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.

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.

A perfect example of where math like this was extremely helpful was the Mini-bot race in 2011. By the halfway point in the season, sub 2 seconds mini-bots began to become the standard for teams playing in the last few matches of any events, with ‘traditional’ mini-bots becoming almost useless by the championship. The secret* behind them was so simple, and once explained was easy to understand, but it’s not something that most people would have come to without understanding the concepts in this thread. (IIRC, 973 - Adam’s Team - Had the fastest mini-bot at the championship (or at least their division) that year.)

With that being said, this is an awesome thread. I think I’m going to borrow some of these equations for later.

*The ‘secret’ was to remove the transmissions, and use a really small diameter roller/wheel - 3/8" OD or so, IIRC.