Weight's effect on acceleration

[jws]

Hello all,

I made a spreadsheet, using the cycling power equation to calculate the separate components of power given input of all the variables. There's some guesswork on the coefficients, but I think it's pretty easy to get reasonably close. The components of resistence are 1)aero, 2)rolling, 3)frictional, 4)gravitational, and 5)inertial, or acceleration.

Out of curiosity, I wanted to compare power requirements at my current weight to my ideal weight. Obviously, gravity is a component affected by weight, but acceleration is also. Even in a flat ride/race, like a crit, weight will increase power requirements because of the accelerations. Keep in mind that I'm about 35 lbs over where I want to be, so the power differences are real.

However, it's hard to nail down the effect of accelerations because they're so variable and frequent. Also, the accompanying decelerations slightly mitigate the effects. But I thought I'd like to try to get a rough guess using a very simple model without differential equations.

I assumed a 0.5 mile, 4-corner course, 4 accelerations of 5sec from 25 to 28 mph each lap. Power from accelerations equals mass*speed*acceleration. Energy during the accelerations would be mass*avg speed*delta speed. Adding the energy for all accelerations and dividing by total time gives the extra power. Using 100kg versus 80kg yields a difference of 18 W over an hour.

Decelerations complicate things because even in a very simple model, extra mass means less power needed during decelerations. So that 18 W difference would be reduced in my example to maybe about 10 W.

Of course it's very rough, but does this approach seem reasonable?

 

[frenchyge]

I'm sneaking a response in while I'm here at work, but here are a couple quick thoughts:

1) Isn't the energy change during the accelerations is 1/2*mass*(V2^2 - V1^2)? I'm not sure that's the same as what you have, but maybe it is.

2) In the crits I've run, the decelerations are produced by braking rather than by resistance working against inertia, unless you are *extremely* smooth in your technique or willing to ride at the front the entire time. If you're using your brakes to slow down, then that would negate any advantage a heavier rider would have from increased inertia and eliminate the need to calculate that side of the equation.

 

[RapDaddyo]

The 18w number seems reasonable, but I think the physiological demands of the crit accelerations is different from the incremental power demands of, say, a larger frontal area (on the flat) or higher weight (on a climb) over a long duration. According to Andy, increasing power > sustainable power for less than 15 secs doesn't trigger the exponential lactate/power response. So, I don't think an 18w higher power demand for short accelerations is the same as an 18w higher power demand for a longer duration.

 

[flapsupcleanup]

Well, the classic equation is F=M*A. force equal mass times acceleration. Force for us is torque and if you're at a relatively constant cadence then you could correlate torque to power. The bottom line is that yes a heavier rider has to produce higher peaks of power to follow those minor accelerations that happen in a pack. And although the physics says you get much of that back in your inertia, I suspect you lose more in lactic acid/fatigue in a longer ride that way. I guess ideally, a heavier rider should stay towards the front of the pack where that doesnt happen as severely.

Braking is another one to think about. Every time you use brakes, you are putting your energy into brake heat rather than into getting you down the road. Mostly you've got no choice but for instance, when you see a stop or slowdown coming up start coasting early if you can. Saves your energy and it does add up on a ride.

The things we think about when we're on a long ride.

 

[RapDaddyo]

Thinking about this a little more, I'm not sure the extra power required for the accelerations would have a practical effect on race performance. It depends on whether the average power after the accelerations is at or close to one's sustainable power for that duration (say, 30 mins). Let's say that my sustainable average power for 30 mins is 280w, the average power required after accelerations is 250w and that the accelerations are <15 secs at 400w. I think the recovery is linear and thus, if I keep the accelerations <15 secs, I can recover at 250w in 60 secs (120/30 x 15). Of course, this analysis breaks down if the accelerations are more frequent than 75 secs, because I would never recover from the prior acceleration before I have to do it again.

 

[jws]

You all made good points. Regarding braking, I totally agree that some deceleration comes from braking, but I was ignoring that to simplify things a bit. In fact, I fudged a bit on the discount(18 to 10 W) to account for some braking. There are so many assumptions in my scenario that I thought close was close enough.

Also, the power equation yields rolling and frictional resistances of 11 W and 4 W, respectively, lower at 80kg than 100kg. That's more than I expected compared to the acceleration factor. Overall, that's about 30W, ignoring gravity(climbing).

I certainly agree that physiologically, it's much more complex than my calc's; I use NP normally, so those accelerations may have a greater effect if they are surrounded by near threshold power for 30s or so.

It's a starting point, and time(and weight loss) will tell the real story, but I thought it was interesting to look into.

Ciao, Jimmy

 

[RapDaddyo]

I certainly agree that physiologically, it's much more complex than my calc's; I use NP normally, so those accelerations may have a greater effect if they are surrounded by near threshold power for 30s or so.

Actually, I think the short duration of the accelerations keeps it simple (linear). I forgot to look at your course description. That's a short course, with frequent accelerations (I estimate one every 18 secs). If the acceleration duration/at speed duration ratio is >2:1, you could accelerate at a power delta of 2 x your "power cushion" (your FT minus the at-speed average power). So, if you have a power cushion of, say, 30w, you could accelerate for 5 secs at FT+60w and recover before the next acceleration.

 

[palewin]

Can't resist joining in on this thread, since in NJ we seem to live on a diet of crits; due to the difficulties in closing roads, you can count the number of RRs on one or two hands. First, looking at my PT files for last Sunday (rode the 55+ and 45+ Master's crits) the power peaks (accelerations) are all around 600-700 watts, or since my pet peeve with these postings is trying to make them less weight-dependant, 9.6-11.2 watts/kg. Interestingly, the peaks were higher in the 45+ race even though, due to the much larger field, I was being happily sucked along, and didn't feel like I had to accelerate all that much, and for which the avg power was 20 watts lower than our "old guys" race where the smaller field meant everyone was out in the wind a lot more! Anyway, just wanted to suggest that the 400 watt accelerations in RDs posting are way low compared to my experience. Since the point of the thread seems to be an attempt to determine the impact of rider weight on crit performance, the empirical test would be for riders of different weights, riding the same or similar crits, to compare their power peaks. [It seems to me that I have similar 600-700 watt peaks in most of my crits, so perhaps for a given rider these are relatively constant? In that case, we could simply compare our PT results from typical crits.] What I don't have a good feel for is whether it is the watts/kg or absolute watts which are more significant. My rough "instinctual" response is that the smaller rider (me) is not at a disadvantage cornering, since his lower absolute wattage is offset by the lower weight which must be accelerated. Unfortunately, though, absolute wattage becomes the critical factor in breakaways (i.e. speed on the straights) and in the finishing sprint. In those cases we know the issue is watts/frontal area, and typically the larger rider comes out ahead. Also, interestingly, in the "harder crit", my Norm Power was pretty close to my 1-hour sustainable as measured in TT-type tests (with my paltry absolute power, I avoid "real" TTs like the plague!) In the 45+ crit, we 55+ types all stayed mid-pack to rear-pack to avoid messing up the true 45+ riders (this was the State Championships) and since riding in a pack lowers the power requirement by ~30%, Norm Power was much lower than 1-hr sustainable.

 

[RapDaddyo]

Anyway, just wanted to suggest that the 400 watt accelerations in RDs posting are way low compared to my experience.

Actually, my main point was that the short duration of the accelerations would not trigger the exponential lactate/power curve as it relates to the impact on normalized power. The 400w acceleration was just by way of illustration. But, now that you mention it, the OP said that the accelerations were from 25-28mph. I also accelerate at 600-900w, but usually from a much slower speed exiting a corner (e.g., 15-16mph). I wonder if it's necessary to accelerate at 600w+ to go from 25-28mph? And, for a 5 sec acceleration, I wonder if there is truly a major difference in the physiological response for 400w vs. 600w? I know that when I accelerate for a short burst (e.g., 5 secs), it doesn't seem to matter much whether I accelerate at 400w or 600w.

 

[frenchyge]

Watts/kg simplifies the whole question of 'how much of an effect does weight play', but unfortunately it is not a real physical property that is easily visualized. Saying that losing 35 lbs takes you from 3.6 W/kg up to 4.6 W/kg sounds promising, but it's not easy to picture the magnitude of the difference.

The inverse approach would be for the OP to determine his power during a real-world crit that he's already ridden (NP would work best) and assume he'll hold that power after he drops the weight. Calculate the W/kg at the lighter weight, and then multiply by the heavier weight kg to determine how much 'effective power' it would have felt like he had in his real world crit if he'd been 35 lbs lighter.

 

[jws]

I just got back from our weekly crit which originally inspired this thread. I want to try some more examples with different numbers and see what kind of magnitude of difference there is. When I get home tomorrow, I'll report back. I'm too tired now to read replies, much less respond, so until then, Ciao and Thanks.

 

[ric_stern/RST]

In flat races, such as generally happens with crits, you're probably best of scaling to the power of 0.67 rather than 'straight' power to mass ratio. That is W/kg^0.67

Ric

 

[Peka]

Couldn't you just add 35lb of weight to the bike (or in a backpack or something....), and see what difference that makes to your data? I'm not suggesting you do a crit with the extra weight but you could do some sprints with and without the extra 35lb and compare the data...

 

[frenchyge]

Sure, but he wants to model himself as 35 lbs lighter than his current weight, not heavier. That's a little trickier to accomplish.

 

[palewin]

the OP said that the accelerations were from 25-28mph. ... And, for a 5 sec acceleration, I wonder if there is truly a major difference in the physiological response for 400w vs. 600w? I know that when I accelerate for a short burst (e.g., 5 secs), it doesn't seem to matter much whether I accelerate at 400w or 600w.

Ah, the joys of CyclingPeaks, you can review almost anything! The 45+ crit averaged 26.5mph, and typical accelerations were from 20-21mph entering the turns to 26-28mph exiting the turns. So for the mathematical modeling, I suspect the start speed of 25mph is a bit high, and/or the 3mph differential is a bit low (unless you're at the absolute front of the field, and hardly slowing at all for the turns). Also, I tend to agree with RD that when the accelerations are short, the peak wattage doesn't seem to make that much difference; its only when the graph changes from "sawtooth" to "squared off peaks" that life becomes hard.

 

[RapDaddyo]

Ah, the joys of CyclingPeaks, you can review almost anything! The 45+ crit averaged 26.5mph, and typical accelerations were from 20-21mph entering the turns to 26-28mph exiting the turns. So for the mathematical modeling, I suspect the start speed of 25mph is a bit high, and/or the 3mph differential is a bit low (unless you're at the absolute front of the field, and hardly slowing at all for the turns). Also, I tend to agree with RD that when the accelerations are short, the peak wattage doesn't seem to make that much difference; its only when the graph changes from "sawtooth" to "squared off peaks" that life becomes hard.

I think you're right about the typical accelerations -- 20-21 to 26-28 seems more likely unless the corners are pretty wide. Also, I think the physiological response to accelerations is more complex than simply <> 15 secs. I feel like the <15 sec accelerations need to be further broken down into duration categories. I feel like really short bursts (<5 secs) are completely different from longer bursts (e.g., 5-15 secs), or as you say, the sawtooth points vs. the squared off peaks. It really points up the price of having to close a gap coming out of a corner.

 

[frenchyge]

Those accelerations can be smoothed out with good technique. I downshift 2 gears entering the corner, stay seated, and pick up my pedalling in the middle of the corner to bring speed back up sooner, but slower and more evenly. In our training crits, it's not unusual for me to slip past 1 bike per corner by keeping momentum up while the other riders are standing and cranking like mad to accelerate out of the corners.

 

[Blackie]

Some good scientific thinking going on here - phew!

The drift of the thread is along the lines of something I'd been thinking about - the paradox that although F=ma, and that accelerations are crucial in crits, more than road races, little guys don't win. On the contrary, big guys do (especially in sprints).

How then does one decide one's optimal weight? Should we all just aim for a bmi or 22ish (the healthy average for the population, and the average for previous top champs), or is there a more scientific way of finding out?

Or for the pros - do they tend towards certain weights or do they deliberately aim for a target weight (presumably to maximise W/kg), or for classics riders aim for a mix of optimum W/kg and absolute sustainable Watts?

Cheers

 

[frenchyge]

Some good scientific thinking going on here - phew!

The drift of the thread is along the lines of something I'd been thinking about - the paradox that although F=ma, and that accelerations are crucial in crits, more than road races, little guys don't win. On the contrary, big guys do (especially in sprints).

How then does one decide one's optimal weight? Should we all just aim for a bmi or 22ish (the healthy average for the population, and the average for previous top champs), or is there a more scientific way of finding out?

Or for the pros - do they tend towards certain weights or do they deliberately aim for a target weight (presumably to maximise W/kg), or for classics riders aim for a mix of optimum W/kg and absolute sustainable Watts?

Ummm.... I think when the big guys win, it's because of their muscles and not their body fat. Lowest body fat possible (well, within reason but certainly less than 22%) would be my target since the fat is just along for the ride. Even the 'big' pros tend to have very little body fat.

No matter how big or small you are, if you drop fat, your W/kg will go up.

 

[jws]

I ran the numbers using an acceleration from 20 to 25mph over 5sec and the other numbers the same: 80kg versus 100kg (keep in mind this includes bike and equipment), a total of 200 accelerations over an hour.

I agree that's probably a more typical acceleration, though 200 of them is a lot. I used that because our weekly crit course is a half mile. Anyway, I get a 25W difference. Fewer accelerations over the hour would yield a proportionally lower wattage difference, e.g., 100 of them would mean 12 W difference. This compares with 18W when accelerations were from 25 to 28.

Using 23 to 28 mph yields a 28W difference and 25 to 30mph, 30W. Again, this is all highly simplified and doesn't consider climbing, rolling, and frictional resistances. For that matter, it might all be wrong; but it seems ballpark to me.

Thanks for the good discussion, guys, and if you want to see the spreadsheet, let me know and I'll send it.

Jimmy