Tools › Aerodynamics › Propulsion › Propeller and Jet Thrust › Example
NACA Report 640 propeller 5868-9, three blades, 10 ft, set 20° at 0.75R, 1,000 rpm at 100 mph: blade-element momentum theory against the measured curves
| Tool | Propeller and Jet Thrust |
| Source | Hartman, E. P., and Biermann, D. (1938). The Aerodynamic Characteristics of Full-Scale Propellers Having 2, 3, and 4 Blades of Clark Y and R.A.F. 6 Airfoil Sections. NACA Report 640, National Advisory Committee for Aeronautics, Washington, DC. Figure 2 (blade-form curves of the 5868-9 blade) and Figures 9, 11 and 12 (thrust coefficient, power coefficient and efficiency of the three-blade propeller against V/nD). |
| Level | Undergraduate |
Problem
The three-blade 10 ft propeller 5868-9 of Clark Y section, whose chord, thickness and pitch distributions are given in Figure 2 of Report 640, is set 20° at 0.75R and runs at 1,000 rpm at 100 mph at sea level. Find the thrust, torque, power and efficiency by blade-element momentum theory with Prandtl's tip-loss factor and a stated Clark Y polar, the radial distributions, the efficiency map against the advance ratio J, the zero-thrust J and the static thrust, and compare with the report's measured curves.
Inputs to Enter
- Model: propeller, blade-element momentum; altitude 0 ft (1976 Standard Atmosphere), V 100 mph, D 10 ft, N 1,000 rpm, 3 blades, hub 0.2 R, geometry NACA 5868-9 (Report 640), beta 20° at 0.75R
- Section polar: a_0 5.73/rad, alpha_L0 −5° (from the flat face of the Clark Y, NACA's blade-angle reference), C_d0 0.008, C_dt 0.10, k_d 0.010, C_l,md 0.35, C_l,max 1.35
Answers
- J = V/(nD) = 146.67/(16.667 × 10) = 0.880; T = 248.7 lb, Q = 409.0 lb-ft, P = 77.86 hp; C_T = 0.03767, C_P = 0.03892, C_Q = 0.006194, η = J C_T/C_P = 0.8517 (ideal efficiency of the same C_T and J 0.971)
- Map at 20°: zero thrust at J = 1.049 (Report 640 curve 1.04), peak efficiency 0.854 at J = 0.84 (measured 0.831 at 0.85–0.9); static thrust 1,055 lb at 132.9 hp
- Against the report at 20°: C_T theory 0.1127 / 0.0944 / 0.0546 / 0.0333 at J 0.5 / 0.6 / 0.8 / 0.9 vs measured 0.1107 / 0.0926 / 0.0520 / 0.0308; η theory 0.706 / 0.772 / 0.850 / 0.847 vs measured 0.659 / 0.731 / 0.826 / 0.830 (the theory carries no nacelle)
- SI: T = 1,106 N, Q = 554.5 N-m, P = 58.06 kW at V = 44.70 m/s
Notes
The tool's default inputs are this case; press Submit. The report prints no tables (its test data were available on request), so the geometry and the measured points were digitized from its figures (References/Propeller-Jet-Thrust/README.md states the accuracy); the theory's numbers are checked in test_propeller_jet_thrust.php against an independent numpy/scipy solution (1e-8), the momentum-theory bound and the report's zero-thrust advance ratios (within 1.2 %), and the same test reproduces the report's appendix thrust table for the two-blade propeller to the printed digits. The jet-cycle part of the tool is checked against the ideal-turbojet closed forms at 20 parameter sets and the NASA Glenn polynomials against the NIST-JANAF tables.