The Cost of Speed
Since the whole resistance, in either type of flying machine, is approximately proportional to the square of the velocity; and since horse-power (work) is the product of resistance and velocity, the horse-power of an air craft of any sort varies about as the cube of the speed. To increase present speeds of dirigible balloons from thirty to sixty miles per hour would then mean eight times as much horse-power, eight times as much motor weight, eight times as rapid a rate of fuel consumption, and (since the speed has been doubled) four times as rapid a consumption of fuel in proportion to the distance traveled. Either the radius of action must be decreased, or the weight of fuel carried must be greatly increased, if higher velocities are to be attained. Present (independent) aeroplane speeds are usually about fifty miles per hour, and there is not the necessity for a great increase which exists with the lighter-than-air machines. We have already succeeded in carrying and propelling fifty pounds of total load or fifteen pounds of passenger load per horse-power of motor, with aeroplanes; the ratio of net load to horse-power in the dirigible is considerably lower; but the question of weight in relation to power is of relatively smaller importance in the latter machine, where support is afforded by the gas and not by the engine.
The Propeller
Very little effort has been made to utilize paddle wheels for aerial propulsion; the screw is almost universally employed. Every one knows that when a bolt turns in a stationary nut, it moves forward a distance equal to the pitch (lengthwise distance between two adjacent threads) at every revolution. A screw propeller is a bolt partly cut away for lightness, and the “nut” in which it works is water or air. It does not move forward quite as much as its pitch, at each revolution, because any fluid is more or less slippery as compared with a nut of solid metal. The difference between the pitch and the actual forward movement of the vessel at each revolution is called the “slip,” or “slip ratio.” It is never less than ten or twelve per cent in marine work, and with aerial screws is much greater. Within certain limits, the less the slip, the greater the efficiency of the propeller. Small screws have relatively greater slips and less efficiency, but are lighter. The maximum efficiency of a screw propeller in water is under 80%. According to Langley’s experiments, the usual efficiency in air is only about 50%. This means that only half the power of the motor will be actually available for producing forward movement—a conclusion already foreshadowed.
In common practice, the pitch of aerial screws is not far from equal to the diameter. The rate of forward movement, if there were no slip, would be proportional to the pitch and the number of revolutions per minute. If the latter be increased, the former may be decreased. Screws direct-connected to the motors and running at high speeds will therefore be of smaller pitch and diameter than those run at reduced speed by gearing, as in the machine illustrated on page [134]. The number of blades is usually two, although this gives less perfect balance than would a larger number. The propeller is in many monoplanes placed in front: this interferes, unfortunately, with the air currents against the supporting surfaces.
There is always some loss of power in the bearings and power-transmitting devices between the motor and propeller. This may decrease the power usefully exerted even to less than half that developed by the motor.