How Low drag Is attained

The molecule has to accelerate vertically to give way for body when flow is interrupted by a body then retard to remain at boundary at vertical extreme of the body. When crosssection starts reduce air has to accelerate inward and again retard to remain at the boundary at trailing edge. If this change in acceleration and retardation are not smooth very high instantaneous acceleration is required for air to remain in boundary and this causes anomalies in pressure near boundary resulting in separation of flow. In the cycloid design the vertical component of acceleration at leading edge starts from 0 to maximum then to 0 and then retardation starts and then to maximum retardation and then to zero at the top most part of body. Then vertical component of acceleration at trailing edge starts from 0 to maximum then to 0 and then retardation starts and then to maximum retardation and then to zero at the end of the body.

Aerofoil Velocity vectors at trailing edge

You can see below that at aerofoil’s trailing end velocity vectors are not horizontal that means vertical component of velocity is not zero this causes turbulence.

Cycloid Wing Velocity vectors at Trailing edge

Force is required to initiate vertical component of velocity and impact of air molecule to body causes a vertical component of velocity in air. This continues until acceleration profile at front changes smoothly to retardation. Here pressure is low. Then cross section of body decrease and air at above initiates a downward velocity on air below due to pressure difference. This continues until acceleration profile at back changes to retardation. At this point pressure is high. At the end of retardation profile air losses its vertical component of velocity by hitting body and body gains most of the forward momentum it lost during initiation of vertical component of velocity of air at the leading edge. Due to this, stream lines at the bottom and top at the end of trailing edge is all horizontal and parallel and they do not cross each other (no crossing of upper stream line to bottom stream lines occurs) and this reduces turbulence. Since acceleration changes very smoothly from positive to negative there will be fewer anomalies in air flow near boundary. This reduces the chance of separation of flow. Anywhere near the boundary air molecules do not have to accelerate rapidly to fill the gap because of the smooth transition from acceleration to retardation through zero acceleration zones. If the acceleration curve is not smooth the air has to accelerate or retard rapidly to reach the boundary to equalize pressure.

Horizontal velocity at trailing edge assures that all the kinetic energy given by moving body to air to initiate vertical velocity in air(For body to pass through)at leading edge is given back to body by air before leaving trailing edge.

We can modify the Sears Haack body based on cycloid design in such a way that cross-sectional area of the body changes smoothly as a cycloid. Equation for it is given below y= ((80*((90-x)/90-(sin(2*pi*(90-x)/90))/(2*pi))) )^(1/2) for x=1 to 90

Other form of Cycloid wing can be designed using cycloid as a thickness function with a appropriate camber.

Separation happening at high speeds can be eliminated by plasma flow control. Thus Air will follow the cycloid body profile even at high speeds.

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