Yes, of course. I was acrually thinking it would depend on the relative velocities, and there’d be a crossover point…and then I thought I’d need to write it down and then I couldn’t be bothered anymore. 
I think bestbikesplit or mywindsock might be able to tell you what is better?
Doesn’t it sorta depend on whether you’re training or racing, and if racing, what kind? I remember a pro TT guy (not Dowsett) saying you won if you covered the distance the quickest – not if you put out the most or smoothest power. I dunno. Don’t race anything but dogs.
This can, and had been modelled - best bike split, my windsock, and the opposite to what you suggest is faster.
I don’t race but I always pedal downhill because FAST IS FUN.
I’m never going to get any KOMs going up hills but I always go as fast as I can on the downs 
Could you link to this?
Other way around amigo.
Would be grateful for explanation of why, that discusses cost of higher aero drag losses. Definitely interested in being shown the light here.
That’s pretty broad. I’m not familiar with this site. Could you link to a specific modeling example that indicates higher power into headwind is the ideal. I can’t wrap my head around it because of the exponentially increasing drag energy losses. I would love to be corrected. Fastest way to be right is understand when wrong, so I’m pretty keen to do an about-face here.
Interesting point, but I think this misses an important distinction between the downhill and headwind cases. As a rider, you care about your speed relative to the ground, while aerodynamically what matters is your speed relative to the air.
That means, for example, that when you’re coasting downhill at 40 km/h, the extra 300 W you would have to put out to hit 55 km/h aren’t really worth it. But when you’re facing a 40 km/h headwind, those 300 W are the difference between sitting still on the tarmac and crawling forwards at 15 km/h.
So really, you can’t make the call unless you know the wind speed. What you really want to do is look at the fractional change in speed.
Of course, none of this considers the effect this extra speed will have on your finishing time (which is ultimately what matters). That depends on the course itself, and I don’t think you can really draw general conclusions.
By the way, for interest, I plugged some numbers in and got the following plot, which shows the gain in speed you get for putting out an extra 300 W, as a function of aerodynamic speed (speed relative to the air). Note that it does not depend on how much power you were already putting out.
The numbers I put in are very rough guesses, and I’m not accounting for rolling resistance and other factors. This is just intended to show the relationship between speed gain and wind speed.
P.S., Note that the power from aerodynamic drag scales with the cube of the speed, not the square. The drag force scales with square of the speed, but power is the time derivative of force × distance, and you end up with a cubic scaling.
Sadly I can’t do a good job of explaining it, I’d figured it out racing on the club 10s before modelling TTs was a thing.
But I googled “why is it faster to ride hard into a headwind” and found this article https://www.bikeradar.com/features/why-its-faster-to-ride-hard-into-a-headwind-than-with-a-tailwind/
Don’t worry about aero drag losses, because that isn’t the point of a TT, you need to consider time to cover distance.
In the comments there is a worked example:
Actually, you missed a few steps to calculate that it’s faster to ride hard into the headwind.
Take 225W, 12mph(headwind) gives 13.85mph
225W, -12mph(tailwind) gives 28.71mphIf we want to average 225W on a 40K out and back, we need to equalize the time spent at 200W with the time spent at 250W.
So, as follows:
Ride even at 225W both ways
Out @ 225W for 12.4miles / 13.85mph = 0.895hr
In @ 225W for 12.4miles / 28.71mph = 0.432hr
Total - 1.327hr (1:19:37.2)Ride hard into headwind
Out @ 250W for 9.628miles / 14.61mph = 0.659hr
Out @ 200W for 2.772miles / 13.03mph = 0.213hr
In @ 200W for 12.4miles / 27.79mph = 0.446hr
Total = 1.318hr (1:19:04.8)Ride hard with tailwind
Out @ 200W for 8.726miles / 13.03mph = 0.670hr
Out @ 250W for 3.674miles / 14.61mph = 0.252hr
In @ 250W for 12.4miles / 29.55mph = 0.420hr
Total = 1.342hr (1:20:31.2)So, riding hard into the headwind is faster than the baseline by 32.4seconds and riding hard into the tailwind is slower than the baseline by 54seconds
Thank you for the links. I read the article and all comments. I stand corrected.
This pure engineering analysis is informative. The comment below it in the article comments is important:
the optimisation problem that involves both the physics and physiological constraints.
The magnitude one should increase power into a headwind is probably 10x smaller than the magnitude of increased power that might be valuable when riding uphill. Reasons: duration, and time gain per watt, and physiological cost.
The benefits of pushing power when slow due to uphill gradient is vastly larger than benefit that could be had by pushing into headwind. So much so that they almost shouldn’t be in the same sentence.
I may have been mistaken in inferring that the recommendation was to make the same or similar power increase, based mostly on the magnitude of speed reduction caused by either headwind or uphill, which is definitely an unwise proposition.
Nonetheless, I was wrong. I appreciate being corrected! Thank you, @jnye131.
Nice to see the math…I assumed this was the case just on my own experience. There just seemed more to be gained by riding harder into a headwind just due to decreasing the time you are slower.
Maybe not so much, because you’re also racing against people that don’t pace a race perfectly, say by easing off into a head wind. So good to gain time on them there too.
So especially when riding a TT close to FTP/LT2 it will be a balancing act depending on your physiology and if overall your condition and resulting time suffers more when riding unevenly (NP to AvgP higher) than you gain by riding stronger into headwind.
In this scenario I guess it’s just a couple of watts difference and depends how fast you recover from work above threshold. Seems like it’s ~threshold into headwind and just below threshold with tailwind. (The cited example makes a point for the overall time calculation but at the same time is a bit confusing or misleading as with ~80min 225watt (maybe just below FTP) you can’t just go 250 half the way…it will cook you.)
As duration grows it seems that NP to AvgP ratio could grow more.
Generally it’s a soft pedal. However, if I’m testing then I will keep working as best I can. Even if I am not spun out, I find it more challenging to keep the power up while going downhill – I’m thinking more of a head game. Since I’m going fast I think I must be putting out the watts but when I look it is rarely the case.
I always try to pedal on downhills…even if I’m not doing power, it’s just for keep the blood on movement.
I hate the feeling of rock or hard legs just after a descent with no pedaling…
Also helps clear lactate you’ve built up on the ascent.
