Singlespeed & Fixed Gear - A post about brakes

A Preface:

This is NOT intended to claim anyone is wrong for choosing to ride with or without brakes.

^^ Read that again, I mean it.
I wrote this to give everyone an idea of the dynamics of what exactly happens when you have to decelerate your bike. If you are curious, read on.

A quick description of how a bike brakes on a level road, with as little “engineer speak” as possible. A couple assumptions: 1)The bike is “traction limited” (the rider can lock the wheel, through brakes or skidding) and 2)Aero drag is neglected, as it is relatively small compared to braking force and it would be the same for the brake or brakeless rider.

Here is a diagram of the relevant forces acting on a bike during braking.
http://img.photobucket.com/albums/v628/sac02/bikebraking.jpg

W is the combined weight of the rider and bike acting at the center of mass, positioned approximately halfway along the wheelbase of the bike, at height ‘h’.

Wf and Wr are the weights at each wheel, before braking. During braking, weight will shift to the front wheel and we will call these new weights Wfb and Wrb.

Ff and Fr are the friction forces between the tires and road that are actually slowing the bike.

The friction force at the wheel can be approximated by multiplying a friction coefficient, ‘u’, by the weight on the wheel. So during braking,

(eqn1) Ff=u*Wfb

at the front wheel. In other words, more weight on the wheel means more friction force.

I’ll spare you the DiAllembert and summation of moments stuff. The weight on the front wheel when the rider brakes is described as:

(eqn2) Wfb = Wf + W*(a/g)*(h/L)

And similarly the rear wheel:

(eqn3) Wrb = Wr - W*(a/g)*(h/L)

The easy way to describe this equation is the weight on the wheel during braking equals the ‘original’ weight plus or minus (in respect to front or rear wheel) the weight transferred from the effect of braking.

In the case of front wheel only braking, the summation of forces equation is:

Ff = W(a/g)

Substitute eqn1:

u*Wfb = W(a/g)

Substitute eqn2:

u*( Wf + W*(a/g)*(h/L)) = W(a/g)

Solve this equation for (a/g) and the answer is your deceleration in g’s:

(a/g) = (u*(Wf/W)) / (1-u*(h/L))

For the case of rear wheel braking only, the deceleration is:

(a/g) = (u*(Wr/W)) / (1+u*(h/L))

Make up some weights and dimensions:

W = 200 lbs (rider and bike)
Wf = Wr = 100 lbs (using the assumption the center of mass is at the center of the wheelbase)
L = 40 inches
h = 40 inches
u = 0.7

These values show the front brake rider could decelerate at 1.17 g’s and the brakeless rider could only manage 0.206 g’s. Quite a difference.

The brake-equipped bike can’t really decelerate quite that fast. Substitute this deceleration, a/g = 1.17, into eqn3 and you will see that the weight on the rear tire is negative – huh? In other words, the rear wheel has come off the ground and the rider has (possibly) gone over the bars.

Yes, there are TONS of variables I didn’t include in this explanation: condition of the brakes, the skidder shifting his weight, etc. Still, it should give you an idea of just why a brake-equipped bike can stop quicker than its brakeless equivalent. If a brakeless rider tells you he can stop faster than a bike with brakes, recite this explanation to him, and ask him why Mr. Newton’s laws don’t happen to apply to him. :)

I am open to any comments, questions, corrections, flames, smart-ass comments that you all have for me. Again, please believe me when I say I did not write this to upset anyone. I truly believe everyone out there should ride the bike that makes them happy, brakes or not. I’m just trying to give a little something back (in the form of engineering-nerd knowledge) to a forum I really enjoy reading every day.

Mac

thanks, i haven't had a physics lesson since HS.

but seriously, this makes sense with or without equations added to it. honestly, if you get a brake rider and a brakeless rider and have a stop-off on a level stretch of road, i'd put my money on the brake rider. i don't really know anyone who wouldn't.

i don't really know anyone who wouldn't.

Retem

if you think riding bikes is something that can be reduced to mute equations then you are missing many many whole points

A Preface:

This is NOT intended to claim anyone is wrong for choosing to ride with or without brakes.

^^ Read that again, I mean it.
I wrote this to give everyone an idea of the dynamics of what exactly happens when you have to decelerate your bike. If you are curious, read on.

A quick description of how a bike brakes on a level road, with as little “engineer speak” as possible. A couple assumptions: 1)The bike is “traction limited” (the rider can lock the wheel, through brakes or skidding) and 2)Aero drag is neglected, as it is relatively small compared to braking force and it would be the same for the brake or brakeless rider.

Here is a diagram of the relevant forces acting on a bike during braking.
http://img.photobucket.com/albums/v628/sac02/bikebraking.jpg

W is the combined weight of the rider and bike acting at the center of mass, positioned approximately halfway along the wheelbase of the bike, at height ‘h’.

Wf and Wr are the weights at each wheel, before braking. During braking, weight will shift to the front wheel and we will call these new weights Wfb and Wrb.

Ff and Fr are the friction forces between the tires and road that are actually slowing the bike.

The friction force at the wheel can be approximated by multiplying a friction coefficient, ‘u’, by the weight on the wheel. So during braking,

(eqn1) Ff=u*Wfb

at the front wheel. In other words, more weight on the wheel means more friction force.

I’ll spare you the DiAllembert and summation of moments stuff. The weight on the front wheel when the rider brakes is described as:

(eqn2) Wfb = Wf + W*(a/g)*(h/L)

And similarly the rear wheel:

(eqn3) Wrb = Wr - W*(a/g)*(h/L)

The easy way to describe this equation is the weight on the wheel during braking equals the ‘original’ weight plus or minus (in respect to front or rear wheel) the weight transferred from the effect of braking.

In the case of front wheel only braking, the summation of forces equation is:

Ff = W(a/g)

Substitute eqn1:

u*Wfb = W(a/g)

Substitute eqn2:

u*( Wf + W*(a/g)*(h/L)) = W(a/g)

Solve this equation for (a/g) and the answer is your deceleration in g’s:

(a/g) = (u*(Wf/W)) / (1-u*(h/L))

For the case of rear wheel braking only, the deceleration is:

(a/g) = (u*(Wr/W)) / (1+u*(h/L))

Make up some weights and dimensions:

W = 200 lbs (rider and bike)
Wf = Wr = 100 lbs (using the assumption the center of mass is at the center of the wheelbase)
L = 40 inches
h = 40 inches
u = 0.7

These values show the front brake rider could decelerate at 1.17 g’s and the brakeless rider could only manage 0.206 g’s. Quite a difference.

The brake-equipped bike can’t really decelerate quite that fast. Substitute this deceleration, a/g = 1.17, into eqn3 and you will see that the weight on the rear tire is negative – huh? In other words, the rear wheel has come off the ground and the rider has (possibly) gone over the bars.

Yes, there are TONS of variables I didn’t include in this explanation: condition of the brakes, the skidder shifting his weight, etc. Still, it should give you an idea of just why a brake-equipped bike can stop quicker than its brakeless equivalent. If a brakeless rider tells you he can stop faster than a bike with brakes, recite this explanation to him, and ask him why Mr. Newton’s laws don’t happen to apply to him. :)

I am open to any comments, questions, corrections, flames, smart-ass comments that you all have for me. Again, please believe me when I say I did not write this to upset anyone. I truly believe everyone out there should ride the bike that makes them happy, brakes or not. I’m just trying to give a little something back (in the form of engineering-nerd knowledge) to a forum I really enjoy reading every day.

Mac

Are you just tryin to say brakes work?
I think all brakeless riders know that. They just dont care. Im a brake lover but ive been riding brakeless. Ive had alot more fun.

if you think riding bikes is something that can be reduced to mute equations then you are missing many many whole points

I don't think the OP was making that claim, but obviously you can't cheat the laws of physics no matter how much of a zen ninja you may think you are. At any rate, crashing into a bus without brakes looks way cooler than flipping over your bars because your front braked stopped you too fast.

Heres a new acronym: STBO

Yes, there are TONS of variables I didn’t include in this explanation: condition of the brakes, the skidder shifting his weight, etc.
Weight shifting is the biggest thing that isn't taken into account. Since the primary cause of the changes between your two equations is the rider's weight being moved forward, shifting the weight back would cause a huge difference in the two. The main thing that made me realize this was your free body diagrams. When braking (hand brake or drivetrain), my arms are pushing the bars away.

I'm not saying your physics isn't good and stuff, I'm just saying your quantifications might be a little off. I'd bet the factor of difference is more like 1.5 or 2 and not 6. But that's just an armchair physicists view. :)

if you think riding bikes is something that can be reduced to mute equations then you are missing many many whole points


+1. stopping quickly, with or without brakes is as much a matter of skill as mechanics. even a bike with handbrakes requires skills such as knowing when and to apply pressure and how much to apply, weight distribution, etc. the biggest variable is the rider.

Weight shifting is the biggest thing that isn't taken into account. Since the primary cause of the changes between your two equations is the rider's weight being moved forward, shifting the weight back would cause a huge difference in the two. The main thing that made me realize this was your free body diagrams. When braking (hand brake or drivetrain), my arms are pushing the bars away.

I'm not saying your physics isn't good and stuff, I'm just saying your quantifications might be a little off. I'd bet the factor of difference is more like 1.5 or 2 and not 6. But that's just an armchair physicists view. :)


true. also, a good skidder will know how to skid while basically seated.

+1. stopping quickly, with or without brakes is as much a matter of skill as mechanics. even a bike with handbrakes requires skills such as knowing when and to apply pressure and how much to apply, weight distribution, etc. the biggest variable is the rider.


except that anyone who is a half decent rider can stop faster with brakes then the best brakeless rider can so it really isn't unless you are talking about rank noobs and kids who just lock up the rear wheel in which case they are stopping about as fast as the best brakeless rider anyway.

I already knew that, even without all the formulas......but thanks...:D

except that anyone who is a half decent rider can stop faster with brakes then the best brakeless rider can so it really isn't unless you are talking about rank noobs and kids who just lock up the rear wheel in which case they are stopping about as fast as the best brakeless rider anyway.

but... the best riders, brakeless or not, don't need to stop.

true. also, a good skidder will know how to skid while basically seated.

and a good braked rider will brake while actually seated or even behind the seat. The center of bike com should be about where the com is when seated. On a track bike it will probably shift forward a little bit as will most of the popular hipster bar setups. If anything the vast majority of brakeless riders will probably have a far worse com then the one used in these models.

No matter what your stopping method is, the COM is going to move forward when stopping from a decent speed. Your body isn't completely locked into the same frame of reference as the bike and carries a lot more inertia.

All that really matters is this:
1. You can stop your bike.
2. You are comfortable stopping your bike at any given moment.

Avoidance is best, but not always an option.

I don't think the OP was making that claim, but obviously you can't cheat the laws of physics no matter how much of a zen ninja you may think you are. At any rate, crashing into a bus without brakes looks way cooler than flipping over your bars because your front braked stopped you too fast.


Too bad that isn't the point for (most) brakeless riders. If you want to follow a bus ridiculously close and feel safe with your brakes that is fine. The true spirit of brakeless I think doesn't relate to riding the same way with brakes, but compensating and problem solving. There are more ways to avoid danger than franticly mashing at your brakes. Just learn to ride, DEWWWWWD!

I'm constantly amazed by how many skilled riders seem totally unable to operate handbrakes or wrap handlebars.

except that anyone who is a half decent rider can stop faster with brakes then the best brakeless rider can so it really isn't unless you are talking about rank noobs and kids who just lock up the rear wheel in which case they are stopping about as fast as the best brakeless rider anyway.


but the rider is such a big variable, you can't quantify that. how are you going to prove that statement? you can't. let's say you have a braked bike and a brakeless bike compete in a quick stop. the braked bike wins. that could mean the braked bike is better. it could also mean the brakeless rider is teh sux00rz. and if the brakeless bike wins, the opposite would be true. if the same rider tries both methods and is better at one than the other, that proves only that they can use one better than the other, not that one is inherently better than the other. the formula may prove efficiency, but not necessarily an accurate analysis of the advantages/disadvantages of the two methods in ever day riding. that's about the rider, not the machine.

i know people who suck at riding road bikes. they could suck at track bikes, too. or they could rule on them. i know people who suck at track bikes. same goes for road bikes with them. it has as much to do with avoidance and technique as it does with any mechanical advantage. yes, there is that mechanical edge as the formula above proves. whether or not it will be of any practical value in every day situations is a matter that is dependent wholly upon the rider.

Most skilled riders will scrub speed and carve around or avoid the obstacle compleletly, braked or brakeless.

i know people who suck at riding road bikes. they could suck at track bikes, too. or they could rule on them. i know people who suck at track bikes. same goes for road bikes with them. it has as much to do with avoidance and technique as it does with any mechanical advantage. yes, there is that mechanical edge as the formula above proves. whether or not it will be of any practical value in every day situations is a matter that is dependent wholly upon the rider.
oh please

with very little effort nearly anyone could learn to use a handbrake to stop faster and with more control than even a good brakeless rider

someone who "sucks at riding road bikes" should try a little harder learn a little more or smoke a little less

dont tell me your friends dont have hands

Your body isn't completely locked into the same frame of reference as the bike and carries a lot more inertia.
It really should be (or damn near it) unless you are trying to endo.

but the rider is such a big variable, you can't quantify that. how are you going to prove that statement? you can't. let's say you have a braked bike and a brakeless bike compete in a quick stop. the braked bike wins. that could mean the braked bike is better. it could also mean the brakeless rider is teh sux00rz. and if the brakeless bike wins, the opposite would be true. if the same rider tries both methods and is better at one than the other, that proves only that they can use one better than the other, not that one is inherently better than the other. the formula may prove efficiency, but not necessarily an accurate analysis of the advantages/disadvantages of the two methods in ever day riding. that's about the rider, not the machine.

i know people who suck at riding road bikes. they could suck at track bikes, too. or they could rule on them. i know people who suck at track bikes. same goes for road bikes with them. it has as much to do with avoidance and technique as it does with any mechanical advantage. yes, there is that mechanical edge as the formula above proves. whether or not it will be of any practical value in every day situations is a matter that is dependent wholly upon the rider.


What you seem to miss is that the BEST ANY brakeless rider can do is shift their weight as little forward or up as possible while locking their rear wheel. This is roughly equivalent to the worst any braked rider can do. Watch a novice cyclist make a panic stop sometime... They do exactly what you claim the best brakeless riders do: "keep their weight close to where it would be when they are in the saddle."

Avoidance and technique are fine but there are plenty of situations where stopping fast is all that matters. Your previous claim had even less to do with that however since you claimed that "stopping quickly with or without brakes is as much a matter of skill as mechanics." That simply isn't true outside the fantasy land brakeless rider use to justify their choice.

Retem

thanks man like I have said before once I am riding in a manner that is out of my comfort zone the front brake goes on

It really should be (or damn near it) unless you are trying to endo.

True,
After I posted that I thought:
**** I posted in a brakeless thread. After that I thought, it's probably not enough to really matter. I was also thinking about panic stops from 15-20MPH.

whether or not it will be of any practical value in every day situations is a matter that is dependent wholly upon the rider.

So your argument is that a rider can have mad skidding skillz but cannot competently operate a handbrake.

You can't concede the physics (which you DID do) and then argue that it's all about the rider.


------------

Just say you don't care if you can't stop as well. Everyone's fine with that. Pretending that you can is a lie, to both yourself and the forum.

If I don't ride my bike it'll just lie there otherwise.

I just love these threads and debates! Maybe we will have factionalization in the FG forum in '07 and see it split into two different subgroups. How will we symbolize which group we are in when away from our bikes? Colored bandanas? Tattoos? Maybe carrying a caliper or a hand brake stick?

wiggly fingered signs?. :lol:

i will shoot the next person i see brakeless

http://img.photobucket.com/albums/v628/sac02/bikebraking.jpg


This stick man's bike is far too tall for him. He can't even reach the pedals!

who is away from their bikes?

Four floors below.....it's waiting for me......

http://www.useit.com/alertbox/20021223_05_mistake.gif

the mountain bike i'm building is mere feet from me.

anyway, i dunno...i hate these threads. i know, i conceded the physics, but perhaps i should have said something like "i concede the physics, all things being equal", but of course...they never are.

all i know i stop just fine on my bike with no handbrake, and from riding with others i know i stop at least as quickly as road bikes, and so do other brakeless riders i know, which is mere anecdotal evidence, but even so, controverts the premise that it's impossible for that to happen. seen it, done it, you can't convince me it's impossible.

oh, by the way, the fixed mtb i'm working on will have a handbrake, if anyone's curious. i'm not visciously anti-brake. i'm anti-anti-brakeless.

i'm anti-anti-brakeless.
Word... I ride with brakes, and am constantly blown away by brakeless, it's simply not for me.

heh, it's funny...this fixed mtb will have the first handbrake i've used in over a year. i just hope i can remember to grab it when i need to. i don't see skidding on 2 inch knobbies working very well....hope i remember to use my hands to stop as well as my feet.

Hey guys, a few replies to some of the responses I've gotten.

1) To those who infer that becasue I posted some equations on a message board I must enjoy riding my bike less than them: Oh really? I didn't realize that enjoyment of engineering/physics and cycling were mutually exclusive! In fact, I propose to you (all in fun :)): Because I have taken the time to understand the "how and why" of cycling, I might enjoy it more than you! (I'm not really making that argument, but I hope you get my point.)

2) I'm glad to see that this hasn't degenerated completely into a brakes vs non flame war. Civilized discussion is always good, that's what I was hoping for.

3) Things that will affect the model that people have commented on:

The lower a rider gets during braking, the less weight will transfer from the rear to front. If a rider gets further back on the bike, the rear tire will be more heavily weighted and can provide higher tractive force which in turn results in higher decelleration.

My estimations of the best case scenario for the brakeless rider: If the rider can shift his center of mass 3/4 of the way to the rear of the bike (that would be several inches behind the bottom bracket) so that Wr = 150, and get his CoM really low (the top tube on my bike is 31 inches high) so that h = 31 inches, he could produce a deceleration of 0.340 g's.

A quick summation of forces for a rider using a braking system front and rear:

Ff + Fr = W*(a/g)

substitute tire friction model:

u*(Wf) + u*(Wr) = W*(a/g)

algebra:

u*(Wf + Wr) = W*(a/g)

since Wf + Wr is simply the combined weight of the bike and rider, this becomes:

u*W = W*(a/g)

and algebra simplifies this to:

(a/g) = u

So, with two brakes (or front brake and rear skidding, same thing) a rider can stop with a decelleration (in g's) approximately equal to the available coefficient of friction between the tire and road.

Comparing 0.7 to 0.34, the rider with brakes can stop about twice as fast.

Sorry I didn't go through this in the original post. I didn't mean to imply that a rider with brakes can stop six times faster than a brakeless rider. When re-reading my OP I see how that part may be misleading and I should have clarified this.

Mac

and from riding with others i know i stop at least as quickly as road bikes, and so do other brakeless riders i know, which is mere anecdotal evidence, but even so, controverts the premise that it's impossible for that to happen. seen it, done it, you can't convince me it's impossible.

right because they weren't stopping as fast as they could. riding with other you just don't do that unless that the only way to avoid a serious crash. In fact you never do that I haven't for 2 weeks since some ***** cut into the bike lane and stopped in front of me. If you really think that you could stop as fast as them and they aren't tiding brake pads left on since the 80's you are ****ing clueless.

lots of people dont have much experience riding ya know? or the skills that go with it

somebody who spends hours a day riding around doin runs and hustlin packages knows alot more about brakeless than some recreational rider most of the time, usually knows alot more about riding period

Word... I ride with brakes, and am constantly blown away by brakeless, it's simply not for me.

I've been wanting to put a brake on my commuter, but theres no room in the middle of the bars for a cross lever, and I don't have my hands at the ends of the bullhorns that often, so a time trial lever there wouldn't be too useful. Its all just so much work!

heh, it's funny...this fixed mtb will have the first handbrake i've used in over a year. i just hope i can remember to grab it when i need to. i don't see skidding on 2 inch knobbies working very well....hope i remember to use my hands to stop as well as my feet.

I tried to lock up the back wheel with my legs when my fixed mtb was running 2.1" slicks.

It hurt. You'll learn quick.

ha ha, yeah...i think i will!

i'm assuming the greater rolling resistance will make initializing and holding a skid harder, even though you could say the friction would be greater...

and dutret....i really don't want to talk to you anymore. i want to keep it civilized, and it would probably turn into a flamewar if we kept on, and that's exactly what i hate about these threads.

ha ha, yeah...i think i will!

i'm assuming the greater rolling resistance will make initializing and holding a skid harder, even though you could say the friction would be greater...

and dutret....i really don't want to talk to you anymore. i want to keep it civilized, and it would probably turn into a flamewar if we kept on, and that's exactly what i hate about these threads.


actually my friend has a fixed mtb that I have ridden a couple times and it is geared 36~32 16 and it is way easy to skid its a really fun bike

hc, just for the record, rolling resistance is only in effect when your tire is rolling. When skidding (or attempting to skid) it's the coefficient of friction between the tire and surface that you're trying to overcome.

The Cf of rubber on dirt should be (is) much smaller than on pavement, making it easier to skid. But knobby tires can generate traction in other ways - by actively deforming the dirt "road" surface the tire can improve traction, so it's not strictly about the Cf.

Mac

Yes, the real question is at what point does this limited braking ability put you and others in danger or become impractical? Its pretty clear that bikes with brakes can stop faster than bikes without brakes. How much of that braking power do we use? A jaguar is faster than a saturn but they will get you from A to B in about the same time. I can still stop faster than cars on my brakeless bike. I haven't been in any collisions that could have been avoided had I have had a brake. I can stop quickly enough for almost every situtation I come across. Sometimes I miss a turn because I cannot brake fast enough, but that is because I am riding fast with someone who suddenly tells me we have to turn.

hc, just for the record, rolling resistance is only in effect when your tire is rolling. When skidding (or attempting to skid) it's the coefficient of friction between the tire and surface that you're trying to overcome.

The Cf of rubber on dirt should be (is) much smaller than on pavement, making it easier to skid. But knobby tires can generate traction in other ways - by actively deforming the dirt "road" surface the tire can improve traction, so it's not strictly about the Cf.

Mac

good to know. i assumed rolling resistance would come into play with a fixed gear when stopping the rolling motion as well.

I don't have my hands at the ends of the bullhorns that often, so a time trial lever there wouldn't be too useful.

Why not? I don't ride with my hands on the hoods 100% of the time, but the lever's still there if I need it.

Yes, the real question is at what point does this limited braking ability put you and others in danger or become impractical? Its pretty clear that bikes with brakes can stop faster than bikes without brakes. How much of that braking power do we use? A jaguar is faster than a saturn but they will get you from A to B in about the same time. I can still stop faster than cars on my brakeless bike. I haven't been in any collisions that could have been avoided had I have had a brake. I can stop quickly enough for almost every situtation I come across. Sometimes I miss a turn because I cannot brake fast enough, but that is because I am riding fast with someone who suddenly tells me we have to turn.
I agree that it one feels confident in their ability to ride brakeless safely, and they enjoy it, that they should do it. But... your assertion that you can stop faster than a car is not possible. The derivation and equations I gave for the bike are identical to those used to figure vehicle decellerations. A car with front a rear brakes stop with a decelleration (in g's) approximately equal to the available coefficient of friction between the tire and road, exact same as a bike.

Truly, I do not doubt that you regularly stop faster than the cars around you. But that is not because you have a better braking system than them. They are not braking at full capacity. I've been an amatuer race car driver for about ten years, and an instructor for four. One of the drills we do with our students is to put them on a course with a line of traffic pylons at the end, tell them to get up to 70 or 80 mph, and instruct them to hit the brakes hard at the proper time, to stop the car as close as possible (inches) to the orange cones. Without fail, they always stop way short - several car lengths short. The point is, 99% of people have no clue what the true braking capacity of their car is, much less use it, especially in day-to-day driving. Sorry that this was a little OT...

Mac

Why not? I don't ride with my hands on the hoods 100% of the time, but the lever's still there if I need it.

Good question! I guess I'm just trying to justify riding brakeless and I'm too lazy to buy and install brakes. I'd have to unwrap my bars and since I slid some oury's right up to the stem it would be tough, plus I have electrical tapes so many gashes in the tape I'd have to just slice it off. I'd also have to reinstall my front fender true my wheel. I already have a full time job, cmon!

good to know. i assumed rolling resistance would come into play with a fixed gear when stopping the rolling motion as well.
As I mentioned, (and as the name implies) rolling resistance only comes into play when the wheel is rolling. If you are skidding (or locking up a wheel in any manner) there is no rolling resistance.

If you are braking at a point less than threshold (lockup), then rolling resistance is one of the forces slowing your bike. But the rolling resistance force is very small compared to the other forces in action. It is small enough that it will often be ignored with little loss of accuracy in order to simpplify calculations.

Mac