Adrian Bejan | Lifetime of Vehicles and Animals, from Design in Nature
In this lecture, Adrian Bejan returns to the model he built earlier for movers, where a vehicle is treated as the same thing as an animal, the motor stands for muscle mass and the fuel stands for the food carried in the body. He first recalls the two organ model, in which the mass of the mover is dominated by the fuel load and the motor, and shows how the balance between them is settled by the constructal law. He then makes the model heavier by adding the dead weight of the chassis, the seats, the roof and the occupants, and finds that the conclusion survives unchanged. Finally he divides life travel by speed to arrive at lifetime, and explains why the bigger animals and vehicles live longer.
A vehicle is an animal: Bejan asks the audience to treat vehicles and animals as the same kind of mover, where the motor means muscle mass and the fuel means the food in the stomach, or the grains a bird gathers in the sack under its beak. This is why the same reasoning covers runners, birds and fish as well as land vehicles, air vehicles and ships.
Two organs and one degree of freedom: In the earlier model the mass of the mover was assumed to be dominated by two organs, the fuel load and the motor, with the total mass held fixed, so the only freedom left is the relative size of these two parts. The burned fuel delivers its heating value as a heat input, the motor turns part of it into work, and that efficiency is greater when the motor is bigger, which is the predicted phenomenon of economies of scale.
Movement is what the design maximizes: Bejan calls the product of the body mass and the travel movement, and according to the constructal law an object that has the freedom to change will change in the direction that makes this quantity greater. Working out that balance gives the motor and the fuel as fixed fractions of the total mass, so the more muscular birds are the ones flying from Alaska to New Zealand on larger stores of fat, and the bigger movers travel farther.
Adding the dead weight does not change the answer: The new step in this lecture is a three part model, where the chassis, the seats, the roof, the occupants and the suitcases are counted as dead weight and taken as a fixed fraction of the total size, the way a shipyard states the size of a cargo ship in tons of dead weight, the shell alone. The longer algebra ends at exactly the same conclusion, which is what Bejan means when he calls a result robust.
Lifetime is life travel divided by speed: Since the bigger movers travel farther and also move faster, whether they are runners, birds, fish or land, air and maritime vehicles, the two effects combine into a lifetime that grows with body size. The exponent that falls out of this back of the envelope sketch is comparable with one half or two thirds.
The data were waiting in the zoology books: Only after the sketch is finished does Bejan open the books of zoology, which are full of plots of lifetime versus body size, and the dots line up along a power law with this kind of exponent. Those books report the exponent without explaining it, and his point is that the exponent is the real question, because everybody knows that the bigger live longer but very few question what everybody knows.
I enjoy putting together Umit Gunes on the Constructal Law, and I’m glad to share it with you for free. I hope you find it engaging and worthwhile. Preparing each post takes considerable time and effort, so if you appreciate Umit Gunes on the Constructal Law‘s content and can support it, please consider choosing one of the paid subscription options.