# What would be the mathmatical equation to explain dog exercise? (see details)

Asked by Dog (25152) June 11th, 2009 from IM

While wandering about Manhattan I saw several dog walkers. Many had multiple dogs of all sizes from Great Dane to Maltese. The little dogs were practically running as the large dogs sauntered along. I have two questions. One is what mathmatical equation would reveal the increase of energy expelled by the little dog vs the big one. Secondly- could the reason smaller dogs on average live longer than larger dogs be attributed to the increased exercise?

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Technically both the little dog and the big dog do the same exact amount of work, and thus use up the same amount of energy.

Ivan (13479)

How can it be the same amount of work? The Maltese was panting and running and the big dog looked bored.

Dog (25152)

I don’t believe they use the same relative energy, but there may be a similar caloric expenditure. The little dog isn’t moving a lot of bulk, but it’s moving it hella fast. The big dog is lumbering along while moving an enormous amount of meat. I’d be interested to see a real analysis done.

ru2bz46 (6743)

@Dog

The same way that rolling a boulder up a low-angled ramp does takes the same amount of work as lifting straight up into the air does.

Ivan (13479)

@Ivan is technically correct. Both accomplished the same work – barring wind resistance and the energy spent accelerating both to the same velocity. However, if you are looking to determine the calories expended you have to consider the issue of efficiency. To determine that I went to the (US taxpayer funded) USDA site Mypramid.gov and ran some numbers for humans. You can try it yourself. In my example I compared two, 50 year old males, 5’ 9”. One was 140 pounds, the other 200. Both are “Walking at 3.5 mph, brisk, level ground on a hard surface” for 1 hour. The model said the 140 pound male expended 239 calories while the 200 pound male expended 342 calories. I’m sure you can find other extreme examples.
The site has all kinds of activities listed. I was hoping to find “hot, wild, action ” so I could explain to my better half that I really am doing it for our health benefit.
Unfortunately the duration chart did not go below 8 minutes.

Lupin (4385)

@Lupin Yes, the 200 lb guy and 140 lb guy are going to have different caloric expenditure because their legs are moving at the same rate, so one is moving more mass the same distance on each step.

However, the maltese is moving small mass with fast steps while the ‘dane moves large mass at a relaxed pace. It’s more like comparing a baby (the other white meat) running away from Fat Bastard.

ru2bz46 (6743)

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