# "The 33"-Road Bike Racing - Help from the physicists!!

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View Full Version : Help from the physicists!!

DrWJODonnell
04-03-08, 06:38 PM
Ok, I have taken physics, but that does not mean I know anything. I figured you engineering types with your TI-88 (or whatever calculus calculators are out there now) could explain this to me. I might be right, i might be wrong. What I want to know is the truth.

My coach has asked me for this saturday's TT to go harder into the headwind even if it means positive splitting and not doing as well wattage-wise in the tailwind section.

My feeling is that negative splitting is better from a physiological standpoint with the exception of hills. As such, regardless of the wind, I am thinking to go out at a determined wattage and come back at a slightly higher determined wattage.

I do understand that of course a headwind will make me slower and thus if I was splitting according to distance (versus time) I would have a longer 'out' and shorter 'back'. But if I split according to time, this seems to me to be irrelevant.

With hills, I understand zooming on the uphills a bit hot and "recovering" on the downhills. I guess I assumed this was due to gravity causing most of the resistance and taking aerodynamics out of the equation on uphills, yet aerodynamics plays a very important role on the downhills. With a headwind/tailwind, won't aerodynamics play an equal role both ways? In other words, even though you may go 5 mph faster with a tail wind, you still have the same equilibrium point(frontal resistance), as most of the wattage you use (and thus the max speed you can attain) is sucked up by wind resistance. Am I wrong? Should I consider a headwind/tailwind to be the same as an uphill/downhill situation?

Thanks for any help.

kukusz
04-03-08, 06:42 PM
When I was reading the last TT pacing discussion I was wondering the same thing. Enthalpic or Agnelle will know.

edit: some of the studies cited in this blog entry might help, trying to find the originals http://www2.trainingbible.com/joesblog/2008/03/more-on-pacing.html

Ok, trying to work it out...

Power to Overcome Wind Resistance = ˝*(air_density)*CdA*V_wind^2*V_road.

04-03-08, 06:48 PM
Can't you shut the F up and just come out and crush everyone's soul?

ElJamoquio
04-03-08, 07:08 PM
As most of your resistance is from the aerodynamics, and rolling resistance is roughly linear with speed, you gain a smaller amount from attempting to 'cheat' the wind - going harder into the headwind - when compared to cheating hills.

DrWJODonnell
04-03-08, 07:11 PM

VosBike
04-03-08, 07:13 PM
The same effect as on hills will exist, but to a much smaller degree.

So yes, you should push slightly higher wattage into the wind and slightly lower wattage with a tailwind. However, short of hurricane force winds the effect will pale in comparison with the amount of time to be saved by going over threshold on uphills.

wanders
04-03-08, 07:14 PM
"Dr O'Donnell's CdA just went negative!"

http://img207.imageshack.us/img207/9759/backtothefuturefc2.jpg

CastIron
04-03-08, 07:15 PM
*not a physics geek by a drunken longshot* but, if aerodynamic drag increases exponentially with airspeed, then I'm thinking the gains as tailwind have a much shallower curve.

Frankly, I'd love to some hopped up graph on the concept. Where's our local mad scientist WaterRockets?

04-03-08, 07:21 PM

At least it will be pouring rain Sat AM. So you have that going for you.

Learn to look at the Sunny Side. Oh wait, I guess that means there is no Sunny Side. Which would typically segway into me telling you that you are F'd, but this is a bicycle race. That means your opponents are F'd.

I am not one of them. I will cheer you on with the other old farts.

ElJamoquio
04-03-08, 07:21 PM

Cough. I don't think you're going to see a 20 MPH headwind, for reasons I've argued in the past.

I was trying a 6 MPH headwind and saw no (real) advantage going from a 350 watts there and back versus 370 out and 320 back (normalized power for those assumptions = 350). You have a really good CdA. I'll try again 10 MPH headwind.

mollusk
04-03-08, 07:26 PM
I'm an engineer, but I don't think this is really an engineering problem. It isn't all charts and graphs and watts/kg. A huge amount of this just "will" and pain management. There is a deeper thing going on deep inside that science and engineering doesn't understand.

Lot's of guys have recently posted that they put out a lot more watts going uphill than they ever could on flat ground. Do you really think that there is some sort of inclinometer inside those guys that turns the "governor" off when going up hill? I don't think so. I believe that they associate hill climbing with pain and have learned to cope with the pain because they expect it, but haven't learned how to cope with the pain when riding on flat ground where it is so easy to turn the pain off by just riding a bit slower.

For me headwinds are like hills. I expect pain when riding into them and somehow I can summon up extra watts when riding into them. Every month or so I "test" myself over 40 K. My best times are always when I start into a headwind and then return with a tailwind. The first half of the ride is always pure Hell. The return is just hell (lower case). For some reason I can put out a lot more watts into a headwind then I can with a calm wind or with a tailwind. Perhaps I have learned to embrace that kind of pain and make it my ally. Maybe your coach has sensed that you are one of those guys that can deal with the pain better when there is a headwind and is using it to get the optimal time out of you.

Of course this could all be BS. There is no science here.

04-03-08, 07:26 PM
The last time the Sandy Hook Seashore had a 6mph headwind was before JFK's assassination. Yes, you can safely assume a 20mph headwind in that location. This is the Atlantic Ocean beach, not some Great Lakes Wussyfest. Dr. W. will go 22mph into it and 34mph coming back. Subtract 3-4mph from those numbers to get my speeds.

04-03-08, 07:27 PM
Of course this could all be BS. There is no science here.

You think?

ElJamoquio
04-03-08, 07:29 PM
10 MPH show same - no advantage.

Let's put it this way - against the headwind, you're actually going faster, aerodynamically speaking, than with a tailwind. So, to go faster, you have to fight the V^3 termed - which is counter-productive.

DrWJODonnell
04-03-08, 07:29 PM
You are right. they changed the forecast in the last day. More rain, less wind. Now they say 13 mph with 22mph gusts. that is down from yesterday when they said 24mph wind and 38 gusts.

Oh, did I mention this is essentially at sea level, exposed in the atlantic ocean? Yes, it gets windy.

ElJamoquio
04-03-08, 07:30 PM
Do you really think that there is some sort of inclinometer inside those guys that turns the "governor" off when going up hill?

Part of it is psychological, part of it is physiological. I see a ~5-10% drop in power from the hoods to the aero-bar.

mollusk
04-03-08, 07:30 PM
You think?

Yeah. Not a whole lot of Nobel Laureates are winning TdF stages, though.

04-03-08, 07:34 PM
You are right. they changed the forecast in the last day. More rain, less wind. Now they say 13 mph with 22mph gusts. that is down from yesterday when they said 24mph wind and 38 gusts.

Oh, did I mention this is essentially at sea level, exposed in the atlantic ocean? Yes, it gets windy.

Understatement of the Month.

Racer Ex
04-03-08, 07:35 PM
I think the question needs a constant to really be hashed out, which would be the actual wind speed. If you consider the wind speed to be a factor in the actual measure of the course in distance, the higher the wind, the longer in effective distance the headwind leg is, so if you apply more watts there, you should have a faster overall time, because you're applying it for a longer period to the turn around.

Say 20 minutes out and 10 minutes in, your net applied wattage, assuming your CDA is the same, would be greater hammering the front leg than the back.

Plus if it's howling, from a pure "dude on the bike" POV, you're going to be spun out coming back and I find it much harder to stay on top of the gear.

ElJamoquio
04-03-08, 07:37 PM
Say 20 minutes out and 10 minutes in, your net applied wattage, assuming your CDA is the same, would be greater hammering the front leg than the back.

I took that into account when calculating an equivalent normalized power (370 out, 320 back, instead of 350).

Is there any sort of ground cover/trees/buildings at this event... or is it right on the oceanfront/etc?

ElJamoquio
04-03-08, 07:38 PM
With a headwind/tailwind, won't aerodynamics play an equal role both ways?

Roughly. For the intent at hand, the answer is yes.

DrWJODonnell
04-03-08, 07:44 PM

Think maybe some trees, but not enough to protect anything. The whole place is a 4 feet above sea level and exposed on all sides.

waterrockets
04-03-08, 08:12 PM
Racer_Ex has a good point about not being able to go hard on the tailwind coming back.

There are also the physiological and psychological points about pushing hard against intense resistance, just like a hill -- it's easier to keep the watts high.

The physics, which a couple of you have hit has a large impact too.

Extreme case here (to obviate the differences):

If you're fighting a 30mph headwind, doing 10mph, you're in a 42mph apparent wind. If you go harder and get 1 mph out of it, you're going 10% faster (!!!), but you've only increased your apparent wind by 2.4%. The cube of the wind increase is the power requirement, so that would require a 13.8% power increase.

Compare that to still air, going 30mph (this is DrWJO). To go 1mph faster, it's only 3.3% faster, but it increases the apparent wind by the same amount. The wind speed takes the cube of the increase in power, so that would require 36% more power!

So, in the headwind, 13% more power gets you 10% more speed. In the still air, 36% more power only gets you 3.3% more speed.

Of course, we're talking about a 5% variance, so the real-world numbers won't be quite so dramatic.

Ok, so where'd I mess up?

Scummer
04-03-08, 08:29 PM
TI-88? Old school... TI-89 is where it's at.

DrWJODonnell
04-03-08, 08:44 PM
Racer_Ex has a good point about not being able to go hard on the tailwind coming back.

There are also the physiological and psychological points about pushing hard against intense resistance, just like a hill -- it's easier to keep the watts high.

The physics, which a couple of you have hit has a large impact too.

Extreme case here (to obviate the differences):

If you're fighting a 30mph headwind, doing 10mph, you're in a 42mph apparent wind. If you go harder and get 1 mph out of it, you're going 10% faster (!!!), but you've only increased your apparent wind by 2.4%. The cube of the wind increase is the power requirement, so that would require a 13.8% power increase.

Compare that to still air, going 30mph (this is DrWJO). To go 1mph faster, it's only 3.3% faster, but it increases the apparent wind by the same amount. The wind speed takes the cube of the increase in power, so that would require 36% more power!

So, in the headwind, 13% more power gets you 10% more speed. In the still air, 36% more power only gets you 3.3% more speed.

Of course, we're talking about a 5% variance, so the real-world numbers won't be quite so dramatic.

Ok, so where'd I mess up?

So I understand the headwind and from that standpoint and it makes sense to power ahead to get more speed. and so just to make sure, the opposite applies with a tailwind? so essentially yes the same as the uphill downhill phenomenon? So I should positive split with the headwind?

Enthalpic
04-03-08, 08:48 PM
Purchase/find me a copy of this journal and I will try my best to program the "up-to-date mathematical model" for you. Maxima and minima are pretty easy to calculate if you know the eq and all the constants & conditions.

Atkinson et al. 2007. Variable versus constant power strategies during cycling time trials: prediction of time savings using an up-to-date mathematical model. J Sports Sci 25(9):1001-1009.

curveship
04-03-08, 08:52 PM
10 MPH show same - no advantage.

Try a smaller power differential and you'll see a slight gain. 103%/95% (=100% normalized) saves about 5 seconds over 40k, using some rough assumptions for DrW's power, CdA, Crr, etc etc. Not big by any means, but something.

curveship
04-03-08, 09:02 PM
Ok, so where'd I mess up?

Very funny, WR. Are you just trolling after the 38mph thing? :D

ElJamoquio
04-03-08, 09:05 PM
Racer_Ex has a good point about not being able to go hard on the tailwind coming back.

There are also the physiological and psychological points about pushing hard against intense resistance, just like a hill -- it's easier to keep the watts high.

The physics, which a couple of you have hit has a large impact too.

Extreme case here (to obviate the differences):

If you're fighting a 30mph headwind, doing 10mph, you're in a 42mph apparent wind. If you go harder and get 1 mph out of it, you're going 10% faster (!!!), but you've only increased your apparent wind by 2.4%. The cube of the wind increase is the power requirement, so that would require a 13.8% power increase.

Compare that to still air, going 30mph (this is DrWJO). To go 1mph faster, it's only 3.3% faster, but it increases the apparent wind by the same amount. The wind speed takes the cube of the increase in power, so that would require 36% more power!

So, in the headwind, 13% more power gets you 10% more speed. In the still air, 36% more power only gets you 3.3% more speed.

Of course, we're talking about a 5% variance, so the real-world numbers won't be quite so dramatic.

Ok, so where'd I mess up?

#1. No one can put up 10 MPH against an actual 30 MPH headwind. EDIT - after checking math, I'm wrong.
#2. Working 13% harder, for DrWJO - would require about 400 watts. At 11 MPH, assuming only a 5 mile out/5 mile back, you'd still be pushing 30 minutes. Asking him to output that much more is a dubious strategy. Assuming he can...
#3. You're still exceeding your normalized-power target for the entire interval.

ElJamoquio
04-03-08, 09:07 PM
Try a smaller power differential and you'll see a slight gain. 103%/95% (=100% normalized) saves about 5 seconds over 40k, using some rough assumptions for DrW's power, CdA, Crr, etc etc. Not big by any means, but something.

I'll try tomorrow, but looking for 5 seconds through mucking against a person's default power output scheme (i.e., negative splits for DrWJO) seems to be asking for trouble.

FYI, I was considering anything that small to be equal ("rough" comments above).

waterrockets
04-03-08, 09:33 PM
#1. No one can put up 10 MPH against an actual 30 MPH headwind.
#2. Working 13% harder, for DrWJO - would require about 400 watts. At 11 MPH, assuming only a 5 mile out/5 mile back, you'd still be pushing 30 minutes. Asking him to output that much more is a dubious strategy. Assuming he can...
#3. You're still exceeding your normalized-power target for the entire interval.

Yeah, I called it out as an exaggerated example. I'm just trying to demonstrate how the math works out such that dialing it up into the wind is beneficial. You wouldn't want to make any more than a 5% or so change in either direction. With lower wind speed and smaller power changes, the math still comes out to be more efficient to hit it into the wind. I just wanted to exaggerate so it was more clear what's going on.

DRWJ: yes, it works for the tailwind too -- just like a downhill. Go harder into the wind and up the hills. If it's gusty, fight the gusts as they hit. Not enough to screw with your pacing too much, but make it intentional.

FWIW, I hit the local 8-mile TT course like this last week. It was headwind out, tailwind back (for most of the course). It felt really strange on the way back pushing only 300W or so, but it was really hard to go any harder because the speed was so high. In the end, my power was 5W lower than I expected, but I beat my best time by 46 seconds...

DrWJODonnell
04-03-08, 09:39 PM
Ok, there you have it. I will push into the headwind. I actually negative splitted into the headwind last year (not as strong) and was still 30 seconds ahead of the guy behind me. Of course I came back at an average of around 33mph. Some people have difficulty powering at higher speeds. I don't fortunately. I saw a lot of guys who had better splits out.

snoboard2
04-03-08, 10:58 PM
hah! I did 6x12s in Panama City over spring break so I know what it feels like to hammer into a headwind. I completely agree with hammering into the wind. go hard in the hard parts; on the way back you'll have fun seeing how fast you can go with that tailwind...

Idioteque
04-03-08, 11:02 PM
Ok, there you have it. I will push into the headwind. I actually negative splitted into the headwind last year (not as strong) and was still 30 seconds ahead of the guy behind me. Of course I came back at an average of around 33mph. Some people have difficulty powering at higher speeds. I don't fortunately. I saw a lot of guys who had better splits out.

33mph average?

QQ is all i've got to say

Bob Dopolina
04-04-08, 05:12 AM
Math aside you've got to think about what the other riders are doing. Most people will do what seems most logical - save energy into the wind (out) and nail it home.

If you do the opposite (as it seems you will) you will start to catch people. I find this to be a great motivator. My best TTs have been ones where I have caught my minute man early and then set my sights on my 2 minute man. Somehow it makes the pain that much more tolerable.

TTs are as much mental as physical but I'm pretty sure you already know this. Even without the math I would instinctively ride it that way.

brianappleby
04-04-08, 08:46 AM
It's more of a math question than a physics one.

To avoid writing a novel:

Average Velocity is the ultimate goal of TT's.

Since Average velocity is Distance/Time and not speed/distance, this means that slower speeds are weighted more in your average speed. For example, if you go 10mph for 10 miles then 20mph for 10 miles, your average won't be 15, it'll be 13.3 mph.

Pushing harder into a headwind decreases the amount of time spent at slower speeds. Of course an equal power loss into the tailwind will also make you go slower w/ the tailwind, but since slower speeds are weighted more in the average, your overall average velocity will increase.

In short, speeding up your slowest speeds is more good than slowing down your fastest speeds is bad.

Exactly how much you should split your power is a much harder question to answer and likely requires more biology than physics.

Hope this is helpful to you.

B.

ElJamoquio
04-04-08, 09:06 AM
http://i179.photobucket.com/albums/w309/eljamoquio/DrWJO.jpg

ElJamoquio
04-04-08, 09:09 AM
The relatively small temporal (\$0.50) return, combined with the fourth-order normalized power function, minimizes the effect of front-loading your power output into the headwind.

waterrockets
04-04-08, 09:11 AM
Cool, nice work.

What if you re-run it with DWJO's normal negative power splits on the "constant power" section. ~345 out, ~355 back (vary those to get the 350 avg.). The OP was asking if he should sacrifice this pacing strategy to fight the wind.

jooaa
04-04-08, 09:17 AM
I did some calculations that should help.

I rephrased the problem as: Given a certain capacity to produce power, riding straight into then straight out of the wind, what is the optimal choice of power for both legs of the ride?

Here's what I did. Split the race into two legs: out 10 miles with wind in your face, in 10 miles with wind at your back. I assumed that over the race you can average 400W. Average power for the whole ride is (Power_out*time_out+Power_in*time_in)/(time_out+time_in).

Then I punched a bunch of numbers into http://www.kreuzotter.de/english/espeed.htm. Assumed a TT bike and 5'10" 170lbs. I input varying power levels into the wind to get speed into the wind, from which I calculated the time into the wind. For each of those power levels, I then calculated the power you'd need to ride for the leg back out of the wind. You have to iterated because time_out changes. I can give details if you like.

Here are the results. I did two cases, one with no wind and one with the 10mph wind. The power plot shows your power riding into the wind on the x-axis. The y-axis is then the power you'd need out of the wind so that the average power for the whole ride is 400W. With no wind, you ride 400W in both directions.

The speed plot is where things get interesting. With no wind, optimal strategy is (obviously), ride 400W in both directions. >>With wind, optimal strategy is to ride faster into the wind<<. As you start to go above 400W into the wind, you gain a lot of time on that leg, but dropping a few W with the wind doesn't change your speed much. If you increase your wattage into the wind too much, you get diminished returns on your power and the losses out of the wind outweigh the gains into the wind.

Two important caveats. 1. The "average power" assumption may not be valid. Probably if you increase your power for one leg you'll have to decrease the average power for the whole ride a bit. 2. These aren't your real numbers.

That said, the conclusion is pretty clear: Hammer into the wind.

Cleave
04-04-08, 09:19 AM
Racer_Ex has a good point about not being able to go hard on the tailwind coming back.

There are also the physiological and psychological points about pushing hard against intense resistance, just like a hill -- it's easier to keep the watts high.

The physics, which a couple of you have hit has a large impact too.

Extreme case here (to obviate the differences):

If you're fighting a 30mph headwind, doing 10mph, you're in a 42mph apparent wind. If you go harder and get 1 mph out of it, you're going 10% faster (!!!), but you've only increased your apparent wind by 2.4%. The cube of the wind increase is the power requirement, so that would require a 13.8% power increase.

Compare that to still air, going 30mph (this is DrWJO). To go 1mph faster, it's only 3.3% faster, but it increases the apparent wind by the same amount. The wind speed takes the cube of the increase in power, so that would require 36% more power!

So, in the headwind, 13% more power gets you 10% more speed. In the still air, 36% more power only gets you 3.3% more speed.

Of course, we're talking about a 5% variance, so the real-world numbers won't be quite so dramatic.

Ok, so where'd I mess up?

Hi,

OK, the basic concepts above are correct, but the math has me a bit puzzled. If you're riding 10 mph into a 30 mph wind, your relative speed through the air is 40 mph. (I don't think that Dr. WJ is riding fast enough to use Einstein's relativity theories to calculate speed. ;) )

Also the increase in power to overcome aerodynamic drag increases as a function of your relative velocity through the air cubed (v^3). I'm not sure how you're calculating those power requirements.

Since I have to get myself to work, I give you some scenarios and you assess the power requirements yourself. If you are riding 25 mph into a 10 mph headwind, your power requirements will be the same as riding 35 mph with no wind. If you are riding 25 mph with a 10 mph tailwind, your power requirements will be the same as riding 15 mph with no wind.

Riding up hill is a different set of equations but the basic physics is the same since Power equals Force times Velocity. So Power always increases as a function of v^3. It's just that the absolute Power number is different because the largest force acting on a rider going up hill is due to gravity (though there are smaller aerodynamic forces involved too) while on the flats, the greatest force acting on a rider is aerodynamic.

Clear as mud? ;)

jooaa
04-04-08, 09:19 AM
http://i179.photobucket.com/albums/w309/eljamoquio/DrWJO.jpg

Independent verification!

ElJamoquio
04-04-08, 09:30 AM
Cool, nice work.

What if you re-run it with DWJO's normal negative power splits on the "constant power" section. ~345 out, ~355 back (vary those to get the 350 avg.). The OP was asking if he should sacrifice this pacing strategy to fight the wind.

http://i179.photobucket.com/albums/w309/eljamoquio/DrWJO2.jpg

ElJamoquio
04-04-08, 09:31 AM
The delta changed a little because I reduced the rolling resistance assumption from 0.006 to 0.004.

ElJamoquio
04-04-08, 09:36 AM
So, from 345/355 to 370/313, there's about a 5 second difference. If I were WJO I wouldn't chance it.

waterrockets
04-04-08, 09:40 AM
Yeah, I'm seeing a similar big gap between negative splits and constant power. I ran it over at Kruezotter, with pretty different assumptions. The relative differences are similar though (4.8s savings for variable vs. negative split):

http://img88.imageshack.us/img88/2838/postew8.png

waterrockets
04-04-08, 09:42 AM
Another note is that DRWJO will probably recover on the way back. How long would he need to really be at 313W before he could go harder? I guess you can't beat your mean maximal power, but there should be some resurgence there.

ElJamoquio
04-04-08, 09:44 AM
(4.8s savings for variable vs. negative split):

OH YEAH?!? MY model says 4.77 seconds.

ElJamoquio
04-04-08, 09:46 AM
Another note is that DRWJO will probably recover on the way back. How long would he need to really be at 313W before he could go harder? I guess you can't beat your mean maximal power, but there should be some resurgence there.

I don't know... if I go 20 watts over my 300-ish FTP for twenty minutes, I'm pretty beat. I guess the next five minutes I'd have to take 'a break', terrible in a TT sense, of maybe 200 watts, before I could dial it back up to 260-ish consistently.

waterrockets
04-04-08, 09:52 AM
OH YEAH?!? MY model says 4.77 seconds.

:roflmao: I had to use the "Superman Position," and that still only got down to 2.04 CwA

I don't know... if I go 20 watts over my 300-ish FTP for twenty minutes, I'm pretty beat. I guess the next five minutes I'd have to take 'a break', terrible in a TT sense, of maybe 200 watts, before I could dial it back up to 260-ish consistently.

Yeah, that mean maximal power for a duration is pretty much the limit unless fitness improves. The exception, of course would be WRI™, where my MMP went up when I started going psycho on the front end.