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Ten-passenger executive jet of NASA RP-1060: constraint diagram, match point, fuel fraction and take-off weight
| Tool | Aircraft Sizing and Constraints |
| Source | Loftin, L. K., Jr. (1980). Subsonic Aircraft: Evolution and the Matching of Size to Performance. NASA Reference Publication 1060, National Aeronautics and Space Administration, Washington, DC. Chapter 4, pp. 176-221: Tables 4.I to 4.V, aircraft variant 1, match point 1. |
| Level | Undergraduate |
Problem
Size a twin-engine executive jet for ten passengers, a crew of three and 500 lb of cargo (3,165 lb in all) over 2,174 n. mi. plus 500 n. mi. of reserve at Mach 0.8, with a FAR balanced take-off field length of 6,000 ft, a FAR landing field length of 5,000 ft at 80 percent of the take-off weight, and the one-engine-inoperative climb gradients of 2.4 percent after take-off and 2.1 percent in the approach. Find the wing loading and thrust-to-weight ratio, the fuel fraction, the take-off, empty and fuel weights, the wing area and the thrust.
Inputs to Enter
- C_D0 0.0220, aspect ratio 7, e 0.85 clean and 0.70 with flaps; C_Lmax 2.30 take-off and 2.87 landing; flap drag increments 0.020 take-off and 0.045 approach with gear
- Two engines, thrust lapse T/T_0 = sigma^1 with a cruise rating of 0.84 (0.216 at 39,200 ft, engine D of Table 4.III); SFC 0.823 lb/lb-h
- Field lengths by the report's correlations: k_TO 37.7 ft per lb/ft^2 (6,000 ft at a take-off parameter of 159), k_L 0.3 ft/kt^2 (5,000 ft at 129 knots)
- Cruise 460.8 knots at 39,200 ft at the take-off weight; cruise legs 2,174 and 500 n. mi. at L/D 14.45; payload 2,550 lb, crew 615 lb; empty-weight fraction 0.560 (useful-load fraction 0.440), no reserve fraction
Answers
- (L/D)max = 0.5 sqrt(pi e A / C_D0) = 14.57 at C_L 0.641 (report 14.6 and 0.64)
- Landing: V_A = sqrt(5,000/0.3) = 129.1 kt, W/S limit 119.78 lb/ft^2 (report 120.16 at C_L,A 1.7); take-off parameter 6,000/37.7 = 159.2 lb/ft^2
- Design point where the take-off and cruise lines cross: W/S = 116.48 lb/ft^2, T/W = 0.3182 (report match point 1, read from its charts: 118.0 and 0.315); second-segment climb needs 0.3081, approach climb 0.2732
- Fuel fraction 1 - exp(-2,674 c / (V L/D)) = 0.2814 (report 0.281, Breguet factor 8,090.6 n. mi.)
- Take-off weight 3,165 / (1 - 0.2814 - 0.560) = 19,961 lb, empty 11,178 lb, fuel 5,618 lb (report 19,906, 11,147 and 5,594 lb with the fuel fraction rounded to 0.281)
- Wing area 171.4 ft^2, span 34.63 ft, thrust 6,352 lb (report 168.7 ft^2 and 6,270 lb at its match point); growth factor 6.31 lb per lb of payload
- Range-payload: 2,674 n. mi. at full payload, 2,997 n. mi. with tanks 10 percent larger than the mission fuel and 1,988 lb of payload, 3,409 n. mi. ferry
Notes
The tool's default inputs are this aircraft; press Submit. Choosing Design Point = Entered with 118 lb/ft^2 and 0.315 gives the report's wing area and thrust to 0.3 percent (the page then says the point lies 2.3 percent under the take-off line and 1.0 percent under the cruise line of its own models). test_aircraft_sizing.php (1,549 checks) reproduces Tables 4.I to 4.V row by row and compares 19 parameter sets with an independent scipy implementation. The report lists a speed of sound of 576 knots at 39,200 ft; the 1976 atmosphere gives 573.6, so 460.8 knots is Mach 0.803 here.