In the year 1810, a steam engine weighed something over a ton to the horse-power. This was reduced to about 200 pounds in 1880. The steam-driven dirigible balloon of Giffard, in 1852, carried a complete power plant weighing a little over 100 pounds per horse-power; about the weight of a modern locomotive. The unsuccessful Maxim flying machine of 1894 brought this weight down to less than 20 pounds. The gasoline engine on the original Wright machines weighed about 5 pounds to the horse-power; those on some recent French machines not far from 2 pounds.

Pig iron is worth perhaps a cent a pound. An ordinary steam or gas engine may cost eight cents a pound; a steam turbine, perhaps forty cents. A high grade automobile or a piano may sell for a dollar a pound; the Gnome aeroplane motor is priced at about twenty dollars a pound. This is considerably more than the price of silver. The motor and accessories account for from two-thirds to nine-tenths of the total cost of an aeroplane.

A man weighing 150 pounds can develop at the outside about one-eighth of a horse-power. It would require 1200 pounds of man to exert one horse-power. Considered as an engine, then, a man is (weight for weight) only one six-hundredth as effective as a Gnome motor. In the original Wright aeroplane, a weight of half a ton was sustained at the expenditure of about twenty-five horse-power. The motor weight was about one-eighth of the total weight. If traction had been produced by man-power, 30,000 pounds of man would have been necessary: thirty times the whole weight supported.

Under the most favorable conditions, to support his own weight of 150 pounds (at very high gliding velocity and a slight angle of inclination, disregarding the weight of sails necessary), a man would need to have the strength of about fifteen men. No such thing as an aerial bicycle, therefore, appears possible. The man can not emulate the bird.

The power plant of an air craft includes motor, water and water tank, radiator and piping, shaft and bearings, propeller, controlling wheels and levers, carbureter, fuel, lubricating oil and tanks therefor. Some of the weight may eventually be eliminated by employing a two-cycle motor (which gives more power for its size) or by using rotary air-cooled cylinders. Propellers are made light by employing wood or skeleton construction. One eight-foot screw of white oak and spruce, weighing from twelve to sixteen pounds, is claimed to give over 400 pounds of propelling force at a thousand turns per minute.

The cut shows the action of the so-called “four-cycle” motor. Four strokes are required to produce an impulse on the piston and return the parts to their original positions. On the first, or suction stroke, the combustible mixture is drawn into the cylinder, the inlet valve being open and the outlet valve closed. On the second stroke, both valves are closed and the mixture is highly compressed. At about the end of this stroke, a spark ignites the charge, a still greater pressure is produced in consequence, and the energy of the gas now forces the piston outward on its third or “working” stroke, the valves remaining closed. Finally, the outlet valve is opened and a fourth stroke sweeps the burnt gas out of the cylinder.

In the “two-cycle” engine, the piston first moves to the left, compressing a charge already present in the cylinder at F, and meanwhile drawing a fresh supply through the valve A and passages C to the space D. On the return stroke, the exploded gas in F expands, doing its work, while that in D is slightly compressed, the valve A being now closed. When the piston, moving toward the right, opens the passage E, the burnt gas rushes out. A little later, when the passage I is exposed, the fresh compressed gas in D rushes through C, B, and I to F. The operation may now be repeated. Only two strokes have been necessary. The cylinder develops power twice as rapidly as before: but at the cost of some waste of gas, since the inlet (I) and outlet (E) passages are for a brief interval both open at once: a condition not altogether remedied by the use of a deflector at G. A two-cycle cylinder should give nearly twice the power of a four-cycle cylinder of the same size, and the two-cycle engine should weigh less, per horse-power; but it requires from 10 to 30% more fuel, and fuel also counts in the total weight.

The high temperatures in the cylinder would soon make the cast-iron walls red-hot, unless the latter where artificially cooled. The usual method of cooling is to make the walls hollow and circulate water through them. This involves a pump, a quantity of water, and a “radiator” (cooling machine) so that the water can be used over and over again. To cool by air blowing over the surface of the cylinder is relatively ineffective: but has been made possible in automobiles by building fins on the cylinders so as to increase the amount of cooling surface. When the motors are worked at high capacity, or when two-cycle motors are used, the heat is generated so rapidly that this method of cooling is regarded as inapplicable. By rapidly rotating the cylinders themselves through the air, as in motors like the Gnome, air cooling is made sufficiently adequate, but the expenditure of power in producing this rotation has perhaps not been sufficiently regarded.

Possible progress in weight economy is destined to be limited by the necessity for reserve motor equipment.

The engine used is usually the four-cycle, single-acting, four-cylinder gasoline motor of the automobile, designed for great lightness. The power from each cylinder of such a motor is approximately that obtained by dividing the square of the diameter in inches by the figure 2-1/2. Thus a five-inch cylinder should give ten horse-power—at normal piston speed. On account of friction losses and the wastefulness of a screw propeller, not more than half this power is actually available for propulsion.

The whole power plant of the ClÉment-Bayard weighed about eleven pounds to the horse-power. This balloon was 184 feet long and 35 feet in maximum diameter, displacing about 100,000 cubic feet. It carried six passengers, about seventy gallons of fuel, four gallons of lubricating oil, fifteen gallons of water, 600 pounds of ballast, and 130 pounds of ropes. The motor developed 100 horse-power at a thousand revolutions per minute. About eight gallons of fuel and one gallon of oil were consumed per hour when running at the full independent speed of thirty-seven miles per hour.

The Wellman balloon America is said to have consumed half a ton of gasoline per twenty-four hours: an eight days’ supply was carried. The gas leakage in this balloon was estimated to have been equivalent to a loss of 500 pounds of lifting power per day.

The largest of dirigibles, the Zeppelin, had two motors of 170 horse-power each. It made, in 1909, a trip of over 800 miles in thirty-eight hours.

The engine of the original Voisin cellular biplanes was an eight-cylinder Antoinette of fifty horse-power, set near the rear edge of the lower of the main planes. The Wright motors are placed near the front edge. A twenty-five horse-power motor at 1400 revolutions propelled the Fort Myer machine, which was built to carry two passengers, with fuel for a 125 mile flight: the total weight of the whole flying apparatus being about half a ton.

The eight-cylinder Antoinette motor on a Farman biplane, weighing 175 pounds, developed thirty-eight horse-power at 1050 revolutions. The total weight of the machine was nearly 1200 pounds, and its speed twenty-eight miles per hour.

The eight-cylinder Curtiss motor on the June Bug was air cooled. This aeroplane weighed 650 pounds and made thirty-nine miles per hour, the engine developing twenty-five horse-power at 1200 turns.

Resistance of Aeroplanes

The chart on page 24 (see also the diagram of page 23) shows that the lifting power of an aeroplane increases as the angle of inclination increases, up to a certain limit. The resistance to propulsion also increases, however: and the ratio of lifting power to resistance is greatest at a very small angle—about five or six degrees. Since the motor power and weight are ruling factors in design, it is important to fly at about this angle. The supporting force is then about two pounds, and the resistance about three-tenths of a pound, per square foot of sail area, if the velocity is that assumed in plotting the chart: namely, about fifty-five miles per hour.

But the resistance R indicated on pages 23 and 24 is not the only resistance to propulsion. In addition, we have the frictional resistance of the air sliding along the sail surface. The amount of this resistance is independent of the angle of inclination: it depends directly upon the area of the planes, and in an indirect way on their dimensions in the direction of movement. It also varies nearly with the square of the velocity. At any velocity, then, the addition of this frictional resistance, which does not depend on the angle of inclination, modifies our views as to the desirable angle: and the total resistance reaches a minimum (in proportion to the weight supported) when the angle is about three degrees and the velocity about fifty miles per hour.

This is not quite the best condition, however. The skin friction does not vary exactly with the square of the velocity: and when the true law of variation is taken into account, it is found that the horse-power is a minimum at an angle of about five degrees and a speed of about forty miles per hour. The weight supported per horse-power may then be theoretically nearly a hundred pounds: and the frictional resistance is about one-third the direct pressure resistance. This must be regarded as the approximate condition of best effectiveness: not the exact condition, because in arriving at this result we have regarded the sails as square flat planes whereas in reality they are arched and of rectangular form.

At the most effective condition, the resistance to propulsion is only about one-tenth the weight supported. Evidently the air is helping the motor.

Resistance of Dirigibles

If the bow of a balloon were cut off square, its head end resistance would be that given by the rule already cited (page 19): one three-hundredth pound per square foot, multiplied by the square of the velocity. But by pointing the bow an enormous reduction of this pressure is possible. If the head end is a hemisphere (as in the English military dirigible), the reduction is about one-third. If it is a sharp cone, the reduction may be as much as four-fifths. Unless the stern is also tapered, however, there will be a considerable eddy resistance at that point.

If head end resistance were the only consideration, then for a balloon of given diameter and end shape it would be independent of the length and capacity. The longer the balloon, the better. Again, since the volume of any solid body increases more rapidly than its surface (as the linear dimensions are increased), large balloons would have a distinct advantage over small ones. The smallest dirigible ever built was that of Santos-Dumont, of about 5000 cubic feet.

Large balloons, however, are structurally weak: and more is lost by the extra bracing necessary than is gained by reduction of head end resistance. It is probable that the Zeppelin represents the limit of progress in this direction; and even in that balloon, if it had not been that the adoption of a rigid type necessitated great structural strength, it is doubtful if as great a length would have been fixed upon, in proportion to the diameter.

The frictional resistance of the air gliding along the surface of the envelope, moreover, invalidates any too arbitrary conclusions. This, as in the aeroplane, varies nearly as the square of the velocity, and is usually considerably greater than the direct head end resistance. Should the steering gear break, however, and the wind strike the side of the balloon, the pressure of the wind against this greatly increased area would absolutely deprive it of dirigibility.

A stationary, drifting, or “sailing” balloon may as well have the spherical as well as any other shape: it makes the wind a friend instead of a foe and requires nothing in the way of control other than regulation of altitude.

Independent Speed and Time Table

The air pressure, direct and frictional resistances, and power depend upon the relative velocity of flying machine and air. It is this relative velocity, not the velocity of the balloon as compared with a point on the earth’s surface, that marks the limit of progression. Hence the speed of the wind is an overwhelming factor to be reckoned with in developing an aerial time table. If we wish to travel east at an effective speed of thirty miles per hour, while the wind is blowing due west at a speed of ten miles, our machine must have an independent speed of forty miles. On the other hand, if we wish to travel west, an independent speed of twenty miles per hour will answer.

Again, if the wind is blowing north at thirty miles per hour, and the minimum (relative) velocity at which an aeroplane will sustain its load is forty miles per hour, we cannot progress northward any more slowly than at seventy miles’ speed. And we have this peculiar condition of things: suppose the wind to be blowing north at fifty miles per hour. The aeroplane designed for a forty mile speed may then face this wind and sustain itself while actually moving backward at an absolute speed (as seen from the earth) of ten miles per hour.

We are at the mercy of the wind, and wind velocities may reach a hundred miles an hour. The inherent disadvantage of aerial flight is in what engineers call its “low load factor.” That is, the ratio of normal performance required to possible abnormal performance necessary under adverse conditions is extremely low. To make a balloon truly dirigible throughout the year involves, at Paris, for example, as we have seen, a speed exceeding fifty-four miles per hour: and even then, during one-tenth the year, the effective speed would not exceed twenty miles per hour. A time table which required a schedule speed reduction of 60% on one day out of ten would be obviously unsatisfactory.

Further, if we aim at excessively high independent speeds for our dirigible balloons, in order to become independent of wind conditions, we soon reach velocities at which the gas bag is unnecessary: that is, a simple wing surface would at those speeds give ample support. The increased difficulty of maintaining rigidity of the envelope, and of steering, at the great pressures which would accompany these high velocities would also operate against the dirigible type.

With the aeroplane, higher speed means less sail area for a given weight and a stronger machine. Much higher speeds are probable. We have already a safe margin as to weight per horse-power of motor, and many aeroplane motors are for stanchness purposely made heavier than they absolutely need to be.

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.