The lift coefficient calculator will return the coefficient of lift using the lift force and the dynamic conditions around the wings such as fluid density and flow speed. Aeronautical engineers and RC aircraft enthusiasts use the lift equation to estimate the wingspan/area or the lift coefficient to determine their design's performance. Read on to understand the lift coefficient formula, how to calculate coefficient of lift and how to use our calculator.

What is lift coefficient?

The lift coefficient is defined as the ratio of lift force to the product of surface area and dynamic pressure around the lifting surface. It is a dimensionless quantity that has no units. Mathematically, the lift coefficient CL for a surface having surface area A, fluid dynamic pressure q and lift force F can be written as:

CL = F / (A * q)

The dynamic pressure q for a fluid having density ρ and flow speed V can be written as:

q = 1/2 * ρ * V2

Therefore, the lift coefficient formula becomes:

CL = 2 * F / (A * ρ * V2)

How to calculate coefficient of lift?

Follow four simple steps to use the coefficient of lift equation. Pro-tip: Before you start, convert inputs like density and speed into appropriate units. Use the dropdown menu to select different units to enter.

  • Step 1: Enter the lift force value.
  • Step 2: Input the flow speed.
  • Step 3: Enter the surface area of the lifting surface.
  • Step 4: If the medium is other than air, change the default value of density of air to your desired number.
  • Step 5: The calculator will now use the coefficient of lift equation to return the lift coefficient value.

Example: Using the lift equation to calculate the lift coefficient?

Find the lift coefficient for the wing having surface area of 1 m2, moving at a speed of 100 m/s and generating 800 N of lift force.

  • Step 1-4: Enter the given data as per the problem.
  • Step 5: Using the lift equation, we get:
CL = 2 * F / (A * ρ * V2) =
2 * 800 / (1 * 1.225 * 1002) = 0.1306

The lift coefficient for the surface is 0.1306.

Alternatively, you can also use this calculator to estimate the lift force if you know the surface's lift coefficient. For instance, let's find the lifting force for a wing having a surface area of 2 m2, a lift coefficient of 0.52 and moving at a speed of 150 m/s.

  • Step 1: Enter the lift coefficient as 0.52.
  • Step 2: Input the speed as 150 m/s.
  • Step 3: Use the surface area value as 2 m2.
  • Step 4: Using the lift equation, we get the lift force as:
F = CL * A * ρ * V2 / 2
F = 0.52 * 2 * 1.225 * 1502 / 2 = 14333 N or 14.33 kN

The lift force for the wing is 14.33 kN.

Factors affecting lift force of an aircraft

The lift force needed to fly depends on several factors such as:

  • Weight – How much does the aircraft weigh? This includes empty weight and any onboard cargo. It is also used to estimate wing loading.
  • Speed – The speed at which it is flying. If it moves too slow, it might not be enough to generate enough lift force for it to fly. That's why every aircraft has a stall speed. The stall speed is defined as the minimum speed required to achieve level flight.
  • Density – Aircraft exhibit different performance with variations in the density of air. These variations in air density are caused by changes in altitude, temperature, and other meteorological factors. That is why different types of aircraft have different service altitude ceiling values.

You can also adjust one parameter to compensate for the other. For instance, if you want your design to carry more weight, you can compensate for that by having a higher velocity, which you can achieve by using more powerful engines or motors. You can also adjust the wingspan accordingly. However, it is impractical after a certain value. The coefficient of lift also changes with change in cross section of wing i.e. the aerofoil. Additionally, there's a separate constant for projectiles such as ballistic coefficient.

FAQ

What is coefficient of lift?

Lift coefficient or coefficient of lift is defined as the ratio of lift force and product of surface area and dynamic pressure.

What is the lift formula?

The lift formula is lift force, F = CL × q × A, where CL is lift coefficient, A is area, and q is dynamic fluid pressure.

How do I calculate coefficient of lift?

To calculate coefficient of lift:

  1. Multiply fluid pressure by velocity squared and divide the product by 2.
  2. Multiply the surface area with the preceding product.
  3. Divide the lift force by the product.

What are the factors that affect lift force?

Lift force depends on three major factors:

  1. Weight
  2. Speed
  3. Density of fluid
Rahul Dhari
Lift force (F)
lbf
Flow speed (V)
ft/s
Surface area (A)
in²
Density (ρ)
lb/cu ft
Lift coefficient (Cₗ)
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