Wind resistance is roughly based on the square of your speed, so double your speed, quadruple the wind resistance.
but the power it takes is actually closer to the cube. takes 200 watts to go 20, and over 1,400 to go 40… because not only is the instantaneous resistance squared …. you’re going twice as fast, encountering twice as much of it per unit of time.
"Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome aerodynamic drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW).[16] With a doubling of speed the drag (force) quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power."
here are the ways to really increase range
1) go slow
2) reduce your drag. get down low on the bike, wear smooth and tightly fitted clothes, a tapered and smooth helmet, a bike with narrow and deep section wheels, streamlined frame, no junk on the bars or your back etc etc etc. most of the drag comes from the rider, so the most important part is that the shape of the bike allows the rider to get as aero a profile as possible
3) keep your speed steady. don’t use the brakes unless absolutely necessary, especially going downhill. you built up a huge amount of potential energy going up, don’t waste it to heat!
4) minimize rolling resistance. no integrated gear hubs, motors must be disengaged when not under power, supple tubeless tires with smooth or no tread, well lubricated and maintained drivetrain, etc.
5) use the motor only when you need it (hills and wind!) and, if it’s a mid drive, make sure you are pedaling with a cadence that allows it to operate where it’s most efficient. motor efficiency falls off a cliff at very low or very high RPM.
basically, you want to do all the things people who want to go far fast on a regular bike do. they’ve done them for decades, much has been learned.
the longest ride i’ve done on my e-bike is about 118 miles with about 6,700 feet of climbing. winds were fierce in spots so it wasn’t a super efficient ride. i used 26% of the bike’s battery (83 watt hours) and contributed about 1,300wh of human power, for about 11.7wh/mile at an average speed of 15mph. it ought to be possible to get that number down to around 7.5wh/mile at the same speed with a steadier pace, less hills, wind, and better aerodynamics.
at 12mph, it should be possible to get down to 5wh/mile. if the rider supplies half (almost no work at all!) and the motor the other half, a 700wh battery would go 200+ miles. but that’s no fun!