Adrian Bejan | Fuel load, engine size, range, from Design in Nature
In this video, Adrian Bejan explains that body mass has two parts: the fuel load and the engine. He points to an airplane, where the fuel load is in the wings, and the wings are the burden relative to the empty fuselage. He connects one idea from burning the fuel to heat, then to the engine, and then to the power that drives the airplane, and he defines the relationship between heating and work through the efficiency of the engine. He returns to economies of scale and says that in bigger engines, the passages are wider and heat exchangers have greater surface areas, so engines must be more efficient as they get bigger, but at a decreasing rate, which makes a concave curve. He uses these predictions to relate fuel load, engine size, and travel, and then says they are tested against data from many airplane designs and agree with the figures in the book. He ends by answering questions about the cheetah and the elephant, steady movement and one-shot movement, and lifespan, and he repeats that size matters in speed and in living longer.
The fuel load and the engine are related because fuel generates heat, and the engine converts that heat into work and power. The work requirement is proportional to the body weight and the range or travel length.
The efficiency of the engine forms a cloud of data with engine size, and it cannot punch through a ceiling tied to reversible operation. Engines become more efficient as they get bigger, but the rate decreases, so the curve is concave.
The movement of a piece of material called capital M to a distance L traveled increases when the engine is bigger and when the fuel is more voluminous. These two things do not change independently because they add up to the indicated size of the whole airplane.
From minimization with a capital M constant, he derives results for the mass fraction occupied by fuel and the fuel-to-engine ratio. He also says that every organ scales in proportion to the total size of the capital M, and that these predictions match the airplane measurements shown in the book's figures.
For the cheetah and the elephant, he says that average speed over daily life falls where it should on a line of assumed constant speed V, and he separates steady movement from one-shot movement. Regarding lifespan, he says larger things live longer, and he links this to the range, which increases monotonically with size.
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.