## speed relationship between wheel and bike

tonylai   1 µW

Posts: 4
Joined: May 09 2021 2:03am

### speed relationship between wheel and bike

Hello everyone, I am a student from Taiwan and I am wondering:
1.How to convert the wheel speed(rad/s or RPM) to the e-bike(two wheel drive) speed(m/s or km/hr)?
2.Is there any formula or equation that can represent the relationship between wheel speed(rad/s or RPM) and e-bike(two wheel drive) speed(m/s or km/hr)?
3.I had saw a formula : v=(n*60*L)/1000 where v is e-bike speed, n is wheel's rpm and L is the perimeter of the wheel. Can this formula used for two wheel drive e-bike?

PS:Assume that two wheel's speed are synchronous.

john61ct   100 GW

Posts: 7683
Joined: Dec 18 2018 2:06pm

### Re: speed relationship between wheel and bike

Obviously the two wheels will have the same RPM

unless they are different outermost circumference, even very different tire pressure wojld be significant.

tonylai   1 µW

Posts: 4
Joined: May 09 2021 2:03am

### Re: speed relationship between wheel and bike

john61ct wrote:
May 09 2021 4:34am

Obviously the two wheels will have the same RPM

unless they are different outermost circumference, even very different tire pressure wojld be significant.
But when the e-bike turns, two wheels will have different dynamic equations which might probability make some different or even generate slip ratio, at this moment, will the wheels still remain the same RPM?
And the speed while turning, how to calculate with the wheels' RPM?

E-HP   10 MW

Posts: 2319
Joined: Nov 01 2018 9:20pm

### Re: speed relationship between wheel and bike

tonylai wrote:
May 09 2021 2:09am
Hello everyone, I am a student from Taiwan and I am wondering:....

PS:Assume that two wheel's speed are synchronous.
tonylai wrote:
May 10 2021 5:52am
...will the wheels still remain the same RPM?
Are you changing the assumptions? Does this bike have both wheels on the ground so the wheels spin at the same rate, or is it flying through the air, so the wheels can spin at different rates? I'm guessing your studies are not in science or engineering.

john61ct   100 GW

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Joined: Dec 18 2018 2:06pm

### Re: speed relationship between wheel and bike

tonylai wrote:And the speed while turning, how to calculate with the wheels' RPM?
There are literally hundreds of pages at the link I gave you that give you all the details

tonylai   1 µW

Posts: 4
Joined: May 09 2021 2:03am

### Re: speed relationship between wheel and bike

E-HP wrote:
May 10 2021 9:42am
tonylai wrote:
May 09 2021 2:09am
Hello everyone, I am a student from Taiwan and I am wondering:....

PS:Assume that two wheel's speed are synchronous.
tonylai wrote:
May 10 2021 5:52am
...will the wheels still remain the same RPM?
Are you changing the assumptions? Does this bike have both wheels on the ground so the wheels spin at the same rate, or is it flying through the air, so the wheels can spin at different rates? I'm guessing your studies are not in science or engineering.
I'm just curious about the dynamic state of the wheels, but your right, my assumption has changed.
The situation I assume is:
At first, two wheels are speeding synchronous for a while(given the same throttle) and the e-bike speed is unknown which I would like to know how to calculate through wheels' speed(RPM).
Second, when I am turning, steering angle and camber angle will needed to be considered also and at that moment, are there any formula that can represent the e-bike speed with these angles?
Third, because of the turning, the speed of two wheels' might be different, and if it happens, are there any formula that can represent the e-bike speed with this situation?

For example, assume the speed can be calculated as V=r*sinӨ*sinφ*ω, where Ө is steering angle, φ is the camber angle, r is the wheels' radius and ω is the angular speed of the wheel.
If I am not turning, Ө and φ will be 0 which makes sinӨ*sinφ=1 and if I am turning, the speed will be changed because of the changes of Ө and φ.
The correct formula is what I'm searching for.

john61ct   100 GW

Posts: 7683
Joined: Dec 18 2018 2:06pm

### Re: speed relationship between wheel and bike

the number of wheels should make no difference at all, if they are all the same size.

Nor does electric motor(s) matter as a factor, vs leg power or petrol or. . .

RPM vs bike speed

is what I thought you wanted help with.

One of those being known obviously (to me) is required

bike speed being unknown?

now I am completely confused. . .

Ianhill   100 MW

Posts: 2528
Joined: Sep 25 2015 5:55pm

### Re: speed relationship between wheel and bike

Heres what goes on the wheels on the bus go round round round lmao but they turn at the same speed theres no synchronous stuff to worry about on a bike in a straight line and bends turn in speed up fractional and turn out slow down but they equal out mostly but every ride will never have equal rights and left turns so there will be a slighy variance in the front wheel and the back wheel never truly follows the front wheels path but from the eyes point of view its the same.

What you would find is if you accurately plotted distance traveled of both wheels it wont be the same one will have gone a bit further than the other but i dont see where this is going mind its 2 wheels not 4 so no diffs required.

Ianhill   100 MW

Posts: 2528
Joined: Sep 25 2015 5:55pm

### Re: speed relationship between wheel and bike

I think the effort it takes on the bars proves that turn in is easy one finger but turn out requires more effort and at that point there maybe a little wheel variation on the front but i cant say for sure im not reading all that.

Posts: 7354
Joined: Sep 03 2010 5:28pm

### Re: speed relationship between wheel and bike

There can’t be a formula that will be exact. First you bother about meaningless factors like steering angle and camber, because bikes don’t need steering to turn or, if little of it they ever do, it is a slight counter steering that initiate the turn. Bikes need steering to turn, only at very low speed. It is the rider’s weight transfer that is making a bike turn.

The difference of rotation between the front and the rear, if both wheels are equal in all factors, is related to balance and weight distribution. Braking, you will load the front and the tire deformation will make the front wheel a smaller effective diameter, thus it will spin a little faster than the rear. In acceleration you will load the rear, so the rear wheel will spin faster than the front. Still, riding a constant speed it is likely that the weight distribution is not perfectly centered and makes a slight difference, that can vary with the rider’s position, equipment, luggage.

Now, if your bike is not really a bike, rather a trike or a quad, then it is another story.
Make it fool-proof, and I will make a better fool.

tonylai   1 µW

Posts: 4
Joined: May 09 2021 2:03am

### Re: speed relationship between wheel and bike

I'll think about for what I've learned and what you guys said.

E-HP   10 MW

Posts: 2319
Joined: Nov 01 2018 9:20pm

### Re: speed relationship between wheel and bike

May 11 2021 4:47pm
There can’t be a formula that will be exact. First you bother about meaningless factors like steering angle and camber, because bikes don’t need steering to turn or, if little of it they ever do, it is a slight counter steering that initiate the turn. Bikes need steering to turn, only at very low speed. It is the rider’s weight transfer that is making a bike turn.
Yup, and with motorcycles, at anything greater than walking speed, you turn the handlebars the opposite direction as you want the bike to turn, since motorcycles turn by leaning, and countersteering is what makes you lean further into a turn.

Ianhill   100 MW

Posts: 2528
Joined: Sep 25 2015 5:55pm

### Re: speed relationship between wheel and bike

Some eye opening points made well beyond my imagination.

Thats why i like reading here theres alot to learn and many willing to show.