That little rectangle is the cross sectional area of your motor. The rubber strip comes in a standard thickness of about 0.042″. That means the motor size is defined by length and width. How long should the motor be and what width of strip should we use?
For those of you who are curious about why each airplane has a different size motor, this section gives you some ideas. Some day some of you will be designing your own airplanes and you will want to know this. If all you want to do is make the motor from strip, go to “Making a Rubber Motor”.
There are two measures of motor size, length and cross sectional area. These two determine the volume of rubber, which, together with the density of the rubber, determine its weight. Cross sectional area is the product of the thickness of the rubber strip, times the width of the strip times the number of strands. Our little indoor airplanes are powered by a single loop of rubber having two strands. Put the two ends together and look at them straight on.
The motor must meet several conditions to do its job. The motor is the fuel for your airplane. You want it to carry as much energy as possible. That means the biggest motor you can get on the airplane. But the motor also has weight that pulls the airplane down, the bigger motor pulls it down faster. As in every area of engineering, there is a balance. Here it is between the energy to go up and the weight pulling down. There is a duration equation that tells us that the optimum motor weight is twice the weight of the airframe. In addition, the motor must turn the propeller with enough force to pull the airplane through the air. A thicker motor will produce more turning force, called torque, than a thinner motor. It will take more torque to fly an airplane with a heavier motor. You also want the motor to turn for as long as possible. A longer motor will take more turns, but will also be heavier. A thinner motor will take more turns per inch before breaking than a thicker motor, but it won’t produce as much torque. Again, there is a balance between torque to fly and running out of turns too fast. You must also consider the effect of the weight of the motor on the center of gravity (sometimes called the balance point). If the center of gravity is too far forward, the airplane will dive. If it is too far aft, it will nose up and stall. You want the center of gravity to be at the place that produces the minimum sinking speed. If it is only a little too far forward or aft, the airplane won’t fly as long as it could. If you can move the wing, you can make adjustments to compensate for varying center of gravity locations, to some extent. But if the wing is fixed, that alone may require a certain motor weight, unless you can change the weight distribution by lightening parts or adding ballast weight. And last, but perhaps most importantly, the motor must fit and work in the space available. On each airplane, there is a distance between the propeller hook and the motor hook or peg. A motor with a length equal to this distance will be easy to finger wind without a winder, but it will not take very many turns. A longer motor will not wind properly unless the motor is pulled back to be in line behind the propeller shaft. You can do this by running the motor around your finger to take up some slack. You can have a person or device to hold one end of the motor as you wind from the other end. You can finger wind the prop, but a long motor will take many more turns that are convenient to wind by hand. You will want to stretch wind with a winder. You can actually get more turns into a motor by stretching it to several times its relaxed length while winding. A motor about twice the distance between the hooks seems to be best. At 3 times that distance, the motor knots up when wound and put into the airplane, the knots hit the stick or the inside of the fuselage, wrap around the prop hook and the prop doesn’t turn well. At 4 times the length, the motor turns into a knotted ball of tangles that hangs down, won’t turn the prop at all and sometimes twists itself entirely off the hook. On the Dandiflyer, the motor that only balances energy against weight would be 9 times the hook to peg distance. Nice idea, but it won’t work. The motor has to meet all the required conditions to do its job.
To size the motor for a new airplane I do level flight tests. Before that I do glide tests to trim the airplane for minimum sinking speed. I wind the motor up different amounts, launch it at shoulder height and adjust the number of turns until it comes back to me at the same shoulder height. I measure the torque before and after the flight. I average the torque at the beginning and end of the level flight. I also weigh the whole airplane. This gives me the ratio of level flight torque to weight. From these tests I can figure out how thick the motor must be to fly level at different weights. The thickness and length may result in a motor weight that requires adjustment to get the center of gravity in the right place. If other adjustments are not possible, the motor length must be set to get the required motor weight for proper center of gravity.
There is a relationship between the number of turns in a rubber motor as it unwinds and the torque. This may be found by winding the motor until it breaks, then making an identical motor, winding it until just before it breaks, then unwinding and measuring the torque every few turns during the unwinding. These points are plotted to produce an unwinding torque curve.
There is a direct relationship between the torque curve of the motor and the flight trajectory of the airplane. The plane will be flying level at the highest point of its trajectory. Before reaching the highest point, the plane will be climbing with more than level flight torque. After the highest point, the torque will be less than level flight torque and the plane will descend. I find that I get the best flight times (in still air) when the motor cross section is such that level flight torque falls at about 60% of breaking turns or about 1/5 of breaking torque.