Accelerating into the Wind = Optimal strategy?

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I'll go through the math and consider the energy costs. But I see two reasons off hand why that might be the case:

1. From a math/physics standpoint, it's better to spend less time going slowly.

2. People are less efficient runners at higher speeds.

Here's some math:

Ok, well let's say you're running at X+/-Y mph (with or against the wind) with a Z mph tailwind or headwind. Say the force against you is proportional to a*v^2, where a is a constant and v is the relative velocity. The assumption here is that the only thing that matters are the fluid dynamics, that your body's efficiency or running economy isn't terribly important. This makes sense in the limit of small wind velocities. And let's say the track is just out and back (forget about the curves). Then the time it takes you to finish a lap is time = distance / velocity, or

T = d/(X+Y) + d/(X-Y)

T = 2dX/(X^2-Y^2) (1)

and remember that Y has to be less than X

The amount of work done is a*(X+Y-Z)^2*d+a*(X-Y+Z)^2*d = d*a*(2X^2+2Y^2+2Z^2-4XZ-4YZ)

W = 2da*(X^2+Y^2+Z^2-2XZ-2YZ) (2)

I guess I'll try to plug equation 2 into equation 1, first rearrange 2:

W = 2da*(X^2+Y^2+Z^2-2XZ-2YZ) (2)

W/2da-Y^2-Z^2+2Z(X+Y) = X^2

Plug in:

T = 2dX/(W/2da-Y^2-Z^2+2Z(X+Y)-Y^2)

T = 2dX/(W/2da-2*Y^2-Z^2+2Z(X+Y)) (3)

So for a given amount of work, what's the fastest time you can run? What we would want to know is: Should Y be greater than Z, equal to Z, or smaller than Z to minimize T?

We want to maxmize the denominator, which means we want to minimize the quantity

2Y^2+Z^2

this is minimal when Y is less than Z.

So from a fluid dynamics standpoint, you want to put some extra effort into fighting against the wind; you don't want it to slow you down by the entire wind velocity Z. And you also don't want to go faster against the wind than you would have ordinarily (this corresponds to switching the sign of Y, it would make the denominator smaller because of the last term in equation 3).

The optimal strategy is to run at a constant effort. Noakes peddles lab science without regard to its real-world merit. Any acceleration expends energy, and any deceleration wastes that expended energy. But what do I care? The more idiots accelerating into the wind down the backstretch, the fewer people will beat me!

This makes absolutely no sense, why would you ever decelerate when the wind is at ur back?

Re: all that math you did above, how do you know how much energy to expend in accelerating against the wind?

The obvious strategy is to draft behind another runner when against the wind and weave around the track or road so nobody can draft off of you when running with the wind.

Seriously, I ran my best roadrace this summer in moderately windy conditions. I was able to tuck behind a group for about 1.5 miles of a 4 mile race. It was run in a rectangle. The last 1.2 miles I had the wind at my back and ran a serious negative split. I am sure I ran faster than if there was no wind at all.

In another race (5k) a strong wind was going to be blowing against us from about 2 miles to 2.6 miles. It was 87° and very hot. I was in a group of 3 when we got to this point. I had thought about tucking in and letting them break the wind when it hit me that the wind would feel really good since it was so hot. I took off right when we made the turn and gapped them so much, they never came after me.

It really isn't about always doing one thing. You have to let the race and circumstances dictate whether you take off or tuck in.

uhhhh wrote:

This makes absolutely no sense, why would you ever decelerate when the wind is at ur back?

Re: all that math you did above, how do you know how much energy to expend in accelerating against the wind?

You speed up when the wind is at your back, but don't expend as much effort. You slow down when the wind is at your front, but you should expend more effort. According to my calculation, it should NOT be constant effort -- but of course I may have made a mistake. And when you take physiology into account, the actual difference in effort might be very small.

Does that make sense?

I don't know how much energy is optimal to expend because I don't know how to calculate how the energy your body requires to run translates to actual running speed, and I don't know the aerodynamic cross section of your body, or the speed you're running.

Oh, of course I agree with this.

Sorry, sometimes it's hard for me to explain a calculation to normal people.

[quote]easdjfsdf wrote:

Here's some math:

Ok, well let's say you're running at X+/-Y mph (with or against the wind) with a Z mph tailwind or headwind.

Why do you start your analysis with the assmption that an optimal result will only arise when the increase/decrease in speed ie Y is the same in both directions?

Why not let speed with the wind be p and against be q and rework the analysis and see if you draw any different conclusions?

[quote]easdjfsdf wrote:

Here's some math:

Ok, well let's say you're running at X+/-Y mph (with or against the wind) with a Z mph tailwind or headwind.

Why do you start your analysis with the assmption that an optimal result will only arise when the increase/decrease in speed ie Y is the same in both directions?

Why not let speed with the wind be p and against be q and rework the analysis and see if you draw any different conclusions?

best strategy is to reverse course and run with the wind. you'll run faster. hope this helps.

best strategy wrote:

best strategy is to reverse course and run with the wind. you'll run faster. hope this helps.

This is obviously not correct. Turning around and running backwards against the wind will put the wind at your back and you will run much faster. You can't always just run the other way.

I think "accelerate" and "decelerate" are used incorrectly here. Increased effort and decreased effort are what I think he was going for. This doesn't necessarily go against any rules for running your best/maintaining your pace, etc.

I ran a couple 5,000 intervals two days ago with very strong (and frustrating) wind on the track. I assure you that increased/decreased effort was quite natural into/with the wind.