bruceha2000 wrote: Jimmydreams wrote:
Now, someone smarter than myself would have to determine if a 1/4mile hill in coast (and gaining 7mph) is a savings when applied to the next hill OR of regening down that 1/4mile hill at 63mph and then applying that gained energy on the next hill is more beneficial when it comes to total distance available in the battery pack.
Clearly not necessary, you already got it right. NO way you can get as much out as you generate via regen. The only reason to regen down that hill would be if you went over the speed limit enough to get a ticket. Clearly in your scenario, you won't be passing anyone. 75 is the de facto minimum in a 65 zone in CA unless there is too much traffic.
While I think you are right in this case bruceha2000, it is not quite that clear. Since aerodynamic drag is roughly proportional to the square
of the speed, you loose more energy when you coast faster. So, while you are absolutely right when you say "NO way you can get as much out as you generate via regen." It is also true that there is NO way you can get as much out as you gain by coasting to a higher speed.
Because of the complexities of this example (not only varying speed but varying acceleration down the hill and then again up the hill) and mainly because I'm way
out of practice doing dynamics problems, I'm not going to try to calculate a precise answer to this example. Instead I'll just do some simple calculations:
If you travel at 63 mph for a given distance you only use 81% as much energy to push air as you would at 70 mph (63^2 / 70^2 = .81). You could say that traveling at 70 compared to 63 is only 81% efficient.* In a roundabout way, you could compare this to the efficiency of the full regen cycle (regen and then back to power at the wheels). If the regen cycle is more efficient than 81% (not likely) then it might compare well to the extra speed method. Again, this is a really-really rough comparison, a lot more calculations would be needed before anything definite could be said.
However, one more thing: As the hill gets longer, and the speed difference increases, things move in favor of regeneration. Take 50 and 70 mph. Here 70 is only 51% as efficient as 50 mph (50^2 / 70^2 = .51). Regen might
be able to beat this.
* I am ignoring rolling resistance throughout this post because: 1. It is relatively small compared to air resistance at higher speeds, and 2. It is basically linear with respect to speed.