"Aircraft Propeller Design", written by Fred E. Weick and published by McGraw Hill Book Company in 1930 makes reference to wind tunnel test results for a series of propellers with pitch to diameter ratios between 0.5 and 1.1, see pages 105 to 108 . The tests of these 13 propellers performed by W. F. Durrand and Everett Lesley are reported in "TESTS OF THIRTEEN NAVY TYPE MODEL PROPELLERS", NACA TR 237, 1926 . You can find out more about the tests at Durand Lesley Propeller Collection and download the test report at NACA TR 237 .
In 1994 I, Chris Stoddart, developed and posted to the internet a mathematical model based on these tests and Fred Weick's Representative Section / Blade Element theory, weick.tk. The model made use of MiniTK a free version of the TK Solver, a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc. , see TK_Solver at Wikipedia and UTS . The free version can still be used as a DOS application in Windows and with Linux. You can download MiniTK from MINITK and the Weick.tk mathematical model from Weick.TK .
Weick.TK allows the examination of many interactions on propeller performance on parameters such as efficiency, power and thrust as effected by pitch, diameter, velocity, and rotational speed and other factors. The program can select an optimal propeller to match a flight condition. It gives reasonable answers to queries ranging from rubber power to control line speed.
The Rule, Variable, and Unit sheets of Weick TK appear below.
Rule Sheet
| Status | Rule |
|---|---|
| Comment | ;Program - Weick.tk, Written by Chris Stoddart, July 23, 1994 |
| Satisfied | eta=TAN(PHI)/TAN(PHI+GAMMA) |
| Satisfied | C_p=QGF*B*WR*J^2*((TAN(PHI)+TAN(GAMMA))/(TAN(PHI)*SIN(PHI)))*C_L |
| Satisfied | C_s=J/C_p^0.2 |
| Satisfied | C_s = V*(rho/(P*(N/(2*pi()))^2))^.2 |
| Satisfied | eta=C_t*J/C_p |
| Satisfied | BETA=ATAN((4*PoverD)/(3*PI())) |
| Satisfied | TAN(PHI)=V/((3*D/8)*N) ;-- use without inflow |
| Satisfied | ALPHA=BETA-PHI |
| Satisfied | C_L=0.355+4.3*ALPHA-3*(ALPHA+0.075)^2 ;-- use without inflow |
| Satisfied | GAMMA=0.47*ALPHA+0.0073/(ALPHA+0.075) ;-- use without inflow |
| Satisfied | GAMMA=ATAN(1/LovrD) |
| Satisfied | T=(rho*C_t*N^2*D^4)/(2*pi())^2 |
| Satisfied | P=(rho*C_p*N^3*D^5)/(2*pi())^3 |
| Satisfied | Q=P/N |
| Satisfied | M_0=T/P |
| Satisfied | J=V/(D*N/(2*pi())) |
| Satisfied | PoverD = Pitch/D |
| Satisfied | WR = Chord/D |
| * Undetermined condition | IF OPT = 'yes THEN ALPHA = .8/57.3 |
Variable Sheet
| Status | Input | Name | Output | Unit | Comment |
|---|---|---|---|---|---|
| File Name: weick.tk July 23, 1994 | |||||
| .579 | D | m | Diameter | ||
| .722 | Pitch | m | Geometric pitch | ||
| Chord | .06948 | m | Chord at 3/4 distance to tip | ||
| 2 | B | Number of Blades | |||
| .12 | WR | Width ratio at 3/4 distance to tip | |||
| PoverD | 1.24697754749568 | Aerodynamic Pitch over Diameter | |||
| 8 | N | rev/s | Angular velocity | ||
| 5 | V | m/s | Forward velocity | ||
| T | 1.06051082397811 | N | Thrust | ||
| P | w | Absorbed Power | |||
| Q | .129313391262165 | N*m | Absorbed Torque | ||
| M_0 | .163155511381247 | Figure of Merit [T/P in N/w] | |||
| J | 1.07944732297064 | Advance ratio V/(N*D) | |||
| eta | 81.5777556906235 | % | Efficiency | ||
| C_t | .120262549489696 | Thrust Coefficient | |||
| C_p | .159132947457634 | Torque Coefficient | |||
| C_s | 1.55901190738972 | Speed/Power Coefficient | |||
| BETA | .486760145073151 | rad | Geometric Angle of Attack | ||
| PHI | .429595614242357 | rad | Relative Wind Angle | ||
| ALPHA | .0571645308307935 | rad | Aerodynamic Angle of Attack | ||
| C_L | .548405092943241 | "Lift Coefficient" Correlation | |||
| LovrD | 12.1526639689179 | "Lift/Drag ratio" Correlation | |||
| GAMMA | .0821015133831694 | rad | Angle who's tangent is Drag over Lift | ||
| 1.226 | rho | kg/m^3 | Air density | ||
| .366372781256872 | QGF | Overall torque grading factor (0.366) | |||
| OPT | To find optimal Pitch given D,HP,N,V | ||||
| enter 'yes, otherwise leave blank |
Units Sheet
| From | To | Multiply By | Add Offset | Comment |
|---|---|---|---|---|
| m | in | 39.37 | ||
| ft | in | 12 | ||
| m | mm | 1000 | ||
| kg | g | 1000 | ||
| rad/s | RPM | 9.549296585513721 | ||
| m/s | ft/s | 3.280833333333333 | ||
| w | hp | .001342281879194631 | ||
| rad | deg | 57.29577951308232 | ||
| N*m | lbf*in | 8.850748065226473 | ||
| lbf*in | ozf*in | 16 | ||
| lbf | ozf | 16 | ||
| w | J/s | |||
| N | lbf | .2248090247334889 | ||
| N/w | lbf/w | .224809024733 | ||
| lbf/w | ozf/w | 16 | ||
| rev/s | rad/s | 6.283185307179586 | ||
| ft/s | MPH | .6818181818181818 | ||
| w | HP | .001342281879194631 | ||
| lbf*in | gf*cm | 1153.16 | ||
| - | % | 100 | ||
| lbf | gmf | 454 | ||
| ozf*in | gmf*cm | 72.07250000000001 |
