FRC Motor Selection for Disc Launcher

Selecting a motor for the disc thrower will need to account for:

The necessary output speed of the wheel launcher
The torque applied to the wheel.

System:
The disc weighs 0.18kg (http://www.andymark.com/FIRST-Choice-p/fc13-141.htm)
Field = 50' max

Speed of Launcher:
Our team did several trials for how fast a disc must be thrown to not drop over 50feet (~15.4meters) to cross the game field. 
The trials results ranged from 1.2seconds to 1.5seconds. 

We use the 1.2seconds as the time to cover 15.4meters.
This provides a linear speed of 15.4m/1.2s = 12.82m/s

A wheel travels it's circumference(pi*diameter) every revolution (distance/rev).
This provides Pi*Diameter/Revolution

Our team examined 6", 8" and 12" wheels

(39.354"/meter)
Now determine how fast the launcher must spin to achieve a linear speed of >12.82m/s

diameter circumference
6" 18.84955592
8" 25.13274123
12" 37.69911184
=pi*diameter

Then convert inches to meters for units
meters/rev
0.478974334
0.638632445
0.957948667
=circumference/39.354

Then use the linear speed of 12.82m/s to determine the rev/sec needed for each diameter wheel
rev/sec
26.76552605
20.07414454
13.38276302
=(linear speed)/(meters/rev)

Then, for compatibility with motor units convert the rev/sec to rev/minutes
rev/min
1605.931563
1204.448672
802.9657814
=60*(rev/sec)

If there is any gear ratio between the motor output and the launching wheel then that must also be included in the rpm to the motor.

The actual excel sheet is a little easier to see the diameter linked to the output:
diameter circumference meters/rev rev/sec rev/min
6 18.84955592 0.478974334 26.765526 1605.931563
8 25.13274123 0.638632445 20.0741445 1204.448672
12 37.69911184 0.957948667 13.382763 802.9657814

The spinning objects are measured several ways. 
Cycles per second = Hertz
Radians per second = 2*pi*Hertz
Revolutions per second = RPS = Hertz
Revolutions per minute = RPM = Hertz*60

Motors are usually rated in Revolutions per minute (RPM)
The units for linear speed is meters/second


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