With your current gears and the right battery I would say you should be able to go 10mi/hr up that hill.John and Cecil said:I would like to know about what speed (if it is even possible) a 750w motor can climb an approximately 8% paved grade (aprox 40' elevation change in approximately 500' distance)with a total load (bike, rider, and gear) of about 250 lbs. Has anyone climbed a hill such as this with their 750w motor on throttle only? I am trying to figure out gearing, my 11-32 rear with 42 front is perfect for cruising speeds but appears to be severely lacking in hill climbing abilities, especially with pudgy little Cecil on the back! Thanks![]()
The calculation below is all theory, but I'm quite confident it's close because I regularly have gone 5mi/hr up a 10% hill with 300 lbs total load with my old 250W TSDZ2 plus maybe 150W of my own pedaling (no throttle).
Here goes:
If your bike is in the right gear, the motor works at its optimum working point and provides 750W, the motor and gear train are 100% efficient and if we ignore aerodynamic drag, the bike would go the following speed:
750 W / (250 lbs x .0454 lbs/kg x 9.81m/s2) = 0.67 m/s vertically.
On an 8% slope that would correspond to a speed of around 0.67m / 0.08 = 8.4 m/s. That would be close to 30 km/hr.
With electrical and mechanical losses and aerodynamic drag it might be half of that, so maybe 15 km/hr (almost 10 mi/hr).
If the diameter of your tire is 28", that would be a diameter of 28" x 0.0254 m/inch = 0.71m.
The circumference would be 0.71m x pi = 2.2m.
If your speed is indeed half of 8.4 m/s, that would be 4.2 m/s, so the wheel would go 4.2m/s / 2.2m = 1.9 revolutions per second. In your lowest gear (32) the pedals would go 1.9 revs x 32 / 42 = 1.45 revs/s. That is 87 revs/min, at the top end of what he TSDZ2 will do, and where it is powerful and efficient. So the gearing seems good, as long as your chain-line allows you to use the lowest gear. You might even go to the second gear.
Maybe your battery is too small, as gggplaya suggested. Some of the losses will be electrical, so for the motor to deliver 750W mechanical power you may have to draw 1000W from the battery. At 50V, that means your battery needs to be able to deliver 20A. Preferably continuously, but certainly for the 35 seconds that it would take to go 500' at 4.2 m/s. Maybe something like this:
https://lunacycle.com/52v-mighty-mini-cube-ebike-battery-pack-panasonic-pf-5-8ah-affordable/
FWIW, I've never done business with Lunacycle so I can't vouch for them.
By the way, I don't have the throttle, and I'm not sure if it will give you the full 750W. You may have to put in some work yourself to get the 750W help from the motor!