Lift-induced drag

Lift-induced drag, also called induced drag, vortex drag, or drag due to lift, is an important idea in aerodynamics. It is a type of force that happens when something moving, like an airplane, changes the direction of the air around it. This happens because the wings or other parts of the airplane push air down to make the plane go up, which is called lift.

This special kind of drag happens not just in airplanes but also in cars that have special parts called airfoils to push air down and make the car stick to the road better, known as downforce.

One interesting thing about lift-induced drag is that for a plane to stay in the air with the same amount of lift, it can actually use less energy if it flies faster, up to a certain speed. This might seem strange, but it is true! Another way to reduce this type of drag is to have wings that are wider or to add special devices at the ends of the wings, called wingtip devices.

Explanation

When an airplane flies, the force pushing it up is called lift, and the force slowing it down is called drag. Lift happens when the wings change the direction of the air moving past them. This change in direction means the air is speeding up or slowing down in a new way, which creates a force.

In slow flight, airplanes can create a lot of drag. By flying faster and adjusting the wings, the airplane can keep the same lift while using less drag. This helps the airplane be more efficient.

Vortices

When a wing creates lift, the air below it is pressed down, while the air above it is lighter. This difference in air pressure causes the air to flow from below the wing, around the wingtips, and up to the top. This movement twists the air and creates spinning currents called vortices behind the wing.

These vortices make it harder for the wing to generate lift. To get the same amount of lift, the wing must tilt upward more, which pushes the force backward and creates extra drag. Even though this tilt is small, it adds to the drag, and this extra drag grows with the amount of lift the wing creates. The vortices quickly combine and follow behind the wing as it moves.

Calculation of induced drag

For a flat wing with an even spread of lift, we can figure out the induced drag, written as (D_i). The formula looks like this:

(D_i = \frac{L^2}{\frac{1}{2} \rho_0 V_E^2 \pi b^2})

Here’s what each part means:

• (L) is the lift the wing creates.
• (\rho_0) is the normal density of air at sea level.
• (V_E) is the equivalent airspeed the plane feels it’s moving at.
• (\pi) is the number we get when we divide the distance around a circle by its width.
• (b) is how long the wing is from tip to tip.

This shows that induced drag changes based on how much lift there is, how fast the plane is going, and how long the wings are. If a wing isn’t flat or doesn’t spread lift evenly, we adjust the calculation using something called the span efficiency factor.

We can also compare induced drag to other kinds of drag by using special numbers called coefficients. This helps us see that longer, thinner wings (high aspect ratio) help planes fly more efficiently. As the plane tilts upward more (higher angle of attack), induced drag gets bigger.

This way of calculating induced drag comes from ideas developed by Prandtl's lifting-line theory. Similar methods work for wings that aren’t flat or for different lift patterns.

Reducing induced drag

To reduce the drag that happens when a plane creates lift, one way is to make the wings longer. The Wright brothers used special curved edges on their wings. Modern planes often have winglets at the ends of the wings, which help lower this type of drag and also make the wing taller.

For planes with a certain amount of wing space, wings that are longer and narrower create less of this drag than shorter, wider wings. For big planes flying at steady speeds, this kind of drag makes up a big part of the total drag the plane feels. Lowering it helps save money and reduces effects on the environment.

Combined effect with other drag sources

In 1891, Samuel Langley tested flat plates and found that plates with a higher aspect ratio created more lift and had less drag than those with a lower aspect ratio.

Induced drag needs to be added to parasitic drag to find the total drag on an aircraft. The combined drag of these two types has a lowest point at a certain speed, called the minimum drag speed (V_MD). Flying at this speed helps airplanes be the most efficient. This speed changes as the airplane gets lighter during a flight.

Airplanes can fly higher where the air is thinner, which allows them to go faster using the same amount of fuel. The best speed for flying the farthest distance is just a little slower than the speed for the farthest distance, allowing pilots to go a bit faster with only a small drop in distance traveled.