Tuesday, October 15, 2013

Mathematics defended

The distribution of length added to a run by height is a power distribution given by the formula:
T1=(T-y)+(y2+x2Where T1 is the enhanced length, T is the flat distance, y is the flat distance below sections of the run going up or down, and x is the total ascent/descent.
The distribution below shows the effect based on T=6km and x=600 (i.e a total measured ascent of 300m) which are typical figures for our runs.
The effect is less than 100 meters until the flat distance under the up/down sections falls below 1700 meters. At that point the average gradient would be greater than 35%, which means that allowing for some gentle slopes near the base of hills, the steeper bits would be steep enough to fall off!
Bart's right, if we want to add distance to our runs we'd be better off chasing each other round the beer truck for 20 seconds than adding hills!

6 comments:

  1. All I can say about this formula is that Stick Insect should not be allowed to carry Squealer. That's just so wrong in so many ways.

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  2. I agree. I think she needs a chaperone. I suggest Stick Insect must also carry Superpig at the same time. Go for the hill Bart!

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  3. Damn! My argument is counter acted. Bring on the mere mountains.

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  4. And another thing . . . Pythagoras was clearly not a hasher or he would have recognized that 1 vertical meter is not equivalent to √2-1 (or whatever it is) horizontal meters, at least not in terms of energy expenditure. So Mr. Egg-bloody-head Newton, kindly modify your formula to account for the pernicious effects of gravity.

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  5. That's why you will get to carry Gan Yao, so you get the full "experience"

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  6. Nonsense, the equation can be simplified to:

    Hills=Hurt

    On On, but only on the flat

    Gan Yao

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