Measurement [edit]

The aerodynamic center of an airfoil is usually close to 25% of the chord behind the leading edge of the airfoil. When making tests on a model airfoil, such as in a wind-tunnel, if the force sensor is not aligned with the quarter-chord of the airfoil, but offset by a distance x, the pitching moment about the quarter-chord point,   is given by

where the indicated values of D and L are the drag and lift on the model, as measured by the force sensor..

Coefficient [edit]

The pitching moment coefficient is important in the study of the longitudinal static stability of aircraft and missiles.

The pitching moment coefficient   is defined as follows^[3]

where M is the pitching moment, q is the dynamic pressure, S is the planform area, and c is the length of the chord of the airfoil.   is a dimensionless coefficient so consistent units must be used for M, q, S and c.

Pitching moment coefficient is fundamental to the definition of aerodynamic center of an airfoil. The aerodynamic center is defined to be the point on the chord line of the airfoil at which thepitching moment coefficient does not vary with angle of attack,^[2] or at least does not vary significantly over the operating range of angle of attack of the airfoil.

Roll moment

In a vehicle suspension, roll moment is the moment of inertia of the vehicle's sprung mass (the portion of its weight supported by the suspension). The roll moment is the product of the sprung mass and the square of the distance between the vehicle's roll center and its center of mass. If the vehicle is subjected to centrifugal forces, such as in a turn, the roll moment will cause the body to rotate (lean) towards the outside of the turn.

In aeronautics, the roll moment is the aerodynamic force applied at a distance from an aircraft's center of mass that causes the aircraft to undergo angular acceleration about its roll axis. The roll axis is usually defined as the longitudinal axis, which runs from the nose to the tail of the aircraft. A roll moment can be the result of wind gusts, control surfaces such as ailerons, or simply by flying at an angle of sideslip. See flight dynamics.

19. Write the formula of experimental aerodynamics for lift, to term values, which recontained in this formula

Lift coefficient [edit]

Main article: Lift coefficient

If the lift coefficient for a wing at a specified angle of attack is known (or estimated using a method such as thin airfoil theory), then the lift produced for specific flow conditions can be determined using the following equation:^[89]

where

• L is lift force,

• ρ is air density

• v is true airspeed,

• A is planform area, and

•  is the lift coefficient at the desired angle of attack, Mach number, and Reynolds number^[90]

Kutta–Joukowski theorem [edit]

Main article: Kutta–Joukowski theorem

Lift can be calculated using potential flow theory by imposing a circulation. It is often used by practising aerodynamicists as a convenient quantity in calculations, for example thin-airfoil theoryand lifting-line theory.

The circulation   is the contour integral of the tangential velocity of the air on a closed loop (also called a 'circuit') around the boundary of an airfoil. It can be understood as the total amount of "spinning" (or vorticity) of air around the airfoil. The section lift/span   can be calculated using the Kutta–Joukowski theorem:^[45]

where   is the air density,   is the free-stream airspeed. Kelvin's circulation theorem states that circulation is conserved for any circuit moving with the fluid.^[91] When an aircraft is at rest, circulation is zero.

The challenge when using the Kutta–Joukowski theorem to determine lift is to determine the appropriate circulation for a particular airfoil. In practice, this is done by applying the Kutta condition, which uniquely prescribes the circulation for a given geometry and free-stream velocity.

A physical understanding of the theorem can be observed in the Magnus effect, which is a lift force generated by a spinning cylinder in a freestream. Here the necessary circulation is induced by the mechanical rotation acting on the boundary layer, causing it to induce a faster flow around one side of the cylinder and a slower flow around the other. The asymmetric distribution of airspeed around the cylinder then produces a circulation in the outer inviscid flow.^[92]