Keep On Truckin’

Wednesday, May 20, 2009

This is not about a weight-loss program; it’s about something much more fascinating: Numeracy!

I am trying to persuade my friend Bill to switch from walking to bicycling; I figure that it is still exercise, but with the advantage of exploring the many bike trails near our homes.

Bill says that bicycling is too much work, but I figure it is less work (and hence, perhaps, a poorer form of exercise).

Here are my calculations for the walking side of the equation, based on a human body weighing 180 pounds, walking at 5,000 paces per hour. I think that that is a brisk walk.

The table above summarizes my figures; below I shall elaborate.

Assume a person weighs 180 pounds; obviously quantities may vary. Myself I am (ahem!) well under 180 lbs.

Assume that each step I take (off the balls of my feet) raises me one inch above the ground. Some people seem to bob up and down more than they go forward; some people seem to glide across the ground, but I’m using one inch.

Assume that each (“brisk walk”, remember) pace is two feet six inches, that’s 30 inches.

Assume too that you stride out at 5,000 paces per hour. I measured myself with a pedometer for a few days; I recall that it came out to about 5,000 per hour.

Each step that I take raises me one inch, that is, it raises 180 pounds one inch. I’ve done 180 pound-inches of work. Dividing by twelve (inches to the foot) yields a figure of 15 foot-lbs for each step that I take.

Since I take 5,000 steps per hour, I’m doing 75,000 ft-lbs of work each hour.

That seems like a lot! No wonder walking is a good form of exercise!

From my university vacation days working on the wheat farms of Western Australia, I know that a bushel of wheat weighs 60 pounds, and that three bushels make a sack. I had trouble lifting sacks of “seconds” (cracked wheat) onto the flat-bed truck, but my boss Frank McGinnis could heft ‘em up as easily as I cradle a one-gallon tub of ice-cream.

My 5,000 steps per hour therefore translate into the equivalent of lifting a sack of wheat one foot off the ground 417 times. I figure that the bed of the truck was three feet above the ground, so an equivalent amount of work would be to hoist 139 bags of what onto a truck.

I couldn’t do that then, and I know I couldn’t do it now.

Which would you rather do, load 139 bags of wheat onto a truck, or walk for one hour with a good friend?

I did the distance calculation to verify some of my assumptions. Five thousand paces at 30 inches per pace would see me cover almost two and a half miles in an hour, whereas I think a brisk walk sees me cover four miles in an hour. Either my paces are longer, or my steps are more frequent.

Nonetheless, my figures are within bounds, so I’ll stick with 139 bags of wheat hoisted for now.

There’s a homework exercise for you:

Repeat the calculations for cycling.

Assume that only your legs move (up and down), and that each leg weighs 18 pounds, and that you make a complete cycle of the pedals (each foot goes around once) 5,000 times an hour.

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