then from (1)

thence,

Whether T means drifts, head resistance and thrust for climbing, or drift and head resistance only, the following calculation is the same, only in the latter case, of course, we must add the horse-power required for climbing to the result to obtain the total horse-power.

Now, when we know the total thrust, we shall find the horse-power in the following manner:

We know that the

in kilograms, or in English measure,

where

When P × r = M, then

thence,

or in English system

Now the power on the circumference of the propeller will be reduced by its radius, so it will be M/r = p. A part of p will be used for counteracting the air and bearing friction, so that the total power on the circumference of the propeller will be (M/r) × ? = p where ? is the mechanical efficiency of the propeller. Now ?/tan a = T, where a is taken on the tip of the propeller.

I take a at the tip, but it can be taken, of course, at any point, but then in equation p = M/r, r must be taken only up to this point, and not the whole radius; but it is more comfortable to take it at the tip, as tan a = Pitch/r2p (Fig. 1, C).

Now we can write up the equation of the thrust:

thence

The computations and formulÆ given are of most value to the student engineer rather than matters of general interest, but are given so that a general idea may be secured of how airplane design influences power needed to secure sustained flight. It will be apparent that the resistance of an airplane depends upon numerous considerations of design which require considerable research in aerodynamics to determine accurately. It is obvious that the more resistance there is, the more power needed to fly at a given speed. Light monoplanes have been flown with as little as 15 horse-power for short distances, but most planes now built use engines of 100 horse-power or more. Giant airplanes have been constructed having 2,000 horse-power distributed in four power units. The amount of power provided for an airplane of given design varies widely as many conditions govern this, but it will range from approximately one horse-power to each 8 pounds weight in the case of very light, fast machines to one horse-power to 15 or 18 pounds of the total weight in the case of medium speed machines. The development in airplane and power plant design is so rapid, however, that the figures given can be considered only in the light of general averages rather than being typical of current practice.

WHY EXPLOSIVE MOTORS ARE BEST

Internal combustion engines are best for airplanes and all types of aircraft for the same reasons that they are universally used as a source of power for automobiles. The gasoline engine is the lightest known form of prime mover and a more efficient one than a steam engine, especially in the small powers used for airplane propulsion. It has been stated that by very careful designing a steam plant an engine could be made that would be practical for airplane propulsion, but even with the latest development it is doubtful if steam power can be utilized in aircraft to as good advantage as modern gasoline-engines are. While the steam-engine is considered very much simpler than a gas-motor, the latter is much more easily mastered by the non-technical aviator and certainly requires less attention. A weight of 10 pounds per horse-power is possible in a condensing steam plant but this figure is nearly double or triple what is easily secured with a gas-motor which may weigh but 5 pounds per horse-power in the water cooled forms and but 2 or 3 pounds in the air-cooled types. The fuel consumption is twice as great in a steam-power plant (owing to heat losses) as would be the case in a gasoline engine of equal power and much less weight.The internal-combustion engine has come seemingly like an avalanche of a decade; but it has come to stay, to take its well-deserved position among the powers for aiding labor. Its ready adaptation to road, aerial and marine service has made it a wonder of the age in the development of speed not before dreamed of as a possibility; yet in so short a time, its power for speed has taken rank on the common road against the locomotive on the rail with its century’s progress. It has made aerial navigation possible and practical, it furnishes power for all marine craft from the light canoe to the transatlantic liner. It operates the machine tools of the mechanic, tills the soil for the farmer and provides healthful recreation for thousands by furnishing an economical means of transport by land and sea. It has been a universal mechanical education for the masses, and in its present forms represents the great refinement and development made possible by the concentration of the world’s master minds on the problems incidental to internal combustion engineering.

HISTORICAL

Although the ideal principle of explosive power was conceived some two hundred years ago, at which time experiments were made with gunpowder as the explosive element, it was not until the last years of the eighteenth century that the idea took a patentable shape, and not until about 1826 (Brown’s gas-vacuum engine) that a further progress was made in England by condensing the products of combustion by a jet of water, thus creating a partial vacuum.

Brown’s was probably the first explosive engine that did real work. It was clumsy and unwieldy and was soon relegated to its place among the failures of previous experiments. No approach to active explosive effect in a cylinder was reached in practice, although many ingenious designs were described, until about 1838 and the following years. Barnett’s engine in England was the first attempt to compress the charge before exploding. From this time on to about 1860 many patents were issued in Europe and a few in the United States for gas-engines, but the progress was slow, and its practical introduction for power came with spasmodic effect and low efficiency. From 1860 on, practical improvement seems to have been made, and the Lenoir motor was produced in France and brought to the United States. It failed to meet expectations, and was soon followed by further improvements in the Hugon motor in France (1862), followed by Beau de Rocha’s four-cycle idea, which has been slowly developed through a long series of experimental trials by different inventors. In the hands of Otto and Langdon a further progress was made, and numerous patents were issued in England, France, and Germany, and followed up by an increasing interest in the United States, with a few patents.

From 1870 improvements seem to have advanced at a steady rate, and largely in the valve-gear and precision of governing for variable load. The early idea of the necessity of slow combustion was a great drawback in the advancement of efficiency, and the suggestion of de Rocha in 1862 did not take root as a prophetic truth until many failures and years of experience had taught the fundamental axiom that rapidity of action in both combustion and expansion was the basis of success in explosive motors.

With this truth and the demand for small and safe prime movers, the manufacture of gas-engines increased in Europe and America at a more rapid rate, and improvements in perfecting the details of this cheap and efficient prime mover have finally raised it to the dignity of a standard motor and a dangerous rival of the steam-engine for small and intermediate powers, with a prospect of largely increasing its individual units to many hundred, if not to the thousand horse-power in a single cylinder. The unit size in a single cylinder has now reached to about 700 horse-power and by combining cylinders in the same machine, powers of from 1,500 to 2,000 horse-power are now available for large power-plants.