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FRC Motor Selection

Overall system capabilities, independent of a particular motor:
The max electrical power per motor that the robot can sustain is dictated by the 40Amp current limit on the motor controllers (Jaguars).
The Worst case battery voltage occurs when the battery is towards the end of it's charge. 
The batteries start out between 13-14v fully charged and end up around 11V when mostly discharged (empty)

A) Multiply the current limit by the worst case battery voltage to get the available electrical power. 
11v*40A = 440 Electrical Watts per motor
B) most motors are 40-60% efficient when converting electrical energy to mechanical energy so multiply by 0.4 again to convert the electrical power to mechanical power.
440Watts per motor * 0.4 = 176Watts maximum sustainable mechanical power available per motor. 

The overall system is capable of delivering 176 Mechanical Watts for each motor

Work = Force*Distance
We have a ~45kg robot to move 1.6meters. 

First we need to convert the weight to a Force
Force = Mass*Acceleration, in this case the Mass is the robot weight and the acceleration is from Gravity.
45kg*9.8m/s^2 = 441 Newtons

Then multiply the Force*Distance to get Joules of Work
441N * 1.6m

This is ~713 Joules of work to be done.

Power  = Force*Distance/Time
If we want to climb the tower in 10seconds that sets the time in this equation and it's easy to calculate the Power.

713Joules/10seconds = 71.3Watts of mechanical power.

Picking a motor. 
Here are the motors available in the Kit of Parts (KOP):

1) The system determines the load (robot weight)
2) Identify the load torque at the motor output and speed required by the motor with any gear reduction required
3) Find a motor that can deliver this from the available motors in the document
The power available is listed in a column "Max Power" in the document link above
Any motor with max power above the 176Watts is unusable for sustained periods of time*
You can use the motor, just not all the power will be available.

4) Divide the "Max Power" by 2 and that's probably what we can get the motor to deliver.

There are 7 motors available with >100W output.
The Denso Motors, mentioned for the climber because of backdrive, are only rated at 23Watts.

Next, we need to identify a motor that can produce the proper output at a speed sufficient for climbing the tower.
See the documents in: Motor Curves Primer for FRC

* The Jaguars can do: 100A for 1/2second for "bind condition" 60A for 2 seconds, also for "bind condition" and then 40A all day long. Bind condition refers to the "short circuit" condition while a motor gets up to speed. The starting torque allowed is limited to the torque associated with 100A