All the cool kids in London ride fixed gear or single speed bikes these days. Fact. Well, all the cool kids…..and me. However, there’s a trend for removing both front and back brakes on a fixed gear bike and using rear wheel braking only via the pedals. Riding a fixed gear bike allows you to control your speed and come to a stop easily without ever touching the brakes. If you lock your legs up when riding then you can even skid the rear wheel to stop when you want to. this is (incorrectly) considered to be a faster way of stopping a fixed gear bike and comes with the added down side that it wears out your tyres quickly. If you talk to any brakeless rider they’ll tell you that they can stop whenever they want in the same time/ distance as a normal bike. I guess, you’d have to think that before hitting busy streets on a bike with no brakes in the first place. So, my question is:

*How safe/ stupid is it to ride a bike with no brakes and can you really stop in the same distance/ time as a normal bike in an emergency?*

To answer this we’re only going to look at the mechanical efficiency of rear wheel braking vs front wheel braking. We will assume that a proficient fixie skidder can react as quickly with their legs as the rest of us can with a hand operated rim brake so reaction times are not an issue. I know I can’t react as quickly with my legs but I don’t regularly ride fixed. In fact, the brakeless bregade could argue that the friction and brake cable extension from the brake lever to the rear wheel and potential water on the brake pads on a rim brake causes a much bigger delay and would require faster reactions. But that is another topic altogether.

First we need a model of a bike and rider to base our analysis on. The figure below shows the combined centre of gravity (COG) of the rider and bike. This moves forwards, backwards, up and down as the rider changes position. A typical 58cm frame might have a wheelbase of 1020mm (L_{1 }+ L_{2}) and with the rider in a normal riding position the combined COG will be located at around L_{1} = 600mm and L_{2} = 420mm at a height above ground of around H = 1100mm.

You can measure the position of your COG quite easily by standing on some scales holding the bike to get the overall mass (M). Then, put the front wheel on the scales whilst sitting in your preferred riding position and, balancing against a wall, read off the weight measurement (M_{f}). Do the same for rear wheel as a double check (you probably need someone else to read off the weight as it will alter your position if you try to read it). The front and rear weights should add up to give you the same as the total and the COG position can be calculated using only the front measurement:

L_{1} = Wheel Spacing x (1- M_{f}/M)

The vertical position is a bit trickier to measure but will generally be located around the level of your hip in a normal riding position.

Let’s start with the bike with front and back brakes. Braking is limited by 2 factors. Firstly by the friction that can be developed between the bike tyre and the road and secondly by the stability of the rider on the bike. We all know that if you pull the front brake too hard you’ll end up over the handlebars. Friction between the bike tyre and the road is calculated by **F _{Fr} = μR**. Where F

_{Fr }is the friction force, μ is the friction coefficient between the road and the tyre and R is the reaction force at the point of friction as shown by R

_{f}and R

_{r}on the sketch above.

The friction coefficient varies depending on the road surface, tyre surface and whether the two friction surfaces are static or sliding (kinetic). Here are some typical values for bike tyres on an asphalt road:

Dry (Static) = 0.8

Wet (Static) = 0.5

Ice (Static) = 0.1

Dry (Kinetic) = 0.65

Wet (Kinetic) = 0.4

Ice (Kinetic) = 0.08

The friction force causes the bike and rider to decelerate. The act of decelerating causes more weight to be applied to the front wheel then the back wheel due to the momentum of your body, which is why it is easy to go over the handle bars if you decelerate too sharply. Using Newtons 2nd Law (Force = Mass x Acceleration) the deceleration force on the bike and rider is M x a. Using the front brake alone, at the point where the back wheel lifts off, all the weight is on the front wheel. If we take moments about the base of the front wheel at this split second then the overturning force from the horizontal deceleration is balanced by the weight acting downwards or: MaH = MgL_{1} which can be rearanged to give

a_{max} = gL_{1}/H

Using the numbers above a_{max} = 9.81×600/1100 = *5.35m/s*^{2}. Which is equivalent to stopping from 20mph in 0.7s over a distance of 7.5m.

Note, that at this point the rear brake has no effect whatsoever as there is no weight on the back wheel. The friction force developed between the tyre and the road is Ma_{max} or MgL_{1}/H whilst the maximum friction force theoretically available would use our whole weight mg. So, the smaller the ratio L_{1}/H gets the less stable the bike becomes during braking. Recumbent riders can actually skid the front wheel because L_{1}/H > 1 so the wheel skids before the bike toples over.

Now, let’s do another calculation for braking, this time using the back brake only. We know that we can skid the back wheel without overbalancing so the maximum braking force we can get is F_{Fr} = μR_{r} this also equals the deceleration force so balancing the horizontal forces:

Ma = μR_{r}

We don’t know what the reaction on the back wheel is as it is a function of the deceleration force so taking moments about the front wheel:

MaH + R_{r }(L_{1 }+ L_{2}) = MgL_{1}

If we rearange the first equation and substitute R_{r} into the second then we get:

a_{max} = gL_{1} compared with a_{max} = gL_{1}/H for front wheel braking

. .H+(L_{1}+L_{2})/μ

Using the numbers as before this gives a_{max} = 9.81×600/(1100+(1020/0.8)) = **2 .48m/s**

^{2 }Or a 20mph stopping distance of 16.1m in 1.5s.

So, using rear wheel braking is 2.2 times worse than front wheel braking without skidding or overbalancing. Let’s make this a bit more realistic because we don’t all brake so hard that we’re at the point of overbalancing even when you have to do an emergency stop. We’d be walking round with a lot more cycling injuries if that was the case, so let’s take 80% of the front wheel braking figure (4.28m/s^{2}). In the same way that it’s very easy to overbalance when braking hard on the front wheel, it is very easy to skid the back wheel when you slam on the brakes. This changes your stopping force from static friction to kinetic friction which is about 80% of the static value (max deceleration is now 2.21m/s^{2}). So, assuming that our front brake rider doesn’t want to head over the handlebars and our back brake rider either doesn’t want to skid or can’t help skidding **the front brake is still 1.9 times more effective than the back brake**.

You’ll also remember that this article started off with a discussion of the ultra cool, brakeless, fixie skidders. In the process of starting a skid, most riders shift their weight forwards to take weight off the rear wheel and make it easier to initiate the skid. This reduces the dimension L_{1} and makes the rear wheel even less effective. This is taken to the extreme in a skid competition where the winning skidder will be the one to get their weight the furthest forward over the handlebars. Following the calculations above, if you shift your centre of gravity by only 100mm forwards to help initiate a skid then your maximum deceleration drops to 1.83*m/s*^{2} which is now **2.3 times worse than a front brake**.

So, the brakes (well the front one for sure) are staying firmly on my bike and I will continue to despair at the brakeless (clueless) riders out on the streets. I’m also sure that my suggestion that Newtons Second Law shows that you shouldn’t ride brakeless will fall on deaf hipster ears!

Another interesting thing to note from this is that because bike riders (with a front brake!) are limited by trying not to overbalance, rather than being limited the friction coefficient between the road and the front tyre, you can NEVER brake as quickly as a car because bbecause a car’s L_{1}/H ratio is much higher than that of a bike. I guess we’ve all experienced a close shave (actually a couple of crashes for me) when following a car too closely when they brake suddenly but now you have the proof…. and I still don’t learn.

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It it seems it is actually you who is clueless if you’ve actually managed to crash into the back of cars a couple of times.