Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/352

§ 219 Now, the essential power will be given by the expression $$W\ \gamma\ V ,$$ where $$\gamma$$ (assumed to come within the definition of a small angle) is expressed in circular measure. Now, if $$\gamma$$ is constant in respect of $$V ,$$ as has been proved to be the case so long as the body resistance is regarded as negligible, or separately computed, the following deductions may immediately be made:—

(1) The energy required to travel from point to point is independent of the velocity and is constant.

(2) The power (horse-power) required is directly as the velocity.

(3) From (1) it follows that the maximum range of flight of a flying machine must depend upon the fuel carrying capacity, the energy value of the fuel, and the total efficiency of the prime mover and propelling mechanism, and is independent of the speed of flight.

(4) From (2) it follows that the velocity of flight is limited by the relation of horse-power to weight, and, other things being equal, is proportional to the horse-power per unit weight of the prime mover.

These conclusions are of considerable importance, and are illustrated in the Tables as follows:—

Table XV., column (1), gives, for values of $$\gamma^\circ =$$ 6°, 7°, 8°, 9°, and 10°, the distance that could be run if an aerodrome had at its disposal the total energy of its own weight of hydrogen taken as giving 48,000,000 foot lbs. per lb. Column (2) gives the same information for petroleum spirit, taken as equal 16,000,000 foot lbs. per lb.; column (3) is based on the assumption that 25 per cent, only of the total heat is available, as representing the thermal efficiency of the petrol engine. Column (4) the distance after an allowance of 75 per cent, mechanical efficiency of engine and transmission, and a 66.6 per cent, efficiency of propulsion. Lastly, column (5) gives the actual range, or maximum possible distance, on the basis of columns (2) to (4) on the assumption