Lift Force Calculator

Lift is the force that keeps an aircraft in the air. It is a component of the force experienced by a moving object from a fluid, which acts perpendicular to the direction of flow and pushes the object upwards. Unlike drag, lift does not slow down the object. This tool calculates this force using the standard lift equation with inputs for density, velocity, wing area, and a lift coefficient that takes into account the shape of the wing and its angle of attack. One of the five input fields can be left blank, which will cause the tool to calculate the corresponding value. For example, you could use the same tool to determine the dimensions of a wing, find the required airspeed for a given amount of lift, or derive the lift coefficient from a known force.

What is lift?

When a wing moves through a fluid medium the air is deflected downwards and produces a thrust while the wing experiences an equal but opposite reaction force. Both explanations describe the same effect. Bernoulli's explanation states that the acceleration of the airflow along the curved upper surface of the wing results in lower pressure on the top surface compared to the bottom, which causes the wing to be lifted by this pressure difference.

The Newtonian explanation is that the wing deflects the oncoming air downward, and according to Newton's third law of motion, the air reacts by pushing the wing upward. The values resulting from both explanations are identical. Lift always acts perpendicular to the direction of flow, which distinguishes it from drag. Drag opposes the motion, while lift is a force that supports the motion.

There are four factors that determine the amount of lift generated: the density of the fluid, the velocity of the wing moving through it, the area of the wing exposed to the airflow, and a lift coefficient that combines shape and angle of attack into a single number. The most significant factor is the velocity, because it appears in the equation squared.

Here's how to use this calculator.

If you enter the fluidity, velocity, area and lift coefficient, the tool will give you the resulting lift. Conversely, if you leave blank the field for the desired parameter and fill in values for the other four parameters, it will calculate that value. No mode selection is required; the engine calculates the value of the blank input field.

This can be used for everyday tasks, such as determining the wing size based on target loading, finding a speed that produces enough lift, or checking coefficients from airfoil tables. By enabling "Lift/Drag Ratio" you can add drag coefficient and determine glide ratio. By enabling "Takeoff" and adding weight you can calculate minimum flying speed.

Lift equation:

Lift is derived from the standard lift equation, which combines all effects of shape and angle into a single coefficient.

Here, $\rho$ is the fluidity, $v$ is the speed, $A$ is the area and $C_L$ is the lift coefficient. Let's take an example of a Cessna 172 flying near sea level: The wing area is about 15 m$^2$, the flight speed is 50 m/s and the lift coefficient is 0.5.

This is equivalent to about 2580 pounds of force, which is almost the weight of this small plane, so the wings are carrying the entire airplane. The following table shows each symbol and its value for this example.

Whether you accelerate the same Cessna from 50 m/s to 100 m/s, lift does not double but is about 45900 N, which is four times the original value. This is because the speed factor is squared. Therefore take-off and landing speeds must be carefully controlled.

Formula transformation to calculate any values:

The lift equation is a simple product and can therefore be easily rearranged. The tool uses the following form and allows you to select the appropriate form for the missing element.

The first equation calculates the coefficient that a wing must have based on known lift and speed. The second equation shows the required speed to carry a given load, which is central for takeoff calculations. The third equation determines the wing area from a target lift.

Dynamic pressure and lift pressure:

In addition to force, the tool also displays two types of pressure. Dynamic pressure $q = \tfrac{1}{2}\rho v^{2}$ is the pressure that a moving fluid has and it's what actually drives lift and drag.

The average lift pressure $L/A = q\,C_L$ is a dynamic pressure scaled by a coefficient. It represents the resulting upward force between the bottom and top of an airfoil, expressed as a single number to quantify Bernoulli's effect. When this value is spread over the entire surface area of the wing, it results in total lift.

Lift coefficient

The lift coefficient is a dimensionless quantity that summarizes the shape of an airfoil, its angle of attack and flow conditions into one number. For thin airfoils at small angles of attack it is close to zero when the angle of attack is zero. As the angle of attack increases, the lift coefficient increases up to some limit.

If the critical angle of attack is exceeded, flow separates from the top surface of the wing causing a sudden drop in lift coefficient and the wing stalls. This is why there is an upper limit to the amount of lift that can be produced by any given airfoil at a particular speed. Typical values are listed below for reference.

Fluidity and Height

Since the lift equation applies to any fluid, density is a value that distinguishes air from water. At equal speeds, a denser fluid will generate more lift. The density of water is about 800 times that of air. Thus, underwater wings with a relatively small wing area can still lift a ship at moderate speeds.

Air density decreases with altitude and is lower on hot days. Thus the lift generated by a wing at high altitudes or when it is hot will be less than the lift on a cold morning at sea level. Pilots refer to this as density altitude. For that reason, a fully loaded airplane requires a longer runway for takeoff from an airport in the mountains on a hot day.

Lift/drag ratio and angle of attack

By enabling the "Lift/Drag Ratio" option and adding a drag coefficient, you can check the efficiency of an airfoil. The lift/drag ratio is the ratio of the lift coefficient to the drag coefficient.

This ratio is also the glide angle. If the ratio is 24, this means that a wing will travel about 24 meters forward for every meter it descends, and the corresponding glide angle is small. The tool reports the current drag at the given speed as well as the corresponding glide angle. As a reference: modern gliders achieve values of 40 to 60, commercial airliners have about 17 in cruise flight, light aircrafts about 10, and flying birds have a range from 10 to 20 on approach.

Detachment speed and flow detachment speed

If you turn on the "Takeoff" option and specify the weight that the wing has to carry, then you can calculate the minimum speed at which an airplane can fly. In a steady level flight, lift must equal weight. Solving for $L = m g$ in the equation yields the following formula for minimum flying speed:

At flight speeds below this value the wing will not generate enough lift and stall. This value is close to the takeoff limit speed, and the entered lift coefficient for calculation is used. The tool also outputs the wing loading, which is the weight divided by the wing area. This is an indicator of how much load the wings are carrying.

Applications of lift

The use of lift is not limited to aircraft. Underwater wings raise the ship with underwater wings and reduce drag at high speeds. The rotor blades of wind turbines are rotationally symmetric profiles that are optimized for lift, and sails are vertical surfaces that propel a boat against the wind.

The wings of race cars generate a negative lift, which presses the tires down on the road and increases grip. This is why their lift coefficient is negative. Even a soccer ball or frisbee that floats in the air follows the same equation. In these applications, the tool is mainly useful in early phases of design and validation and supports decision making before extensive wind tunnel tests or simulations.

Tips for a correct estimation

Choose a reference area that matches the lift coefficient chosen. Published values are usually associated with a particular area, often the wing area. Use an appropriate fluidity and conditions for the medium, not always sea level air.

If a certain accuracy is required, you should find the lift coefficient from an airfoil database or wind tunnel measurements as it varies with angle of attack and airfoil profile. Note that these results are meant to be reliable estimates for initial design phase or educational purposes.