# B Power from two sources, electrically assisted bicycle

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1. Mar 31, 2016

### Matt atkinson

So I'm just doing a project where i have a electrically assisted bicycle and im struggling working out the power when the bike is going uphill.

If i have a certain force provided by the rider, and a force provided by an electrical motor; can I do $$Power=F_{motor}* v_{motor}+F_{rider}*v_{rider}$$

where the $v_{motor}$ and $v_{rider}$ are the speeds that the given force will generate, or would it be $$P=F_{total}*v_{total}.$$

sorry if this is a basic question I've just been struggling and needed some reassurance.

2. Mar 31, 2016

### BvU

Both ! Does that offer some reassurance ?

There is a small snag: because of wind resistance, power is not a linear function of $v$ (the force to go twice as fast ($2v$) is more than twice the force for $v$).
So if you on your own go 15 km/h and the motor would give you 10 km/h, the two of you together won't achieve 25 km/h, but for example 20 km/h. But the relative contributions would still be 15/25 (60%) from you and 10/25 (40%) from the motor.

3. Mar 31, 2016

### Matt atkinson

Oh that does, I didn't think of it like that!

So if we are travelling at a set speed (constant) say 40kmph for both the motor + rider contributions it would be better to work the power out using the second method i mentioned by working out the sum of the forces acting on the bike?

4. Mar 31, 2016

### BvU

Yes. The $v_{\rm rider}$ and $v_{\rm motor}$ aren't very meaningful. $F_{\rm total} = F_{\rm rider} + F_{\rm motor}$ is much more sensible.

5. Mar 31, 2016

### jbriggs444

Well, it might be more sensible if one had a definition for the three terms in that formula. No such definition is evident for any of the terms here.

Last edited: Mar 31, 2016
6. Mar 31, 2016

### BvU

I plead guilty to the well-meant reproach in post #5. $F_{\rm total}$ is easily defined: the force needed to maintain the speed $v$. It can be measured, e.g. with a spring balance. And then the other two have to be loosely defined as the (average) fractions times $F_{\rm total}$. Perhaps $F_{\rm motor}$ can be recovered from the specifications.... (or from the time it takes the battery to go empty, an efficiency, etc. etc.). Even exact is relative .

7. Mar 31, 2016

### jbriggs444

I'll buy that. Though this model has limitations. It seems to assume that one has a single-speed bicycle, a constant torque motor and a rider who will exert a constant average force on the pedals throughout a relevant range of speeds.

8. Mar 31, 2016

### Staff: Mentor

I don't see how it makes such assumptions. I only see force, not torque or rpm, so the drivetrain issues just seem to not be addressed. It might just be that the OP hasn't gotten that far yet.

If I were designing a motor assisted bike, I might put the motor on the input side of the drive so it can take advantage of the gears along with the rider.

9. Mar 31, 2016

### BvU

10. Mar 31, 2016

### Matt atkinson

I do have equations for those terms, I was just curious which way was best to approach given my situation where I'm trying to stay at a constant cycle speed.

Thankyou, it works out better this way!

Yeah I haven't got that far yet, i've just been roughing out some physics first thanks for the suggestion.

Matt:
Yes my friend borrowed my account, they wanted to ask for a second opinion. Maybe i didn't explain it well enough thanks all! I need to up my skills as a tutor haha

11. Mar 31, 2016

### jbriggs444

You cannot add force determined by a spring scale attached to a bike at one speed and force determined by a spring scale attached to a bike at another speed and get a number that is meaningful for the purpose at hand if the speeds are different without such an assumption.