Tailwind and speed difference

Fday said:

What is a problem for me here is the answer has to be the same regardless of the frame of reference it is solved from. If we agree that the energy loss here is entirely from the wind resistance then the energy loss going to heat is the same for the rider going 1 mph into a 49 mph headwind and the rider going 50 mph into zero wind. Then the rider must simply put in the power lost to maintain speed. I am having trouble immediatly understanding what the speed of the massless wheel has to do with anything. But, as I said above, I will cogitate on this awhile and see if I can understand your viewpoint or find the flaw in it.

OK, maybe I see your hangup here. Agree that the airstream is losing energy at the same rate in both cases, but that doesn't dictate that the riders have identical power output. A moving airstream loses velocity (and energy) whenever it encounters obstructions, but nothing says the rider must match or restore that energy.

Consider a slightly more extreme scenerio where the slow bike isn't moving at all but just holding a track-stand, like a tree, in a 50 mph wind. How much power is the rider (or tree) putting out then? It would be zero, because the bike pedals (and bike) isn't moving, so no work is being done. The rider is exerting static force, ie, pressing on the forward pedal to hold the bike in the wind, essentially equal to that required to go 50 mph on a calm day, but there is no movement (velocity) and no work as a result. It's just like pushing your bike into the garage wall; no power is exerted via static pressure on the pedals no matter how hard you push.

Energy is being lost by the moving airstream, but the rider sitting in the gale at 0 mph isn't doing any work to replace it; he just let's the moving air go by, letting it compress and heat at the front and then expand/cool in back of him. No law says he has to restore or replace the energy lost by the airstream.

The speed of the rear wheel is important since that determines the speed of the bike, which is half of the power equation. Again, force x velocity is the definition of power. You can use the pedal forces and velocity to compute the rider's power output, or use the rear wheel force/velocity. Both results will be identical as the ratio of force/velocity is established by the relative lengths of the crank arm and wheel radius as well as the ratio of chainring-to-cog.

dhk2 said:

OK, maybe I see your hangup here. Agree that the airstream is losing energy at the same rate in both cases, but that doesn't dictate that the riders have identical power output. A moving airstream loses velocity (and energy) whenever it encounters obstructions, but nothing says the rider must match or restore that energy.

Consider a slightly more extreme scenerio where the slow bike isn't moving at all but just holding a track-stand, like a tree, in a 50 mph wind. How much power is the rider (or tree) putting out then? It would be zero, because the bike pedals (and bike) isn't moving, so no work is being done. The rider is exerting static force, ie, pressing on the forward pedal to hold the bike in the wind, essentially equal to that required to go 50 mph on a calm day, but there is no movement (velocity) and no work as a result. It's just like pushing your bike into the garage wall; no power is exerted via static pressure on the pedals no matter how hard you push.

Energy is being lost by the moving airstream, but the rider sitting in the gale at 0 mph isn't doing any work to replace it; he just let's the moving air go by, letting it compress and heat at the front and then expand/cool in back of him. No law says he has to restore or replace the energy lost by the airstream.

The speed of the rear wheel is important since that determines the speed of the bike, which is half of the power equation. Again, force x velocity is the definition of power. You can use the pedal forces and velocity to compute the rider's power output, or use the rear wheel force/velocity. Both results will be identical as the ratio of force/velocity is established by the relative lengths of the crank arm and wheel radius as well as the ratio of chainring-to-cog.

Got it. Thanks.

rmur17 said:

honestly, it is just high-school physics. Maybe pre-school physics these days!

Yes and that's the worst part of it, I already learned this stuff years ago. Now when I finally seems to get interrested in it, the knowledge is gone. I'm sure somebody told me that "you are going to need that someday", shame on me :-)

koger said:

Yes and that's the worst part of it, I already learned this stuff years ago. Now when I finally seems to get interrested in it, the knowledge is gone. I'm sure somebody told me that "you are going to need that someday", shame on me :-)

okay. since you started the thread, are you comfortable now with the original answer that "no. The increase in speed is not directly proportional to tailwind speed"?

dhk2 said:

OK, maybe I see your hangup here. Agree that the airstream is losing energy at the same rate in both cases, but that doesn't dictate that the riders have identical power output. A moving airstream loses velocity (and energy) whenever it encounters obstructions, but nothing says the rider must match or restore that energy.

Or to put it another way, if the spot at the bottom of the wheel (or point of propulsion, let's say) is allowed to move with the air, then the wind *does* do work by moving the rider. Whereas, if the tire is fixed from sliding then the wind is simply another force that either aids or opposes the rider.

koger said:

Yes and that's the worst part of it, I already learned this stuff years ago. Now when I finally seems to get interrested in it, the knowledge is gone. I'm sure somebody told me that "you are going to need that someday", shame on me :-)

I seem to be having a similar problem. Use it or lose it as they say. :-)

frenchyge said:

Or to put it another way, if the spot at the bottom of the wheel (or point of propulsion, let's say) is allowed to move with the air, then the wind *does* do work by moving the rider. Whereas, if the tire is fixed from sliding then the wind is simply another force that either aids or opposes the rider.

I think I get it now. What is bothering me now is it would seem that wind would have a bigger effect on time-trial results than it seemingly has. I tried going to analytic cycling dot com to run some projected speed effects on an out and back course to see how bad it might really be and couldn't find a page that took into account wind effects.

It may be that we adjust to different conditions to minimize the effects of the wind on performance. For instance, perhaps we try to maximize aerodynamics when going into the wind even at the expense of a lower power while sitting up to maximize power with a tail-wind when aerodynamics are less important. The people who are winning races are probably better at this than those of us at the back, where the "real" effects of wind may be more obvious. Yet, the times we tend to see are only those of the winners so wind seems to be less of a factor than it should be if we couldn't adapt.

Fday said:

I think I get it now. What is bothering me now is it would seem that wind would have a bigger effect on time-trial results than it seemingly has. I tried going to analytic cycling dot com to run some projected speed effects on an out and back course to see how bad it might really be and couldn't find a page that took into account wind effects.

It may be that we adjust to different conditions to minimize the effects of the wind on performance. For instance, perhaps we try to maximize aerodynamics when going into the wind even at the expense of a lower power while sitting up to maximize power with a tail-wind when aerodynamics are less important. The people who are winning races are probably better at this than those of us at the back, where the "real" effects of wind may be more obvious. Yet, the times we tend to see are only those of the winners so wind seems to be less of a factor than it should be if we couldn't adapt.

1. Check out the "Wind on Rider" dynamic model to include wind effects - just take your time with the input form(s) etc. I've had my own custom spreadsheet for years for this sort of thing but it's not suited to multi-segment (grade, bearing) courses and full blown diff. eq. analysis like the ACC model.
   
2. Wind speed at 1m ~ centre of bike resistance level is only about 0.7 of that at the commonly reported 10m elevation. That's for open terrain. Add hedgerows, corn/wheat fields, trees, buildings and the like and a factor of 0.5 or less may be applicable for sheltered areas. IOW, officially reported wind-speed is seldom experienced on the road by the cyclist.
   
3. Pacing is another consideration. Within reasonable bounds set by experience and one's personal power-duration curve (and the length of the head/tail wind segments!), experienced riders tend to apply a bit more power in head & head-cross winds and a bit less power in tail & tail-cross winds. Not a lot of delta power but enough differential to help close the gap over an isopower effort.
   
4. I agree - that at least on road bikes - folks tend to hunker down and tuck better into headwinds and sit up a bit in tailwind conditions. I know I certainly do. On the TT bike ... well one can only tuck so much.
   

rmur17 said:

1. Check out the "Wind on Rider" dynamic model to include wind effects - just take your time with the input form(s) etc. I've had my own custom spreadsheet for years for this sort of thing but it's not suited to multi-segment (grade, bearing) courses and full blown diff. eq. analysis like the ACC model.
   
2. Wind speed at 1m ~ centre of bike resistance level is only about 0.7 of that at the commonly reported 10m elevation. That's for open terrain. Add hedgerows, corn/wheat fields, trees, buildings and the like and a factor of 0.5 or less may be applicable for sheltered areas. IOW, officially reported wind-speed is seldom experienced on the road by the cyclist.
   
3. Pacing is another consideration. Within reasonable bounds set by experience and one's personal power-duration curve (and the length of the head/tail wind segments!), experienced riders tend to apply a bit more power in head & head-cross winds and a bit less power in tail & tail-cross winds. Not a lot of delta power but enough differential to help close the gap over an isopower effort.
   
4. I agree to - that at least on road bikes - folks tend to hunker down and tuck better into headwinds and sit up a bit in tailwind conditions. I know I certainly do. On the TT bike ... well one can only tuck so much.
   

Thanks, I agree with all you say. One other aspect of wind though that people don't talk about is what it does to the riders ability to ride a straight line. Weaving down the road doesn't affect overall speed much (as I have learned in the turning discussions) but it does affect how far the rider has to ride to finish the course. That would slow overall apparent speed also but I expect those who are winning races are much better at compensating for this potential problem than lesser riders.

Fday said:

I seem to be having a similar problem. Use it or lose it as they say. :-)

Glad the explanations worked for you. Now I'm curious to check out that ACC model for some of the detailed calculations on wind effects.

dhk2 said:

Glad the explanations worked for you. Now I'm curious to check out that ACC model for some of the detailed calculations on wind effects.

I went there and got this data for a 4k flat course using his standard inputs, 250 watts.

speed in zero wind, 5 m/s head wind, and 5 m/s tail wind respectively is:

10.72m/s, 7.88m/s, 13.88m/s

so the headwind slows the rider 2.83 m/s and the tail wind speeds him up 3.16 m/s

On a 4km out and back TT this wind would supposedly slow the rider about 30 seconds compared to calm conditions.

Fday said:

I went there and got this data for a 4k flat course using his standard inputs, 250 watts.

speed in zero wind, 5 m/s head wind, and 5 m/s tail wind respectively is:

10.72m/s, 7.88m/s, 13.88m/s

so the headwind slows the rider 2.83 m/s and the tail wind speeds him up 3.16 m/s

On a 4km out and back TT this wind would supposedly slow the rider about 30 seconds compared to calm conditions.

remember the model is dynamic so the time to get up to ~steady-state at 250W power is included there. I would suspect if you're using distance/duratioin or avg. speed that longer legs would allow the true differential to show up somewhat higher than that (-2.9 m/s and + 3.4 m/s) ... but in any case you can play around with that.

rmur17 said:

remember the model is dynamic so the time to get up to ~steady-state at 250W power is included there. I would suspect if you're using distance/duratioin or avg. speed that longer legs would allow the true differential to show up somewhat higher than that (-2.9 m/s and + 3.4 m/s) ... but in any case you can play around with that.

Well, I put in a starting speed close to the average speed, trying to account for that, but even if I didn't do that it still wouldn't be a bad number for such a race as most people almost come to a stop at those turn arounds so there is one acceleration into the wind and one with.

[quote="Fday"]If we agree that the energy loss here is entirely from the wind resistance then the energy loss going to heat is the same for the rider going 1 mph into a 49 mph headwind and the rider going 50 mph into zero wind. QUOTE]

I know that I cannot ride at 50mph on a windless day.

I also know that I can ride at slightly more than 1mph in a 50+mph headwind...

...and no, I'm not going to say that it was riding uphill to school, in the snow, on cobbled/dirt roads (both ways) when I was a lad. :p

[quote="swampy1970"]

Fday said:

If we agree that the energy loss here is entirely from the wind resistance then the energy loss going to heat is the same for the rider going 1 mph into a 49 mph headwind and the rider going 50 mph into zero wind. QUOTE]

I know that I cannot ride at 50mph on a windless day.

I also know that I can ride at slightly more than 1mph in a 50+mph headwind...

...and no, I'm not going to say that it was riding uphill to school, in the snow, on cobbled/dirt roads (both ways) when I was a lad. :p

Fday said:

Well, I put in a starting speed close to the average speed, trying to account for that, but even if I didn't do that it still wouldn't be a bad number for such a race as most people almost come to a stop at those turn arounds so there is one acceleration into the wind and one with.

I did make some other changes to see if it might be possible for a thinking person to improve the situation.

decreasing the frontal area from 0.5 to 0.4 and decreasing the power from 250 to 240 to simulate what one might do into the wind and then increasing the frontal area to 0.6 and increasing the power to 270 (to average about 250 watts for the ride) resulted in an approximate 5 second improvement over the 4 k out and back course. I am sure one could do better than that as those were just guesses as to what is possible.

So, it would appear that we can minimize the damage of wind, just as we can do thing to minimize the impact of hills on a rolling course.

I didn't read all 6 pages but was wondering if this was mentioned.

Did any of you stop think that perhaps there is never a complete sustained unidirectional tail/wind? Even when you swear you just a sustained headwind, it is garranteed that it wasn't a constant speed, in a constant direction.

This would account for the reason that a "4m/s tailwind" won't make you 4m/s faster on flat or negative gradients. Same logic for headwinds.

Wind is very much so not uniform, constantly shifting and changing velocities, even when it appears uniform. Even cycling through a long wind tunnel wouldn't have completely uniform wind.

Also, I believe rolling resistence and mechanical drag should have no impact on the equation, since they are essentially equal at all speeds (with a few exceptions with gear crossovers).

velomanct said:

Also, I believe rolling resistence and mechanical drag should have no impact on the equation, since they are essentially equal at all speeds (with a few exceptions with gear crossovers).

You believe incorrectly though. Otherwise riding faster on rollers would not require more power.

Rolling resistance essentially increases linearly with speed (relative to road surface). Resistance of bearings is nearly linear with speed.

I thought about it, and it makes sense. At higher speeds, the tire is being compressed more often and at a faster rate than at lower speeds.

velomanct said:

I thought about it, and it makes sense. At higher speeds, the tire is being compressed more often and at a faster rate than at lower speeds.

You're both right in a way, depending on whether you're comparing force or power required. In the equations I've seen, rolling resistance (force) is usually considered as a constant factor x weight, independent of speed. But the power needed to "overcome" rolling resistance is linear with speed, because power is always force x velocity.

EG, at a typical coefficient of rolling resistance (CRR) of .006, and a total weight (bike plus rider) of 90 kg, drag force due to tires would be .006 x 90 x 9.8 = 5.3 newtons Since power is just force x velocity, at a speed of say 10 m/sec, power needed for RR is 53 n-m/sec, or 53 watts. Halving the speed would of course halve the watts.

If you think about gearing, it's easy to see why the power needed to overcome a constant drag doubles when the speed doubles. Even though the force needed at the rear wheel doesn't change, we have to either pedal twice as fast at the same force, or use "twice" the gear at the same cadence, meaning we have to push twice as hard on the pedals. Sadly, either way, power output of the rider has to double 😉