How do endplates reduce induced drag?

Question

I have heard the explanation which states that the endplates reduce the tip vortex formation thereby reducing induced drag. From what I understand induced drag is the backwards component of the total force acting on the wing and a consequence of lift creation over a finite span. Thus it depends on the downwash angle. Vortex is an after effect of this lift. I dont understand how induced drag is reduced by suppressing this vortex.

I would appreciate some clarity on this topic or an explanation which doesn't include vortices.

Answer 1

The vortex itself isn't the issue, it's the "leakage" that is resulting in the vortex. The leakage is from the air near the tip being free to flow around it and results in wasted energy.

The wing is moving along driving air down, but near the tip some of the air, instead of being made to accelerate down, is taking the path of least resistance around the tip (being sucked toward the low pressure side you might say) instead and doesn't contribute to the lift force. It was displaced, and energy was consumed, but the displacement was out and around the tip instead of down.

The tip plate is just supposed to inhibit some part of the lateral flow around the tip by blocking it, reducing the leakage and resulting in more of the air package being forced downward than without the tip plate. What is referred to as a reduction in induced drag is just an improvement of the ratio of lift to drag due to less leakage losses, so for a given amount of total lift force, the induced drag is less than for the same lift force without the tip plates.

To do any good, tip plates have to be quite large (because the circulation field extends quite a distance from the wing), which being draggy themselves, cancels out most of the benefit, which is why you don't really see them used very much, except where the end plate effect can be created by default, such as with a T tail where the horizontal stab makes a nice end plate for the top end of the rudder.

Answer 2

Any time you have an object moving through a fluid, you create a disturbance in the fluid (turbulence). The amplitude of disturbance is in proportion to how much energy you are losing (i.e. dissipating into the fluid).

Take a submarine for example. They are designed to optimize the flow of water around the vessel as it moves through the water. This prevents turbulence, which causes noise detectable by Sonar. Creating turbulence, and consequently noise, means that the sub is transferring mechanical energy into it's surroundings. This is wasted energy.

If the vessel (any vessel, boat, airplane, sub) moves faster, typically the turbulence will increase. This means that more energy is being transferred from the sub into the surrounding, and being wasted.

Vortices forming at the wingtips of airplanes is a similar issue. Instead of cleanly "slicing" through the air, the wing is creating turbulence, meaning kinetic energy is being lost to the surrounding air.

Disclaimer: I am not an aerospace engineer.