
for
Single Place, TurboJet Powered
General Aviation Airplane

Georgia Institute of Technology
Atlanta, Georgia
School of Aerospace Engineering

Initial Sizing

Mission Requirements:

Total Cruise of 830 Nm at 20,000 ft. standard day conditions.
Loiter time of 10 minutes at the end of the descent and prior to landing.
Cruise Speed of 242 mph and a dash of 283 mph.
1% unusable fuel.
11% reserve fuel.
Total Payload is 10 lbs.
One pilot weighing 200 lbs.
Engine will be a small Turbojet.
SFC at cruise at 20,000 ft. is .75/lb/lb/hr
SFC at loiter is .45 lb/lb/hr
(L/D)_max = 13.70

Assumptions:

Assume standard day conditions.
Speed of sound at 20,000 ft (STP) is 1037 ^ft/_sec.
Assume that the A/C will be in cruise the majority of the time rather than dash.
The A/C will be constructed of composite material.

# Segment Description Values Fraction

1 W1/Wo Engine Start

Warm Up

Taxi

Take off .998

.998

.998 .9940

2 W2/W1 Climb .995 .995

3 W3/W2 Cruise R=830 Nm

C=.75 lb/lb/hr

V=(.3423*1037)

L/D _cruise = .866(L/D)_max .7792

4 W4/W3 Descent .995 .995

5 W5/W4 Loiter E=10 min

C=.45 lb/lb/hr

(L/D)_max = 13.70 .9945

6 W6/W5 Land

Rollout

Taxi .995 .995

Initial Sizing of Single Seat Homebuilt

Mission Weight Fraction (W6/Wo)	.7588
Mission Fuel Fraction (1-W6/Wo)	.2412
Total Fuel Fraction (1.12*(1-W6/Wo))	.2702

Empty Weight Fraction is given by as provided in the request for proposal.

The total weight is given by where W_crew is 200 lbs, W_payload is 10 lbs, and W_F/Wo is the total fuel fraction given on the previous page as .2702.

Wo	We/Wo	New Wo
50000	0.62381	1981.27
1981.27	0.5198	999.998
999.998	0.5001	914.244
914.244	0.49758	904.296
904.296	0.49727	903.1
903.1	0.49723	902.956
902.956	0.49723	902.938
902.938	0.49723	902.936
902.936	0.49723	902.936

After the iterations of Wo, the total weight of the aircraft is to be 902.936 lbs.

Verification:

W_E	448.97 lbs.
W_F	243.95 lbs.
W_crew	200 lbs.
W_payload	10 lbs
Total Weight	902.9 lbs

Estimation of ^T/_W and ^W/_S

The following values were used:

C_Do = 0.03
e = .94
where AR = 7.627

Dash:

M_dash = .4003
q_dash = 79.8069 PSF
n = 1
Lapse Factor = 1.0
Weight Fraction (W2/Wo) = .9890

Maneuver:

M_man = .2306
q_man = 76.0888 PSF
n = 3.0
Lapse Factor = 0.5
Weight Fraction (W1/Wo) = .9940

The design point was found to have the following values:

(T/W)o = .235

(W/S)o = 31.4 PSF

Landing Data

S_FL = .3*(V_A)² where S_FL is given in the RFP as 2500 ft, thus (V_A)² = 8333.333

V_A = 91.2871 knots

V_SL = V_A/1.3 = 70.2208 knots or 118.5194 ft/sec.

but (W_L/Wo) = 1.0 so

(C_lmax)_landing	(W/S)o ~PSF
1.6	26.7227
1.8	30.0631
2.0	33.4034
2.2	36.7438

Interpolating, this gives a maximum coefficient of lift when landing of 1.88.

Take-off Data

S_TOFL = 3500 ft.

TOP₂₅ = 3500/37.5 = 93.33 lbs/ft²

(W/S)TO			(T/W)TO
	1.2	1.4	1.6	1.8	2
10	0.08929	0.07653	0.06697	0.05952	0.05357
20	0.17858	0.15307	0.13393	0.11904	0.10715
30	0.26787	0.2296	0.2009	0.17856	0.16072
40	0.35716	0.30613	0.26787	0.23809	0.21429
50	0.44644	0.38267	0.33483	0.29761	0.26787

From the design plot, C_Lmax in Take off = 1.4.

Wing

Area, sq. ft. 16.75

Span, ft. 14.81

Centerline Chord, ft. 2.62

Tip chord, ft. 1.26

Taper Ratio, ft. .48

Aspect Ratio 7.627

Mean Geometric Chord, ft. 1.94

Mean Aerodynamic Chord, ft. 2.02

Quarter Chord Sweep, degrees 2.37

Dihedral, degrees 2.0

t/c ratio 0.15

Available Fuel Volume, ft.³ 3.532

Required Fuel Volume, ft.³ 4.979

Weights

Design Take off Weight, lbs. 902.9

Design Empty Weight, lbs. 448.97

Design Fuel Weight, lbs. 243.95

Crew Weight, lbs 200

Payload Weight, lbs. 10.0

Aerodynamic

Clean C_Do 0.03

Cruise "e" 0.94

Engine

Thrust, lbs. 212.205

Core Length, inches 21.935

Core Diameter, inches 13.110

Core Weight, lbs. 72.521

Fuselage

Length, ft. 16.75

#	Segment	Description	Values	Fraction
1	W1/Wo	Engine Start Warm Up Taxi Take off	.998 .998 .998	.9940
2	W2/W1	Climb	.995	.995
3	W3/W2	Cruise	R=830 Nm C=.75 lb/lb/hr V=(.3423*1037) L/D _cruise = .866(L/D)_max	.7792
4	W4/W3	Descent	.995	.995
5	W5/W4	Loiter	E=10 min C=.45 lb/lb/hr (L/D)_max = 13.70	.9945
6	W6/W5	Land Rollout Taxi	.995	.995

Wing
	Area, sq. ft.	16.75
	Span, ft.	14.81
	Centerline Chord, ft.	2.62
	Tip chord, ft.	1.26
	Taper Ratio, ft.	.48
	Aspect Ratio	7.627
	Mean Geometric Chord, ft.	1.94
	Mean Aerodynamic Chord, ft.	2.02
	Quarter Chord Sweep, degrees	2.37
	Dihedral, degrees	2.0
	t/c ratio	0.15
	Available Fuel Volume, ft.³	3.532
	Required Fuel Volume, ft.³	4.979
Weights
	Design Take off Weight, lbs.	902.9
	Design Empty Weight, lbs.	448.97
	Design Fuel Weight, lbs.	243.95
	Crew Weight, lbs	200
	Payload Weight, lbs.	10.0
Aerodynamic
	Clean C_Do	0.03
	Cruise "e"	0.94
Engine
	Thrust, lbs.	212.205
	Core Length, inches	21.935
	Core Diameter, inches	13.110
	Core Weight, lbs.	72.521
Fuselage
	Length, ft.	16.75