Analyzing winglets to find the optimal characteristics to result in the lowest net drag for an aircraft was the goal of University of Illinois researchers Phillip Ansell, Kai James and graduate student Prateek Ranjan. Source: Debra Levey Larson

The winglet may not be a widely known part of a plane, but it is one of the most important parts of the wing. The winglet is at the very tip of the wing, angling upward. The winglet reduces drag, which allows the plane to travel at higher speeds or allows the pilot to throttle back and save fuel. The winglet also reduces wingtip vortices, which can cause issues in flight.

Winglets have been around since the 1970s. They vary in size, shape and construction. University of Illinois researchers set out to find the perfect characteristics for the optimal, lowest drag winglet.

"Many academic studies on non-planar wing designs idealize winglets installed with a sharp 90-degree turn at the tips, though there are a lot of things potentially wrong with having these sharp junctures. Because individual aircraft have a unique set of constraints and requirements, it's difficult to make generalizations about how an aircraft should be designed," said Phillip Ansell, assistant professor in the department of aerospace engineering in the College of Engineering at the University of Illinois. "However, when looking at non-planar wing systems, we distilled the problem to something very specific and canonical. We used a method of multi-fidelity optimization, beginning with very simple mathematical algorithms to better understand the design space within plus or minus 10 percent accuracy, then ran more advanced simulations to understand how the winglet influences the flow field and performance of the wing."

The team found the perfect design: A non-linear design called Hyper Elliptic Cambered Span (HECS) wing configuration. The virtual projection of this design can be mathematically described as the equation of a hyper ellipse.

"We distilled the wing geometry down to something very simple," Ansell said. "We expressed the non-planarity of the wing — how curved it is, how high the wingtips are, etc. — using equations for a hyper-ellipse. Now we can easily change the values in the equation to find the best-performing wing while trading off sharper or smoother curvature as the tip is approached, as well as larger or smaller winglet heights."

When developing the algorithm, the team started with fixed lift, fixed projected span, fixed bending movement of the wing and the fixed weight. This generated a wing with the least amount of drag possible.

"While others have studied non-planar wings with blended winglet designs, most have only looked at the so-called 'inviscid' aspect of the wing drag, ignoring the complex sources of drag introduced by the viscosity of the air," Ansell said. "But that's only about half of the picture. In our formulation, we included these viscous drag sources because it has a substantial influence on the net efficiency of the wing. For example, it is easy to reduce the inviscid drag of the wing by adding very tall winglets at the tips with very sharp junctures. However, there is a distinct viscous drag penalty by doing so that reduces the effectiveness of such a design in practice."

"By performing a rigorous numerical optimization procedure, we were able to systematically explore the space of possible designs, and ultimately obtain designs that may seem unusual, and that we could never have predicted by relying on mere intuition," said Kai James, also an assistant professor in the Department of Aerospace Engineering.

The paper on the new winglet design was published in the Journal of Aircraft.