paper: 4 CIM versus 6 CIM theoretical calculations

[InFlight]

The lead acid batteries used by FIRST are about 17 Amp-Hours. They are certainly capable of discharging in excess of 300 amps for a few seconds.

The roboRIO brown out control is based on a voltage threshold of 6.3 Volts. And thus has 5.7 volts of margin with a fully charged battery.

You could reasonably model this situation as a 12 V voltage source with 0.05 Ohms of resistance to the power distribution board; and 0.3 Ohms of resistance through each of motor controls (Talon SRX) and wiring.

A CIM motor has a stated Stall current of 131 amps at 12 volts. For the instantaneous stall current, you could model the equivalent resistance as R=V/I = 12/131=0.09 Ohms

So each CIM motor circuit would have a Series Resistance of 0.09+0.3=0.39 Ohms.

Parallel resistances are totaled as 1/Rtotal = 1/R1 + 1/R2 +…+ 1/Rn

Four CIMs have a combined parallel resistance of 0.0975 Ohms.
Six CIMS have a combined parallel resistance of 0.065 Ohms

Four CIMS
The Four CIM total Resistance is 0.05+0.0975=0.1475 Ohms

Current:
I=V/R=12V/0.1475=81.4 Amps

The voltage drop at the RoboRio is
V=I*R=0.05*81.4= 4.07 Volts
The roboRIO has 1.63 Volts of margin for a brown out.
12-6.3-4.07=1.63

Six CIMS
The Six CIM total Resistance is 0.05+0.065=0.0115 Ohms

Current:
I=V/R=12V/0.115=104.3 Amps

The voltage drop at the RoboRio is
V=I*R=0.05*104.3= 5.21 Volts
The roboRIO has 0.49 Volts of margin for a brown out.
12-6.3-5.21=0.49


What happens later in the match when the Battery voltage has drooped down to 10.5 Volts?

We will leave the CIM resistance unchanged, even though they are now quite hot. Same with the wiring resistances.


Four CIMS
Current:
I=V/R=10.5V/0.1475=71.2 Amps

The voltage drop at the RoboRio is
V=I*R=0.05*71.2= 3.5 Volts
The roboRIO has 0.7 Volts of margin for a brown out.
10.5-6.3-3.5=0.7



Six CIMS
Current:
I=V/R=10.5V/0.115=91.3 Amps

The voltage drop at the RoboRio is
V=I*R=0.05*91.3= 4.57 Volts
The roboRIO is -0.37 Volts below the brownout voltage.
10.5-6.3-4.57=-0.37

Summary:
Standard four CIM Drives consistently maintain a 1 Volt higher brown out margin than six CIM drives. While a Six total CIM Drive can accelerate 150% faster than a Four CIM drive, it does come at considerable more risk of brownout event. Each team will have to balance drivetrain performance vs. robot reliability for the entire match.