Climbing power, is there a law of diminishing returns?

Discussion in 'Power Training' started by Porkyboy, Jun 8, 2008.

  1. Porkyboy

    Porkyboy New Member

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    Hi

    Is there a simple answer to this question? It seems to me that if you want to go faster uphill you have to put in a whole lot more effort to go what seems like not too much faster! It seems to me that the steeper the gradient is the more potential there is to "waste" a whole lot of energy going a just a tiny bit faster, and possibly pay a heavy price in terms of the rest of the ride.

    Take a bike/rider combination that weighs 85kg riding up a 10% gradient. If the rider produces 300W and is climbing comfortably he (or she) goes up the hill at x speed. So, what if our rider decides to work much harder and manages to push out one third as much power on top, 400W, will the rider's new speed up the hill also be x plus 33.3%?

    What if the same rider decided this is a do or die climb and manages to squeeze out 500W in an eyeballs out effort? Will the rider now go up 66.6% faster?

    I'm sure the answer is obvious to many but I'd like to know the actual facts of the matter and also does the power to climbing speed relationship hold true for any gradient?

    Thanks for any help, just seems to me that if I ease back on my efforts on hills I don't go up much slower and have much more energy left for the rest of the course! I appreciate of course that easing off a bit is not an option if you need to hold onto the back of a pack!

    Thanks.

    PBUK
     
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  2. sogood

    sogood New Member

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  3. daveryanwyoming

    daveryanwyoming Well-Known Member

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    Well of course you've got to ride within your abilities for the duration of the climb and the duration of the overall ride. No sense in trying to go 30% beyond your best sustainable power for 20 minutes on a 20 minute climb, you'll just blow up and lose tons of time.

    But in general climbing is one place where you get nearly a linear increase in speed for extra power as you suggest. Put out 10% more power on a moderate to steep climb where wind resistance is negligible and you'll go about 10% faster. Not true for riding on the flats or on descents where aerodynamics rule and you've got to put out a lot more power to go a bit faster.

    Are you riding with a PM Porky? If not it could be that what you think of as backing off on the climb to save some energy is really just backing off speed to hold nearly the same power. My PM has really helped me come to terms with long climbs and headwinds. You have to back off the speed in those situations to keep the power within your abilities or you risk going way beyond your sustainable power and paying a big price later.

    I used to suffer in headwinds and now I realize I was trying to hold some arbitrary speed and the PM helps me stay in a sustainable range regardless of what speed I'm holding. They've become much easier to deal with when I realize I don't have to maintain a certain speed for good training, only a certain power.

    Anyway, pacing the climbs to avoid going over redline and digging a big hole is smart. Backing off further than that so that you have extra energy for flat sections later on might be a good touring strategy, but a lousy strategy for a competitive cyclist. You'll never be able to get more out of that energy you save while riding fast and flat as you can on the sustained climbs. It's the basis of variable power TT pacing, work hardest where the course is slowest, uphills and into headwinds and work hard enough but not as hard during the easier sections, descents, tailwinds.

    Good luck,
    -Dave
     
  4. Steve_B

    Steve_B New Member

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    For the OP: Yeah, so you may put a lot more power into it (and you may not like the "rate of return" of your investment) but consider that it's harder for everyone and everyone suffers from the reality of physics. It's also another way of looking at why not carrying extra blubber around on your body is helpful.
     
  5. WattsAMatta

    WattsAMatta New Member

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    I agree with working hardest on the climbs, but working hardest into headwinds seem counter-intuitive to me. If you double your effort on a climb, you get roughly double your progress. But, if you double your effort into a headwind, you get much less than double your progress. And although with the increased effort you'd spend less time in the headwind, it doesn't seem like that would make up for it.
    -- Bryan
     
  6. dkrenik

    dkrenik Member

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    This logic came up on another thread and I'm in agreement with you. For example, when I double my speed for a given TT in MachineHead software it shows that ~7.2x the power is required.

    IIRC the power, speed, resistance relationship looks something like: to double speed one must overcome ~4x the resistance and produce ~8x the power to do so.

    To me this clearly shows that working harder into a headwind would be a strategic mistake in TT pacing.

    Dave
     
  7. daveryanwyoming

    daveryanwyoming Well-Known Member

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    Yeah, it's not obvious. But don't take my word for it:

    http://cat.inist.fr/?aModele=afficheN&cpsidt=797655
    http://www.informaworld.com/smpp/content~content=a778564753~db=all~jumptype=rss
    http://www.ncbi.nlm.nih.gov/pubmed/9268969?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_Discovery_RA&linkpos=5&log$=relatedarticles&logdbfrom=pubmed

    -Dave
     
  8. Steve_B

    Steve_B New Member

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    Consider that:

    1. TT's are won by the rider with the highest average speed, not necessarily the rider who uses the least amount of energy to get to the finish. Maximizing speed within practical limits is the goal.
    2. In a 40K ITT, doing 120% of FTP for several 30-second chunks probably won't scuttle the whole TT, if they have adopted a sensible pace for the majority of the TT. OTOH, doing 120% of FTP for a continuous 20 minutes would be a big problem. Those moments where you employ high power have to be dosed out in accordance with the rider's capabilities.
    3. Imagine two riders on the same course with some windy periods. Let’s say that the wind hits them equally, for the sake of explanation. If one rider uses a “flat” power profile (minimizing variation, sticking to one average power for the duration) and the other hits the hills and windy sections harder than other sections, the latter rider should be, if done correctly, losing less speed in those sections than the rider using the “flat” profile. The rider will hit the windy sections hard(er) and recover at other times. Yeah, they are burning some matches doing it but if it’s a sensible application of high power within their capabilities, then it’s fine.
     
  9. swampy1970

    swampy1970 Well-Known Member

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    Go play!

    http://www.analyticcycling.com/ForcesSpeed_Page.html
     
  10. Piotr

    Piotr New Member

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    Headwind sections take more time than tailwind sections (on an out and back or a circuit course). If you lose 2 min on a 25 min headwind section, you won't make up 2 min on a 15 min tailwind section. That's a -2/25 vs. +2/15 speed difference. For all practical purposes you'll run out of road before you can make up the losses.
     
  11. lnyndhlp

    lnyndhlp New Member

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    Piotr raises an excellent point. It's the time spent at the slower speed that really matters. Remember if you fly down a 1 mile hill at 30mph that you climbed at 10mph, your average speed is 15mph (NOT 20!). Because you spent a lot more time going 10mph than 30mph. It's important to minimize the time you spend going slower.

    Increasing your average speed on a climb from 10 to 12 mph will have a more significant effect (on your overall time) than increasing your time on the flat section or descent by 2mph.
     
  12. Krazyderek

    Krazyderek New Member

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    I think you meant..... your avg speed will be 7.5mph, not 15mph.
    2 minutes down, at 30mph
    6 minutes up, at 10mph
    8 minutes total time, 7.5mph average speed

    which is an excellent example of that problem that you can't go fast enough in this situation to offset going slow up the 1 mile hill. Even at the speed of light, you'd get down the hill in 0.0001 minutes, but it would still take 6 minutes to go back up where as if you coasted down the hill say at 25mph and hammered it up at 15mph you'd get a lower over all time and higher average speed.
    2.4 minutes up at 25mph
    4 minutes up at 15mph
    6.4 minutes total time, 9.37mph avg speed

    Weather or not these speeds are attainable for your power capabilities is a whole other investigation, but for a 4 or 5 % grade these numbers would be about right for your average fit cyclist.
     
  13. kmavm

    kmavm New Member

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    You might want to double check that :). 2 miles in 8 minutes really is 15mph. I'd be a little disappointed if, in a ride where I never went any slower than 10 mph, I averaged 7.5mph...
     
  14. daveryanwyoming

    daveryanwyoming Well-Known Member

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    8 minutes, 2 miles (1 up, 1 down) = 15 mph........
     
  15. Addict07

    Addict07 New Member

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    I don't have the time right now to de-bug the math, but it doesn't intuitively make sense that your overall average would be less than the 10 mph climbing speed. Likewise for the second example.



     
  16. frenchyge

    frenchyge New Member

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    For the sake of piling on, this is also wrong! What were you thinking?

    1 mile / 186,282.397 mile per second = .00000537 seconds or .0000000895 minutes

    Please never post this rubbish again. ;) :D ;) :D ;) :D
     
  17. Piotr

    Piotr New Member

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    Derek, you so Krazy! :D
     
  18. lnyndhlp

    lnyndhlp New Member

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    I stand by what I said. It looks like you need to take a refresher course on arithmetic.
     
  19. Krazyderek

    Krazyderek New Member

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    lol my goodness you guys are picky, i obviously forgot to use 2 miles over the total time to calculate the total average speed that's all..... and no, i didn't use the actual speed of light value, it doesn't matter for this discussion..... or many other's for that matter.

    15mph avg for the first scenario was correct, BUT the second scenario is still faster at 18.74999999941mph for all you precision freaks.
     
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