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Old 28th June 2008, 14:57   #20 (permalink)
Brian Abraham
 
Join Date: Aug 2003
Location: Sale, Australia
Age: 65
Posts: 2,193
Dug out my old study notes which explains it thus. The only forces that can act on a body moving through a fluid are those produced by friction (shearing stress in the fluid which is a function of viscosity) or those produced by pressure. Except when minimum drag is considered, the pressure forces are by far the most important, and completely responsible for the production of lift. The ambient or static pressure existing around a body moving through the air, cannot produce a resultant force, so dynamic pressure is left as the fundamental source of aerodynamic forces.

The maximum force that can be produced by dynamic pressure would seem to be,

Force = Dynamic Pressure x Area

Most airfoils are capable of producing a total reaction considerably greater than that suggested by the above formula.

Consider a mass of air travelling at constant velocity that is turned through an angle of 90° by a vane whilst maintaining its constant velocity. A vector diagram of the velocity’s will show that that the resultant (acceleration or change in velocity) will be 1.414 x Velocity (being an equilateral triangle with included angles of 90° and 45°). Newton’s second law suggests then that the force acting in the direction of the resultant (on the vane) will be,

Force = Mass x Change in Velocity

Mass/Unit Time = Rho x Area x Velocity

Therefore Force = Rho x Area x Velocity x 1.414 Velocity

= 2.828 x ½ Rho x Velocity^2 x Area

= 2.828 x Dynamic Pressure x Area

Although an airfoil is unlike the vane in that it is immersed in the airstream, it still produces lift by changing the momentum of the air, and producing a greater force than predicted by the simple “pressure x area” relationship. This is equivalent to saying that the airfoil produces an aerodynamic mechanical advantage. Although the forces may be magnified by mechanical advantage, the total energy remains constant. The dynamic pressure produces the resultant force by altering the value of the local static pressure, with the total pressure remaining constant. Until the airfoil produces a change in momentum to the airflow, the dynamic pressure will not affect the static pressure, or will affect it equally, and no resultant force will exist. Once the angle of attack is set so that the momentum of the airflow is changed, the resulting dynamic pressure will produce an out of balance of the static pressures, and a resultant force will act on the airfoil. The ability of an airfoil to change the momentum of the airstream is a function of airfoil camber and angle of attack.

A helicopter with rotor blades that are free to flap give as good an illustration as you could possibly get of the downwash/lift relationship. With blades at minimum pitch there is no noticeable lift and little downwash and the tip path plane of the blades will be at a given position. As you progressively add pitch you increase both lift and downwash and you will see the tip path plane increase in height (that is, the rotor blades increase their coning angle as the lift, and downwash, progressively increase).

To sum up, the wing throws air at the ground. No downwash, no lift.
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