Isaac Newton's sine-squared law of air resistance is a formula that implies the force on a flat plate immersed in a moving fluid is proportional to the square of the sine of the angle of attack.
More sophisticated analysis and experimental evidence have shown that this formula is inaccurate; although Newton's analysis correctly predicted that the force was proportional to the density, the surface area of the plate, and the square of the velocity, the proportionality to the square of the sine of the angle of attack is incorrect.
The force is directly proportional to the sine of the angle of attack, or for small values of
Ironically, the sine squared formula has had a rebirth in modern aerodynamics; the assumptions of rectilinear flow and non-interactions between particles are applicable at hypersonic speeds and the sine-squared formula leads to reasonable predictions.
[4][5][6] In 1744, 17-years after Newton's death, the French mathematician Jean le Rond d'Alembert attempted to use the mathematical methods of the day to describe and quantify the forces acting on a body moving relative to a fluid.