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Does anyone know?

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Dr. Evil writes a new post.
In there he does the Watt calculations for the recent Vuelta stage, telling us:

This year’s group of favorites, with Piepoli, Sastre and Menchov took 25’30”, with VAM= 1823m/h.
Wind and drafting can always affect the times of the ascent and the ensuing valuations, but assuming the body weights of Sastre, Menchov and Piepoli to be 58, 64, e 52 kg respectively, then the average watts developed would be 364, 402, and 326.

Can anyone walk me (us) through the calculation where he used their VAM, their weight, the UCI bike weight (15.9#) to get their watts? I guess he also used the hill gradient?

I would really like to know how he does this estimation.

Thanks to the super geeks who can show us how this is done.

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About Bush43

“Long time cyclist, skier and purveyor of all that is good in this life.” SLC, Utah, USA

28 Replies to “Does anyone know?”

  1. …hell, i certainly don’t know how to make those calculations… but if it’s gonna lead to more bad doping revelations, don’t tease us, just lay it on the table…

    …we’ve all become used to it, and that is a bloody shame…

  4. Being the political genius you are, you should easily be able to figure it out. I’ll give you a hint… It doesn’t require any real calculus. Unless your paying, I’m not gonna waste my time.

  5. Power = Work * time. Work = mass * gravity * height. So if you know the rider’s weight and how high he climbed and how long it took him then you know how much average power he put out fighting gravity. Add in a fudge for friction and wind resistance and that’s his average power output.

  6. VAM is just altitude gained per hour. The climb was 8.6km @ 9.1%.

    The percent of grade is the vertical climb divided by the horizontal distance. Note that the horizontal distance is not the length of the climb, that is the hypotenuse.

    If you know the % and the length of the climb (we do), to find the elevation climbed, use the following:

    elevation = (% * length of climb)/(sqrt(%^2 +1))

    In this case:
    elevation = (0.091*8.6)/(sqrt(0.091^2+1))
    elevation = .7826/sqrt(1.00828)
    elevation = .7826/1.00413
    elevation = 0.7794km or 779.4m

    Ok, we know the meters climbed, now we need to know in how many hours.
    24min22sec needs converted to hours.
    First divide 22 sec by 60 to convert it into minutes
    22/60=.36666666666666666666666666666666(shout at the devil!)
    So that is 24.3666666666666666666666666 minutes.
    Divide that junk by 60 again to get hours.
    24.366666/60 = 0.4061 hours

    Now, VAM = elevation gained/time
    VAM = 779.4/.4061 = 1919.2 meters per hour.

    You’ll note that this doesn’t coincide with Dr Evil’s calcs, he does it the wrong way, exactly the way you’d expect a MD to do basic trigonometry:
    8.6km*0.091/0.4061 = 1927 meters per hour.

    Ok, now moving onto body weights, he’s just using their published weights, and if they’re not in kilos, just do the conversion. No mystery.

    Of course, he assumes the riders are at the UCI minimum bike weight, this must be added to the rider’s weight to get the total weight.

    Now, to find watts:
    First we must get the weight of the rider+bike (in Newtons), not the mass (grams). The average acceleration of gravity on the earth’s surface is 9.81m/s^2.
    Newtons = kilograms*9.81, in our case (58kg+7.22kg)*9.81=639N.

    A watt is just a Newton * it’s velocity (in meters/second).

    From above, we found the rider’s VERTICAL speed to be 1919.2 meters/hour. To turn that into meters/second, divide by 3600.
    1919.2/3600 = 0.533 meters/second.

    Now to calculate watts, 639N*0.533m/s = 340 Watts.

    You’ll note that my calculations ignore mechanical inefficiency of the bicycle, which is probably around 95%.

    340/0.95 = 359 watts.

    I’ve also ignored aerodynamic drag, b/c I don’t have a reasonable estimate to go by.

    But now you have an example of how the numbers are derived.

    This is basic high school physics & trigonometry.

  8. …jeez, i mean cheese…

    …this is what makes drunkcyclist so worthwhile…a place to rip, rant, fume, joke, laugh, be serious or a little foolish, and yet when something real comes up, there is usually a helpful informative response…

    …there are a lotta hypocrites out there, who can’t face real ideas & emotions, cuz a few “nasty” words are used…people like that, seem to have a limited perspective…

    …fuck ’em, if they can’t take (an open stance)***(a joke)…it’s good to be honest, helpful & humorous w/ all yer brothers & sisters…thanks for the opportunity DC…

  9. Easy there tiger, I sent in a detailed & quite lengthy response with formulae & an example to the original questions last night. The comment appears to be stuck in moderation.

  10. Power = VAM*total mass*9.8/3600. That’s if you ignore wind resistance, so it’s only valid for a perfectly vertical climb. Which is why comparing VAM on different climbs (as the cycling press loves to do) is a waste, since for the same power/mass, VAM goes up with gradient.

  11. Bush43, I’ve got a really simple Excel sheet that will calculate that out for you (yes, I’m an enginerd). Drop me an email and I’ll send it to you.
    pw

  13. As others have pointed out, climbing watts are simple to figure out P=F*T, F=M*A, A=d/t(sup 2) so by combining all the disparate elemnets
    P=(M*(d/t(sup 2)*t, and removing the terms that cancel out P=M*d/t in consistent units. Knowing mass, altitude gain and time one can figure out power.

    Opus

  15. …does anyone still ride a bike for enjoyment ?…

    …how does heart & soul measure into the equation ?…all things being equal, the one w/ the most desire wins the jersey !…

    …too much science = equals = potential, lost in capitulation…

  16. “does anyone still ride a bike for enjoyment ?”
    No, I just sit around and do equations….it’s the coolest.

    “how does heart & soul measure into the equation ?…all things being equal, the one w/ the most desire wins the jersey !”
    Right, all things being “equal”, which they’re not, Dr.Juice’s point was that one of these riders is not like the other, one of them is putting out 10% more power than the others. Who are you putting your money on? or….who’s blood is thicker than the rest?

  17. …p…maybe we should all just shudup, ‘n’ ride more, huh ?…

    …as regards ferrari’s quotes & calc’s in the original post, ya, yer point is taken…w/in the pro ranks, things never seem equal these days…

    …my point regarding “equal” would be that, although amongst ourselves, here on the enthusiast level, there is a lotta knowledge & competency, i’d still bet that one on one, science vs. heart & desire are gonna work out pretty equal…i guess i’m playin’ old school advocate here…

    peter, i want to express something w/out denigrating you in any way as an engineer…it’s simply to better define the science / emotion parallels…
    …as an old ex-industry guy, one of the regularly occurring phenomenas was to meet young gung-ho engineering students powering outta school w/ the thought that they were gonna set the bicycle industry on it’s ear…as you are probably aware, that just hasn’t happened for any company…solid competent evolutionary ideas, whether initiated by scientific fact or ‘need to solve’ emotion, are what drive the industry…the two schools are valuable factors that work hand in hand…

    …anyway, to bring this long winded rant back towards the original point…i would love to see the right money & scientific knowledge utilized in such a way that there would be no available avenues for the cheaters…
    …maybe someday, ‘all things’ will again be equal…

  18. Peter,
    You’re not normalizing out their body masses. A more massive person SHOULD put out more power, b/c they will have more lean muscle mass.

    When you look at watts/kg, they’re all pretty much the same (6.276, 6.281, 6.269, respectively). It’s a 0.2% difference between the highest/lowest.

    bikesgonewild, in other words, the playing field between those 3 is soooo level, you could shoot pool on it.

    Just another engineer cyclist….

  19. mxraceer652, yes I did. The 10% higher gross wattage (not normalized W/kg) comes into play in the long flat ITT, that was mentioned in the article. (difference of the square of the avg speeds because wind drag goes up by the square, blah, blah, 10% difference….etc….winner.)

    Anyway, enough geeking out, I’m going to have to kick my own ass soon.
    First ‘cross race of the season tonight, time to lace ’em up and see if my pidly 4.9 w/kg can keep from getting lapped and still drink beer afterwards without vomiting.

  20. …mxracer652…if you read my last post, you would see i concede to peter’s point, that w/in the “PRO” peleton & the three particular rider’s mentioned, no,indeed, things are not equal…

    …if you’re are a ‘cycling engineer’, please pay attention…questioning my validity says more about you than me…

  21. Peter-agreed.

    bgw-I think something was lost in translation, there is absolutely nothing suspicious or out of the ordinary with Menchov making 10% more watts. He weighs more, will have more lean muscle mass, therefore will make more power.

    Just to be clear, I’m not a cycling engineer, I have nothing to do with the sport professionally, and don’t want it confused as such. I just wanted to let Peter know that I spoke the “language”.

  24. I usually just use this site,
    http://www.analyticcycling.com/ForcesPower_Page.html
    which is pretty awesome. I used to always punch in my hill climb and time trial data into it to see how I was doing.

    I punched in the values reported/used defaults where I didn’t know them, and it gave 415 watts. So this number is almost surely wrong, but you would need some bored engineer type person to figure out by how much.

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