# Measuring Acceleration on a Bike using Phyphox

• luciaalmiron
luciaalmiron
Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: how can I calculate the acceleration of a bike whilst using phyphox?

Calling all physics lovers who are willing to lend a hand,

Hello, I’m busy doing a physics project on the friction force on different surfaces, like asphalt, grass, etc. I need to measure the data using an app called Phyphox, by taping my phone into the wheel of my bike, which gives me a graph of the angular velocity as the bike moves. However, the graph is not steady, it increments and decrements at random points. So how am I meant to calculate the approximate acceleration and THEN calculate the friction force? I was thinking of equaling the Friction force to m•a / m • g but I don’t know if this is correct, as the source I read this on didn’t seem trustworthy. All help would be grately appreciated, as this project is worth a 30% of my grade.

Last edited by a moderator:
OmCheeto
Welcome to PF.

luciaalmiron said:
using an app called Phyphox, by taping my phone into the wheel of my bike, which gives me a graph of the angular velocity as the bike moves.
I hope you didn't really tape your phone to the moving wheel. You can get the motion information by just having somebody hold your phone to film you with that app, I'm pretty sure. Since your tires will likely not be slipping, you can calculate the angular motion of the wheels from the linear motion of the bicycle.

luciaalmiron
berkeman said:
Welcome to PF.

I hope you didn't really tape your phone to the moving wheel. You can get the motion information by just having somebody hold your phone to film you with that app, I'm pretty sure. Since your tires will likely not be slipping, you can calculate the angular motion of the wheels from the linear motion of the bicycle.
Thank you for your answer, I think I’ll give that a try to see if it gives me better results.

luciaalmiron said:
So how am I meant to calculate the approximate acceleration
The experiment you described measures the centripetal acceleration. You need to measure the linear acceleration. You can do that by taping your phone on the bike frame.

luciaalmiron said:
and THEN calculate the friction force?
Define the equation relating the force to the acceleration.

Assuming you are going very slow, this force can be approximated to the actual friction force acting on the bicycle. It is also the actual force you are producing when pedaling. Both are equal. This means that if you are producing the exact same force on asphalt and on grass, you will get the same friction force.

You probably want to know the maximum friction force on a given surface. This means you will need to produce an ever-increasing force when pedaling until you reach a maximum. (Hint: it should be a little bit before the wheel begins to slip.)

Once you find out the maximum friction force, you probably would want to define the equation relating the friction force to the friction coefficient. (Hint: it is related to the normal force acting on the driven wheel which is NOT necessarily the whole weight of the object.)

luciaalmiron said:
I was thinking of equaling the Friction force to m•a / m • g but I don’t know if this is correct,
This is not meant to be the friction force, but the friction coefficient. This equation wouldn't be good for your experiment as it assumes the whole weight acts as the normal force.

You need to solve the following free body diagram to find the normal force acting on the driven wheel ##B_y## , where ##B_x## is the friction force and ##\ddot{x}## is the linear acceleration of the bicycle:

luciaalmiron
jack action said:
The experiment you described measures the centripetal acceleration. You need to measure the linear acceleration. You can do that by taping your phone on the bike frame.

Define the equation relating the force to the acceleration.

Assuming you are going very slow, this force can be approximated to the actual friction force acting on the bicycle. It is also the actual force you are producing when pedaling. Both are equal. This means that if you are producing the exact same force on asphalt and on grass, you will get the same friction force.

You probably want to know the maximum friction force on a given surface. This means you will need to produce an ever-increasing force when pedaling until you reach a maximum. (Hint: it should be a little bit before the wheel begins to slip.)

Once you find out the maximum friction force, you probably would want to define the equation relating the friction force to the friction coefficient. (Hint: it is related to the normal force acting on the driven wheel which is NOT necessarily the whole weight of the object.)

This is not meant to be the friction force, but the friction coefficient. This equation wouldn't be good for your experiment as it assumes the whole weight acts as the normal force.

You need to solve the following free body diagram to find the normal force acting on the driven wheel ##B_y## , where ##B_x## is the friction force and ##\ddot{x}## is the linear acceleration of the bicycle:

Thank you for this explanation, I think your proposed way is more efficient in terms of analysing data. I’ll give it a shot to see if I can get different results for the different surfaces.

luciaalmiron said:
Hello, I’m busy doing a physics project on the friction force on different surfaces, like asphalt, grass, etc.
Please explain more details of what you did. E.g. did you attempt to accelerate as fast possible, producing a skid, so the acceleration of the vehicle would indicate the kinetic friction?
As noted, the acceleration measured at a non-central point on the wheel will be a combination of the linear acceleration of the vehicle and the centripetal acceleration. Since the angle between those two vectors is not constant the magnitude of the net acceleration will not be constant.

Weird. I downloaded the app to my phone and did a similar experiment. While your images indicate data collection roughly every half second, my device collected 250 data points per second!

And the angular velocity in your top graph went from maximum to zero in only 2 seconds? Guessing that was the 'grass' test?

while yours looks like you hit a mole hill or something...

In any event, this is a delightful project your instructor has imposed upon you and your classmates.

berkeman
I think we need to see the assignment so we know how it's worded.

OmCheeto said:
Weird. I downloaded the app to my phone and did a similar experiment. While your images indicate data collection roughly every half second, my device collected 250 data points per second!

And the angular velocity in your top graph went from maximum to zero in only 2 seconds? Guessing that was the 'grass' test?

View attachment 345706
while yours looks like you hit a mole hill or something...

In any event, this is a delightful project your instructor has imposed upon you and your classmates.
Hello! That looks like a more accurate graph than mine, and strangely enough I was riding on a flat road, no grass. What’s the name of that app? I think I’m going to try this one out for more specific results.

Mister T said:
I think we need to see the assignment so we know how it's worded.
The assignment just says to create a physics experiment using the app “Phyphox” to collect data then make a video and present out results. Me and my physics partner have chosen to see the different coefficient of friction on different surfaces using a bike to see the different velocities on different surfaces.

haruspex said:
Please explain more details of what you did. E.g. did you attempt to accelerate as fast possible, producing a skid, so the acceleration of the vehicle would indicate the kinetic friction?
As noted, the acceleration measured at a non-central point on the wheel will be a combination of the linear acceleration of the vehicle and the centripetal acceleration. Since the angle between those two vectors is not constant the magnitude of the net acceleration will not be constant.
To begin my partner was on the bike, I tapped “record” so that the app would start measuring data and then he started cycling in a space of approximately 8 meters. That was all the data that the app gathered, it was more of a “test run” since we are still investigating to see if we can get more accurate results. If I accelerated and then produced a skid would I be able to calculate the kinetic friction for that specific surface?

luciaalmiron said:
To begin my partner was on the bike, I tapped “record” so that the app would start measuring data and then he started cycling in a space of approximately 8 meters. That was all the data that the app gathered, it was more of a “test run” since we are still investigating to see if we can get more accurate results. If I accelerated and then produced a skid would I be able to calculate the kinetic friction for that specific surface?
You are comparing different surfaces. You are not going to detect a difference unless you reach/exceed the limit of static friction.
For the static friction limit, the only way to know you have reached it is by pushing a bit harder and finding that you then exceed it, so that's a bit tricky (unless you have ABS). Easier to investigate kinetic friction, and that means skidding.
An obvious way is to hit the brakes and see how quickly it stops. May be complications with not being sure whether both wheels skidded. Can get around that by only applying the brake on one wheel. As noted, though, you would need to know what the normal force is on the braking wheel, and that will not be the same as when the bike is standing still. Braking increases the normal force on the front wheel and reduces it at the back.

jack action
haruspex said:
You are comparing different surfaces. You are not going to detect a difference unless you reach/exceed the limit of static friction.
For the static friction limit, the only way to know you have reached it is by pushing a bit harder and finding that you then exceed it, so that's a bit tricky (unless you have ABS). Easier to investigate kinetic friction, and that means skidding.
An obvious way is to hit the brakes and see how quickly it stops. May be complications with not being sure whether both wheels skidded. Can get around that by only applying the brake on one wheel. As noted, though, you would need to know what the normal force is on the braking wheel, and that will not be the same as when the bike is standing still. Braking increases the normal force on the front wheel and reduces it at the back.
Thanks, this makes sense, I’ve been thinking of doing this:

F(applied to the pedal) - Fr (friction)= m•a
1.5• weight - m•g•friction = m•a
I could calculate the force applied to the pedal by estimating that it is approximately 1.5 times the riders body weight for a moderate push.

On the other hand perhaps I could do the same but skidding and calculating the deceleration of the skid? I don’t know how accurate these calculations would be.

luciaalmiron said:
Me and my physics partner have chosen to see the different coefficient of friction on different surfaces using a bike to see the different velocities on different surfaces.
Are you measuring the coefficient of sliding (kinetic) friction or the coefficient of rolling friction?

luciaalmiron
luciaalmiron said:
If I [..] produced a skid would I be able to calculate the kinetic friction for that specific surface?
Yes. At low speed.

luciaalmiron
Mister T said:
Are you measuring the coefficient of sliding (kinetic) friction or the coefficient of rolling friction?
I think I’m going to try skidding for the kinetic friction and then do a separate equation for rolling friction, though I need to investigate more about the rolling friction as it requires a different formula and Ím not sure if that would be harder.

luciaalmiron said:
F(applied to the pedal) - Fr (friction)= m•a
That's not how it works.
If a is the acceleration of bike+rider and m is the mass of bike+rider then ma is the net external horizontal force on bike+rider. On a horizontal surface that is the friction. Force applied to the pedal is an internal force in the bike+rider system and is balanced by the reaction from the pedal on the foot.
Without friction you wouldn’t go forward.
There may also be a bit of rolling resistance - the energy lost to deformation of the tyres - and drag, but those are minor here. So your equation is force of friction = ma.
Likewise when braking.

jack action
luciaalmiron said:
Hello! That looks like a more accurate graph than mine, and strangely enough I was riding on a flat road, no grass. What’s the name of that app? I think I’m going to try this one out for more specific results.
Phyphox, like you. I just transferred the data to my laptop and tried analyzing it with a spreadsheet. Unfortunately, it was raining at the time so I did a coast down measurement of my front wheel in the kitchen, measuring the bearing and windage losses. You didn't state in your original post what kind of friction you were talking about so I collected data for a different kind. I was mostly just checking out how the app worked. Pretty neat for a free piece of software. 15,000 data points in just under a minute.

My cell phone doesn't have the centrifugal acceleration sensor that yours has so I opted for the 'acceleration with gravity' mode. I'm fairly certain that by measuring the change in width of the waveform I can determine the angular velocity vs time and deceleration rate. If you notice, between 10 and 15 seconds, there are 7 1/2 rotations, and it loses about 1/2 a rotation for each subsequent 5 second increment. I think ideally I should measure the time between all sets of adjacent peaks. And it looks like something happened at around 32 seconds as the bottom of the waveform took a turn upwards. It's possible I twisted the handlebars or maybe I bumped something and one of the brake calipers started lightly rubbing without me noticing. But this is how science is. Lots of head scratching. Maybe tomorrow I'll do the same experiment on the back wheel. I'm guessing all the extra hardware will cause a much higher drag.

haruspex said:
That's not how it works.
If a is the acceleration of bike+rider and m is the mass of bike+rider then ma is the net external horizontal force on bike+rider. On a horizontal surface that is the friction. Force applied to the pedal is an internal force in the bike+rider system and is balanced by the reaction from the pedal on the foot.
Without friction you wouldn’t go forward.
There may also be a bit of rolling resistance - the energy lost to deformation of the tyres - and drag, but those are minor here. So your equation is force of friction = ma.
Likewise when braking.
OK, so theoretically the coefficient=a/g, since there are m’s on both numerator and denominator. So as long as I push with the same force on each surface the acceleration should be different, therefore giving me different results?

luciaalmiron said:
If I accelerated and then produced a skid would I be able to calculate the kinetic friction for that specific surface?
Yes.

Use the rear brake only. It will be easier to skid and also safer. You then have to solve the same free body diagram as in post #4, except that ##B_x## and ##m\ddot{x}## will be negative (i.e. pointing in the other direction).

OmCheeto said:
Phyphox, like you. I just transferred the data to my laptop and tried analyzing it with a spreadsheet. Unfortunately, it was raining at the time so I did a coast down measurement of my front wheel in the kitchen, measuring the bearing and windage losses. You didn't state in your original post what kind of friction you were talking about so I collected data for a different kind. I was mostly just checking out how the app worked. Pretty neat for a free piece of software. 15,000 data points in just under a minute.

View attachment 345725
My cell phone doesn't have the centrifugal acceleration sensor that yours has so I opted for the 'acceleration with gravity' mode. I'm fairly certain that by measuring the change in width of the waveform I can determine the angular velocity vs time and deceleration rate. If you notice, between 10 and 15 seconds, there are 7 1/2 rotations, and it loses about 1/2 a rotation for each subsequent 5 second increment. I think ideally I should measure the time between all sets of adjacent peaks. And it looks like something happened at around 32 seconds as the bottom of the waveform took a turn upwards. It's possible I twisted the handlebars or maybe I bumped something and one of the brake calipers started lightly rubbing without me noticing. But this is how science is. Lots of head scratching. Maybe tomorrow I'll do the same experiment on the back wheel. I'm guessing all the extra hardware will cause a much higher drag.
That’s strange as my graph only took a few data points, your’s far more detailed than when I exported the data to files on my phone, I’ll give it a shot exporting it to my phone. Yes I suppose there are a lot more factors that influence the accuracy of results, however as I have to write a formal investigation, I’ll include that in the observations section. Hopefully the centrifugal acceleration sensor is more accurate if I export it. When I manage to record the data on a few surfaces I’ll add a few images so you can see if they improved.

OmCheeto
jack action said:
Yes.

Use the rear brake only. It will be easier to skid and also safer. You then have to solve the same free body diagram as in post #4, except that ##B_x## and ##m\ddot{x}## will be negative (i.e. pointing in the other direction).
Thank you very much, I’ll give this a shot later to see if I get accurate results.

luciaalmiron said:
So as long as I push with the same force on each surface the acceleration should be different, therefore giving me different results?
I don’t know what you mean.
By each surface, do you mean where each meets the road?
How do you mean to "push" on those surfaces?
They obviously cannot have different accelerations.

If the normal forces are ##N_{front}, N_{rear}## and both are skidding then the braking force is ##(N_{front}+ N_{rear})\mu_k=mg\mu_k##.

luciaalmiron said:
OK, so theoretically the coefficient=a/g, since there are m’s on both numerator and denominator. So as long as I push with the same force on each surface the acceleration should be different, therefore giving me different results?
You are going to need to be much more clear on what test you are running.

Are you measuring the drag force (rolling resistance) during acceleration?
Are you measuring the kinetic friction during decelleration during a skid to a stop?

The coefficient ##\frac{a}{g}## is applicable to a skidding stop. It will directly tell you the coefficient of sliding friction.

The coefficient ##\frac{a}{g}## will not mean the same thing during slow acceleration. You will be rolling without slipping. Your acceleration will not be limited by static friction but will instead be limited by the torque applied from the pedals. Any drag from rolling resistance will amount to a subtraction from the forward propulsion provided by the drive train.

You may hope that rolling resistance is proportional to weight and insensitive to velocity. There is no assurance that this hope is realistic. For instance, molasses on the road may behave differently from styrofoam, sand, grass or ice. At higher speeds, quadratic drag from air resistance may dominate.

jbriggs444 said:
You are going to need to be much more clear on what test you are running.

Are you measuring the drag force (rolling resistance) during acceleration?
Are you measuring the kinetic friction during decelleration during a skid to a stop?

The coefficient ##\frac{a}{g}## is applicable to a skidding stop. It will directly tell you the coefficient of sliding friction.

The coefficient ##\frac{a}{g}## will not mean the same thing during slow acceleration. You will be rolling without slipping. Your acceleration will not be limited by static friction but will instead be limited by the torque applied from the pedals. Any drag from rolling resistance will amount to a subtraction from the forward propulsion provided by the drive train.

You may hope that rolling resistance is proportional to weight and insensitive to velocity. There is no assurance that this hope is realistic. For instance, molasses on the road may behave differently from styrofoam, sand, grass or ice. At higher speeds, quadratic drag from air resistance may dominate.
Sorry, I don’t think I specified properly, I’m trying to calculate the coefficient of friction (μ)of different surfaces using a bike, where I can calculate the centripetal acceleration using an app. Would skidding and accelerating give me two different numbers for μ? I’m trying to find the most accurate way to do this so I dont know if skidding is best for this or not.

haruspex said:
I don’t know what you mean.
By each surface, do you mean where each meets the road?
How do you mean to "push" on those surfaces?
They obviously cannot have different accelerations.

If the normal forces are ##N_{front}, N_{rear}## and both are skidding then the braking force is ##(N_{front}+ N_{rear})\mu_k=mg\mu_k##.
Apologies I didn’t specify, I mean pushing the pedals with approximately the same force to calculate the coefficient of friction of various surfaces.

jbriggs444 said:
The coefficient is applicable to a skidding stop.
Not if the rear and front braking forces are not balanced with the normal forces acting on the tires, like, for example, when braking with one wheel.

luciaalmiron said:
I’m trying to calculate the coefficient of friction (μ)of different surfaces using a bike, where I can calculate the centripetal acceleration using an app.
Don't use the centripetal acceleration, use the linear acceleration. As far as I know, your app can measure that.

luciaalmiron said:
Would skidding and accelerating give me two different numbers for μ?
Skidding will give you the kinetic friction coefficient and while still rolling, you should be able to get the static friction coefficient. The values obtained in acceleration or deceleration should be similar.

luciaalmiron
jack action said:
Not if the rear and front braking forces are not balanced with the normal forces acting on the tires, like, for example, when braking with one wheel.

Don't use the centripetal acceleration, use the linear acceleration. As far as I know, your app can measure that.

Skidding will give you the kinetic friction coefficient and while still rolling, you should be able to get the static friction coefficient. The values obtained in acceleration or deceleration should be similar.
Ahh okay, this clears things up more, thank you. I’ll give this a shot.

jack action said:
Skidding will give you the kinetic friction coefficient and while still rolling, you should be able to get the static friction coefficient. The values obtained in acceleration or deceleration should be similar.
[Human] power-limited acceleration and friction-limited deceleration should be very different.

luciaalmiron said:
Sorry, I don’t think I specified properly, I’m trying to calculate the coefficient of friction (μ)of different surfaces using a bike, where I can calculate the centripetal acceleration using an app.
As @jack action has indicated, centripetal acceleration has essentially nothing to do with friction -- except to the extent that it could conceivably be used as a surrogate for a speed measurement.

Halve the wheel diameter and you've doubled centripetal acceleration without affecting friction at all.

jack action said:
and while still rolling, you should be able to get the static friction coefficient
Only by increasing the acceleration to the point where increasing it any further would lead to skidding. As I posted, that could be tricky.

jack action
luciaalmiron said:
pushing the pedals with approximately the same force
The force applied to the pedals doesn't tell you anything useful.
How that translates into tractive force when not skidding depends on the gearing and wheel size. When skidding, you can increase the force on the pedals as much as you like without increasing the acceleration or the frictional force.
If both wheels are skidding or both are rolling, all you need to measure is the maximum linear acceleration, nothing else.

luciaalmiron said:
I’m trying to calculate the coefficient of friction (μ)of different surfaces using a bike, where I can calculate the centripetal acceleration using an app.
OP -- sometimes when students try to come up with project ideas, those first ideas are fundamentally flawed. And in those cases, you should strive to see the flaws early and not spend lots of time on those paths and instead learn from the flaws and redirect to better paths.

Designing experiments to find the coefficients of friction involves focusing in on how best to find those coefficients. The classic tilted incline is one such experimental paradigm. Making precise force measurements in a horizontal test bed is another way to do it. Using a cellphone app to try to measure accelerations on a bicycle is not a way to do it, no matter how much work you try to do to shoehorn the friction measurement concept into a cellphone app that measures position as a function of time.

My recommendation would be to take a step back and think more about what you want to do. Since it is a project requirement to use that phone app in the project, think about other tests that you can do with it. If you still want to do friction measurements, you will need to find a better vehicle (sorry for the pun) for them. I don't see how to use the inclined plane paradigm with that phone app*, so you would probably need to think about some other way to demonstrate friction forces. You could try locking up both bicycle brakes in a skid and using the app to measure the deceleration, but that will only work for hard smooth surfaces that don't deform, and will only give you values for dynamic friction and not static friction.

Sometimes you have to step back and realize that the initial path you've chosen for a project is flawed, and revise your plan.

*EDIT/ADD -- Maybe you could use the app to measure the speed of the mass going down the incline after it breaks loose to determine the dynamic friction coefficient...

Last edited:
nasu
luciaalmiron said:
That’s strange as my graph only took a few data points, your’s far more detailed than when I exported the data to files on my phone, I’ll give it a shot exporting it to my phone. Yes I suppose there are a lot more factors that influence the accuracy of results, however as I have to write a formal investigation, I’ll include that in the observations section. Hopefully the centrifugal acceleration sensor is more accurate if I export it. When I manage to record the data on a few surfaces I’ll add a few images so you can see if they improved.
I look forward to it! Per forum rules, I can't share my findings, as that would be kind of like solving your homework problem. I've learned a lot in the last 12 hours, fiddling with and looking at my data. If I were you, I'd write that into your paper, regarding the stumbling blocks which lead to a more refined experiment.

ps. Here's the results of my back wheel coast down experiment from this morning:

acceleration without gravity mode

I haven't started analyzing it yet, but it sure looks different.

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