**Discussion on Facebook**

Interesting that the permanent headwind which blows in your face whatever direction you cycle still operates in the hot weather. Clearly its intelligence does not yet equal its malice and agility.

*I find that crosswinds are treacherous because: a) they have a similar drag effect to a headwind and b) they have a vastly greater angular range than just head on. Unfortunately that pretty much encapsulates any wind direction. Get out early if you can, before the thermals kick in.*

*Have you seen the study that shows the wind is always against you? It’s summarized in New Scientist here and the original paper is here.*

**Further analysis**

OK so now we’ve got onto the purely hypothetical case where you cycle from A to B and then back from B to A and the wind continues to blow from B to A as though nothing had happened. Even so, the analysis in the references above looks rather complicated.

Let’s ignore rolling resistance and consider a cyclist who wants to cycle on the flat from A to B and back again. He cycles with a power P which gives a limiting velocity V **relative to the air**. (In the absence of rolling resistance we ignore interactions with the ground.)

So let’s say as an example B is 10 km from A and V is 20 km/h. In the absence of any wind it takes 0.5 hours to go from A to B, another 0.5 hours to go from B to A, for a total of 1 hour or 60*60 =3600 seconds. Then with P measured in joules/second, the energy expended will be 3600*P J.

Now a wind of 10 km/h blows from B to A. The cyclist’s speed **relative to the ground** is then 10 km/h on the outward leg and 30 km/h on the return leg. So the time taken is 60+20 = 80 minutes or 4800 seconds and the energy expended is 4800*P J.

The cyclist has spent **more time** and expended **more energy** even with a completely unchanging wind.

This analysis clearly applies to any situation where there is a component of the wind along the cyclist’s direction of motion, even if it doesn’t turn round on you…

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Tags: bicycle, headwind, kinematics

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