Originally Posted by

**safe**
I think we are all at least becoming aware of the core equation that applies to regen ... **Regen** (gained) = **Time** (lost)

You can put an equal sign between those two terms, but that doesn't make it a valid equation. I have already given you two counterexamples: First, regeneration user to recover energy during necessary braking; and, second, strategic regeneration that allowing you to go faster by saving energy downhill, then using it uphill where the extra speed makes a bigger difference.

I'm sorry to tell you this, but your premise is fundamentally wrong.

If one recaptures energy on the downhill and uses that energy on the flat to catch up then the added aerodynamic drag (and the fact you have lost connection with the leaders) means you will give most of the energy back to the wind.

In a serious ebike race, you would still ride in a pace line downhill, but you (and your team) would be recovering energy for use on the next climb. The time lost on the downhill section is easily made up by gains on the next climb, as I have already shown.

...there are other scenarios to ponder I'm sure, but the math doesn't look all that great for regen in a situation where time is important. (like in a race)

Didn't you read my last reply??? The math overwhelming supports the use of strategic regeneration - go back and check your work.

Note: One mph out of 30 mph is different than 1 mph out of 7 mph. (on the climb) Basically I don't think that the numbers will work out that way. You need to actually create formulas that include the way electric motors work. Try those ideas again and use 0.5 mph on the climb and then you would probably be closer to the truth. You need to think in terms of energy recaptured by the motor verses energy required to run the motor. The losses are at least 50% in that exchange.

I don't think you are equipped to argue with my example. Work through it before arguing (use the energy calculator I linked and make reasonable assumptions). Come back and apologize for questioning my numbers when you are done. The reason you get a remarkable benefit is that the marginal drag when accelerating from 29 to 30mph is far higher than when going from 6 to 7. Also, increasing your minimum speed has far greater benefit on elapsed time than the cost of decreasing top speed by the same amount, so the net result is a big win, despite some significant inefficiency in regeneration.

By the way, I assumed the net result of regeneration was 25% energy recovery. If 100% of the energy were available, your uphill speed would be 4 mph faster in the example I gave. That would improve your time by almost 4 1/2 minutes in just 2 miles, but, alas, 100% efficiency is not possible.

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I have been making some assumption in defense of regeneration, and I don't mean to say that currently available systems are as good as I would hope. My chain driven ebike (without regeneration) is far more efficient at hill climbing than any hub motor, making it a better choice for just about any race I could imagine (assuming equivalent battery packs) than a hub motor with regen.