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As in the momentum equation there are many variations for applying F, some argue that the mass flow should be corrected in either the axial equation, or both axial and tangential equations. Others have suggested a second tip loss term to account for the reduced blade forces at the tip.
There are two causes of aerodynamic force: [1]: §4.10 [2] [3]: 29 the normal force due to the pressure on the surface of the body; the shear force due to the viscosity of the gas, also known as skin friction. Pressure acts normal to the surface, and shear force acts parallel to the surface. Both forces act locally.
Consider fluid flow around an airfoil. The flow of the fluid around the airfoil gives rise to lift and drag forces. By definition, lift is the force that acts on the airfoil normal to the apparent fluid flow speed seen by the airfoil. Drag is the forces that acts tangential to the apparent fluid flow speed seen by the airfoil.
Lifting line theory supposes wings that are long and thin with negligible fuselage, akin to a thin bar (the eponymous "lifting line") of span 2s driven through the fluid. . From the Kutta–Joukowski theorem, the lift L(y) on a 2-dimensional segment of the wing at distance y from the fuselage is proportional to the circulation Γ(y) about the bar a
Streamlines around a NACA 0012 airfoil at moderate angle of attack. A foil generates lift primarily because of its shape and angle of attack. When oriented at a suitable angle, the foil deflects the oncoming fluid, resulting in a force on the foil in the direction opposite to the deflection. This force can be resolved into two components: lift ...
The distribution of forces on a wing in flight are both complex and varying. This image shows the forces for two typical airfoils, a symmetrical design on the left, and an asymmetrical design more typical of low-speed designs on the right. This diagram shows only the lift components; the similar drag considerations are not illustrated.
In words, the wind axes force is equal to the centripetal acceleration. The moment equation is the time derivative of the angular momentum: = where M is the pitching moment, and B is the moment of inertia about the pitch axis. Let: =, the pitch rate. The equations of motion, with all forces and moments referred to wind axes are, therefore:
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil (and any two-dimensional body including circular cylinders) translating in a uniform fluid at a constant speed so large that the flow seen in the body-fixed frame is steady and unseparated.