In order to determine the amount of cooling required for the battery pack, we must first determine how much heat is produced in the battery box.

Heat in an electrical system is produced by current flowing through a resistance, with the formula P = I²R

The conductors of the battery pack have been designed to have a low resistance and thus not heat up significantly. The major source of heat production in the pack will be the battery cells.

The heat produced in our battery cells also follows the same power equation, with the Resistance term being the internal resistance of the battery cell. This has also been determined by calorimeter experiments in this paper - that the heat is produced by the internal resistance, and the heat of the chemical reactions are insignificant:

Our battery cells have an average DC internal resistance (determined with a current step method) of around 38mOhms.

The power losses below include the power loss of the cells, the nickel strips, and the spot welds.

A few key points for the power loss are in the table below:

Current (A)	Power Loss (W)	Note
15	12.8	Target current for cruising
20	22.8	Safe estimate for cruising current
30	51.3	Max Continuous Current at Nominal Voltage (4kW at 3.635V/cell)
50	142.5	Between max and peak current
76	329.2	Max Peak Current at Nominal Voltage (10kW at 3.635V/cell)
100	570.0	Battery Pack Design Target
130	963.3	BPS Current Limit Hard Cutoff

Doing a linear fit (not a line) to the data, gives us a total pack resistance of 57mOhms. I did this using scipy in python - its a super powerful tool that is handy to know how to use. This was easier than adding up all the resistances individually, but is the exact same in principle.

So, our equation for power loss is below:

POWER = CURRENT² * 0.057 Ohms

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