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Name: Adam
Status: student
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Question:
Two men riding bikes in the Tour de France, one in front of the other, and often the lead man will talk about how he had to exert more effort to "pull" the man behind him. Gravitational attraction aside, does drafting behind someone create an additional force on the person in the lead? It makes it easier for the back man, but does it also make it harder for the front man? What would the force diagrams look like for each rider?



Replies:
Adam

I do not think a force diagram is necessary. Besides it will be really complicated to represent all of the forces. Let us try to do this by a thought experiment.

Both riders are independent bodies passing through a fluid, one behind (in the wake to be nautical) the other. I would like to move this to a comparison of two ships steaming at sea one behind the other to slow the dynamics down for easier understanding. We will assume both ships have the same hull shape, displacement, power plant, etc. etc. We will look at this as an inventory list of the forces.

The interaction of the forces on both bodies will depend on how close they are to each other.

Let us do an inventory of forces in two cases: 1st Case: When the ships are separated at a far distance so the forces from one ship does not effect the other ship, with one traveling in the wake of the other: The 1st ship will have a bow wave that builds as it pushes the water in front of it that cannot easily escape around the side of the ship. The 1st ship will also experience the drag caused by the turbulence of the water as it slips along its sides. The 2nd ship will experience the bow wave but it will have an additional turbulence force caused in the water by the 1st ship. The effect of the turbulence may be to reduce the force of the bow wave. The 2nd ship will also experience the drag of the water slipping around it which might be a little more than the first ship because of the additional turbulence from the lead ship. So in this case, it will take more energy for the 2nd ship to keep up with the 1st ship.

2nd Case: When traveling closely to each other such that their forces interact: The 1st ship will have its bow wave and the slipping water turbulence as before The 1st ship may also experience a push from the reduced 2nd ships bow wave. The 2nd ship will experience its bow wave with the additional turbulence component as before, but the turbulence forces will be stronger because it is following more closely to the 1st ship. The effect of the turbulence may be to reduce the force of the bow wave. The 2nd ship will also experience the drag of the water slipping around it which again will be more intense because of the turbulence of the lead ship.

Now we need to talk about the magnitude of the forces. I am sorry but I do not have numbers to show the magnitude of the forces (lbs-force), but to try to answer the questions:
does drafting behind someone create an additional force on the person in the lead? This does not appear to be the case to me.

It makes it easier for the back man, because of the turbulence of the 1st ship reducing the bow wave of the 2nd ship, but does it also make it harder for the front man? This does not appear to be the case from this analysis to me.

But the real details are the magnitudes of the forces.

Sincere regards,

Mike Stewart


Obviously, the bigger impact is to the second rider. The second rider can stay in the slipstream of the first, thus experiencing significantly less wind drag than the first rider.

I am not sure if the second rider would exert a force on the first person. The sense of 'pulling them along' only happens when the other rider is not taking his/her fair share of the wind (taking equal time in front). It is a sharing-the-workload problem, not a physics problem. Speaking from my own personal experience riding, I do not feel the second person behind me at all. I can hear them, but not feel them.

I suppose it is possible that the second rider can disrupt airflow around the first rider and thereby increase drag, but that would be very much dependent on where the rider is, the angle of the wind, etc. etc. I think the size and shape of riders and bicycles might make that situation rare or impossible. The best I can do is speculate on how/when/if it is significant, I would say it is negligible - kind of like gravitational attraction is very negligible. (technically if the two bikers are moving at the same velocity, all else being equal, the gravitational attraction would not cause a net force opposing their mutual motion).

What would the force diagram look like? It depends on how accurate you would want to be. To be rigorous, the diagram would be enormously complicated. There are many, many different forces applied to each person and each bike because each location is experiencing a different aerodynamic force, and you have lots of small corrections being applied by the rider in multiple locations (pedals, handlebars, etc.). Neither the bike nor the person is rigid. If you aren't interested in taking all those variables into consideration, then I would also ignore any impact to the first rider caused by the second rider.

Hope this helps,

Burr Zimmerman



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