Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/355

Rh resistance increases as $$V^2,$$ so that the angle $$\gamma$$ is no longer constant in respect of $$V .$$ We also know (§ 171) that the influence of the weight of the aerofoil, as additional to the load carried, is to place a lower limit on the velocity that may be usefully employed.

The Equation (5) of § 171 gives the condition of least resistance. The value of $$\gamma$$ can thus be calculated for any set of conditions, and the power data obtained from the Table. By plotting from the equations the conditions other than for least resistance may be examined with equal facility and the $$\gamma$$ values determined.

Before leaving the subject of power expenditure it is desirable to point out the extent to which the future of flight and the uses of a flying machine are circumscribed by economic considerations.

Leaving all attendant difficulties on one side, it is evident that the conveyance of goods by flying machine would be comparable, so far as power expenditure is concerned, with drawing them on a sleigh over a common road, so that where any other method of transport is possible, flight may be regarded as out of the question. In addition to this, the range of a flying machine must, unless after the manner of a soaring bird it derives its energy from wind pulsation, be strictly limited to a few hundred miles between each replenishment of fuel; and consequently we cannot at present regard aerial flight as a means of ocean transport, or even as a means of exploring inaccessible regions where the distance to be accomplished exceeds that stated.

Beyond this the velocity of flight is limited by the horse-power weight factor. If, as an example, we suppose that 25 per cent, of the weight of the machine is taken up by the motor itself, and if the motor weigh only 2$$\tfrac{1}{2}$$ lbs. per horse-power, it is improbable, taking everything into account, that seventy miles per hour can be