Basics of Lift

I'm going to start this off with a short disclaimer: I am not an engineer yet and as such I won't be going in to too much detail about this topic. I'll explain as much as I confidently can, but if you are more knowledgeable and find any inaccuracies the please let me know in the comments! That being said, let's get right into it!

Image of a B-2 Spirit in flight by tusrhode via Suwalls

The Equation

Lift force is, as implied by the name, a force that helps keep aircraft in the air. It is a force that pushes them upwards, negating the gravitational force, and allowing them to fly. The exact math behind finding lift can get complicated, but for now we'll just talk about the equation for lift which on its own is relatively simple to understand.

L = (1/2) x Cl x ρ x V² x A

L = Lift

Cl = Coefficient of Lift

ρ = Density of the air (also denoted as d or r sometimes)

V = Velocity

A = Wing Area

Most of these values are relatively simple to figure out. The wing area can be easily measured, and the velocity at which the aircraft moves is typically determined by the pilot. The density of the air is a bit harder to find out but can be modeled using computers. The lift coefficient however, is determined by the shape of the object. Every object has a unique lift coefficient and this essentially is determined by how good of a wing the object would be. To understand how this is determined, we need to understand a little bit about how lift is produced. There are a lot of things that go into producing lift, but the main two we are going to focus on today are Bernoulli's principle and Newton's third law.

Image from FlyingMag.com

Bernoulli's Principle

Bernoulli's principle is named after Daniel Bernoulli who stated that the a fluid's speed increases with a decrease in pressure or potential energy. This basically means that as any fluid (a liquid or a gas) speeds up it decreases in pressure and vice-versa. This can be seen in the wings of a plane. There are two extremely popular misconceptions as to why the velocity of the air increases above the wing. One of them is that the air has to meet up on the other side of the wing and since the top is longer the air speeds up. The other is that a Venturi nozzle is formed at the front of the wing speeding the air up. To my knowledge, the first theory is wrong because it wouldn't speed the air up enough to cause the necessary lift, and the second is wrong because wings simply aren't a Venturi nozzle. Again, I won't go in-depth on why this is the case but I suggest this link for more information on why the first is incorrect, and this one for the second. Either ways, the speed of the air above the wings is increased which results in lower pressure relative to the air beneath the wing, causing a part of the lift.

Diagram by Mr. Truppi

Newton's Third Law

Newton's third law is the other major factor causing lift. It states that for every action there is an equal and opposite reaction, and by this he means that for every force applied there will be a reaction force in the opposite direction. Newton's second law relates force with mass and acceleration (which itself is just a change in velocity) so really force can be calculated with a mass and a change in velocity. One thing to keep in mind here is that velocity is speed with a direction, so changing the direction of an object counts as accelerating it. So knowing all this, we can think about how Newton's third law might explain lift. When a wing moves through the air, there is a barrage of air molecules hitting its underside and bouncing off in a downwards direction. The direction change means they had a change in velocity and since their velocity changed we know that a force must have been applied on them. That in turn means that they are applying an equal force in the wings in the opposite direction. The same is true of the wind above the wings. As the air reaches the end of the wing, it is angled downwards causing the air to change direction and move downwards. This is called the downwash and it helps create even more force since the air that is now moving down pushes back up on the plane.

Diagram by Michael Paetzold via Wikimedia

It is a combination of these two explanations that allows modern aircraft to soar majestically through the sky. For a more comprehensive explanation of how lift is produced be sure to check out this interactive course from the NASA Glenn Research Center.

I also run a blog where I post all sorts of random information about planes from economics, to regulations, to engineering topics such as this. If you're interested in aircraft or aviation check it out here!