I've been thinking about the weight issue lately too, and I think its VERY important to the performance of an ebike. Consider two ebikes that are identical except one weighs 250 pounds (including rider) and the other weighs 350 lbs:
1) They will have identical wind resistance in ALL situations.
2) When going up a hill, the heavier ebike will require the additional energy necessary to move a 100 lb object up the hill.
3) When accelerating, the heavier bike will require the additional energy to accelerate the additional 100 lbs up to speed.
Note: The physics formulas for going uphill, and accelerating are PROPORTIONAL formulas. THerefore, a bike that's 20% heavier will require exactly 20% more energy to climb a hill and will also require exactly 20% more energy to accelerate. Also, if the motor is outputting the same amount of power, the heavier bike will travel 20% slower uphill, and accelerate 20% slower.
However, these are just the formulas for motion. In the real world there are additional factors that favor the lighter bike. For example, the motor will function more effeciently with the lighter bike because it won't be asked to run a heavy load at a slower speed. Also, you may not be able to accelerate to optimal speeds uphill, straining the motor in a bad way. So in reality, the lighter bike will be significantly more effecient than the heavier one, but the only way to know the exact difference is to test a real bike.
Here's what's important to know:
1) Wind resistance is MUCH less significant at slow speeds. But as you go faster, wind resistance goes up EXPONENTIALLY. So if it takes 100 watts to go 10mph, it may take 500 watts to go 20 mph.
2) Most ebikes will perform great on flat land. On flat land weight is not very important. It will still take more energy to accelerate, but one the bike is moving fast, weight has absolutely no effect. The only issue is wind resistance. And all the motor's power is used to fight the wind.
3) When climbing a hill, wind is much less significant because you slow down, and much of the motor's power is used to pull the bike uphill.
4) A crutial isse is when you must ACELERATE UPHILL. This is where wind resistance is basicly insignificant. Almost all the motor's power is used for acceleration and hill climbing.
I think too many poeple focus on top speed as a measurement of their ebike's performance. I think a better measure of performance should be how well it accelerates uphill. Getting a ebike to go fast on flat land is the easy part. But when using an ebike as a vehicle in the real world, you want a bike that will get you up a hill, and accelerate well in "stop and go" traffic. These are the real issues. Also, if you design a bike to perform well on hills, it should automatically have a good top speed.
Here's an example:
Energy Needed to accelerate 100 lbs to 15mph
100lbs = 45kg
15mph = 6.7 meters per second
Kenetic Energy = 1/2 * Mass * Velocity * Velocity
http://www.csgnetwork.com/kineticenergycalc.html
KE = 1/2 * 45 * 6.7 * 6.7 = 1010 Joules
KE for 350 lb ebike = 3535 Joules
KE for 250 lb ebike = 2525 Joules
So it will take an additional 1010 Joules to accelerate
This is the total energy needed to get each ebike up to 15mph. It is INDEPENDENT of how much time is used to accelerates. For example, you could deliver the energy slowly at 10 watts (1 watt = 1 Joule per second) , and it would take 100 seconds to reach 15 mph. Or you could deliver it in a 1010 watt burst, and it would take 1 secont to reach 15mph.
So suppose you wanted to accelerate to 15 mph in 8 seconds (realistic):
350 lb bike needs (3535 joules / 8 seconds) = 441 watts
250 lb bike needs (2525 joules / 8seconds) = 315 watts
So it takes an additional 126 watts to accelerate the heavier bike to 15mph.
Note: Eventhough both these bikes will accelerate to 15mph in 8 seconds, the heavier bike will still require 1010 more Joules of energy to accelerate. This energy will be missing from the battery, which will reduce the range of the heavyer bike.
Now consider both bikes going up a 100 meter hill that rises 10 meters:
Potential energy = weight * height * 9.8
http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html
Weigh difference = 100lbs = 45 kg
PE = 45 * 10 * 9.8 = 4410 Joules
PE for 350 lb bike = 15435 Joules
PE for 250 lb bike = 11025 Joules
So it takes 4410 more Joules of energy to get the heavier bike up a hill that climbs 10 meters. Again, this number is independant of the time it takes to climb the hill. But suppose you wanted to climb the hill going 15 mph.
15 mph = 6.7 meters per second
100 meter hill / 6.7 meters per second = 15 seconds to climb hill at 15mph
So it will take 15 seconds to rech the top of the 100 meter hill.
So the 350 lb bike will use 15435 Joules in 15 seconds =1029 j/s = 1029 watts. Likewise the 250 lb bike will require 735 watts to climb the hill.
So the heavier bike requires an additional 294 watts to climb the hill.
Now consider accelerating up the 100 meter hill. However, we must adjust the amount of time to accelerate to the top because the bike can't accelerate quickly going uphill, so assume that it will take 20 seconds to climb the hill, and it will reach 15 mph at the top of the hill:
Joules needed for 350 lb bike = energy needed to accelerate to 15 mph + energy needed to climb hill
Energy for 350 lb = 3535 Joules + 15435 Joules = 18970 Joules
Power needed for 350 lb bike = 18970 Joules / 20 seconds = 949 watts
Power for 250lb bike = 677 watts
The best way to understand these numbers is to get a pedal-bike and ride it. How much harder is it to accelerate than to maintain a speed? How much work does it take to get up hills?
I beleive evs must use similar engineering to pedal-bikes. Look at all the effort to make bicycles light. Weigjt is a huge issue. If you ride a bike that has 10 lbs of extra weight, your batteries must accelerate that 10 pounds every time you come to a stop sign. And it has to pull that 10lbs up every hill.
Also remember that if you can shave 20% of the weight from your bike, it will go 20% farther on a charge (provided you drive exactly the same) or it will go 20% faster up hills, or accelerate 20% faster. This is not exact, it will be aslurring of numbers, but its a good guideline.
I'm trying to make my next bike out of aluminum.