So Im making a 1 page quick reference for my team.
If you had a 1 page basic Equation/Reference sheet for FRC/FTC what would you want on it?
Things I’m thinking of
Here’s a short list of equations that I have used in FRC and FTC:
Geometry
sin^2(x)+cos^2(x)=1
C=2*pi*r
Mechanics
F=ma (and its angular complement T=I*alpha)
at^2+vt+k=x
W=Fd (the calculus definition W=integral F ds is also useful)
w=mg
Electricity
V=IR
P=VI
Gears
Ratio = Driving teeth / driven teeth (also true for belts)
Center distance = (Pitch Diameter 1 + Pitch Diameter 2) / 2 + Center Add
Not mechanically oriented so here’s a PID equation:
DC motor equations
^this
DC motor equations, with explanations:
V=I*R
And all of its various derivatives.
for gears: pitch diameter = # teeth / diametrical pitch
for pullies: pitch diameter = (# teeth * pitch) / pi
All you need is F = m*a and you can derive the rest.
It appears you’re talking about for design time.
Along this line:
I’d add some near-pythagorean triplets that are “close enough” to 30 and 45 degree angles to build Versaframe triangles without drilling holes in either gussets or tubes:
30/60/90 triangle: 152 + 262 ~ 302
45/45/90 triangle: 122 + 122 ~ 172
We used 15/26/30 (actually 7.5", 13", 15") on our 2017 robot and 12/12/17 on our 2018 competition robot; the errors were small enough in both cases that we had no problem fitting the rivets. I have also used 30x26 and 15x13 tiling patterns to make honeycomb wallpaper. Also, as it turns out, the 5/12/13 pythagorean triple is close enough to a 22 1/2 degree angle for many practical purposes.
Nickbrickmaster: This really should be ΣF = ma, and you also need F[sub]reaction[/sub] = -F[sub]action[/sub]. All the F’s and a’s should be annotated as vector quantities. Then you can derive the rest. The derivations get shorter if you add ΣΓ = Iα with Γ and α being pseudo-vectors.
I might also add the equation for effective gear ratio of a planetary gearbox with a fixed ring: R[sub]p[/sub] = R[sub]ring[/sub]/R[sub]sun[/sub] + 1.
Pneumatic cylinder equation: F=pA [also works for hydraulics, but not useful for FRC).
Some energy/work equations! Likely some I’m missing, here are a few:
[ul]
[li]E[sub]kinetic[/sub] = mv2/2 or Iω2/2[/li][li]E[sub]gravitational[/sub] = mgh[/li][li]E[sub]spring[/sub] = kx2/2[/li][li]E[sub]pneumatic (slow)[/sub] = pV[/li][/ul]
Edit: even on a one-pager, there should be some room for the key numbers of the legal motors (stall and free current, stall torque, free speed, peak power). Also, some conversion factors. Top of the list: 1 rpm ~ 0.1047 radians/sec.
This, if you’re a district team 
Don’t most people write for their constants to all be positive? If so, shouldn’t the derivative term have the opposite sign?
There are a bajillion forms of the PID equation people use.
From one of my favorite professors and I’m sure a bunch of other places, here are the fundamental equations for a few different engineering disciplines:
Electrical Engineers: V = I*R (Ohm’s Law)
Mechanical Engineers: F = M*a (Newton’s 2nd Law)
Civil Engineers: “if it goes uphill you gotta pump it” (… most civil engineers)
TIL will.i.am is a civil engineer.
More important than all of these equations is knowing how to use them as is the case with just about every equation. Each of these alone is relatively useless if you can’t correlate the problem to the equation correctly.
Just a simple example, ∑F=Ma is an incredibly useful formula, but if you don’t know how to create a Free Body Diagram that accurately depicts how the forces are acting on the bodies the equation won’t get you much further than 1D problems.
That knowledge and understanding takes time and education (self or otherwise), and luckily in this day and age there are a multitude of resources that can help cultivate that knowledge and turn it into a skill.
This includes:
Woah, that sounds like a lot of work! You’re saying that knowledge of every discipline in FRC can’t be boiled down to a single page?
My original post was a joke, but knowing how to derive things from F=ma (ie knowing physics concepts and how they relate) is the far more important part.