# Homework Help: What are the physics/forces behind a bike pedal?

1. Jul 28, 2016

### beterdenu

• Thread moved from the technical forums, so no Homework Help Template is shown
Hi All,

I am working on a project that mounts an accelerometer to the bike pedal, and requires me to calculate the power that the sensor experiences as the bike is being ridden. However, I am having some trouble understanding the forces that the pedal/sensor experiences.

Essentially, I need to calculate power given the acceleration the sensor experiences, mass of the sensor, and time. Here's what I have right now:

Power = Work/time = ½*m*v^2
Power * Time = ½*m*v^2
v = sqrt(2*Power*t/m)
a = dv/dt = sqrt(Power/2*m*t)
Power = a^2*(2*m*t)

While this does give me power, I don't know if this equation is applicable to my project. I'm also thinking that I need to account for the rotational physics as well, which I am not sure how to do. Could someone explain how I could calculate the power at any given moment?

Thanks

2. Jul 28, 2016

### Staff: Mentor

Welcome to the PF.

Your first two equations have the same RHS but different LHSs. How can that be true? You can use dimensional analysis to double-check equations to look for simple mistakes.

Also, I don't think you can calculate power just based on the acceleration and movement of the pedals. Consider the case where you are pedalling on flat ground versus climbing a hill. You may have the same cadence, but the power output by the rider is very different. What else can you use? You almost need to add force sensors to the pedal/foot interfaces...

3. Jul 28, 2016

### sophiecentaur

That, in conjunction with a motion sensor on the crank, to tell the velocity of the foot, would allow you to calculate the power as long as you were measuring the tangential component of force. Perhaps two force meters at right angles could be used on each pedal and the outputs processed together with rotation information.. Alternatively, you could measure the chain tension and its speed.

4. Jul 28, 2016

### CWatters

I think the professional devices to do this have a strain gauge in a special crank.

5. Jul 28, 2016

### houlahound

6. Jul 28, 2016

### Staff: Mentor

Yes, I agree, they would have to. And the strain gauges would need to read out the force in 2 dimensions (up/down and front/back) to capture all of the displacement forces going on. Bike "pedals" for performance bicycles are clip-ins or stirrups, which allow you to add force on the lift-up and push-forward parts of the pedal stroke, in addition to the push-down part of the stroke.

I've only recently learned to use the extra parts of the pedal stroke, and it definitely adds extra power...

7. Aug 1, 2016

### beterdenu

Hi All, Sorry for the late reply

Thanks for the responses! Allow me to clarify my project a bit:

I'm trying to mount sensors on stationary gym bikes, and use the data from the accelerometer, magnetometer, and gyroscope (9-axis motion) for further analysis. This means that I don't need to worry about having a sloped surface. Right now, I am focused on verifying that any data I receive is actually rotation/pedaling data. To do that, I have written a program which checks that the power in the y-axis (up/down) and x-axis (forwards/backwards) and sees that the average power over a short period of time is above some threshold (to be determined after I can accurately calculate power). Also, I recently realized I only need to calculate the power that the sensor experiences, and not necessarily the power that the rider exerts. Does this change the situation enough so that I can calculate power given time, acceleration, and mass?

In regards to my first two equations, I simply left out time on the RHS. Here's how it should be:

Power = Work/time = ½*m*v^2/time
Power * Time = ½*m*v^2
v = sqrt(2*Power*t/m)
a = dv/dt = sqrt(Power/2*m*t)
Power = a^2*(2*m*t)

8. Aug 1, 2016

### sophiecentaur

If you want to know the Power developed on a stationary bike, why not use a dynamometer? It measures the final power delivered to the road but it's very much a known art. It is also not too hard to measure the Power In by the cyclist - using gas analysis.

9. Aug 1, 2016

### beterdenu

From what I quickly looked up about dynamometers, they seem too big and expensive for what my project is trying to accomplish - a relatively cheap and automatic way to track gym exercise. Also, I'm trying to make this all electronic, so I would have no way of taking in data with a dynamometer.

10. Aug 1, 2016

### jbriggs444

A stationary exercise bike almost certainly monitors rotation rate already. It may also be calibrated to know the resistance imposed at the current setting. I know the one I have at home is willing to display Watts. It presumably computes this by multiplying resistance by rotation rate and applying a simple decaying average.

11. Aug 1, 2016

### Staff: Mentor

Exactly. What does your "stationary bike" use for resistance? Or is it just a bike on free-rolling rollers? You just need to figure out what the resistance is on the different settings for your stationary bike, and use RPM as the variable that gives you the power. You don't really need the extra data of the power in the dirrerent parts of the pedal stroke, as long as you have the instantaneous RPM number and the resistance is constant.

12. Aug 1, 2016

### jbriggs444

Mine uses magnetic coupling, hidden under the housing so that the exact mechanism is not revealed. No idea how accurate it is.

13. Aug 1, 2016

### beterdenu

I'm pretty sure the bike uses magnets to increase resistance, although I'm not absolutely certain as partner on this project is working on incorporating resistance into data analysis. Another thing I previously failed to mention is that I'm planning on not using any of the data that the bike already measures by itself (RPM, Speed, Time, etc) since the overall goal of this project is to create a central platform in which users can track ALL of their gym activity. This means I have to take in my own data as I have no electronic access to data that is built in on the biking platform.

I also want to note that my current goal is to simply check that any data I take is actually rotation and not just the pedal being randomly jerked around.

I guess a more general question is this:

How Can I relate Power and Acceleration in an equation?

Thanks!

14. Aug 1, 2016

### sophiecentaur

You appear to be wanting some form of measurement system that's attached to the person? This would be hard as it would have to involve multiple stress and motion sensors actually attached to the body. I mentioned gas analysis as a method for measuring rate of total work by the body. That is an established method, I think.
There are several formulae for Power. It is rate of doing work
Power = Force X Velocity
Power = Torque X Angular velocity
If you want 'acceleration' (?) involved then you can use
F = ma
The m would, presumably be your body mass (plus equipment) and measuring acceleration could be problematical and so why would you want to do that? Do you have a particular idea for this?
I feel that you need to specify in more detail what you envisage if you want to get any useful contributions from PF. There are many people who would be interested in the same sort of project, I am sure. There could be a lot of money in it for somebody to develop such a system.

15. Aug 1, 2016

### Staff: Mentor

That is not enough for your project to succeed.

If you really need to make your school project work without any hooks into the stationary bike (or other exercise equipment), then you will need shoes and gloves that can sense force as well as position and acceleration. With that information you will be able to calculate the power involved. Without that information, you will not. Bottom line.

16. Aug 2, 2016

### CWatters

I don't see how the sensors you mention can be used to measure power. You need to measure the torque and angular velocity or a proxy for those. I can't think of a way to do it with an accelerometer. Where have you installed it?

17. Aug 2, 2016

### CWatters

Your application of these equations appears so wrong/confused I'm struggling to find a way to explain why they are wrong.

The work done by the rider against the friction brake is not 0.5mv^2.

I suspect you may well be recording data that looks like it's related to effort produced by the rider but i bet it's not. For example if a rider turns the pedals at a constant 1 revolution per second the data recorded by an accelerometer in the pedals will vary as the pedals rotate BUT it will not depend on the brake setting.