02/11/2025 13:59

I was recently passing through Gare du Midi in Brussels, where I saw that some fellow travellers were using a bicycle-powered phone charging station to charge their smartphones.

This made me wonder, how much power can we generate by cycling? And how long would it take me to fully charge my iPhone? We can calculate the mechanical power generated by the human force applied, and then use a 50% conversion factor to electricity.

P = F * v

Power is work times speed, and where circular motion is involved speed is wr$wr$. let’s assume the bicycle wheel is 60cm in diameter and rotates 3 times per second, then;

\omega = 2 * \pi * 3  \approx 18 rad s^{-1}

v = wr \approx 18 * 0.3 \approx 6 m/s

It’s tricky to estimate the force applied on average but I’m going to go with ~0.1 your body weight. For a 75 kilo person this will be ~70 Newtons

P = 70 * 6  \approx 400 W 

Can we produce 400W of electricity by cycling? Well, we have to realize that this is 400W of mechanical energy. Generators will only convert about 50% of this energy to electricity, so we are talking about 200W of electrical energy.

How much does my phone need? Well, my iPhone charging cable is rated for 45W (for fast charging - with 5 W being the minimum amount of charge) so a bicycle hooked up to a dynamo could in principle charge 4-5 iPhones at once! This seems quite high…

Reviewing the literature (1) it seems that only elite cyclists can consistently generate 400W of mechanical power, with amateur cyclists generating closer to 100-150W. Let’s assume that the weary traveller is generating 80W of mechanical power continuously. Then the electrical power generated will be about 40W.

The iPhone battery can hold 12Wh (2) of energy, so it would take about 18 mins of cycling to fully charge. No wonder they’re always in use!