# Electric bicycle power rating calculations

#### zazas321

Joined Nov 29, 2015
856
Hey guys. Could any of you give me some help on how to start calculating the power rating needed to run the electric bicycle.
The only given parameters are:
-Able to achieve 20mph on flat
-Can neglect wind resistance and friction.
-Person weighting 80kg.
The task is to select appropriate motor to be able to achieve that speed and the calculations must be provided.
Many assumptions can be made .
Lets assume that i want to accelerate to 20ms in 5 seconds. Newtons law:
F=m*a= 80kg *(20/5) . Thats the force i will need to accelerate to 20 mph.
Now i can calculate the torque that i need to generate using torque and force equation below:
T=F*r
T-torque
F-force

Okay assuming i have calculated that torque. That will be the torque needed to achieve 20mph, but how do i know if the torque to remain constant speed at 20mph will remain the same?

What would be the other step to calculate the motor power rating

#### Alec_t

Joined Sep 17, 2013
12,070
but how do i know if the torque to remain constant speed at 20mph will remain the same?
If you neglect wind resistance and all friction, then Newton's Law says you don't need to expend any energy to maintain 20mph. Unfortunately, real life does involve wind resistance and friction arising from various sources.

#### BobTPH

Joined Jun 5, 2013
3,315
With no friction or wind resistance. any amount of power will get you up to 20 MPH. The power you use will determine how long it takes to get there.

This is, of course, a totally meaningless calculation since tne wind resistance at that speed is very significant.

Bob

#### MrChips

Joined Oct 2, 2009
23,528
As all others before me have stated, you need zero power to run your ebike at 20mph.
Going from my experience you need a 350W motor. The max you will ever need is 500W unless you are a 500lb gorilla.

#### crutschow

Joined Mar 14, 2008
27,212
If you look up the output power of a human peddling a bike, that will give you a good idea of what you need.

#### zazas321

Joined Nov 29, 2015
856
Okay lets assume the friction and air resistance. How would i calculate what power rating would i need to achieve and maintain 20 mph. As i have read motors are most efficient and their high speeds. So to maintain 20 mph and stay efficient i need a motor that would deliver a sufficient amount of torque for the 20mph. I need the calculations and justifications the power calculated thats why i am asking for your help guys.
Lets have a look at wind drag and friction formulaes:
Wind drag = 1/2 * air density * speed^2 * cross-section area * shape constant
Friction with road: normal force * friction coefficient.
Does anyone now what is the normal friction coefficient for casual bicycle?
So can i say that to maintain the 20mph, the total force should be F=Wind drag + Friction