# Technical FAQ: Physics and the bike throw

## How does a sprinter's bike throw actually work? Lennard Zinn dives into the physics of rider weight, bike acceleration, and more.

Dear Lennard,
Per classic Newtonian physics the centre of mass of the bike-rider system will continue moving at the same velocity unless an external force is applied. You’re entirely correct that throwing the rider’s weight rearwards relative to the bike does not apply an external force — only pedaling can do that — but it’s not correct to think that this makes no difference in a sprint finish: Moving a 72kg rider backwards X distance must result in moving an 8kg bike forwards 9x distance; so the centre of the rider will cross the line later but the front of the bike will cross the line earlier.

If we say that Sagan is maybe 2cm behind where he would normally be on the bike he’s gained 18cm on the front wheel. Kristoff looks to me to be 10cm forward to a seated position — if he’d just sat back down he’d have gained 9cm and won the stage; a Sagan-distance throw from where he is would gain him 27cm and make the photo redundant.

The heavier you are compared to your bike the more you can gain with a throw.
— Phil

Dear Phil,
You were one who caught my post early last Tuesday. Thanks for your analysis, which, unlike what I had posted briefly on the subject, is spot on.

Last week, after staring cross-eyed at photo-finish images of riders throwing their bikes at the line into the wee hours of the morning, I started thinking about how the bike throw works. I hadn’t begun digging through my veloqna@comcast.net email box for questions to answer for my column until late at night on Monday, and my column goes up on Tuesday morning. I was happy to find the wonderful question about why spokes are curved on photos from photo-finish cameras, and I set about answering it.

In a sleep-deprived state after answering that question, I thought I had come up with a revelation that the bike throw is a myth. I then went on to write out a wild theory regarding last Monday’s defeat by Peter Sagan of Alexander Kristoff by a hair in a photo finish that was attributed to the Slovak throwing his bike forward better than the Norwegian. Ignoring a lesson that I had learned many times before, namely not sending in an article that I work on late at night until I’ve slept on it, I sent it in right then. I awoke late the following morning with a jolt, wondering, “What was I thinking?”

I hoped that when I looked at VeloNews.com that it would not have yet been posted, but our web team is very efficient, and it was already up. You were among the many dedicated readers (thank you for your dedication!) who saw it before we chopped the bike-throw part off of the curved-spokes-in-photo-finish explanation. Anyway, the theory I put forward there was totally wrong, but there is still a lot going on with the bike throw that I think is fun to think about.

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The reason for doing a “bike throw” at the line is obvious; the rider is trying to push the bicycle out in front of him in order to have the leading edge of the front tire cross the finish line earlier than it otherwise would have, had he not “thrown” it. It is the cycling equivalent of the runner who learns forward in order to break the tape with his or her chest a bit earlier.

Unlike the runner, a bicycle is rolling, and here is where my sleep-deprived mind started veering off into the weeds. I was thinking that as long as its wheels roll on the ground without slipping, the only thing that can get it across the line sooner is by pushing harder on the pedals; the rider cannot generate any other force to cause it to move forward faster. I got excited and wrote on and on in this vein and submitted it for posting while bathed in the soft light of a beautiful full moon. I went to bed with a smile on my face.

My analysis was, of course, wrong. The rider actually stops pedaling for the instant of the bike throw and is coasting. He throws his weight back, pushing against the pedals and the handlebar. The bike moves forward faster than he does for the same reason that a boat on a frictionless lake moves forward if a guy on the boat throws heavy items out the back.

Newton’s first law of motion says that momentum, which is mass times velocity, must be conserved. It gets a little trickier with human-powered bikes moving at this speed, though, because wind resistance is such a massive deterrent to their forward motion. As soon as the rider stops pedaling, the wind is slowing him and the bike down in a big hurry. But ignoring the air for the brief instant of the bike throw, we can say that the combined mass of the bike and rider times their velocity just before the instant of the bike throw must equal the sum of the separate masses of the rider and bike, each times its separate velocity during the bike throw. Or:

(mb + mr)vb+r = mb*vb + mr*vr

Since the bike is so much lighter than the rider, it actually can shoot forward quite rapidly, as Phil describes, if the rider pushes himself back quickly enough. But, in addition to the frictional forces (mainly air resistance) complicating this, the equation is complicated yet more by the fact that the masses and velocities on the right side of the equation are not simple to separate. The “mass of the bike” in this equation is not just the mass of the bike; it also includes the masses of parts of the rider that are moving along at the same speed of the bike, like his hands, forearms, and feet. Consequently, the “mass of the rider” is not his entire mass, and the “velocity of the rider” varies depending on what part of his body you’re talking about; his butt and torso are moving forward the slowest (i.e., moving back relative to the bike the fastest), while his upper arms and lower legs are moving forward closer to the speed of the bike.

Anyway, I had fun thinking about all of this, and I hope you enjoyed it, too, especially those of you who saw the original post this morning and thought what an idiot that Lennard Zinn must be! Below are a few other good responses regarding it, but I got so many that I can’t possibly put them all in here. Have a great recovery from Tour de France withdrawal!
― Lennard

Dear Lennard,
I see you pulled that one … No doubt you will discuss that in a future column… I thought it through a bit more and have I think a cleaner way of describing it … You’re probably close to being right that you can’t speed up or slow down the CENTER OF GRAVITY of the human/bike package… but you can move the parts of that package IN RELATION TO the CG… so you can “rotate” the bike forward by “rotating” the person backwards.
— Jay

Dear Lennard,
I agree in part that you need to put force on the pedals to accelerate the bike (F=ma). However, velocity in a moving body is a center of mass proposition. When you throw your bike you are keeping your velocity the same but putting your center of mass further back by putting your wheel forward. OK I even think after reading this I have proven nothing … What about this, an experiment with a motored road bike, constant speed through constant distance throwing and not throwing to see if there is in fact a “marginal” gain in the time over the distance.
— Dean

Dear Lennard,
About that bike throw: What the rider is really doing by pushing the bike forward is moving his center of gravity back relative to the bike. The center of gravity is what moves consistently up the road so moving this point back relative to the bike puts the front wheel a little further forward of the center of gravity giving the rider’s front wheel a few extra inches at the end of the throw. We are all familiar with this effect in reverse when riding a pace line and the rider in front of you stands up moving his center of gravity forward relative to the bike. You see this as a rapid movement of the leading bike back toward you a few inches. This rapid movement of the center of gravity thus contributes to winning tight bike races and occasional crashes for unwary paceline riders.
— Rodger

Dear Lennard,
Thanks for your great explanation of how photo finishes work. I found it very informative and easy to follow.

As you predicted many would, I am writing to say that I think you’ve made a mistake regarding bike throws. Perhaps you’ve realized this as it seems that this section of the post has been edited out since I read it yesterday. There was a physical impossibility presented in the post involving Sagan’s body moving backward without the bike moving forward (the only thing Sagan can push on to make himself go back is the bike, so the bike must go forward), but physics aren’t necessary to prove that it works. If you are coasting (this is easiest to hear at a slow pace) and keep the pedals stationary and then throw the bike forward (while leaving the wheels on the ground), you can hear the clicking of the cassette momentarily speed up. This means the rear wheel sped up and therefore that the bike is moving faster. If you do the opposite and pull yourself back forward, the cassette clicking slows, proving that the opposite of a bike throw is also true.
— Dave

Dear Lennard,
I was kind of shocked to read the nonsense (sorry!) you wrote about the bike-throw. It not only works in the minds of the people who practice it. It really works and the reason is simple physics. When you’re neither propelling or decelerating the bike you do not create any force that the tires have to transfer to the road. That’s right. So the whole system of rider and bike cannot accelerate just because you do a bike-throw. That’s a consequence of the conservation of momentum. But that does apply to the center of gravity of the system. And if the rider “throws” his bike forward he changes the mass distribution within that system. Both his body and the bike move further away from the COG of the system they’re forming. With the bike being the much lighter part of the system the rider benefits from his body’s inertia. In comparison to the same rider that does not throw his bike and continues to ride parallel to him as a thought experiment the body of the rider throwing his bike only moves slightly backwards but the bike moves considerably forward. Once the bike throw is executed and the rider’s arms are stretched to the max, that movement within the system stops and there is no further “acceleration” of the bike.

Were the bike much heavier than the rider then you were partially right. The bike throw would not be able to move the bike much forward. Only the rider’s body would move backward.

The same effect can be felt when riding closely behind a rider. When that rider goes out of the saddle and does that without taking care of the rider behind him he will push his bike backwards into the following rider’s front wheel. I’m certain you experimented that effect yourself several times. It’s the proof that the bike throw works.
— Horst