Regenerative Braking

Electric cars typically employ regenerative braking to increase their efficiency. So, one question we get asked all the time is, "do the bikes come with regenerative braking?" The short answer is no, but it's not because we haven't evaluated the technology. Regenerative braking for bicycles provides minimal benefit and considerably increases the cost of an electric bicycle. In this blog entry we'll talk about why regenerative braking isn't what it's cracked up to be.

Background
Aerodynamic drag and weight:
A bicycle has relatively high aerodynamic drag and low mass compared to cars. A typical electric bicycle has a drag coefficient of 0.9 and a weight of 25(bike)+30(elec)+180(rider)=235lbs. A Toyota Prius has a drag coefficient of 0.26 and a curb weight of 2765 lbs. Effectively, the bicycle produces 3 times the drag and is a tenth the weight of a car. This higher aerodynamic drag consumes energy whether we are climbing hills or just pedalling along a flat and with our reduced weight electric bicycle momentum can easily be changed with relatively small braking power.

Battery recharge rate:
The other major issue surround regenerative braking is battery recharge rate. The rate energy can be absorbed by the battery is much lower than the rate it can be discharged. A typical NiMh or Li-Ion battery can be charged at 1/10th of it's discharge rate (Note, for new Nano-Li-P04 batteries this rate is much higher). This means, for a typical 20A 36V system like the Crystalyte Cannon only 2A could go back into the battery on a downhill. Even if the power recharge rate were higher, lets say 5A, only 1/4 of the energy of discharged (under ideal conditions) would be reaching the battery pack.

A hill example

To better summarize the effect this

has on electric bicycle regeneration imagine an electric bicycle climbing an 8% grade at 15mph using 20A @ 36V or 720W of power. Let's say, conversion losses from controller, battery, and motor are about 20%, so you are actually only getting 80% of your total energy output to move you forward - this equals about 575W. At 15mph, the bicycle is also overcoming about 125W of rolling resistance and 150W of aerodynamic drag - leaving about 300W for hill climbing.

Now, imagine you are coming back down the same hill with regeneration turned on full (approximately 5A @ 36V or 180W). This slows the bike substantially, removing more than half of the acceleration due to gravity, which means you'll be accelerating down the hill much slower than normal. How slow?
If it took 300W to climb the hill and over 180W is being converted into energy for the battery, it is safe to assume you would lose about half your acceleration coming down the hill. In our example we can assume a 19mph descent, instead of about 35mph without regeneration. Assuming a high efficiency on recharge (let's say 50%), we'd be getting only 90W back to the battery on the way down the hill and only have 75% the time to charge as we did to discharge.
This means, the regeneration downhill only produces 90W/720W * 100 = 12.5% of the energy used to get up. Plus, all the fun of coasting fast downhill is gone ...
At a conversion rate of only 12.5% regenerative braking is a poor way to recover energy coming down the hill and far less efficient than coasting, which essentially suffers from no conversion losses. So instead of regeneration, you could coast down a hill fast and use the speed to help you coast right up the next hill.

Furthermore, if you are interested in extending your range, simply bring a second battery for close to a 100% incrase in range (much higher than 12.5%) at a much lower cost, only $349 for a NiMh battery vs. $500 or more for a system with regeneration. While you'll be carrying approximately 14 lbs. more you'll have the flexibility to leave a battery to recharge while continuing ride or you can pack up both batteries for a long trip. If you're worried about the extra weight of an additional battery consider it doesn't substantially increase your aerodynamic drag, won't substantially increase your rolling resistance and increases your hill climbing power requirement by a mere 21W (on an 8% grade). In fact your total additional power requirement would be only 29W, which only increases power consumption by 4%. That leaves you 96% more power.

Overall we've found that regenerative braking for bicycles is more useful as a marketing gimick than an efficient technology. Although we've done our own independent calculations for this example they match up very nicely with the bicycle vs. power calculator available at http://www.kreuzotter.de/english/espeed.htm. We hope you've found this comparison useful and feel free to comment if you've found any errors in our calculations.