Technical FAQ: The backward bike throw

Lennard Zinn talks about the science behind bike throws and looks at whether there's such a thing as throwing a bike backward.

Does the backward bike throw exist?

Dear Lennard,
In a post last July, you discussed the physics of the forward bike throw. 

My question is whether it is physically possible to throw a bike backward. One very often reads that when a rider stands out of the saddle, the bike is pushed backward into the trailing rider’s front wheel.

I can imagine that this is possible at very low speeds, i.e. the bike’s forward motion slows to a stop and begins to move backward. But can this happen when a bike is traveling at speed? Does the bike physically go into reverse relative to the ground, or does it just slow down and appear to move backward in the eyes of the rider behind, whose forward speed has not changed?

I offer an analogy. Some people think a skydiver moves upward when his or her parachute opens because videos shot from beside the skydiver show the individual disappearing out of the top of the frame when the parachute opens. This is of course an illusion caused by the deceleration of the skydiver relative to the videographer, whose parachute has not yet been deployed.

If physics show that a bicycle does indeed move backward rather than just slow down, albeit sharply, when a rider stands in the saddle, please explain it to me. If not, I will continue to be peeved at statements like this one (taken verbatim from a leading online cycling site):

“What you need to do is shift up one or two gears (harder) just before standing up. Get on top of that gear and then stand up. This will prevent you from throwing your bike backwards into the guy behind you.”

To my mind, standing up has the same effect as hitting the brakes hard. Your bike slows down rapidly. The following rider crashes into you because they weren’t able to quickly scrub off speed to match your new, slower velocity. You don’t get hit by the rider behind you because your bike is suddenly moving in reverse.
— Johan

Dear Johan,
It is as you said; the bike does not move backward relative to the ground, except perhaps at very low speeds. Instead, it moves back relative to the rider in the same way that the bike throw moves the bike forward relative to the rider, and it is analogous to the skydiver example you gave.

For the sake of simplicity, assume that the bike and rider continue to move at constant speed over the instant that the rider stands up. In other words, the center of mass (COM) of the bike and rider move the same speed in the instant just before the rider stands up as in the instant just after he or she stands up. But in standing up, the rider must move forward relative to the bike to get his or her center of mass over or forward of the bottom bracket — and quite a bit forward of the bottom bracket if it’s a steep climb. So, the rider’s COM is moving faster than the COM of the bike and rider together during this split second of standing up in order to get his or her COM ahead of where it would have been if he or she had stayed seated.

If the COM of the bike and rider together is moving at constant velocity during this instant, by Newton’s law of conservation of momentum, the COM of the bike must move back relative to the rider’s COM in order that the COM of both together maintains constant speed. In the case of a modern road racing bike and an adult rider, the bike is much lighter than the rider. In order to keep both sides of the equation balanced, the bike will move backward relative to the COM of the bike and rider much faster than the COM of the rider will move forward relative to the COM of bike and rider.

As you said, Johan, if the rider is rolling along at a speed close to zero when he or she stands up, it is possible for the bike to actually move backward relative to the ground, and if he is stopped, it most certainly will. A trials rider performing stunts at a standstill is a good demonstration of this.

In the case of riding in a paceline, it doesn’t actually matter that the bike does not move backward relative to the ground in order for the rider behind to run into the rider ahead when he or she stands up out of the saddle; all that matters is that the bike has moved backward relative to the rider. Since the COM of the lead bike and rider is moving at the same speed as the rider behind in a paceline, if the lead rider’s bike suddenly decelerates (because standing out of the saddle causes it to suddenly move backward relative to the COM of bike and rider), the following rider can easily crash into the lead rider’s bike if he or she is not paying proper attention and allowing sufficient space.

I guess you’re going to continue to be peeved at online cycling tips like the one you quoted. That tip may have been worded incorrectly, but it did communicate the issue a beginner riding uphill in a paceline should be aware of. Had the last sentence read something more like, “This will prevent your bike from rapidly slowing down right in the path of the guy behind you,” it would have been more accurate. Problem is, the uninitiated, without understanding the explanation above, would assume that meant that the rider was going to be slowing down simply because he or she stood up, rather than that the bike would be slowing down instead. He might not understand why and thus might not appreciate the problem the sentence is attempting to warn him about. The image of throwing the bike backward, however, does communicate the issue to a beginner, even if the bike does not actually go backward relative to the ground. So I think you may want to reconsider being peeved about it; it just might save you someday from some newbie getting out of the saddle right in front of you and your bike running into his.
― Lennard