Tools › Aerodynamics › Rotors and Ducted Fans › Rotorcraft Performance › Example
Helicopter of NACA Report 1266: power required at 180 ft/s with a 300 ft/min climb, hover power and ceilings
| Tool | Rotorcraft Performance |
| Source | Gessow, A., and Tapscott, R. J. (1956). Charts for Estimating Performance of High-Performance Helicopters. NACA Report 1266, National Advisory Committee for Aeronautics, Washington, DC. Pages 3-4: equations (4), (7), (8) and the sample performance calculation. Johnson, W. (2015). NDARC: NASA Design and Analysis of Rotorcraft. NASA Technical Publication 2015-218751, Ames Research Center, Moffett Field, California. Pages 98-101, 108-109. |
| Level | Undergraduate |
Problem
A single-rotor helicopter weighs 4,287 lb; its rotor has a radius of 20 ft, a tip speed of 600 ft/s and a solidity of 0.08, and the airframe has an equivalent flat-plate area of 12 ft^2. Find the power the rotor needs at 180 ft/s (106.65 knots) while climbing at 300 ft/min at sea level, split into induced, profile, parasite and climb power, and compare it with the 371 hp that the report obtains from its charts. With an illustrative tail rotor, transmission and 450 hp engine, find also the hover power, the figure of merit, the hover ceilings in and out of ground effect, the speeds for best endurance and best range, the maximum speed and the autorotative rate of descent.
Inputs to Enter
- Aircraft: helicopter; gross weight 4,287 lb, one rotor, radius 20 ft, tip speed 600 ft/s, solidity 0.08, flat-plate area 12 ft^2 (NACA Report 1266 p. 4)
- Induced power factor 1.15, mean profile drag coefficient 0.00885 (the value that gives the report's chart reading C_Po/C_T = 0.0315), profile power growth by the blade-velocity integral F_P, hover download 3 percent
- Illustrative: tail rotor radius 3.5 ft, tip speed 600 ft/s, solidity 0.12, arm 24 ft, induced factor 1.2, profile drag 0.012; transmission efficiency 0.97; installed power 450 hp falling with the density ratio; 600 lb of fuel at 0.6 lb/hp-h
- Sea level, standard day; rotor height in ground effect 15 ft; flight condition 106.65 knots with 300 ft/min climb
Answers
- Flight condition: drag 462.4 lb, thrust 4,327 lb tilted 6.13 deg, advance ratio 0.2974, induced velocity 4.01 ft/s, profile factor F_P = 1.4217
- Rotor power 374.3 hp: induced 36.3, profile 147.6, parasite 151.4, climb 39.0 hp; C_P/C_T = 0.0793 (report: 0.0067 + 0.0315 + 0.0322 + 0.0084 = 0.0788, 371 hp with ideal induced power)
- With the induced power factor set to 1.0, no download and no tail rotor the page gives 369.5 hp at the rotor (C_Pi/C_T 0.0067, C_Pp/C_T 0.0321, C_Pc/C_T 0.0083), 0.4 percent under the report's 371 hp
- Shaft power at the flight condition 400.9 hp with 14.6 hp for the tail rotor and 12.0 hp of transmission loss
- Hover out of ground effect: v_h = 27.19 ft/s, C_T = 0.00411, induced 251.0 hp, profile 103.8 hp, tail rotor 29.2 hp, shaft power 395.9 hp, figure of merit 0.615
- Ground effect at z/R = 0.75: T/T_inf = 1/(1 - (1/3)^2) = 1.125, induced velocity factor 0.8381, hover power 350.1 hp; hover ceilings 3,911 ft out of and 7,777 ft in ground effect
- Best endurance 52.3 kt (221.8 hp), best range 87.1 kt (278.9 hp), maximum speed 122.1 kt, rate of climb 1,630 ft/min, service ceiling 22,696 ft
- Autorotation: 3,102 ft/min vertically (1.91 v_h), minimum 1,631 ft/min at 50.5 kt, flattest glide 4.19 at 84.8 kt
Notes
The tool's default inputs are this helicopter; press Submit. The report gives only the rotor data and the flight condition; the tail rotor, the engine, the losses, the induced power factor and the download are illustrative. The report's profile power comes from charts built on blade-element theory with a three-term section drag polar, so the mean drag coefficient 0.00885 is a calibration to its chart reading, not an independent result. The report rounds its coefficients to 0.079 and 0.031 before multiplying: unrounded they give 370 hp in place of 371 and 148 hp of profile power in place of 146. test_rotorcraft_performance.php (1,463 checks) reproduces the closed-form steps of the sample to the printed digits and checks the inflow, the profile-power integral, 20 helicopters and 13 multirotors against numpy and scipy.