Lift Theory for Level Flight Using Bernoulli's Principle and Cross-Stream Acceleration
|Title||Lift Theory for Level Flight Using Bernoulli\'s Principle and Cross-Stream Acceleration|
|Keywords||flight, lift force, flow past solids, incompressible fluids, frictionless flow|
The lift force per unit span on a thin circular arc wing at subsonic speeds and at zero angle of attack is found to be directly proportional to the product of the fluid density, the square of the uniform fluid speed relative to the wing and far away from it, and the wing's maximum thickness. The bottom surface of the wing is assumed flat. The lift equation is based on Bernoulli's principle and on the length scale for flow perturbation above the wing, which is calculated to be proportional to the wing's chord. Central to this calculation is the downward fluid acceleration, and its associated pressure gradient, above the top curved surface of the wing. When standard theory is applied to the same wing profile a similar form is found for the lift equation, but the constant of proportionality is significantly larger (3.14 compared to 1.89). An explanation for the discrepancy is given. Extensions of the new lift concept to wing geometries involving combinations of two or more circular arc profiles are outlined. A possible practical consequence of the new theory is suggested.