Mathematical Model of Road Cycling - Martin, Coggan Paper

Since 2001, over 90,000 cyclist's have joined Cycling Forums to discuss topics from general cycling to equipment, training, racing and travel or vacation destinations (especially in europe during the tour de france). We also feature an great deals in our online store, 100's of articles, classifieds and product reviews.

I've been playing recently with the model from this paper:

Martin, J.C., D.L. Milliken, J.E. Cobb, K.L. McFadden, and A.R. Coggan. Validation of a mathematical model for road-cycling power. Journal of Applied Biomechanics, 14(3): 276-291; 1998

It's given me some fun results regarding equipment choices under different conditions.

I was wondering if anyone has a spreadsheet macro that will solve the equation for the requested variable or can recommend the best approach to setting this up. I am happy to try to teach myself some basic programming, but I don't really know where to start.

Also wondering if anyone has Crr data for singles glued with track glue versus road glue?

I know this isn't strictly a power training question but I didn't know where else to put it (plus the people that lurk here seem to be the best on the forum).

Cheers,

RS

I don't have the paper, but modeling isn't too difficult. Just solve the equation of motion - F=m*a (power=F*velocity). You can use something like 4th order Runge-Kutta integration to solve. I've written my own programs to do this but with variable power, wind, hills, ... that I use to better predict Crr and CdA.

I don't have the paper, but modeling isn't too difficult. Just solve the equation of motion - F=m*a (power=F*velocity). You can use something like 4th order Runge-Kutta integration to solve. I've written my own programs to do this but with variable power, wind, hills, ... that I use to better predict Crr and CdA.

So I agree with you that the basic idea behind modelling with an equation isn't too difficult, but the great Cog et al do a particularly good job. I'm wondering more about how to come up with a friendly interface to solve for any given variable - eg, sometimes I'll be interested in lumping together everything except CDA and sometimes I'll want to isolate Crr. I can solve it fairly easily manually, but it would be even better if I had a clean interface that could solve for any given variable, give outputs that could be graphed (eg Crr vs Power req, given speed), and give component breakdowns of power requirements - eg, power to overcome aerodynamics, bearing friction, rolling resistance, intertia, etc. Even better if the program can do a work with heaps of data points so you can model power requirements of variable paced efforts.

I don't think the concepts are super-hard. I just don't have the programming nous. If you made this sufficiently user friendly, I think you'd have a very neat and clean tool to help with equipment selection and aero position tuning.

Thinking about it, maybe a spreadsheet will be a bit clunky. I am going to talk to my friend that works at google about coding up a standalone program.

Peace,

RS

So I agree with you that the basic idea behind modelling with an equation isn't too difficult, but the great Cog et al do a particularly good job. I'm wondering more about how to come up with a friendly interface to solve for any given variable - eg, sometimes I'll be interested in lumping together everything except CDA and sometimes I'll want to isolate Crr. I can solve it fairly easily manually, but it would be even better if I had a clean interface that could solve for any given variable, give outputs that could be graphed (eg Crr vs Power req, given speed), and give component breakdowns of power requirements - eg, power to overcome aerodynamics, bearing friction, rolling resistance, intertia, etc. Even better if the program can do a work with heaps of data points so you can model power requirements of variable paced efforts.

I don't think the concepts are super-hard. I just don't have the programming nous. If you made this sufficiently user friendly, I think you'd have a very neat and clean tool to help with equipment selection and aero position tuning.

Thinking about it, maybe a spreadsheet will be a bit clunky. I am going to talk to my friend that works at google about coding up a standalone program.

Peace,

RS

Andy, this is OK right? I'm thinking that as all the info is in journals it is OK to use it like this? If there are any issues let me know, I don't want to step on toes.

doesn't the programme at www.analyticcycling.com do what you already want? I think it uses a very similar (or perhaps the same) formula as in the Martin et al. paper?

Ric

Andy, this is OK right? I'm thinking that as all the info is in journals it is OK to use it like this?

No problem whatsoever (and the publisher of the journal owns the copyright, anyway).

doesn't the programme at www.analyticcycling.com do what you already want?

My thought exactly.

I think it uses a very similar (or perhaps the same) formula as in the Martin et al. paper?

It's not exactly the same formula, but they're all essentially the same...Jim's is a bit more detailed (e.g., including an estimate of the incremental increase in CdA due to spinning wheels), but you'd be hard-pressed to say that it's really more accurate.

maybe a spreadsheet will be a bit clunky.

It is, but one solution is to use the LOOKUP function...that's how Jim's original spreadsheet was written (he takes great pride in his ability to push Excel to its limits :) ).

doesn't the programme at www.analyticcycling.com do what you already want? I think it uses a very similar (or perhaps the same) formula as in the Martin et al. paper?

Ric

Yep, it is very good. However, I started attacking the problem to assess tubulars vs clinchers in terms of weight penalty and rolling resistance. I have satisfied myself that clinchers are winning, but I'd like to be able to prove it to friends (and paying customers at my friend's bike shop who ask for equipment advice) by actually running numbers on the tradeoffs between moment of inertia and weight. I couldn't find a page on analytic where I could enter moment of inertia. Maybe I missed it? I have satisfied myself that moment of inertia is a very small order effect, but I'd like to be able to show it to others. I think, realistically, this effect is within the margin of error of the formula, but hey, it would still be nice to show people that.

It's not exactly the same formula, but they're all essentially the same...Jim's is a bit more detailed (e.g., including an estimate of the incremental increase in CdA due to spinning wheels), but you'd be hard-pressed to say that it's really more accurate.

It wouldn't be possible to get a coopy of that spreadsheet would it? :p

Yep, it is very good. However, I started attacking the problem to assess tubulars vs clinchers in terms of weight penalty and rolling resistance. I have satisfied myself that clinchers are winning, The biketechreview data are mostly for latex inner tubes. They show quite a mix of rolling resistance, some tubulars better than most clinchers, some clinchers better than most tubulars, very few clinchers better than all tubulars. With butyl tubes, I'm not certain.

Data from the cycling magazine "Le Cycle", compiled by Robert Chung.... to quote him, from another forum:

From a 100 tire comparison test in Le Cycle:

http://anonymous.coward.free.fr/rbr/find-the-tufo.png
T=tubular
C=clincher
P=puncture-resistant clincher
R=rain tire

Slip.angle.wet is measured as angle between bike and pavement (i.e.,
lower slip.angle.wet is better)

Rollout is related to rolling resistance (higher is better). These data indicate tubulars are generally fine, especially considering rolling resistance isn't the only consideration in choosing tires (puncture resistance, handling).

That said, I have tufos glued to my "aero" wheels (Cosmic Carbones). Bad choice, perhaps, but one I made years ago.

The biketechreview data are mostly for latex inner tubes. They show quite a mix of rolling resistance, some tubulars better than most clinchers, some clinchers better than most tubulars, very few clinchers better than all tubulars. With butyl tubes, I'm not certain.

Data from the cycling magazine "Le Cycle", compiled by Robert Chung.... to quote him, from another forum:
These data indicate tubulars are generally fine, especially considering rolling resistance isn't the only consideration in choosing tires (puncture resistance, handling).

That said, I have tufos glued to my "aero" wheels (Cosmic Carbones). Bad choice, perhaps, but one I made years ago.

That's not the most informative graph I've ever seen. It doesn't give any guidance as to which tires are included and it doesn't give crr. Unhelpful.

FWIW, I am yet to see any data that suggests there are better road tires than latex tubes with either a Deda Tre Giro d'Italia, a Vittoria Open Corsa Evo CX or a couple of Veloflex's in terms of Crr. Michelin Pro2 Race are also OK. My experience with these suggests not to run Veloflex's because they flat too easily. The only tubs I've seen data on that roll better than clinchers are track glued silks, and you can only run these on an indoor track if you don't want to be buying a new set in about 5 minutes. The magnitude of difference in power requirements based on calculations from the 1998 paper's formula suggests clinchers are vastly preferable and make a significant difference. Do you have actual crr numbers better than 0.3 for a roadgoing tubular (even one glued with track glue or shellack)? Or even better than 0.38, which I think is a Dedatre tire with a butyl tube (from memory).

Edit: I accidentally wrote clincher where I should have written tub. Makes more sense now.

I suppose all of this is usefull- IF YOU DO IT FOR A LIVING

I suppose all of this is usefull- IF YOU DO IT FOR A LIVING

Personally I just find it very interesting. I don't need to get paid to validate that.

That's not the most informative graph I've ever seen.It's pretty informative if you believe that one type of tire is better than another. The graph was designed for a discussion in another forum, where that was the question: it shows that you shouldn't make blanket statements like "clinchers are {better|worse} than tubulars" -- instead, you have to specify which tubular and which clincher.

It doesn't give any guidance as to which tires are included and it doesn't give crr. Unhelpful.Knock yourself out, big guy: http://www.lecycle.fr/sommaire.php?num=360