Dakota Richline
“Every one of us is, in the cosmic perspective, precious. If a human disagrees with you, let him live. In a hundred billion galaxies, you will not find another.”
― Carl Sagan, Cosmos

# Could Formula E cars run on hydrogen?

Note: I did not research hydrogen-powered racing before writing this article; I wanted to use deductive reasoning and napkin math to satisfy my curiosity

I was curious what Formula E would be like with a fuel cell instead of batteries, so I calculated the energy storage of various cars using different fuels just for giggles.

## Energy storage of various vehicles

A 2nd generation Formula E car has a 54 kW h battery. (I prefer kW h over MJ #sorrynotsorry)

A street-legal Honda Clarity FCEV holds 5.46 kg of compressed hydrogen gas, or 214 kW h:

$$5.46~\text{kg}~\text{H}_2\cdot\frac{1000~\text{g}}{1~\text{kg}}\cdot\frac{1~\text{mol}~\text{H}_2}{2.016~\text{g}}\cdot\frac{285~\text{kJ}}{1~\text{mol}~\text{H}_2}\cdot\frac{1~\text{kW h}}{3600~\text{kJ}}\approx214~\text{kW h}$$

A 2020 F1 car holds 105 kg of premium gasoline, or 1 321 kW h:

$$105~\text{kg}~\text{gasoline}\cdot\frac{1~\text{L}}{0.75~\text{kg}}\cdot\frac{9.5~\text{kW h}}{1~\text{L}}\approx1~321~\text{kW h}$$

## Efficiency and power output

Fuel cells are only 60% efficient according to the US Dept. of Energy , but that’s still ~2.5x the usable amount of energy as a current Formula E car (ignoring the real battery’s internal resistance, so the actual number is even better than 2.5x).

The Clarity’s fuel cell outputs 100 kW continuous, and only weighs 52 kg.  It uses a 1.7 kW h buffer battery to feed the motor, which is similar to the 1 kW h accumulator F1 cars use for their MGU-K boost motor. Formula E cars use their 54 kW h battery for a 45 minute race, so the average power is 72 kW:

$$\bar{P}=\frac{54~\text{kW h}}{0.75~\text{h}}=72~\text{kW}$$

The Clarity fuel cell’s average power output should be sufficient for a race, but the Formula E car would probably need a larger supercapacitor to handle the 250 kW bursts. Luckily, the 52 kg fuel cell would be replacing a 250 kg battery, so there should be plenty of room for a capacitor energy store.