There are some generalizations, rules of thumb, that help estimate prop and motor sizes for free flight rubber powered model airplanes.
There is a relationship between the swept disk (circular) area of the prop and the wing area. The wing generates lift per unit area and the prop generates thrust per unit area. The two are related. McCombs recommends the the prop diameter should be from 1.0 to 1.5 times the square root of the area of the wing. Pitch is best determined by test. Or you can use John Barker’s Prop Picker. Go here, scroll down about 2/3 and click on ‘Prop Picker’.
In horizontal flight, Lift equals Weight.
Trim attack angle establishes a trim Lift to Drag ratio L/D. That and Lift establish Drag. We have some reasonable ballpark guesses for that L/D, usually based on glide tests. For typical rubber models, L/D is probably in the range of 4 to 6. (Trim L/D is not necessarily maximum L/D, usually isn’t, shouldn’t be.)
In horizontal flight, Thrust equals Drag. I know of no way to measure either in flight. L/D under power is not the same as L/D in glide for several reasons; different trim attack angles, prop slipstream. But if that is all you have, try it. It won’t be too far off.
For typical rubber model propellers, there is a range of typical Thrust to Torque ratios. It is difficult to establish values because Thrust is unknown. At the end, we will estimate a value based on typical values for the other numbers.
It is possible to measure level flight torque Q; wind the motor until the plane makes a level circle from launch to catch. Measure the torque at begin and end. The numbers will be close and the average is a good estimate for level flight torque. For a fast, steep climb, torque must be much greater. You can weigh the plane, with motor, and calculate a Torque to Weight ratio Q/W.
Torque relates to motor cross section. Q = Kq x S^2/3 where Q is torque, Kq is a torque coefficient specific to a batch of rubber and S is the cross sectional area of the motor. S^2/3 is the two thirds power of cross sectional area. Use the exponentiation function on your calculator. This allows you to calculate how many strands of what width you will need when you know the required torque. I am measuring torque in gram centimeters and cross section in square inches. Level flight Kq ranges from about 21,000 to 24,000. Adjust as necessary for your units.
This chain of relationships implies a ratio of level flight torque to weight Q/W, which can be measured, as above. For my planes, mostly simple stick models, I find a level flight torque to weight ratio ranges from 0.767 for the Dandiflyer (stick ROG, cambered single tissue wing surface, moderately high aspect ratio) to 1.24 for the AMA Cub and 1.38 for the Squirrel (stick models with flat plate wings of low to moderately low aspect ratio). The Sig Tiger was 1.63 (box fuselage, two surface airfoil wing of moderately high aspect ratio). The Big Pussycat got 0.952 in one test and 1.106 in another (also box fuselage, single tissue surface cambered wing of moderate aspect ratio). I am measuring torque in gram centimeters and weight in grams, so torque to weight ratios are in centimeters. Convert as necessary.
Put this together and we get
Q = (Q/T) (D/L) W
Rearranging gives Q/W = (Q/T) (D/L) and T/Q = (D/L) (W/Q)
This would suggest for a typical value of D/L of 1/5 and W/Q of 1/cm a T/Q around (1/5) 1/cm = 0.2/cm.
For a start, select a cross section that gives a level flight torque in gmcm about equal to the weight of the plane, including weight of motor, in grams, with Kq of around 21,000 to 24,000. This torque coefficient falls in the mid range of the torque curve. The spike will typically be about 5 times higher. The cross section is calculated from rearranging Q = Kq x S^3/2 to S = (Q/Kq)^2/3. Remember that S = n t w where n = number of strands, t = strip thickness and w = strip width. So the number of strands would be n = S/tw. Typical t is 0.042″.
If you want a faster climb, use a greater cross section.
I have just completed a model of a Frog Fawn rubber model
Wing Span 22 inches
wing area 64 sq inches
weight excluding rubber is 45gms.
Hook to pin is 11.5 inches
Prop Diameter 7.5 inches
I have some tan rubber 1/8 or 1/4 inchs
Would you be able to advise me of a suitable motor dimension?
I use a measured torque to weight ratio to calculate motor dimensions. The tests I have range from about 0.71 to about 1.76 for different airplanes. The value depends on the aerodynamics of the aircraft at flight trim and the properties of the propeller. The Fawn is a clean cabin design. I also assume a motor length to hook distance ratio, typically I find it is impractical to use a motor more than about twice the available distance. I can use another ratio if you prefer.
https://outerzone.co.uk/plan_details.asp?ID=578
I notice that the Fawn plan calls for a propeller with flat (untwisted) blades. This would make a very inefficient propeller that would require a thicker motor that would give fewer useful turns, probably a higher revolution rate and short duration. A carved helical prop would be better, the best pitch to diameter ratio is a matter of testing. The wing area suggests a propeller diameter of 8″.
The plan says weight is 3/4 ounce, which is 21.26 grams. The stated weight excluding rubber is 45 grams. The heavier plane will require a thicker motor with fewer turns capacity. Your plane will fly, but flights will be faster and shorter than they would be if you could get the lower weight. After you get some experience with this one, you might build another with lighter wood. Look on the bright side, with the smaller flying places today, a heavy model is safer, less likely to get lost.
I will assume a level flight torque to weight ratio of 1.0, a motor length of 23″ and a motor average torque coefficient of 21,133. Your airplane, propeller and rubber may differ.
The computation assumes an empty airplane weight W and calculates the torque required to fly it level Ql, the cross section S required to develop that torque at average torque, the width w of a two strand motor with 0.042″ strand thickness and the weight of that motor Wr. When we put that motor on the plane, it weighs more and therefore requires a thicker motor, so we redo the calculation with the new total weight, repeating the process until the change in motor weight is less than we can measure. It usually converges by the fifth iteration.
Rubber Motor Iteration
Model Frog Fawn
Date 08/30/21
Weight of airframe 45
Torque/weight ratio 1
Motor length 23
Torque coefficient 21,133
W Ql S w Wr
45 45 0.0165513812 0.1970402521 6.0425677303
51.0425677303 51.0425677303 0.0180017299 0.214306308 6.572060111
51.572060111 51.572060111 0.0181260101 0.2157858347 6.6174322656
51.6174322656 51.6174322656 0.0181366398 0.2159123792 6.6213129606
51.6213129606 51.6213129606 0.0181375489 0.2159232008 6.6216448249
51.6216448249 51.6216448249 0.0181376266 0.2159241262 6.6216732045
51.6216732045 51.6216732045 0.0181376333 0.2159242054 6.6216756314
51.6216756314 51.6216756314 0.0181376338 0.2159242121 6.6216758389
51.6216758389 51.6216758389 0.0181376339 0.2159242127 6.6216758567
51.6216758567 51.6216758567 0.0181376339 0.2159242128 6.6216758582
51.6216758582 51.6216758582 0.0181376339 0.2159242128 6.6216758583
Strands of 1/8” 3.4547874043
Strands of 3/32” 4.6063832058
Strands of 1/16” 6.9095748087
These are all odd numbers of strands. Rounding up is preferred.
If you don’t have a rubber stripper, you could try four strands of 1/8″ rubber 23″ long. This would be a good place to start. It may give a little more power than necessary, may not give as much duration, but will get off to a quick start. You can adjust from there. This design method assumes the motor will be carefully wound to just below breaking turns, will climb to apogee and continue turning all the way to touchdown. This assumes a gradual increase in torque in a series of test flights to trim for proper climb. If the plane lands with many turns remaining, either it was not fully wound or it is too small cross section. If it runs out in the air, the motor is too thick in cross section. Adjust accordingly. Also check the CG with the motor in place. It may be necessary to add ballast and redo the motor calculation. I’m looking at the Fawn plan. Its CG is about midway on the length of the motor, so changes in motor weight won’t make major changes in CG position.