EXAMPLE 11 Dives

Sperm whales (and some other species) regularly hold their breath and stay underwater for an hour. Why can’t we?

In part, it’s because we aren’t as large as whales. A mammal’s breath-holding ability depends on how much air it can hold in its lungs, which is proportional to its mass. It also depends on how fast it uses up air—in other words, on its metabolic rate, which is proportional to the three-quarters power of its mass. Hence, the limit of duration of a dive should be proportional to the volume of the air in the lungs divided by the rate of using up the air, or

For a 90,000-lb sperm whale, this limit is proportional to , while the corresponding figure for a 150-lb human is . So the sperm whale should be able to hold its breath for about times as long. However, most humans cannot hold their breath for one-fifth of an hour (12 minutes)! (The record is 22 minutes; don’t try it—the guy died the next time he attempted it.) This fact tells us the whale has special adaptations to make long dives possible. The stars of the 2005 film March of the Penguins, emperor penguins, weigh 80 to 90 lb but can dive for as long as 20 minutes. Their special adaptations are more blood per pound of body weight, an abundance of myoglobin (which can store oxygen) in their tissues, and the slowing of their heart rate during dives.