CHAPTER VII.

THE SHAPE AND EFFICIENCY OF AEROPLANES.

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 aeroplane _a_ (Fig. 57), would lift a great deal more than _b_, and that _c_, would lift still less. He suggested the arrangement shown at _a′_, _b′_, _c′_, in which _b′_ 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 under _a′_, and that _c′_, 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 between _j_, and _k_, and that he did not take into consideration the mass of air between _k_, and _l_, 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 arrangement _a′_, _b′_, _c′_, as the angle was so sharp, especially at _c′_, that a very large screw thrust would be necessary. I therefore made a compromise on this system which is shown at _a′′_, _b′′_, _c′′_. In this case _a′′_, has an inclination of 1 in 10, _b′′_ an inclination of 1 in 6, and _c′′_ an inclination of 1 in 5. It will be seen that this form, which is shown as one aeroplane at _a′′′_, _b′′′_, _c′′′_, is a very good shape. It is laid out by first drawing the line _c_, _d_, dropping the perpendicular equal to one-tenth of the distance between _c_ and _d_, and then drawing a straight line from _c_, through _e_, to _f_, where another perpendicular is dropped, and half the distance between _d_ and _e_ laid off, and another straight line drawn from _e_, through _g_, to _h_, and the perpendicular _h_, _i_, laid off the same as _f_, _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.

THE ACTION OF AEROPLANES AND THE POWER REQUIRED EXPRESSED IN THE SIMPLEST TERMS.

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, or _à la_ Hargrave’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; 500/10 = 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 × 3,520 ---------- = 5·33. 33,000

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 be 1/6th 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 plane _a′′_, our second plane _b′′_, and the third _c′′_, the same as in Fig. 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 planes _a′′_ and _b′′_, 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 be 1/5th of the lifting effect, and the H.P. required is twice as much per pound carried as with the plane _a′′_, 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 making the 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 weight and 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.

SOME RECENT MACHINES.

Professor S. P. Langley, of the Smithsonian Institute, Washington, D.C., made a small flying model in 1896. This, however, only weighed a few pounds; but as it did actually fly and balance itself in the air, the experiment was of great importance, as it demonstrated that it was possible to make a machine with aeroplanes so adjusted as to steer itself automatically in a horizontal direction. In order to arrive at this result, an innumerable number of trials were made, and it was only after months of careful and patient work that the Professor and his assistants succeeded in making the model fly in a horizontal direction without rearing up in front, and then pitching backwards, or plunging while moving forward.

The Wright Brothers of Dayton, Ohio, U.S.A., often referred to as “the mysterious Wrights,” commenced experimental work many years ago. The first few years were devoted to making gliding machines, and it appears that they attained about the same degree of success as many others who were experimenting on the same lines at the same time; but they were not satisfied with mere gliding machines, and so turned their attention in the direction of motors. After some years of experimental work, they applied their motor to one of their large gliding machines, and it is said that with this first machine they actually succeeded in flying short distances. Later on, however, with a more perfect machine, they claim to have made many flights, amongst which I will mention three: 12 miles in 20 minutes, on September 29th, 1905; 20·75 miles in 33 minutes, on October 4th; and 24·2 miles in 38 minutes, on October 5th of the same year. As there seems to be much doubt regarding these alleged flights, we cannot refer to them as facts until the Wright Brothers condescend to show their machine and make a flight in the presence of others; nevertheless, I think we are justified in assuming that they have met with a certain degree of success which may or may not be equal to the achievements of Messrs Farman and De la Grange. It is interesting to note in this connection that all flying machines that have met with any success have been made on the same lines; all have superposed aeroplanes, all have fore and aft horizontal rudders, and all are propelled with screws; and in this respect they do not differ from the large machine that I made at Baldwyn’s Park many years ago. I have seen both the Farman and the De la Grange machines; they seem to be about the same in size and design, and what is true of one is equally true of the other; I will, therefore, only describe the one that seems to have done the best--the De la Grange. The general design of this machine is clearly shown in the illustrations (Figs. 68 and 69). The dimensions are as follows: The two main aeroplanes are 32·8 feet long and 4·9 feet wide; the tail or after rudder is made in the form of a Hargrave’s box kite, the top and bottom sides of the box being curved and covered with balloon fabric, thus forming aeroplanes. This box is 9·84 feet long from port to starboard, and 6·56 feet wide in a fore and aft direction. The diameter of the screw is 7·2 feet and it has a mean pitch of 5·7 feet. The screw blades are two in number and are extremely small, being only 6·3 inches wide at the outer end and 3·15 inches at the inner end, their length being 2·1 feet. The space between the fore and aft aeroplanes is 4·9 feet. The total weight is about 1,000 lbs. with one man on board. The speed of this machine through the air is not known with any degree of certainty; it is, however, estimated to be 32 to 40 miles per hour. When the screw is making 1,100 revolutions per minute, the motor is said to develop 50 H.P.

In the following calculations, I have assumed that the machine has the higher speed--40 miles per hour. I have been quite unable to obtain any reliable data regarding the angle at which the aeroplanes are set, but it would appear that the angle is about 1 in 10. The total area of the two main aeroplanes is 321·4 square feet. A certain portion of the lower main aeroplane is cut away, but this is compensated for by the forward horizontal rudder placed in the gap thus formed. The two rear aeroplanes forming the tail of the machine have an area of 128·57 square feet. The area of all the aeroplanes is, therefore, 450 square feet. As the weight of the machine is 1,000 lbs., the lift per square foot is 2·2 lbs. Assuming that the angle of the aeroplanes is 1 in 10, the screw thrust would be 100 lbs., providing, however, that the aeroplanes were perfect and no friction of any kind was encountered. Forty miles per hour is at the rate of 3,520 feet in a minute of time, therefore, (3,520 × 100)/33,000 = 10·66 H.P. If we allow another 10 H.P. for atmospheric resistance due to the motor, the man, and the framework of the machine, it would require 20·66 H.P. to propel the machine through the air at the rate of 40 miles per hour. If the motor actually develops 50 H.P., 29 H.P. will be consumed in screw slip and overcoming the resistance due to the imperfect shape of the screw. The blades of the De la Grange screw propeller are extremely small, and the waste of energy is, therefore, correspondingly great--their projected area being only 1·6 square feet for both blades. Allowing 200 lbs. for screw thrust, we have the following: 200/1·60 = 125 lbs. pressure per square foot on the blades. If we multiply the pitch of the screw in feet by the number of revolutions per minute, we find that if it were travelling in a solid nut it would advance over 70 miles an hour. By the Eiffel tower formula P = 0·003 V², a wind blowing at a velocity of 70 miles per hour produces a pressure of 14·7 lbs. per square foot on a normal plane; therefore, assuming that the projected area of the screw blades is 1·6, we have 1·6 × 14·7 = 23·52 lbs., which is only one-fifth part of what the pressure really is when the screws are making 1,100 turns a minute. It is interesting to note that the ends of the screw blades travel at a velocity of 414 feet per second, which is about one-half the velocity of a cannon ball fired from an old-fashioned smooth bore.

VELOCITY AND PRESSURE OF THE WIND.

The pressure varies as the square of the velocity or P ∝ V². The old formula for wind blowing against a normal plane was P = 0·005 × V². The latest or Eiffel Tower formula gives a much smaller value, being P = 0·003 × V², where V represents the velocity in miles per hour, and P the pressure in pounds per square foot.

+---------------------------------+---------+----------------------+ | VELOCITY. |Pressure | | | | on a |Character of the Wind.| +---------+-----------+-----------+Sq. Foot.| | |Per Hour.|Per Minute.|Per Second.| | | +---------+-----------+-----------+---------+----------------------+ | Miles. | Feet. | Feet. | Lbs. | | | 1 | 88 | 1·5 | ·003 | Barely observable. | | 2 | 176 | 2·9 | ·012 |} Just | | 3 | 264 | 4·4 | ·027 |} perceptible. | | 4 | 352 | 5·9 | ·048 | Light breeze. | | 5 | 440 | 7·3 | ·075 |} Gentle, | | 6 | 528 | 8·8 | ·108 |} pleasant | | 8 | 704 | 11·7 | ·192 |} wind. | | 10 | 880 | 14·7 | ·3 | Fresh breeze. | | 15 | 1,320 | 22 | ·675 | Brisk breeze. | | 20 | 1,760 | 29·4 | 1·2 | Stiff breeze. | | 25 | 2,200 | 36·7 | 1·875 | Very brisk breeze. | | 30 | 2,640 | 44 | 2·7 |} High | | 35 | 3,080 | 51·3 | 3·675 |} wind. | | 40 | 3,520 | 58·7 | 4·8 | Very high wind. | | 45 | 3,960 | 66 | 6·075 | Gale. | | 50 | 4,400 | 73·4 | 7·5 | Storm. | | 60 | 5,280 | 88 | 10·8 |} Great | | 70 | 6,160 | 102·7 | 14·7 |} storm. | | 80 | 7,040 | 117·2 | 19·2 | Hurricane. | | 90 | 7,920 | 132 | 24·3 |} | | 100 | 8,800 | 146·7 | 30 |} Tornado. | | 110 | 9,680 | 161·2 | 36·3 | } | | 120 | 10,560 | 176 | 43·2 | } “Washoe | | 130 | 11,440 | 191 | 50·7 | } zephyrs.”[2] | | 140 | 12,320 | 205·3 | 58·8 | } | | 150 | 13,200 | 220 | 67·5 | } | +---------+-----------+-----------+---------+----------------------+

[2] With apologies to Mark Twain.

TABLE OF EQUIVALENT INCLINATIONS.

+------------+----------------+-------------------+ | Rise. | Sine of Angle. | Angle in Degrees. | +------------+----------------+-------------------+ | 1 in 30, | ·0333 | 1·91 | | 1 „ 25, | ·04 | 2·29 | | 1 „ 20, | ·05 | 2·87 | | 1 „ 18, | ·0555 | 3·18 | | 1 „ 16, | ·0625 | 3·58 | | 1 „ 14, | ·0714 | 4·09 | | 1 „ 12, | ·0833 | 4·78 | | 1 „ 10, | ·1 | 5·73 | | 1 „ 9, | ·1111 | 6·38 | | 1 „ 8, | ·125 | 7·18 | | 1 „ 7, | ·143 | 8·22 | | 1 „ 6, | ·1667 | 9·6 | | 1 „ 5, | ·2 | 11·53 | | 1 „ 4, | ·25 | 14·48 | | 1 „ 3, | ·3333 | 19·45 | +------------+----------------+-------------------+

TABLE OF EQUIVALENT VELOCITIES.

+-----------+-------------+-------------+-------------+-------------+ | | | | | | | Miles | Feet | Feet | Metres | Metres | | per Hour. | per Second. | per Minute. | per Minute. | per Second. | +-----------+-------------+-------------+-------------+-------------+ | | | | | | | 1, | 1·5 | 88 | 26·8 | ·447 | | 2, | 2·9 | 176 | 53·6 | ·894 | | 3, | 4·4 | 264 | 80·5 | 1·341 | | 4, | 5·9 | 352 | 107·3 | 1·788 | | 5, | 7·3 | 440 | 134·1 | 2·235 | | 6, | 8·8 | 528 | 160·9 | 2·682 | | 8, | 11·7 | 704 | 214·6 | 3·576 | | 10, | 14·7 | 880 | 268·2 | 4·470 | | 15, | 22 | 1,320 | 402·3 | 6·705 | | 20, | 29·4 | 1,760 | 536·4 | 8·940 | | 25, | 36·7 | 2,200 | 670·5 | 11·176 | | 30, | 44 | 2,640 | 804·6 | 13·411 | | 35, | 51·3 | 3,080 | 938·8 | 15·646 | | 40, | 58·7 | 3,520 | 1,072·9 | 17·881 | | 45, | 66 | 3,960 | 1,207 | 20·116 | | 50, | 73·4 | 4,400 | 1,341·1 | 22·352 | | 60, | 88 | 5,280 | 1,609·2 | 26·822 | | 70, | 102·7 | 6,160 | 1,877·5 | 31·292 | | 80, | 117·2 | 7,040 | 2,145·8 | 35·763 | | 90, | 132 | 7,920 | 2,414 | 40·233 | | 100, | 146·7 | 8,800 | 2,682·2 | 44·704 | | 110, | 161·2 | 9,680 | 2,950·2 | 49·174 | | 120, | 176 | 10,560 | 3,218·4 | 53·644 | | 130, | 191 | 11,440 | 3,486·6 | 58·115 | | 140, | 205·3 | 12,320 | 3,755·1 | 62·585 | | 150, | 220 | 13,200 | 4,023·3 | 67·056 | +-----------+-------------+-------------+-------------+-------------+

To convert feet per minute into metres per second, multiply by ·00508.

TABLE SHOWING VELOCITY AND THRUST CORRESPONDING WITH VARIOUS HORSE-POWERS.

+---------+-------------------------------------------------+ |Velocity | Horse-Power. | |in Miles +------+-------+-------+--------+--------+--------+ |per Hour.| 1 | 10 | 20 | 30 | 40 | 50 | | +------+-------+-------+--------+--------+--------+ | | Thrust in Pounds. | +---------+------+-------+-------+--------+--------+--------+ | 1, |375 |3,750 |7,500 |11,250 |15,000 |18,750 | | 5, | 75 | 750 |1,500 | 2,250 | 3,000 | 3,750 | | 10, | 37·5 | 375 | 750 | 1,125 | 1,500 | 1,875 | | 15, | 25 | 250 | 500 | 750 | 1,000 | 1,250 | | 20, | 18·8 | 187·5| 375 | 562·5| 750 | 937·5| | 25, | 15 | 150 | 300 | 450 | 600 | 750 | | 30, | 12·5 | 125 | 250 | 375 | 500 | 625 | | 35, | 10·7 | 107·1| 214·3| 321·4| 428·6| 535·7| | 40, | 9·4 | 93·8| 187·5| 281·3| 375 | 468·8| | 45, | 8·3 | 83·3| 166·7| 250 | 333·3| 416·7| | 50, | 7·5 | 75 | 150 | 225 | 300 | 375 | | 60, | 6·3 | 62·5| 125 | 187·5| 250 | 312·5| | 70, | 5·4 | 53·6| 107·1| 160·7| 214·3| 267·9| | 80, | 4·7 | 46·9| 93·8| 140·6| 187·5| 234·4| | 90, | 4·2 | 41·7| 83·3| 125 | 166·7| 208·3| | 100, | 3·75| 37·5| 75 | 112·5| 150 | 187·5| +---------+------+-------+-------+--------+--------+--------+

+---------+--------------------------------------------+ |Velocity | Horse-Power. | |in Miles +--------+--------+--------+--------+--------+ |per Hour.| 60 | 70 | 80 | 90 | 100 | | +--------+--------+--------+--------+--------+ | | Thrust in Pounds. | +---------+--------+--------+--------+--------+--------+ | 1, |22,500 |26,250 |30,000 |33,750 |37,500 | | 5, | 4,500 | 5,250 | 6,000 | 6,750 | 7,500 | | 10, | 2,250 | 2,625 | 3,000 | 3,375 | 3,750 | | 15, | 1,500 | 1,750 | 2,000 | 2,250 | 2,500 | | 20, | 1,125 | 1,312·5| 1,500 | 1,687·5| 1,875 | | 25, | 900 | 1,050 | 1,200 | 1,350 | 1,500 | | 30, | 750 | 875 | 1,000 | 1,125 | 1,250 | | 35, | 642·8| 750 | 857·1| 964·3| 1,071·4| | 40, | 562·5| 656·3| 750 | 843·8| 937·5| | 45, | 500 | 583·3| 666·7| 750 | 833·3| | 50, | 450 | 525 | 600 | 675 | 750 | | 60, | 375 | 437·5| 500 | 562·5| 625 | | 70, | 321·4| 375 | 428·6| 482·1| 535·7| | 80, | 281·3| 328·2| 375 | 421·9| 468·8| | 90, | 250 | 291·7| 333·3| 375 | 416·7| | 100, | 225 | 262·5| 300 | 337·5| 375 | +---------+--------+--------+--------+--------+--------+

PHILIPPS’ EXPERIMENTS.

+----------+----------+------------+------------+------------+------+ | DESCRIP- | SPEED OF | DIMENSIONS | LIFT. | DRIFT. | | | TION | AIR | OF | | | LIFT | | OF | CURRENT. | AEROPLANES.| | | DI- | | FORM. +----+-----+ +------+-----+------+-----+ VIDED| | |Feet|Miles| |Whole | Lbs.|Whole | Lbs.| BY | | |per | per | |Plane.| per |Plane.| per |DRIFT.| | |sec.|hour.| | Ozs. | sq. | Ozs. | sq. | | | | | | | | ft. | | ft. | | +----------+----+-----+------------+------+-----+------+-----+------+ |Plane sur-| | | | | | | | | |faces, | 39 |26·59| 16" × 5" | 9 |1·013| 2 |0·225| 4·5 | |Fig. 1, | 60 |40·91| 16" × 1·25"| 9 |4·05 | 0·87 |0·392| 10·3 | | „ 2, | 48 |32·73| 16" × 3" | 9 |1·688| 0·87 |0·163| 10·3 | | „ 3, | 44 |30 | 16" × 3" | 9 |1·688| 0·87 |0·163| 10·3 | | „ 4, | 44 |30 | 16" × 5" | 9 |1·013| 0·87 |0·098| 10·3 | | „ 5, | 39 |26·59| 16" × 5" | 9 |1·013| 0·87 |0·098| 10·3 | | „ 6, | 27 |18·41| 16" × 5" | 9 |1·013| 2·25 |0·253| 4 | | | | |Area sq. ft.| | | | | | |Rook’s | | | | | | | | | |wing, | 39 |26·59| 0·5 | 8 |1·0 | 1·0 |0·125| 8 | +----------+----+-----+------------+------+-----+------+-----+------+