The Lift Formula

The lift formula is one of the very few formula that you have to remember or work with at the basic level of learning to fly.

Whilst we don't need to actually work out how much lift is being generated, a good knowledge of the lift formula greatly assists in understanding what's going on in a changing environment, and knowing what to expect as a result.

OK, Here's the Formula:

 lift formula dets

Let's Look at Each of the Terms Individually.

On the left side of the equation, we have the total lift produced, Lift. In level flight, this must always be equal to the total weight, otherwise the aircraft would climb or descend, so it wouldn't be level flight! We'll come back to this.

The first term on the right side is the Coefficient of Lift, CL. This is simply a number between zero and two, which depends on the Shape of the Wing, and the Angle of Attack. Practically, it can't be zero, because that would give us no lift (anything multiplied by zero equals zero), so no flight!

Whenever the pilot changes the shape by extending the flap, the the Coefficient of Lift, CL is increased, and, if nothing else changes, the Lift will increase and the aircraft will start to climb. [The same thing will happen when the pilot operates the ailerons, but as the ailerons operate in opposite directions, (one down, the other up) Lift increases on one wing and decreases on the other, causing the aircraft to roll. The wing with the down-going aileron produces more Lift, and the wing with the up-going aileron produces less Lift.]

The other component of the Coefficient of Lift, CL, is the Angle of Attack, which is also controlled by the pilot. Have a read of the tutorial on Angle of Attack if you're not sure what this means. Pulling back on the stick increases the Angle of Attack, which increases the Coefficient of Lift, CL, which in turn increases the Lift causing the aircraft to climb. [This only happens up to the stalling Angle of Attack, when the wing stalls, CL decreases rapidly and Lift reduces.]

The next term in the equation is the Air Density, 1/2ρ. The symbol ρ is the Greek letter rho, which is used to denote air density. In level flight, the Air Density will remain practically constant. It will change as pressure systems move across the country, but not in the short term.

The next term is V for velocity, or true airspeed. Notice that this term is squared, so that if we increase the airspeed, the Lift will be increased in proportion to the square of the airspeed, so airspeed has a greater effect on the lift than any one of the other components.

The final term in the equation is S, for Surface Area of the wing. Again, in practical terms, the surface area doesn't change for the type of aircraft we're considering, training aircraft such as the Jabiru 160.

Some Practical Applications

Since all the elements on the right side of the equation are multiplied together, a change in any one of them will produce a change in the Lift, so we'll no longer be in straight & level flight. However if we change two or more elements, say increase one and decrease another by a corresponding amount, then no change to the lift occurs, and straight & level flight continues.

Angle attack



If we want to fly straight & level but slowly, we can reduce power, which will reduce airspeed, but we'll have to move the stick back to increase the Angle of Attack and keep the lift constant so we don't descend. We're sort of "trading off" lift from speed, for lift from angle of attack.





AoA flap



If we want to fly even slower, we can trade off the lift from the reduced airspeed by extending flap, and gaining more lift from the changed shape of the wing, thus keeping total Lift constant. However, as the changed shape alters the position of the chord line of the wing, and increases the Angle of Attack too, we'll need to counter this with forward stick to prevent the lift from increasing, causing the aircraft to climb. See the next paragraph.





AoA flap corrected


If we move the stick forward as the flap extends, we can prevent the Angle of Attack from changing, so leaving the lift unaffected, and the aircraft remains in level flight.
How do we know we've got just the amount of stick movement? Only by monitoring the performance to make sure the aircraft doesn't climb or descend.
It takes a lot of practice to be able to do this smoothly and accurately.