Physics reveals the optimal roof ratios for energy efficiency

Whereas serving as a visiting professor in Benevento, exterior Naples, Italy, Adrian Bejan seen one thing in regards to the native structure: All of the roofs seemed the identical. With what appeared like too-shallow peaks on smaller, older constructions clustered collectively, maybe it was simply the fashion of the instances.

Or maybe the traditional Roman builders had been onto one thing. An professional in thermodynamics and the motion and movement of warmth, Bejan, the J.A. Jones Distinguished Professor of Mechanical Engineering at Duke, was the proper particular person to sleuth out a solution.

Sitting down with pencil and paper, Bejan went by the equations and calculations that govern warmth movement and switch inside two related shapes: a protracted roof with a triangular cross part and a round cone.

The outcomes, obtained in collaboration with Pezhman Mardanpour, assistant professor of mechanical and supplies engineering at Florida Worldwide College, are published in Worldwide Communications in Warmth and Mass Switch. They confirmed that there are certainly roof shapes that maximize warmth retention—the older era of Italian architects knew what they had been doing.

“Pockets of air are good insulators, and attics are basically just differently shaped pockets of air,” Bejan stated. “Whereas energy conservation is a well-liked buzzword in the present day, in years long gone it was a matter of survival.”

The small print of how squat or tall a roofline decide how the air inside it would act. Given a single peak on an A-frame or round cone, if that peak is lower than three toes tall, the air will movement easily and uniformly throughout it like water careening down the facet of a sink. But when the height is greater than three toes tall, the air will tumble round chaotically like smoke waving wildly within the wind.

Primarily based on the physics of those airflows and heat transferif a roof peak is shorter than roughly three toes, it needs to be about three or 4 instances wider than it’s tall to reduce warmth loss. And if a roof peak is taller than three toes, it needs to be an equilateral triangle with a height-to-width ratio of 1.

Maybe unsurprisingly, these are roughly the identical ratios that may be present in numerous older, modest dwellings created the world over. And they’re fairly near the rooflines that Bejan noticed that day in southern Italy.

“This type of insight is not hard to rationalize, but it’s easy to overlook even though there are examples everywhere,” Bejan stated. “It’s important for our students—and their professors—to open their imaginations and ask why things are the way that they are.”

Whereas Bejan doubts that architects from days passed by had been making use of thermodynamics to their roof designs, he would not suppose their shapes had been unintended, both. It is not troublesome to think about, he says, discovering that one neighbor’s house is hotter than one other’s and copying its design repeatedly throughout a few years.

It is a lesson, he says, that trendy architects might stand to think about as properly.

“Today’s homes and buildings are being designed to be as energy efficient as possible,” Bejan stated. “But to my knowledge, nobody is considering the physical shape of the building, or any ‘thing’ like a vehicle or animal, as a variable that could help with that efficiency, and perhaps we should be.”