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[This discussion is based on W. Biddle, "Skeleton Alleged in the Stealth

Bomber's Closet," _Science_ (May 12, 1989)]

Managerial economics is of great use in the aerospace industry, but this

does not mean that errors sometimes will not occur. The B-2 "Stealth" bomber

has cost billions to develop. According to Joseph Foa, an emeritus professor

of engineering at George Washington University, its design is fundamentally

flawed because two aerodynamicists made a mistake: they mistook a minimum

point for a maximum point.

The B-2 is basically a jet-powered "flying wing" aircraft. In a secret study

for the Air Force, the two aerodynamicists, William Sears and Irving Ashkenas

(then at the Northrop Corporation), used mathematical formulas to determine

how an aircraft's volume should be proportioned between wing and fuselage

in order to maximize its range. Taking the derivative of range with respect

to volume, they found that this derivative equaled zero when the total volume

was almost all in the wing. Hence, they concluded that a "flying wing" design

would maximize range.

But, in a subsequent analysis, Foa showed that the second derivative was

positive, not negative, under these circumstances. Thus, the "flying wing"

design minimized range; it didn't maximize it. In Foa's words, "The flying

wing was the aerodynamically worst possible choice of configuration."

This is a very interesting example of how important it is to look at the

second derivative to make sure that you do not confuse a maximation point

with a minimization point. While the backers of the B-2 bomber claim that

it is a good plane despite this error, no one denies that the error is an

embarrassment.