Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/450



§ 131 a suggestion is made that leads to a new method of treatment of problems in fluid resistance.

Let us imagine a modification of the medium of Newton in which the particles, instead of being at rest, are in a state of agitation, and in the first instance let us suppose that all the particles, moving in directions at random, have the same velocity.

Taking first the case of a normal plane travelling at a velocity greater than that of the particles, we have the resistance proportional to the energy per unit volume (§ 131), the energy being reckoned only in respect of motion in the direction of flight, of either plus or minus sign. This energy is made up of two parts, the corpuscular energy of the medium, of which one third only counts as being in the direction of the axis of flight, and the energy of translation.

Now the corpuscular energy is constant in respect of the velocity of flight, and the energy of translation varies as the square of this quantity, consequently the law of resistance for this modified Newtonian medium will be. P = k V2 + n, where k and n are constants.

If the velocity of the plane, instead of being greater than that of the particles, be less, the medium will exert a pressure on the back of the plane as well as on the face, and the resistance will be due to the pressure difference.