Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/202

§ 130 results obtained by the two methods are strikingly different, and the discrepancy in the value of the constant as given by different writers may be to a certain extent explained.

§ 131. Wind Pressure Determinations.—One of the characteristics of the aerial disturbance which we know as wind is the continual fluctuation both as to direction and velocity; this characteristic is so well known as to have found expression in the vocabulary of every civilised nation—“gust of wind,” “coup de vent,” etc. Wind may be said to consist of a general motion of translation with a superposed motion of turbulence (§ 37), the result being that at no point does the velocity or direction remain constant for any length of time.

One immediate consequence of this variability is that for a wind of known mean velocity $$= V,$$ the mean value of $$V^2$$ is higher than would be the case if the problem were one of uniform air current having the same mean velocity, and therefore the pressure (which depends upon $$V^2$$) will also be higher. If we neglect the secondary effect due to the components of motion of the air in directions parallel to the pressure plane (§ 146 et seq.), so that the mean pressure on the plane is due only to the normal component of motion of the wind, then it would appear that the pressure will be proportional to the energy per unit volume; for dimensionally:—

That is to say, the pressure is proportional to the energy per unit volume.

Now the average energy per unit volume in the wind is the sum of the separate energies of mean velocity and of turbulence (the latter for our present purpose being reckoned only in respect of motion in the direction at right angles to the pressure plane), and in a wind possessing such energy of turbulence, the mean pressure will be greater than would be the case for the simple