Ok, so since I took physics this past semester, every time I go out for a walk I'm constantly thinking about physics x_x. I've been hiking quite a bit lately, and over the past week I heard it said that, "For every extra pound your boots weigh, you lift the equivalent of one extra TON of weight per mile..." What was meant by that is that if you take about 2000 steps per mile, and your boots weight an extra pound each, every step you take you are lifting an extra pound of weight. Lift that weight 2000 times, and it's roughly the same amount of work done as if you lifted a ton.
This got me to thinking, so if the effect of adding weight to the feet is that great, then what sort of added calorie expenditure must there be? If you look at most websites on the web in regards to adding ankle weights and how many extra calories you'll burn, they tell you that the amount is negligible. They are perfectly correct, when only considering your translational (horizontal) motion. When you walk, your center of mass moves across a horizontal distance, but its height above the ground essentially remains the same, unless you go up/down a hill. This is the rationale for how your calorie expenditures are usually calculated for walking/running. The estimate is calculated based upon the total mass moved over a horizontal distance. Of course adding only 2 pounds to your total body mass will make a negligible difference in how much energy it takes to move your whole body one mile down the road, considering 2 pounds would be less than 3% of your total weight.
However, this leaves out a very important factor in the motion of a human body. While the center of mass stays much the same height above the ground while moving, the feet DO NOT. For every step you take, what happens? You lift your foot UP off the ground and further in front of you. Your foot, and to some extent your legs, undergo a vertical motion, doing work against the force of gravity. What this means is that adding weight to your feet totally changes the equation governing how many calories you use up walking/running.
I haven't calculated the amount of energy just required to move a body down a mile myself, so I can't tell anyone how that differs from the estimations on most calories calculators on the web, or if they would even take into account the weight of the average person's foot and how much energy it takes just to lift that for every step. But lets assume they're fairly accurate in calculating how many calories you burn walking with no added weight anywhere on your body.
For me (I weight 180 pounds), I burn about 100 calories per mile while walking. When I walk a mile, I take about 1700 steps (conservative approximation, probably closer to 2000). I think it's safe to say that I lift my foot at least 2 inches for every step. It takes a specific amount of energy to lift the weight on my foot a certain distance above the ground, easily calculated with the gravitational potential energy equation as follows:
mass x gravity x height = (1 lb weight on each foot/.454 kg) x (9.8) x (2 inches/5.08 cm/.0508m) = .226 Joules
Now, there are 4.184 Joules in 1 calorie/.239 cal per J, so:
.226 x .239 = .054 calories
Thus, each step with an extra pound weighing down upon your feet requires .054 extra calories. Multiply this by the number of steps I take each mile and I get:
.054 x 1700 = 91.8 calories per mile~108 cal per mile (using 2000 steps per mile)
In conclusion, by merely adding 1 pound of weight to each foot, I could essentially DOUBLE my calorie expenditure for walking/running. *This does not take into account a host of other physical and biological factors that play an important role in how much energy the body uses for such activity, but should represent a good baseline*
Would any of you physics oriented people please correct me if I'm wrong?