Rubber Motor Turns Tables Formula

Motor turns tables are limited to the lengths and cross sections listed. Those of us who cut and strip rubber to other than standard size need something more general.

I use a formula.

Caution; the breaking turns are affected by many things. Every batch of rubber has different properties, warmer temperature stresses the rubber, lubrication, stretching, rate of winding, cooling, previous stretching, braiding, contamination and other things affect how many turns a motor will take. Winding heats the rubber, it heats faster as torque increases and every turn puts in more work. Slow your winding as you get close to full to let it dissipate the heat.

Formulas can be a useful guide to winding under standardized conditions.

My formula is:

T = 10.64/Sqrt(S)

T is breaking turns per inch. Multiply that by the length of your motor to get breaking turns for that motor.
S is motor cross section in square inches. Multiply strip thickness (0.042″) by motor width times number of strands.
Sqrt( ) is square root. Look on your pocket calculator. Most computers have a calculator window.
10.64 is an empirical coefficient. It is the result of testing some pretty good Tan II. Lou got exactly the same for some Tan SS. Purely coincidence.

You can establish your own formula by winding a short test motor under standard conditions and using the formula to calculate a new coefficient. “Good” rubber will run from 9 to 13.

Here is an example of a turns table I made up for a motor.

Denny Dart II, 7″ NP Prop, 17″ loop of 0.083″, 127.4 tpi

% Breaking Turns        Number

100                                  2166

95                                  2058

90                                  1950

85                                  1841

80                                  1733

75                                  1625

70                                  1516

If you are using a 15:1 winder, divide those turn numbers by 15 to get the number of cranks on the winder.

Gary Hinze

8 thoughts on “Rubber Motor Turns Tables Formula

  1. Hello
    Thanks for that formula. Very useful. I used that formula to complete the table for the maximum rubber turns in Don Ross’s book for 1/16 and 3/32 rubber bands.
    Although there is a little difference, results for both methods are very close(formula and numbers in table).
    Can I use that template of the formula for any type of rubber band?
    Albeit I know I should change the constant 10.64 for any different rubber but I am not sure about that square root.
    Thanks

    1. The 10.64 is an empirical coefficient based on tests. It is good for that particular batch of pretty good Tan II rubber. I think it is a little bit on the safe side. Every batch of rubber may be different. The variation within current batches of Super Sport is said to be much less than previous kinds of rubber. If you are not pushing your rubber to the limit in competition, an average coefficient might be good enough. You should use this number as a guide, not expect to wind to that exact number every time. When you approach this number, you slow your winding. Winding heats the rubber, which makes it push back. Pausing allows it to cool, letting it relax and permitting more turns to be put in. You can judge the stiffness of the rubber by letting it cool and giving little tugs on it. With experience, you will be able to judge when the rubber is going up on the torque spike and when to stop winding.

      The square root is based on physics and should not be varied.

      1. Thanks.
        Here in my country, the FAI rubber is rarely available and expensive (Due to the economic problems of my country).
        I teach kids building and flying simple gliders and after that rubber power models like AMA cub and SkyBunny.
        But I want to give them something more than just building and flying.
        I think when kids use some simple theory and math in their models, they feel they have learned more professional content.
        So I try to formulate other types of available rubber.
        If they don’t know the square root yet, but can multiply the length of their rubber in maximum (turn/inch) number.

        1. Rubber testing would be important then, to select the best from what is available. On the old Comet plans, the instruction was to cut rubber strip from bicycle inner tube!

          One of the advantages of model aviation is that it provides opportunities for kids to learn basic science, math and engineering skills while having fun. It engages their mind and motivates learning. It is very satisfying to see how ideas can be realized in practice.

          Most pocket calculators have a square root function. Square roots can be done on a slide rule. There are also tables. In the old days we used log tables to calculate things like square roots. There is also a formula for calculating square roots that is similar to long division. Search the Internet.

  2. Denny Dart II, 7″ NP Prop, 17″ loop of 0.083″, 127.4 tpi

    If 0.083″ is the width of the rubber you used in your example table, I can’t get 127.4 tpi using the empirical coefficient of 10.64 that is listed in your formula, I’m confused? I get 10.64/(.083*.042)^.5 = 180.2 tpi.

    Is it possible that your table is based on a empirical coefficient of 7.52?

    1. I am pleased that someone is reading this closely enough to try the numbers. It makes me feel that my effort is justified. Sometimes I make a mistake, so I carefully reviewed the calculation.

      Your discrepant number is the result of an easy oversight. The width of 0.083″ is the width of a single strand of rubber. There will be two strands in the loop used in the motor. So the cross section is twice the width times the thickness.

      This number is a rough guide. Every batch of rubber is different and motors cut from the same batch may differ noticeably. The width and thickness may vary slightly. When winding a motor, you can wind up to about 90% of this number, then you can stretch check. You will find that energy may be stored in two ways, by torsion and by tension. The sum has a limit. As you approach the limit in torsion, you will feel the motor stiffening in tension. As you approach maximum turns, you should wind slowly and stop occasionally. Let the motor cool and then give light tugs to the motor to see how it responds to stretching. When it doesn’t want to stretch with a light tug it is a good time to stop winding. The decision is a matter of judgement based on experience. You wind this hard only in competition. If you wind this hard you probably will prestretch the motor once and fly it once, then discard it. It will likely break the next time you wind that hard. For sport flying, 70% to 80% of maximum turns is preferred. That will allow many flights from the same motor.

      1. Ughhh, it never dawned on me that a loop is two strands. I appreciate your feedback, I couldn’t let a clever concept like this go, Thanks!!!

        (10.64)/[(2 strands*0.083*0.042)^.5] = 124.7 tpi…. Sweet : )

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