Double the size of an Airbus A380? No problem, aerodynamicists say.
- By Michael Milstein
- Air & Space magazine, July 2006
How big can an airplane get?
Airbus Industrie’s A380, undergoing certification tests now, has racked up some impressive statistics: a length of 239 feet, a tail as high as an eight-story building, and a 262-foot wingspan. It can carry 853 passengers on two levels, if you cram them all into economy seats. It has 17 restrooms, is heavier than 16 semi trucks (1.23 million pounds fully loaded), and can accommodate 81,893 gallons of fuel and 6,492 mini-bottles—or thereabouts.
But the A380 is not as big as an airplane can get.
An airplane can be as big as you want, say researchers who have tested the question against the laws of aerodynamics. The Russian Antonov An-225, a six-engine jet produced in 1988 to carry the Russian space shuttle, is bigger than the A380, with a span of 290 feet and a takeoff weight of 1.32 million pounds. Howard Hughes’ Spruce Goose is even bigger. And Airbus is already hinting at a stretch A380. When it comes to hauling people through the air, size is an advantage. But at some point, does size become a handicap?
At about the time Airbus committed to the A380, Ilan Kroo, a Stanford University professor of aeronautics and astronautics and a leading aircraft designer, tried to answer that question.
Kroo worked with several other aerodynamicists on a NASA-sponsored study to evaluate the effects of size on aircraft performance and cost. He and his colleagues first believed that the growth of an aircraft would bump up against the square-cube law, a principle first outlined by Galileo that suggests that everything has a maximum size. In mathematical terms, the law states that when an object increases in size, its weight multiplies faster than the strength of the structure that supports it. In the case of an airplane, the engineers feared that the weight of a hypothetical craft would grow faster than the lifting ability of its wings until at some point you couldn’t build wings long enough and sturdy enough to get the whole thing into the air.
But the square-cube law turned out not to limit the size of airplanes until the craft grow much bigger than the A380. “The basic physics that makes flying insects common and flying elephants impossible is not the main factor limiting the size of future aircraft,” Kroo says. He measured the lift-to-drag ratio—the aerodynamic efficiency—for aircraft ranging in size from a 92,000-pound weakling with a span of 75 feet to a whopper that would weigh about 2.5 million pounds on takeoff, about twice as much as the A380. Its wings would stretch 392 feet, half again as long as the Airbus’ and almost twice those of a 747. You’d need a roadmap to find your seat. It had a better lift-to-drag ratio than the smaller designs.
That a larger wing is more efficient may seem counterintuitive, since a longer wing on a heavier aircraft will need added structure to handle the increased loads from lifting that weighty fuselage. But Kroo found that the weight added to strengthen the wing was only a modest fraction of the airplane’s overall weight—modest enough not to impose a significant penalty. Given a fixed span, in this case a very long one, the aerodynamicist would strengthen the wing by lengthening its chord (the distance from its leading to its trailing edge) and making it thicker—creating a deeper, structural box. Increasing size also confers some advantage in Reynolds number, a parameter that reflects how the size and speed of an object affect the resistance it meets from the fluid (in this case, air) it moves through. The airplane’s larger wings experience less drag per square foot of area.