Thursday, February 25, 2010

The One-Second Workout

Hitchhiker: You heard of this thing, the 8-Minute Abs?
Ted: Yeah, sure, 8-Minute Abs. Yeah, the exercise video.
Hitchhiker: Yeah, this is going to blow that right out of the water. Listen to this: 7... Minute... Abs. 

Scene from There’s Something About Mary, as quoted on IMDB.

We turn now to weight loss. Forget “Eight-Minute Abs” and “Ten-Minute Buns,” we have something that’ll even eclipse Ben Stiller’s sketchy hitchhiker friend. How fast would you have to run to burn 10 lbs of fat in one second?

If we learned anything from the cannibal estimation, it’s that biology is not my strong suit. Be that as it may, there’s still a fairly straightforward way to at least estimate an upper bound for this problem. In order to lose fat, we have to convert it into energy. There are 9.0 Calories per gram or about 3.8×107 J/kg in fat. That means there are about 1.7×108 J of energy in 10 lbs (~4.53 kg) of fat.

When we run, we convert chemical energy into kinetic energy. Kinetic energy is the energy of motion and can be computed using the formula,

energy = (person’s mass) · (speed)2 / 2.

If we start from the stop position and accelerate to some speed, the chemical energy we use will be at least as big as our kinetic energy. Not all of the chemical energy gets converted to kinetic energy. Since our bodies aren’t 100% efficient, some of the chemical energy gets converted into heat. Moreover, not all of the kinetic energy helps us move forward, since we’re also using some of it to swing our arms and legs. In short, we use more chemical energy than we get out, but we can use this fact to compute an upper bound on how fast we’d need to run to lose 10 lbs in a second. I’ll assume the person’s mass is 75 kg (~165 lbs).1 We can solve the equation above for velocity to estimate the speed a person would need to run to lose 10 lbs in a second,

speed = [ 2 · (energy) / (person’s mass) ]1/2
= [ 2 · (1.7×108 J) / (75 kg) ]1/2
= 2100 m/s

If you neglect the sonic boom and air friction that would surely kill most mere mortals, you could lose at least 10 lbs in one second by accelerating to 2100 m/s, or about Mach 6 (i.e. six times the speed of sound).2

[1] This is technically the average mass since the person is losing mass as he runs.
[2] Before you start burning fat, you use the chemical energy from ATP and glycogen. Rigorously speaking, this means you might have to run a little faster. However, given that you’d likely deplete your ATP and glycogen storage well before you’d lose 10 lbs in a single workout, I stand by this result as an upper bound.

1 comment:

  1. Sprinting is generally an anaerobic exercise because it takes the body a while to begin to break down the fat with Oxygen. This is mostly when you use things like ATP and basic sugars (which don't need oxygen to break down). Your body also generally stores these in the muscle cells themselves so that they're readily available. Good sprinters try to get their adrenaline going right before a race for an even bigger boost.

    Running for long durations (an aerobic exercise) is when your body mostly breaks down fat and more complex carbohydrates.