Scientists are often trained to seek out the absolute best solution to a given problem. On a chalk board, this might look something like drawing a graph to find a function’s minimum or maximum point. When designing a turbojet engine, it might mean tweaking the rotor blades’ angles a tiny degree to achieve a tenth of a percent increase in efficiency.
Adrian Bejan, the J.A. Jones Distinguished Professor of Mechanical Engineering at Duke University, was busy demonstrating the former for a class full of students when a thought struck him: this is not how nature operates. Evolution is a sequence of design changes happening on their own in a discernible direction; it never weds itself to a single point on a drawing board. An evolving system or animal is free to simply go with what works. Not so much that its performance suffers greatly, but enough that it opens access to other options near the so-called optimal design.
With science often looking to nature for clues to solve challenges, Bejan wondered if he might look the opposite way, to predict nature before looking at it. If problem solvers and builders were free to miss the absolute highest mark, how much greater might be the range of designs they consider plausible?
That’s the question that Bejan posits in a new paper published online May 16 in the journal Biosystems. Using two relatively simple examples — walkways ferrying passengers off a train and a bird flapping its wings — he discovers that the answer is, “quite a lot.”
“In engineering, design, theater, architecture or even the organization of this university, any form of design benefits from the ability to make good but imperfect decisions and the freedom to move on and contemplate other opportunities for improvement,” Bejan said. “If one is wedded to the idea of the absolute best, nothing new will ever be created.”
In the paper, Bejan first looks at the example of passengers arriving by train and walking across a room with many exit points. With the total area of the room remaining constant but the length and width of the room free to change, he solves for the optimal shape of the room to get all passengers where they’re going the quickest. With the solution equations in hand, he shows that providing even 1% wiggle room for imperfection away from the best performance opens the design space by 28%.
In his second example, Bejan looks at the flapping motion of birds at nearly constant altitude and speed. Considering the various forces involved — drag during gliding, lift created by wing size, speed and body size, among others — he formulates an equation for the rhythm of wings needed to maintain constant speed with minimum effort. While an optimal answer does exist, Bejan once again shows that allowing for just 1% imperfection above the theoretical minimum effort opens the design space by 20%.
Bejan says that he chose these examples because they involved changing only a single variable, a single degree of freedom — the shape for a room or the flapping rhythm for a wing. In more complex examples that involve many variables, these tiny tolerances for imperfection create an even wider range of “good enough” solutions.
The lesson learned is that science now has a predictive idea of how nature works. By focusing less on finding absolute optimal designs, researchers may use the freedom to iteratively move toward entirely new design concepts that wouldn’t otherwise have been within their sight. It also gives designs, methods and entire fields of study the ability to adapt to a changing world.
“The doctrine of chasing the best design is not helpful,” Bejan said. “The teaching of science should go hand-in-hand with the freedom to take a shot, hit the vicinity of the mark and move on. The end goal isn’t just to hit a bullseye, but to keep more arrows in your quiver to keep taking shots over a long period of time.”
This work was supported by a grant from CaptiveAire Systems.