What is the lift formula or equation?

By Aerodynamics Leave a comment

The lift formula or equation is CL ½ p V2 S.

This formula is used to quantify the factors or components that influence lift production.  The factors are coefficient of lift, air density, velocity, and surface area.  Not all factors of the equation are equal.

CL is the coefficient of lift.  In general, this is the angle of attack on the rotor blade.  Until the stalling angle is reached, an increase in the CL will produce more lift.

½ p V2 This section of the formula is Dynamic Energy or Kinetic Energy.  Basically, dynamic/kinetic energy is derived from the movement of air.  The p is for pressure or air density.*  The greater the density (lower pressure altitude) the more lift produced.

V2 is for velocity or the rotor RPM with regards to helicopter flight.  As referenced by the squared component, velocity is a major factor in lift production.  A slight change in velocity can have a significant impact on lift.  This fact is one reason that low rotor RPM is a significant issue with helicopters.

S stands for surface area.  In helicopter flight, the surface area of the rotor blades does not change.  Unlike fixed-wing aircraft, rotor systems do not have flaps that can increase or decrease the surface area.**

* The p is m for mass in some equations.  With reference to lift, mass is the density of the air.
** There are some experimental systems, but in general these are not available to most pilots.  In addition, this discussion does not consider stabilizers or other systems that may change the surface area slightly, as these are not a significant factor in helicopter flight.

Reference(s):

Principles of Helicopter Flight, 2nd Edition, pg. 18

Other Helicopter Aerodynamic Principles

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3 Comments

  • Daniel Stockdale Reply

    This formula is deficient. Two rotors can have the same surface area but different lengths and widths. The velocity of the rotor tip of the longer, narrower rotor will be greater than the shorter, wider rotor when both have the same rpm.

    • ETL Reply

      You are correct in that a longer rotor blade would have a greater velocity. As “velocity” is squared in the lift formula, changes in length would have a greater impact to lift than other changes, such as surface area alone. However, I disagree that the formula itself it deficient.

  • Daniel Stockdale Reply

    According to the lift equation when you double your speed, the lift is quadrupled so the tip of a rotor moves twice as fast as it’s halfway point and produces 4X the lift. A rotor with a value of 100 square feet could be 50X2 or 25X4. The tip of the longer one is producing much more lift than one that is 1/2 the length even if it is only 1/2 the width. Thomas Edison told us that a helicopter would need to jave a long narrow rotor even before the first one flew. The lift equation only applies to fixed wing aircraft.

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