MadSci Network: Physics

Re: Would we run faster if the wind helped us. It can deley us if itīs coming a

Date: Tue Jun 19 12:08:16 2001
Posted By: Tom Cull, Staff, Clinical Sciences MR Division, Marconi Medical Systems
Area of science: Physics
ID: 992008230.Ph


The simple answer is yes: wind can either help or hinder a runner at any distance. When the wind is from behind (tailwind) it will help the runner, and when the wind is from the front (headwind) it will hinder the runner. Think of it as vector addition.

The olympic committee (IOC) and other track and field governing bodies will not allow records to be achieved with any wind above a certain speed for some events. There thinking is that the wind could aid the athletes in an unfair way when compared to athletes performing the same event in still wind.

The effect is just about cancelled from running in circles or ovals. If the force from wind resistance is proportional to the relative velocity (the case of low Reynolds number), then the effect would be canceled exactly if the runner runs the same speed all the way around and the wind also stays constant. The way to picture this is imaging that parts on opposite sides of the track cancel each other out. But, usually force due to air resistance is proportional to speed squared for interactions with air for everyday speeds (10's of miles per hour) and objects of macroscopic size.

John Link, another physics moderator and I discussed this question. I credit the following to him.

Assume the force on a runner is proportional to the square of the relative air velocity against the runner (this is a close enough approximation at low speeds). If the runner's speed is r and the wind speed is w, then the force while the runner is going with the wind is proportional to (r-w)^2 while the force against the wind is proportional to (r+w)^2. If the wind speed is zero then the force is proportional to r^2. On a closed track which is symmetrical we can assume that the distances travelled against and with the wind are the same, so the work done around the track is (r-w)^2 * d + (r+w)^2 * d, where d is half the distance around the track, and I have dropped any constants of proportionality. The question is "Is the total work done around the track the same regardless of the wind speed?", or
"Is (r-w)^2 * d + (r+w)^2 * d = 2 * r^2 * d ??"
Dividing through by d and doing the algebra we get
2 * r^2 + 2 * w^2 = 2 * r^2
which shows that the answer to the question is "No!" The extra work done when there is a wind is proportional to 2 * w^2.

[end of section provided by John Link]

The effect of wind is more pronounced when traveling in mostly one direction. I think it pretty difficult to measure the effect on running races, but the effect of tailwind, headwind, or even crosswind is much more exaggerated for airplanes. In the USA, the prodominant wind at 5000 - 12000 meters is west to east. It is pretty strong something on the order of 55 km/hr (35 miles/hr). The airplane is traveling relative to the air. A west to east moving plane is getting a boost of 55 km/hr for free. Conversely a east to west plane is getting slowed by 55 km/hr. A crosswind will be beneficial/harmful depending on which way the plane is trying to go relative to the crosswind.

I fly Cleveland to St. Louis pretty frequently. These cities are 901 km (560 miles) apart by car and maybe 735 km (460 miles) apart by direct path. The flight from St. Louis to Cleveland typically takes about 80 minutes and the flight from Cleveland to St. Louis typically takes about 110 minutes (30 minute difference), this is the announced times anyway.

Using the numbers here in the equation:

Time = distance /speed

I get:

STL->CLE : 735 km/(Speed + 55) km/hr = 1.33 hr

CLE->STL : 735 km/(Speed - 55) km/hr = 1.83 hr

I get a Speed of 501 km/hr STL->CLE and

Speed of 456 Km/hr CLE->STL.

These are average speeds from my estimations, so they seem to agree pretty well. The planes average speed is in the neighborhood of 450 to 500 km/hr (280 to 312 mph). I assumed that the planes are flying the same distance. They don't. Anyway, you can see the effects of headwind/tailwind. Remember the speed of sounds is around 340 m/s.

Maybe you could try this with a runner. Guess the wind and runner's speed. Plug in a distance and see what the time difference would be.


Tom "Carry On Baggage" Cull

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