Experience From - Matt Mahoney, Eric Robinson,
Steve Patt wrote:
I did some rough mental calculations and started concluding that 1000 ft gross ascent/descent on a run was equivalent to an extra mile of distance.
That's funny. I sometimes run faster on hilly courses than on flat ones. I've noticed this at distances of 5K to 24 hours, but the results are mixed. For instance at the VT 100 last year my 24 hour split was 87 miles, 3 more than my best 24 hour track run, but a few months later I did 94 miles on a track.
I once tried to calculate the effect of hills on speed and concluded that it takes 12 times more energy to move upwards than horizontally, i.e. climbing 1000 feet has the same effect as running an extra 12,000 feet. Then my own tests on a treadmill suggested the ratio was really about 9 to 1. Then other people reported even smaller ratios like 6 or 8 to 1.
It's well known that we burn 2/3 calorie per mile per pound of body weight in running or walking on flat terrain regardless of speed (i.e. 100 calories/mile for a 150 pound person). I calculated that climbing uses 8 calories per vertical mile per pound (12x horizontal) based on physics and assuming that your muscles are 21.5% efficient at converting food into mechanical energy. That's the efficiency ratio I got by comparing watts (work done) and calories/hour (fuel used) on the Concept II rower and the PT-4000 Stairmaster. The results above suggest the actual muscle efficiency is 30-40%. That's pretty good since your car engine is only about 12% efficient.
As for downhill running, it's not possible to do the same analysis. In theory, running downhill should return energy back to your body, or at worst, using your muscles as brakes should dissipate energy as heat but not consume any fuel. What actually happens is that your muscles have negative efficiency during eccentric contraction. You use energy when lowering a weight in addition to the energy dissipated through resistance. However, I've noticed that it's easier to lower a weight quickly than slowly, which suggests that running downhill fast uses less energy than running slow.
About eighteen months ago, I did the same calculations on my logs and determined that 700' of gain takes me the same amount of time as a flat mile. But then, I am a relatively weak climber. The 1000' you arrive at is the figure most often suggested by backpacking guides.
It's even more interesting to take splits on a hilly route and divide each time not by mileage but by "equivalent mileage". When I am training, these are very consistent, with "equivalent pace" sloping slightly upward in a straight line. But I found that when racing, my speed on the uphills degenerated much more rapidly than my speed on downhills. I was taking the early ones too hard and not realizing it.
This realization led me to pace myself better on the uphills -- and I now know that the early ones should feel "restful" if I want to maintain the same speed on the later climbs. I think Dana R. was onto something when he described himself naturally optimizing with a pattern of "rest the ups" during Hardrock.