Fig. 44.—Shows the position of the blades of a hélicoptère as they pass around a circle, when the angle of the shaft and the angle of the blades are the same.
Fig. 44.—Shows the position of the blades of a hélicoptère as they pass around a circle, when the angle of the shaft and the angle of the blades are the same.
Fig. 44.—Shows the position of the blades of a hélicoptère as they pass around a circle, when the angle of the shaft and the angle of the blades are the same.
InFig. 43, I have shown a plan of a hélicoptère machine in which two screws are employed rotating in opposite directions,a,a, being the port screw;b,b, the starboard screw; andd,d, the platform for the machinery and operator. The screws should be 20 feet in diameter and made of wood. Suppose now that the pitch of these screws is such that the extremities of the blades havean angle of 5°; if now we tilt the shaft forward in the direction of flight to the extent of 5°, we shall completely wipe out the angle of inclination of the blades when atb(Fig. 44), whereas it will be observed that the pitch as regards the horizontal will be increased to 10° ata, on the outer side, and remain unchanged atc, andd. If the peripheral velocity of the blades is, say, four times the velocity at which the machine is expected to travel, the blades will get a good grip on the air atc,d, but when they travel forward and encounter air which is travelling at a high velocity in the opposite direction, they assume the position shown atb. If the pitch of the screw blades was a little more than the angle of the shaft, the blades atbwould also produce a lifting effect, and as the velocity with which they pass through the air is extremely high, a very strong lifting effect would be produced even if the angle was not more than 1 in 40. By tracing the path and noting the position of the ends of the blades as they pass completely around the circle as shown (Fig. 44), it will be observed that they very closely resemble the motion of a bird’s wing. I have no doubt that a properly made machine on this plan would be highly satisfactory, but one should not lose sight of the fact that even with a machine of this type, well designed and sufficiently light to sustain itself in the air while flying, it would still be necessary forit to move along rapidly when starting in order to get the necessary grip on the air. Upon starting the engine, in a machine of this kind, a very strong downward draught of air would be produced, and the whole power of the engines would be used in maintaining this downward blast, but if the machine should at the same time be given a rapid forward motion sufficiently great to bring the blades into contact with new air, the inertia of which had not been disturbed, and which was not moving downwards, the lifting effect would be increased sufficiently to lift the machine off the ground. It would, therefore, work very much like an aeroplane machine. It would also be possible to provide a third screw of less dimensions and running at a less velocity, to push the machine forward, so as not to render it necessary to give such a decided tilt to the shafts.
As before stated, great care should be taken in designing and making the framework of flying machines, and no stone should be left unturned in order to arrive at the greatest degree of lightness without diminishing the strength too much; then, again, elasticity should be considered. If we use a thin tube all the material is at the surface, far from the neutral centre, and great stiffness is obtained, but such a tube will not stand so much deflection as a piece of wood; then, again, wood is cheaper than steel, and in case of an accident, repairs are very quickly and easily made. Wood, however, cannot be obtained in long lengths absolutely free from blemishes. It therefore becomes necessary to find some way of making these long members of flying machines of such wood as may be found suitable in the following table.
The relative value of different kinds of wood is shown in this table, and it will be observed that some are much more suitable for the purpose than others. The true value of a wood to be used in flying machines is only ascertained by considering its strength in comparison with its own weight—that is, the wood which is strongest in proportion to its weight is the best. It will be seen that Honduras mahogany stands at the head of the list, but American white pine is very good for certain purposes, as it is light, strong, easily obtained, and takes the glue very well indeed. InFig. 45, I have shown a good system of producing the long members necessary in flying machines. I will admit that it costs something to fit up and produce the kind of joints which I have shown, but when themembers are once made, they are exceedingly strong and stiff.Fig. 46shows sections of the struts, and these may be made of either straight-grained Honduras mahogany or of lance wood; either answers the purpose very well,because being very strong and straight-grained, permits the struts to be made of such a shape and size as to offer very little resistance in cutting their way through the air. The framework of the aeroplane unless carefully designed will offer great resistance to being driven through the air. Suppose that the bottom member of the truss (Fig. 47) is straight, and the top one curved in the direction shown; no matter how taut the cloth may be drawn, the pressure of the air will cause it to bag upwards between the different trusses, so as to present very nearly the correct curve which is necessary to produce the maximum lifting effect, and without offering too much resistance to the air; however, one must not forget for a single moment that the air flows over both sides of the aeroplane. When the aeroplane is made very thick in the middle and sharp at the edges (Fig. 48), with the bottom side dead level, it produces a decided lifting effect no matter which way it is being propelled through the air. This is not because the bottom side produces any lifting effect of itself, but because the air running over the top follows the surface. The aeroplane encounters air which is not moving at all. The air is first moved upwards slightly, but it also has to run down the incline to the rear edge of the aeroplane, so that, when it is discharged, it has a decided downward trend; therefore, the air passing over the top side instead of under the bottom side, produces the lifting effect, showing that the top side of an aeroplane as well as the lower side should be considered. The top side should, therefore, be free from all obstructions.
Fig. 45.—System of splicing and building up wooden members. When they have to be curved and to keep their shape, they should be bent at the curve at the time of being glued together, and joined in the middle as atd.
Fig. 45.—System of splicing and building up wooden members. When they have to be curved and to keep their shape, they should be bent at the curve at the time of being glued together, and joined in the middle as atd.
Fig. 45.—System of splicing and building up wooden members. When they have to be curved and to keep their shape, they should be bent at the curve at the time of being glued together, and joined in the middle as atd.
Fig. 46.—Cross-section of struts.
Fig. 46.—Cross-section of struts.
Fig. 46.—Cross-section of struts.
Fig. 47.—Truss suitable for use with flying machines, having aeroplanes about 6 feet to 8 feet wide.Fig. 47 enlarged(30 kB)
Fig. 47.—Truss suitable for use with flying machines, having aeroplanes about 6 feet to 8 feet wide.
Fig. 47.—Truss suitable for use with flying machines, having aeroplanes about 6 feet to 8 feet wide.
Fig. 47 enlarged(30 kB)
The top of the aeroplane as well as the bottom should be covered with some light material, if the very best results are to be obtained. In another chapter I have shown a form of fabric-covered aeroplane, made by myself, that was not distorted in the least by the air pressure, and produced just as good effects as it would have done if it had been carefully carved out of a piece of wood. On more than one occasion Lord Kelvin came to my place; he said that my workshop was a perfect museum of invention. At the Oxford Meeting of the British Association for the Advancement of Science, Lord Salisbury in the chair, I was much gratified when Lord Kelvin said that he had examined my work, and found that it was beautifully designed and splendidly executed. He complimented me very highly indeed. While at my place, he said that the most ingenious thing that he had seen was the way I had prevented my aeroplanes from being distorted by the air. He spoke of this several times with great admiration, and, I think, if the fabric-covered aeroplane is to be used at all, that my particular system will be found altogether the best.
Fig. 48.—The paradox aeroplane that lifts no matter in which direction it is being driven.
Fig. 48.—The paradox aeroplane that lifts no matter in which direction it is being driven.
Fig. 48.—The paradox aeroplane that lifts no matter in which direction it is being driven.
Fig. 49.—The Antoinette motor.
Fig. 49.—The Antoinette motor.
Fig. 49.—The Antoinette motor.
Regarding the motors now being employed, I think that there is still room for a great deal of improvement in the direction of greater lightness, higher efficiency and reliability. At the present time, flying machine motors have such small cylinders, the rotation is so rapid, and the cooling appliances so imperfect, that the engine soon becomes intensely heated, and then its efficiency is said to fall off about 40 or 50 per cent., some say even 60 per cent. This is probably on account of the high temperature of the cylinder, piston, and air inlet. The heat expands the air as it enters, so that the actual weight of air in the cylinder is greatly reduced, and the engine power reduced in a corresponding degree. There is no trouble about cooling the motor, and a condenser of high efficiency may be made that will cool the water perfectly, and, at the same time, lift a good deal more than its own weight. All the conditions are favourable for usinga very effective atmospheric condenser (seeFigs. 30and31).
Water may be considered as 2400 times as efficient as air, volume for volume, in condensing steam. When a condenser is made for the purpose of using water as a cooling agent, a large number of small tubes may be closely grouped together in a box, and the water pumped in at one end of the box and discharged at the other end through relatively small openings; but when air is employed, the tubes or condensing surfaces must be widely distributed, so that a very large amount of air is encountered, and air which has struck one tube and become heated must never touch a second tube (seeFigs. 30and31, alsoAppendix).
Fig. 50.—Section showing the Antoinette motor, such as used in the Farman and De la Grange machines.
Fig. 50.—Section showing the Antoinette motor, such as used in the Farman and De la Grange machines.
Fig. 50.—Section showing the Antoinette motor, such as used in the Farman and De la Grange machines.
Fig. 51shows a pneumatic buffer which I have designed, in whicha,a, is a steel tube highly polished on the inside;b, a nozzle for connecting the air-pump, which is of the bicycle variety;c, a nipple to which is attached a strong india-rubber bulb;d, a piston which is made air-tight by a leather cup; andf, the connection to the lever carrying the wheels on which the machine runs. While the machine is at a state of rest on the ground, the piston-rodd, is run out to its full extent, and supports the weight of the machine—the pressure being about 150 lbs. to the square inch. When, however, the machine comes violently downto the earth, the piston is pushed inward, compressing the air, and by the time it has travelled, say, one-half the stroke, the air pressure will have mounted to 300 lbs. to the square inch. At this point, the rubber bulbc, ought to burst and allow the compressed air to escape under a high pressure. Air escaping through a relatively small hole absorbs the momentum of the descent and brings the machine to a state of rest without a destructive shock. It is, of course, necessary for the navigator to select a broad and level field for descent, and then to approach it from the leeward and slow up his machine as near the ground as possible, tilting the forward end upwards in order to arrest its forward motion, and touching the ground while still moving against the wind at a fairly high velocity. If all these points are studied, and well carried out, very little danger will result; then, again, the aeroplanesb,b, and the forward rudderd(Fig. 41), should be so arranged that, in case of an accident, their outward sides may be instantly turned upwards, in such a manner as to prevent the machine from plunging, and keep it on an even keel while the engines are not running.
Fig. 51.—Pneumatic buffer—a,a, cylinder;b, attachment for pumping up;c, air outlet, covered with a rubber thimble made to burst under about 300 lbs. pressure;d, the piston.
Fig. 51.—Pneumatic buffer—a,a, cylinder;b, attachment for pumping up;c, air outlet, covered with a rubber thimble made to burst under about 300 lbs. pressure;d, the piston.
Fig. 51.—Pneumatic buffer—a,a, cylinder;b, attachment for pumping up;c, air outlet, covered with a rubber thimble made to burst under about 300 lbs. pressure;d, the piston.
A ship at sea has only to be steered in a horizontal direction; the water in which it is floated assures its stability in a vertical direction; but when a flying machine is once launched in the air, it has to be steered in two directions—that is, the vertical and the horizontal. Moreover, it is constantly encountering air currents that are moving with a much higher velocity than any water currents that have ever to be encountered. It is, therefore, evident that, as far as vertical steering is concerned, it should be automatic. Some have suggested shifting weights, flowing mercury, and swinging pendulums; but none of these is of the least value, on account of the swaying action which always has to be encountered. A pendulum could not be depended upon for working machinery on board a ship, and the same laws apply to an airship. We have but one means at our disposal, and that is the gyroscope. When a gyroscope is spun at a very high velocity on a vertical axis, with the point of support very much above the center of gyration, it has a tendency to maintain a vertical axis; a horizontal or swinging motion of its support will not cause it to swing like a pendulum. It therefore becomes possible by its use to maintain an airship on an even keel. In a steam steering apparatus, such as is used on shipboard, it is not sufficient to apply steam-power to move the rudders, unless some means are provided whereby the movement of the rudder closes off the steam, otherwise the rudder might continue to travel after the effect had been produced, and ultimately be broken; and so it is with steering a flying machine in a vertical direction. Whenever the fore and aft rudders respond to the action of the gyroscope and are set in motion, they must at once commence to shut off the power that works them, otherwise they would continue to travel. In the photograph (Fig. 52) I have shown an apparatus which I constructed at Baldwyn’s Park. It will be seen that the gyroscope is enclosed in a metal case; a tangent screw, just above the case, rotates a pointer around a small disc, which admits of the speed of the gyroscope being observed. Steam is admitted through a universal joint, descends through the shaft and escapes through a series of small openings placed at a tangent, so as to give rotation to thewheel after the manner of a Barker’s mill. The casing about the rotating wheel is extremely light as relates to the wheel, so that, when the gyroscope is once spun on a vertical axis, the rest of the apparatus may be tilted in any direction, while the gyroscope and its attachments maintain a vertical axis. The gyroscope and its attachments are suspended from a long steel tube, which in reality is a steam cylinder. The sleeve which supports the gyroscope moves freely in a longitudinal direction, and the whole is held in position by a triple-threaded screw on the small tube above the cylinder. The steam is admitted through a piston value operated by a species of link motion, as shown. The piston-rod extends to each end of the cylinder, and regulates the rudders by pulling a small wire rope, the travel of the piston being about 8 feet. At the end of the cylinder (not shown) the piston-rod is provided with an arm and a nut which engages the small top tube—this tube being provided with a long spiral—so that, as the piston moves, the top tube is rotated, and thereby slides the gyroscope’s support, and changes its position as relates to the piston valve. It will, therefore, be seen that the action is the same as with the common steam steering gear used on shipboard. A little adjusting screw at the right hand of the print is shown. The upward projecting arm of the bell crank lever is for the purpose of attaching the wooden handle, making it possible to move the connecting-rod instantly into a position where the steam piston will move the rudders into the position shown (Fig. 56).
I copy the following from a description which I wrote of this apparatus at the time:—
“Gyroscope Apparatus for Automatically Steering Machine in a Vertical Direction.
“This apparatus consists of a long steam cylinder which is provided with a piston, the piston-rod extending beyond the cylinder at each end; the ropes working the fore and aft rudders are attached to the ends of this piston-rod, and steam is supplied through an equilibrium valve. The gyroscope is contained in a gunmetal case, and is driven by a jet of steam entering through the trunnions. When the gyroscope is spinning at a high velocity, the casing holding it becomes very rigid and is not easily moved from itsvertical position. If the machine rears or pitches, the cylinder and valve are moved with the machine while the gyroscope remains in a vertical position. This causes the steam valve to be moved so as to admit steam into the cylinder and move the piston in the proper direction to instantly bring the machine back into its normal position. As the fore and aft rudders are moved, the long tubular shaft immediately over the steam cylinder is rotated in such a manner as to move the whole gyroscope in the proper direction to close off the steam. The apparatus may be made to regulate at any angle by adjusting the screw which regulates the position of the tubular shaft. The link that suspends the end of the steam valve connecting-rod is supported by a bell crank lever, and while the machine is moving ahead, the lever occupies the position shown in the photograph (Fig. 52); but if the machinery and engine stop, the bell crank lever may be moved so as to throw the connecting-rod below the centre, when the steam will move the piston in the proper direction to throw both the rudders into the falling position, as shown inFig. 56.”
Fig. 52.—Gyroscope, used for the control of the fore and aft horizontal rudders, thus keeping the machine on an even keel while in the air.
Fig. 52.—Gyroscope, used for the control of the fore and aft horizontal rudders, thus keeping the machine on an even keel while in the air.
Fig. 52.—Gyroscope, used for the control of the fore and aft horizontal rudders, thus keeping the machine on an even keel while in the air.
Fig. 53.—In order to adjust the lifting effect so that it was directly over the centre of gravity, and to test the action of my fore and aft horizontal rudders, I ran the machine along the steel raili,i, and adjusted my weights and aeroplanes in such a manner that, when the machine was run at a speed of 30 miles an hour along the track, with the rudders adjusted in the manner shown, the front wheelj, was raised from the steel track and the small wheelm, brought into contact with the upper trackh. When the rudderb,b, is in this position, it produces a strong lifting effect, while the rudderc,c, does not lift at all.Fig. 53 enlarged(66 kB)
Fig. 53.—In order to adjust the lifting effect so that it was directly over the centre of gravity, and to test the action of my fore and aft horizontal rudders, I ran the machine along the steel raili,i, and adjusted my weights and aeroplanes in such a manner that, when the machine was run at a speed of 30 miles an hour along the track, with the rudders adjusted in the manner shown, the front wheelj, was raised from the steel track and the small wheelm, brought into contact with the upper trackh. When the rudderb,b, is in this position, it produces a strong lifting effect, while the rudderc,c, does not lift at all.
Fig. 53.—In order to adjust the lifting effect so that it was directly over the centre of gravity, and to test the action of my fore and aft horizontal rudders, I ran the machine along the steel raili,i, and adjusted my weights and aeroplanes in such a manner that, when the machine was run at a speed of 30 miles an hour along the track, with the rudders adjusted in the manner shown, the front wheelj, was raised from the steel track and the small wheelm, brought into contact with the upper trackh. When the rudderb,b, is in this position, it produces a strong lifting effect, while the rudderc,c, does not lift at all.
Fig. 53 enlarged(66 kB)
Fig. 54.—This shows the rudders placed in such a position thatb,b, does not lift at all, whilec, is placed at such an angle as to produce a strong lifting effect, especially so as it is in the blast of the screwsd,d. With the rudders in this position, and at a speed of 30 miles an hour, I was able to lift the rear wheelsk,k, off the steel rails and to bring the small wheell, in contact with the upper trackh. These experiments showed that the machine could be tilted in either direction by changing the position of the rudder.Fig. 54 enlarged(60 kb)
Fig. 54.—This shows the rudders placed in such a position thatb,b, does not lift at all, whilec, is placed at such an angle as to produce a strong lifting effect, especially so as it is in the blast of the screwsd,d. With the rudders in this position, and at a speed of 30 miles an hour, I was able to lift the rear wheelsk,k, off the steel rails and to bring the small wheell, in contact with the upper trackh. These experiments showed that the machine could be tilted in either direction by changing the position of the rudder.
Fig. 54.—This shows the rudders placed in such a position thatb,b, does not lift at all, whilec, is placed at such an angle as to produce a strong lifting effect, especially so as it is in the blast of the screwsd,d. With the rudders in this position, and at a speed of 30 miles an hour, I was able to lift the rear wheelsk,k, off the steel rails and to bring the small wheell, in contact with the upper trackh. These experiments showed that the machine could be tilted in either direction by changing the position of the rudder.
Fig. 54 enlarged(60 kb)
Fig. 55.—When the rudders were placed in the position shown, and the machine was run over the track at a rate of 40 miles an hour, all the weight was lifted off the wheels,j, andk, and both the small wheelsm, andl, engaged the upper track.Fig. 55 enlarged(62 kB)
Fig. 55.—When the rudders were placed in the position shown, and the machine was run over the track at a rate of 40 miles an hour, all the weight was lifted off the wheels,j, andk, and both the small wheelsm, andl, engaged the upper track.
Fig. 55.—When the rudders were placed in the position shown, and the machine was run over the track at a rate of 40 miles an hour, all the weight was lifted off the wheels,j, andk, and both the small wheelsm, andl, engaged the upper track.
Fig. 55 enlarged(62 kB)
Fig. 56.—In case of a breakdown or failure of the engines when the machine is in flight, it is necessary to place the rudders in the position shown, in order to prevent the machine from diving to the earth. When the rudders are in this position, a rapid and destructive descent is not possible, as the machine will preserve an even keel while falling.Fig. 56 enlarged(50 kB)
Fig. 56.—In case of a breakdown or failure of the engines when the machine is in flight, it is necessary to place the rudders in the position shown, in order to prevent the machine from diving to the earth. When the rudders are in this position, a rapid and destructive descent is not possible, as the machine will preserve an even keel while falling.
Fig. 56.—In case of a breakdown or failure of the engines when the machine is in flight, it is necessary to place the rudders in the position shown, in order to prevent the machine from diving to the earth. When the rudders are in this position, a rapid and destructive descent is not possible, as the machine will preserve an even keel while falling.
Fig. 56 enlarged(50 kB)
In Prof. Langley’s lifetime, we had many discussions regarding the width and shape of aeroplanes. The Professor had made many experiments with very small and narrow planes, and was extremely anxious to obtain some data regarding the effect that would be produced by making the planes of greater width. He admitted that by putting some two or three aeroplanes tandem, and all at the same angle, the front aeroplanea(Fig. 57), would lift a great deal more thanb, and thatc, would lift still less. He suggested the arrangement shown ata′,b′,c′, in whichb′is set at such an angle as to give as much additional acceleration to the air as it had received in the first instance by passing undera′, and thatc′, should also increase the acceleration to the same extent. With this arrangement, the lifting effect of the three aeroplanes ought to be the same, but I did not agree with this theory. It seemed to me that it would only be true if it dealt with the volume of air represented betweenj, andk, and that he did not take into consideration the mass of air betweenk, andl, that had to be dealt with, and which would certainly have some effect in buoying up the stream of air,j,k. Prof. Langley admitted the truth of this, and said that nothing but experiment would demonstrate what the real facts were. But it was a matter which I had to deal with. I did not like the arrangementa′,b′,c′, as the angle was so sharp, especially atc′, that a very large screw thrust would be necessary. I therefore made a compromise on this system which is shown ata′′,b′′,c′′. In this casea′′, has an inclination of 1 in 10,b′′an inclination of 1 in 6, andc′′an inclination of 1 in 5. It will be seen that this form, which is shown as one aeroplane ata′′′,b′′′,c′′′, is a very good shape. It is laid out by first drawing the linec,d, dropping the perpendicular equal to one-tenth of the distance betweencandd, and then drawing a straight line fromc, throughe, tof, where another perpendicular isdropped, and half the distance betweendandelaid off, and another straight line drawn frome, throughg, toh, and the perpendicularh,i, laid off the same asf,g. We then have four points, and by drawing a curve through these, we obtain the shape of the aeroplane shown above, which is an exceedingly good one. This shape, however, is only suitable for velocities, up to 40 miles per hour; at higher velocities, the curvature would be correspondingly reduced.
Fig. 57.—Diagram showing the evolution of a wide aeroplane.
Fig. 57.—Diagram showing the evolution of a wide aeroplane.
Fig. 57.—Diagram showing the evolution of a wide aeroplane.
In designing aeroplanes for flying machines, we should not lose sight of the fact that area alone is not sufficient. Our planes must have a certain length of entering edge—that is, the length of the front edge must bear a certain relation to the load lifted. An aeroplane 10 feet square will not lift half as much for the energy consumed as one 2 feet wide and 50 feet long; therefore, we must have our planes as long as possible from port to starboard. At all speeds of 40 miles per hour or less, there should be at least 1 foot of entering edge for every 4 lbs. carried. However, at higher speeds, the length may be reduced as the square of the speed increases. An aeroplane 1 foot square will not lift one-tenth as much as one that is 1 foot wide and 10 feet long. This is because the air slips off at the ends, but this can be prevented by a thin flange, orà laHargrave’s kites. An aeroplane 2 feet wide and 100 feet long placed at an angle of 1 in 10, and driven edgewise through the air at a velocity of 40 miles per hour, will lift 2·5 lbs. per square foot. But as we find a plane 100 feet in length too long to deal with, we may cut it into two or more pieces and place them one above the other—superposed. This enables us to reduce the width of our machine without reducing its lifting effect; we still have 100 feet of entering edge, we still have 200 feet of lifting surface, and we know that each foot will lift 2·5 lbs. at the speed we propose to travel. 200 × 2·5 = 500; therefore our total lifting effect is 500 lbs., and the screw thrust required to push our aeroplane through the air is one-tenth of this, because the angle above the horizontal is 1 in 10. We, therefore, divide what Prof.Langley has so aptly called the “lift” by 10;50010= 50. It will be understood that the vertical component is the lift, and the horizontal component the drift, the expression “drift” also being a term first applied by Prof. Langley. Our proposed speed is 40 miles per hour, or 3,520 feet in a minute of time. If we multiply the drift in pounds by the number of feet travelled in a minute of time, and divide the product thus obtained by 33,000, we ascertain the H.P. required—
50 × 3,52033,000= 5·33.
It therefore takes 5·33 H.P. to carry a load of 500 lbs. at a rate of 40 miles per hour, allowing nothing for screw slip or atmospheric resistance due to framework and wires. But we find we must lift more than 500 lbs., and as we do not wish to make our aeroplanes any longer, we add to their width in a fore and aft direction—that is, we place another similar aeroplane, also 2 feet wide, just aft of our first aeroplane. This will, of course, have to engage the air discharged from the first, and which is already moving downwards. It is, therefore, only too evident that if we place it at the same angle as our first one—viz., 1 in 10—it will not lift as much as the first aeroplane, and we find that if we wish to obtain a fairly good lifting effect, it must be placed at an angle of 1 in 6. Under these conditions, the screw thrust for this plane will be1⁄6th part of the lift, or 8·88 H.P. against 5·33 H.P. with our first aeroplane. In order to avoid confusion, we will call our first planea′′, our second planeb′′, and the thirdc′′, the same as inFig. 57. Still we are not satisfied, we want more lift, we therefore add still another aeroplane as shown (c′′,Fig. 57). This one has to take the air which has already been set in motion by the two preceding planesa′′andb′′, so in order to get a fair lifting effect, we have to place our third plane at the high angle of 1 in 5. At this angle, our thrust has to be1⁄5th of the lifting effect, and the H.P. required is twice as much per pound carried as with the planea′′, where the angle was 1 in 10; therefore, it will take 10·66 H.P. to carry 500 lbs. As there is no reason why we should have three aeroplanes placed tandem where one would answer the purpose much better, we convert the whole of them into one, as shown (a′′′,b′′′,c′′′,Fig. 57), and by makingthe top side smooth and uniform, we get the advantage of the lifting effect due to the air above the aeroplane as well as below it. The average H.P. is therefore 5·33 + 8·88 + 10·66 ÷ 3 = 8·29 H.P. for each plane, or 25 H.P. for the whole, which is at the rate of 60 lbs. to the H.P., all of which is used to overcome the resistance due to the weightand the inclination of the aeroplanes, and which is about half the total power required. We should allow as much more for loss in screw slip and atmospheric resistance due to the motor, the framework, and the wires of the machine. If, however, the screw is placed in the path of the greatest resistance, it will recover a portion of the energy imparted to the air. We shall, however, require a 50 H.P. motor, and thus have 30 lbs. to the H.P.
From the foregoing it will be seen that at a speed of 40 miles an hour, the weight per H.P. is not very great. If we wish to make a machine more efficient, we must resort to a multitude of very narrow superposed planes, or sustainers, as Mr. Philipps calls them, or we must increase the speed. If an aeroplane will lift 2·5 lbs. per square foot placed at an angle of 1 in 10, and driven at a velocity of 40 miles an hour, the same aeroplane will lift 1·25 lbs. if placed at an angle of 1 in 20, and as the lifting effect varies as the square of the velocity, the same plane will lift as much more at 60 miles per hour, as 60² is greater than 40²—that is, 2·81 lbs. per square foot instead of 1·25 lbs. At this high speed, providing that the width of the plane is not more than 3 feet, it need be only slightly curved and have a mean angle of 1 in 20.
An aeroplane 100 feet long and 3 feet wide would have 300 square feet of lifting surface, each of which would lift 2·81 lbs., making the total lifting effect 843 lbs. 843 ÷ 20 = 42·15, which is the screw thrust that would be necessary to propel such a plane through the air at a velocity of 60 miles per hour. 60 miles per hour is 5,280 feet in a minute, therefore the H.P. required is 42·15 × 5,280 ÷ 33,000 = 6·7 H.P. Dividing the total lifting effect 843 by 6·7, we have 843 ÷ 6·7 = 125·8, the lift per H.P. If we allow one-half for loss in friction, screw slip, etc., we shall be carrying a load of 843 lbs. with 13·4 H.P. It will, therefore, be seen that a velocity of 60 miles an hour is much more economical in power than the comparatively low velocity of 40 miles an hour; moreover, it permits of a considerable reduction in the size and weight of the machine, and this diminishes the atmospheric resistance.