January 19, 2018, ©. Leeham Co: In the last Corner, we described how the boundary layer theory lead to the understanding of Friction drag for aircraft. The mechanisms behind Induced drag was understood about the same time.
Once again Prandtl was involved, but it was an English person who first postulated the physical root of induced drag, Fredrick Lanchester.
Lanchester observed how the air flowed around a flat plate, Figure 2. He saw the air turning up ahead of the plate, then down on top and bottom sides and finally straighten out.
From a theoretical point, he argues in his 1907 book, Aerodynamics, this can be thought of as a linear flow combined with a circular flow. On the topside, the flows augment each other; the air flows faster in a downward curve and the pressure drops (according to Bernoulli’s equation, which was accepted at the time).
On the bottom side of the plate the flows are opposed and the air slows and turns down. At the trailing edge, the two streams meet and at some length behind the plate the circular motion is finished, the air follows the free stream again.
This basic idea was used by Zhukovsky and Kutta to independently formulate the circulation theory of lift (the plate’s contribution to the free stream is adding the circulating motion, by it creating lift).
Lanchester also understood what happened at the tips of the plate/wing. He observed tip vortices and understood these were created by a flow which went from the higher pressure on the bottom of the wing to the lower pressure on the top of the wing.
This circular motion combined with the free stream created “vortex trunks”, shedding from the wing tips, Figure 3.
Lanchester didn’t formulate any theory how to estimate the effect of these circulations. It was left to Kutta-Zhukovsky for their infinite wing circulation theory and to Prandtl for the finite wing circulation theory.
It’s important to understand, induced drag is coming from the global spanwise change of direction of the air around a wing, Figure 4.
The global spanwise circulation around the wingtips is the source of induced drag, not the very visible wingtip vortices. The air behind a wing creating lift is forced down into a giant vortex sheet (Figure 5) which continuous down behind the aircraft.
In air where the low pressure of the high-speed air causes condensation or at cloud tops, one can see this gigantic vortex sheet left by the aircraft, Figure 6.
Induced drag is highest at low speed, friction drag at high speed, Figure 7. A high aspect ratio wing is therefore important for take-off and initial climb performance.
Here how the different drag components affect a typical airliner flight:
As the aircraft increases speed toward cruise Mach, transonic drag sets in. This we will cover in the next Corner.