Force of Lift

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Equation / Last modified by KurtHeckman on 2018/04/17 17:47
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MichaelBartmess.Force of Lift
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The Force of Lift calculator uses the equation L = ½•A•ρ•CL•V² to compute the lifting force on a wing based on the surface area, DragForce-illustration.pngairframe forcesthe velocity of the wind, the density of the air and a lift coefficient.

INSTRUCTIONS: Choose units and enter the following:

  • (CL) - This is the dimensionless lift coefficient that characterizes the amount of lift generated for a surface given the mass density of the fluid through which the surface moves, it's surface area and its velocity
  • (A) - This is the wing surface area
  • (V) - This is the velocity of the wind through the air
  • (ρ) - This is the density of air (default is the dry air density)

Force of Lift (L): The calculator returns the force of lift in Newtons.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

Bernoulli's principle is based on the conservation of energy, which dictates that in a steady flow of a fluid (lacking any substantial turbulence) the sum of all mechanical energy along a line of flow, a streamline, is the same at all points on that flow path. This , in turn means the sum of the potential and kinetic energy must remain constant and so with increased velocity of the flow, there is an decrease in static pressure.

From this same Bernoulli's principle we can derive the equation to calculate the lift force on a wing surface (airfoil). When the air flowing past the top surface of an aircraft wing moves faster than the air flowing past the bottom surface, Bernoulli's principle defines a difference in pressure on the two surfaces of the wing, with the lower pressure being on the upper surface where the faster flow exists.

The difference in pressure sums to a net upwards lifting force, as calculated in this equation.  The formula for the force of lift is:

      L = ½•A•ρ•CL•V²

where:

  • L is the force of lift
  • A is the wing surface area
  • ρ is the density of fluid
  • CL is the lift coefficient
  • V is the velocity of flow

Density of Air

The density of air, ρ (Greek: rho) (air density), is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in temperature or humidity. At sea level and at 15 °C, air has a density of approximately 1.225 kg/m3 (0.001225 g/cm3, 0.0023769 slug/ft3, 0.0765 lbm/ft3) according to ISA (International Standard Atmosphere).

See Also

References

  • Wikipedia - http://en.wikipedia.org/wiki/Density_of_air