How to Pump Your Bike, According to Physics

Have you ever wondered how pumping works? Why pushing downwards into the ground helps to propel you forward? I did, but for a long time I was satisfied with a very common explanation that went something like this: when you’re pushing into the down-slope of a roller, you’re making your bike heavier, and when you let the bike come towards you as you go up the next roller, the bike is lighter. That’s what propels you forward — it’s almost like you’re turning gravity up and down to your advantage.
But a couple of things made me realize this explanation was wrong. And this misunderstanding was causing my pumping technique to suffer.

The first was the realization that you could pump around corners. Not just to generate traction or to do a sweet cuttie; pushing into a berm can actually generate speed. In fact, it’s possible to pump while snaking side to side on flat ground, as demonstrated in this Skills With Phil video, which is great fun by the way. But a turn isn’t downhill or uphill. So how does that work?
The second revelation came when a coach told me I was pumping too early. Instead of pushing into the steepest part of the down-slope, he got me to wait a fraction longer and push into the curved transition at the end of the slope. The difference was palpable.

When I thought about it more, pushing into the down-slope can’t be what’s pushing you forward. Imagine you’re going down a hill with a constant gradient. Gravity accelerates you down the slope because the vertical force of gravity is not at right angles to the slope. But, if you extend your legs and push into the ground, you’re pushing at right angles to the ground underneath your wheels, which doesn’t help propel you forward at all. A lot of pumping explanations talk about pushing vertically downward onto a down-slope, but because the only thing to push against is the floor, the reaction force you’re generating is always at right angles to the ground, and to direction you want to accelerate.

Physics 101

So how is it that pumping helps to generate speed in a corner or through a set of rollers? It’s all to do with conservation of angular momentum.

This is a classic physics demonstration where someone spins around with heavy weights in both hands. Then, as he pulls the weights in towards the center of rotation, he spins faster. On first glance, it might look like the weights only rotate faster because they’re describing a smaller circle, but the weights are actually speeding up.

The same is true of a pirouetting ice-skater, a spiral coin machine, the orbits of the planets, or the water draining from your bathtub: as the radius decreases, the speed increases. This is explained very neatly by the law of conservation of angular momentum. For a mass that is moving around a circle or a corner with a constant radius, the angular momentum is given by its mass, times the radius of the turn, times its velocity. (Angular momentum=MVR). In the absence of friction or other external forces, this quantity always stays the same.

So if the radius of curvature decreases (like the weights getting closer to the axis of rotation) then in order to conserve angular momentum, the velocity has to increase. In fact, if you halve the radius of the circle, the velocity must double. Let’s apply this to pumping.

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Imagine you’re in a berm or a trough which has a radius of five meters. It has a center of curvature, the point that’s always five meters away from any point on the curve. If you extend your arms and legs to push away from the ground, your center of mass will move towards the center of rotation. So as far as your body weight is concerned, the radius of curvature has decreased, and by conservation of angular momentum, your speed will increase. So when you’re pumping through a set of rollers, it’s the radius of curvature of the rollers that’s important, not the down slope or the up slope. Picture the concave, U-shaped part of the rollers — the trough between the peaks. That is when you want to extend your arms and legs because you can move your center of mass towards the center of curvature about which the ground is curving. Similarly, when you’re going over the crest of the rollers, you want to contract your arms and legs such that you move towards the center of curvature, which is now somewhere beneath the ground.
This is why I used to suck at pumping. You don’t want to extend your arms and legs when you’re on the steepest part of the down slope, but the most tightly curved part of the transition. Sometimes the difference in timing can be quite subtle, but if you have a long down-slope before the transition, it pays to be patient and push only once the ground starts to curve. Similarly, it’s the crest of the roller where you want the bike to come up towards you, not the steepest part of the up-slope.
A more thorough explanation

But the law of conservation of angular momentum is not really an explanation: a law is just a relationship between some variables, not a cause. So if you want a better explanation of why angular momentum is conserved, check out this video from Vsauce.
To summarize, if you have a mass going around a circle with one radius, and then you pull that mass in towards a narrower radius, (like the rider pumping into a berm, or an ice skater pulling her arms in), it doesn’t go instantly from one radius to a narrower radius, it moves in a spiral pattern. And when that happens, the path it follows is no longer perpendicular to the line drawn from the mass to the center of rotation. That means if you pull towards the center of rotation, you’re no longer pulling that mass perpendicular to its direction; you’re pulling it slightly ahead, and that is what causes the mass to speed up. It’s being pulled slightly forwards as well as radially inwards. This explains why a mass will speed up when it’s drawn towards the center of curvature.

On a bike, as you push away from a berm, your center of mass moves in a spiral instead of an arc with a constant radius. And when you do that, you’re pushing not only towards the center of the turn; you’re also pushing your mass slightly forwards.

The transition giveth and the transition taketh away

It’s worth remembering that the opposite is also true. If you allow your center of mass to move towards the ground in a compression, you will lose speed, just as an ice skater who extends her arms and legs away from the axis of rotation will slow down. Centrifugal force will naturally cause your arms and legs to collapse slightly unless you make a conscious effort, and your suspension will compress too, pulling you further from the center of curvature. So if you’re on a full suspension bike you have to work even harder to counter this and to maintain speed. But remember that even if you only maintain your speed by pumping through a turn or compression, that’s a win compared to the speed you would lose if you rode passively.

Also, pumping is not “free speed”. The work you do pushing yourself away from the ground against the centrifugal force is what provides the energy that accelerates you down the trail. Anyone who’s ridden a few laps of a pump track knows this energy is not “free”.

Of course this doesn’t just apply to a pump track. I find pumping most fun when finding natural corners and compressions to gain speed from. Just remember to look for the curves not the slopes.