Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/451

Rh Taking the velocity as very low, then, the pressure being due to the bombardment of the particles, it may be easily demonstrated that the pressure difference and therefore the resistance must vary directly as the velocity. This may be regarded as the equivalent of "Stokes stage" in the case of a real fluid.

If the particles of the medium have different velocities the same general principles apply, only if the method is to be interpreted quantitatively the problem becomes a trifle more complex as involving the integration of a series of some kind.

In the case of a normal plane such as we have so far considered, the components of the motion of the particles transverse to the direction of flight have no influence. In the case of a solid body or curved lamina this is not the case, the lateral bombardment cannot be without effect on the total resistance.

Without examining the problem analytically, it appears obvious to the author that if (as is the case in a real gas) the energy of the particles is equally distributed in the three "degrees of freedom," that is in the directions of the three co-ordinate axes, the resistance at high velocities will not, in respect of the corpuscular energy, depend upon the form of the surface in presentation, but will depend upon the cross sectional area only; and any relief that can be obtained by rounding off or pointing the surface in presentation will take effect only in respect of the portion of the resistance that varies as V2. That is to say, in the expression, P = k V2 + n, giving easy entrance lines will diminish the constant k, but will have no influence on the value of the constant n.

The modified Newtonian medium of our present hypothesis resembles in many ways the perfect gas of kinetic theory, but differs in one very important respect. The molecules of a perfect gas are not only in a state of motion, but are undergoing frequent encounters one with another. Whether these encounters are due to gross impact or to some kind of action at a distance is immaterial from the point of view of the present discussion. The particles or corpuscles of the hypothetical medium have no