Aerodynamic Forces | Lift And Drag Forces In Wind Turbine | Pitching Moment
Aerodynamic Forces and Moments acting on the Vehicle Body
In order to analyse the various aerodynamic forces and moments acting on the vehicle body, consider the vehicle as a mass having six degrees of freedom. Now the various aerodynamic forces acting on the vehicle body can be summarized as follows:
Px — Force of air drag in the direction of motion with wind angle along the longitudinal axis
Py — Cross wind force
Pz — Aerodynamic lift
Longitudinal Air Drag
The longitudinal component of the resultant of pressure distribution is called as “Longitudinal Air Drag”. The magnitude of this component can be represented by,
Px = Cx ρ A V2 / 2
where,
Cx — Longitudinal wind force dimensionless coefficient
ρ — Air density in kg/m3
V — Velocity of wind in m/s
A — Cross sectional area of the vehicle viewed from the front in m2
Cross Wind Force
Cross wind force is formed by the asymmetric flow of air around the vehicle body when the wind angle is not equal to zero. The cross wind force can be given as
Py = Cy ρ A V2 / 2
where,
Cy — Cross wind force dimensionless co-efficient
Aerodynamic Lift
Aerodynamic lift is the vertical component of the resultant of the pressure distribution over the vehicle body due to flow of air around it. The aerodynamic lift can be represented as
Pz = Cz ρ A V2 / 2
where,
Cz — Lift co-efficient
The lift will tend to reduce the pressure between the wheels and the ground, which causes losses of steering on the front axle and the loss of friction on the rear axle. The magnitude of this lift and its distribution over the front and rear is a function of ground clearance, the contours of the body and the underbody and the angle of attack of the air on the vehicle body.
Since these factors are not acting at the centre of gravity (C.G) of the vehicle body but at the centre of pressure, they create the following three aerodynamic moments:
Mx — Rolling moment
My — Pitching moment
Mz — Yawing moment
Rolling Moment
This movement is caused by the cross wind force Py about the longitudinal axis. The magnitude of this rolling moment is given by
Mx = Py a = Cmx ρ A L V2 / 2
where,
a — Height of centre of thrust above CG
Cmx — Rolling moment co-efficient
L — Reference length
The rolling moment effects the weight distribution on the wheels. This effect is dangerous for tall vanes where the side force acts much above the CG. The only near solution to reduce rolling moment is to increase the wheel track.
Read More Info Regarding This Post : Vehicle Aerodynamics | Reducing Drag On A Car
Pitching Moment
Pitching moment is caused about y axis by cross wind force Py or the longitudinal force Px. The pitching moment My is given by
My = Px b = Cmy ρ A L V2 / 2
where,
b — Distance between CG and CP
Cmy — Pitching moment co-efficient
L — Reference length of the wheel base
The pitching moment is usually negative I.e. nose down and this moves. The rear axle lifts off the ground and further reduces the available traction.
Yawing Moment
Yawing Moment is caused about z axis by cross wind force Py. The yawing moment Mz is given by
Mz = Py c = Cmz ρ A L V2 / 2
where,
c — Distance between CG and CP
Cmz — Yawing moment co-efficient
L — Reference length
These moments adversely affects the directional stability of the vehicle at high speed. The use of stabilizer fins at the rear of the vehicle gives a very good reduction in yawing moment.
Note:
Centre of Gravity is the point where the whole mass of a system is assumed to be act
Centre of Pressure (CP) is the point where the total pressure acts on the system.
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