# Calculating Linear Force from Motor Torque?

You could build a regional winning FRC bot this year with no one in your team having more than a 8th grade math education, given a few people on the team fairly familiar with FRC rules of thumb. Frankly, I think you might even be able to get away with a 4th grade math education.

However, this fact completely misses the point of FRC. FRC is one of the few places where students are actually asked to challenge themselves and apply what they’ve learned. It’s been awesome for me to see how different things I’ve learned in math class (trig, differential equations, etc) apply to robot design, and it’s motivated me to continue to do well in the classroom.

If you want to build a well engineered robot (which isn’t necessary to win a regional), these types of calculations are extremely important. In fact, you can argue that this discussion of DC motors only scratches the surface in terms of design for DC motors (current draw, changes in performance at different voltages, factoring in acceleration of the motor under load, etc are all great things to look into). Without this type of basic knowledge, you’re flying blind. If you don’t want to rebuild gearboxes a few times each season because you’re cooking motors, do your homework, and actually look at torque requirements and safety factors. It looks like Adam’s presenting the math a bit formally (which is really the right way to do it), but don’t get scared by a few equations. It’s honestly not that hard.

Adam, although I’ve never built an elevator, a FOS of 4 sounds a bit conservative. I’d assume a FOS of 2 would work well from just general FRC experience. Of course, I’m sure you’ve had a lot more experience with elevators than me.

You are correct, I assumed it was 80 on drum.

I didn’t recommend any specific factor of safety, and I generally do these calculations without them as they are kind of meaningless in this case.

For example, why design for 25% motor load with a FOS of 2, when you can call that 12.5% motor load.

It’s a style preference, I just don’t use FOS here (Although I use it a lot elsewhere).

AS for what % stall is okay, that’s tough to say and depends on how often it’s used and what motor you’re using.

To be quite honest, I think most folks who managed to pass high school algebra could do engineering math quite easily. But if you asked them what they were doing, or how the equation they’re dealing with is derived, they’d be totally lost–which is why engineering is a 4-year (or more) curriculum with math through about 4 semesters worth of calculus and differential equations.

As far as safety factor, what a “good” one is varies by what you’re dealing with, and other similar things. If I’m designing something to carry people, I’ll use a higher safety factor than if people aren’t involved, for example. For an FRC

robot, the more critical the system, the higher the FoS should be–to a point. (You probably want somewhere between 1 and overkill, but where overkill is depends a lot on your design, where in the design you’re working, what material shape you’re using, and how well you made your bumpers this year.)

You have to be careful with safety factors. Otherwise you start with a mouse built to government specification—A elephant.

Airplanes are another example of competing safety factors. You don’t want wings falling off, but you want your lift to weight ratio much greater than 1.