June 1, 2023, ©. Leeham News: Last week, we examined ways to lower the dominant drag of an airliner, the air friction drag (Figure 1).
Now we look at the second largest drag component, the Induced drag, and how it can be reduced. We go through the fundamentals of the drag to understand how to affect it. Then we look at aircraft changes to reduce Induced drag and if these make sense on an overall aircraft efficiency level.
If air friction drag can be called “ drag due to size” of an airplane, the Induced drag is “drag due to weight”. So the first action one can take to reduce Induced drag comes from this simplification, reducing the airplane’s weight.
Weight is the downward force caused by the earth’s gravity pulling on the airframe mass. It’s measured in lb in the Imperial system and Newton in the SI system. Note that lb is often used instead of the correct slug to denote mass in the Imperial system, whereas SI here uses kg. It’s why we use lbf for weight and other forces in our series.
Induced drag comes from the air’s desire to stream from a higher-pressure region below the aircraft’s wing to a lower-pressure region above the wing when flying, Figure 2.
The forward speed and the air circulation around the wings cause a wide rolling-up wake behind the aircraft, Figure 3. In the image, we can see the air downstream of the aircraft is affected over six wingspans wide.
An aerodynamicist that has described the widespread effects of an aircraft on the surrounding air is Doug McLean in his excellent book “Understanding Aerodynamics.”
McLean debunks several myths in the book. Examples: wingtip devices working by local modification of the airstream; aspect ratio is related to Induced drag, and the Prandtl box wing works beyond an in-the-vertical plane staggered wing.
The Induced drag of aircraft is dependent on the parameters in the Induced drag formula;
Induced drag = Lift^2 divided by 0.5 * Air density * Speed^2 * Pi * Wingspan^2
Let’s look at these relationships and understand what they mean:
Figure 4 shows there is an ideal speed for the lowest drag where Induced drag and Parasitic drag (where friction drag dominates) are equal. This is called the green dot speed in an airliner, and it’s the speed at which waiting patterns are flown. As an airline has many costs that increase with time, the cruise speed is higher than the speed of lowest drag.
Low air density increases Induced drag, but it’s not squared. Therefore, airliners fly high as a lower air density reduces air friction drag. An airliner gains in total drag by flying high, as this brings the two drags closer to the center in Figure 4 (Induced drag increases and Parasitic drag decreases).
The Induced drag equation is valid when the lift distribution of the wing is elliptical. As this is seldom the case in practice, an “Oswald’s efficiency factor” e is added to the denominator.
A practical airliner wing seldom has an ideal elliptical lift distribution as mechanical or other aerodynamic constraints deviate the wing from an ideal elliptical lift distribution. Engines on the wings also affect lift distribution, propeller engines in a major way, and jet engines to a lesser degree. With typical e values of 0.8 to 0.9 for modern airliner wings, it increases the Induced drag by 11% to 25%.
We now know we can reduce the Induced drag by:
We will look at aircraft architectures that use these four factors to reduce Induced drag in the next Corners. We will also use our Airliner Performance Model (APM) to calculate the gains from different architectures.