![]() For nontailed rotor missiles, the asymmetric distortion of the boundary layer and the asymmetric separation of flow in the leeward region are the main causes of the Magnus force. Rotating missiles produce the Magnus effect during flight. The absolute value of the pitch moment coefficient of the missile body decreased with the increasing altitude. Under a high angle of attack, the Magnus moment direction of the missile body changed with the increasing altitude. As lateral force directions of the missile body and the tail were opposite, the Magnus moment direction changed noticeably. Consequently, Magnus moments generated by different boundary layer thicknesses at the front and rear of the missile body decreased and the Magnus moment generated by the tail fin became larger. With the increasing altitude, the position of the boundary layer with a larger thickness of the missile body moved forward, making the lateral force distribution of the missile body even. When the angle of attack was 20°, the interference of the tail fin to the lateral force of the missile body was different from that for other angles of attack, leading to an increase of the lateral force of the rear part of the missile body. The Magnus force direction did not change with the change of the altitude and the angle of attack at low angles of attack however, it changed with altitude at an angle of attack of 30°. At a low altitude, with the increase of the angle of attack, the Magnus moment direction changed from positive to negative however, at high altitudes, with the increase of the angle of attack, the Magnus moment direction changed from positive to negative and then again to positive. It was found that the Magnus moment direction of the missiles changed with the increase of the angle of attack. ![]() You can find a discussion on the accuracy of this approximation here.The Magnus moment characteristics of rotating missiles with Mach numbers of 1.3 and 1.5 at different altitudes and angles of attack were numerically simulated based on the transition SST model. ![]() There are also very simple approximations to these formulas, like Where values for the constants $m$ and $T_n$ depend on temperature and are tabulated: ![]() You can refer to this question for more detail on the origin of this formula (based on the Magnus approximation), but if you do some algebra to the expression there for dew point ( $TD$) as function of temperature ( $T$) and relative humidity ( $RH$), you get ![]()
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