FOOTNOTES.

FOOTNOTES.[2]“Experiments in Aerodynamics,”Smithsonian Contributions to Knowledge, Vol. 27, 1891.[3]This chapter was written almost entirely by Mr. Langley in 1897.[4]1897.[5]In this statement, of course, no account is taken of the “internal work of the wind.”[6]Ten years prior to 1897.[7]Communication to the French Academy. Extract from the Comptes Rendus of the Sessions of the Academy of Sciences, Vol. 122, Session of May 26, 1896.(Translation.)A Description of Mechanical Flight. By S. P. Langley.In a communication which I addressed to the Academy in July, 1891, I remarked that the results of experimental investigation had shown the possibility of constructing machines which could give such a horizontal velocity to bodies resembling in shape inclined planes, and more than a thousand times heavier than air, that these could be sustained on this element.While I have elsewhere remarked that surfaces other than planes might give better results, and that absolutely horizontal flight, which is so desirable in theory, is hardly realizable in practice, so far as I know there has never been constructed, up to the present time, any heavy aerodrome, or so-called flying-machine, which can keep itself freely in the air by its own force more than a few seconds, the difficulties encountered in absolutely free flight being, for many reasons, immeasurably greater than those experienced when the flight is controlled by the body’s pressing upward against a horizontal track, or whirling-arm. No one is unaware that many experimenters have been engaged in trying to execute free mechanical flight, and although the demonstration which I furnished in 1891 [“Experiments in Aerodynamics,” 1891] of its theoretical possibility with means then at our disposition, seemed conclusive, so long a time has elapsed without practical results, that it might be doubted whether these theoretical conditions are to be realized. I have thought it well, then, to occupy myself with the construction of an aerodrome with which I might put my previous conclusions to the test of experiment.The Academy will, perhaps, find it interesting to read the narrative given here by an eye-witness, who is well known to it. I am led to present it not only by the request with which he honors me, but by the apprehension that my administrative duties may put a stop to these researches, so that it seems to me advisable to announce the degree in which I have already succeeded, although this success be not as complete as I should like to make it.The experiments took place on a bay of the Potomac River, some distance below Washington. The aerodrome was built chiefly of steel, though lighter material entered into the construction, so that its density as a whole was a little below unity. No gas whatever entered into the construction of the machine, and the absolute weight, independent of fuel and water, was about 11 kilos (24 pounds). The width of the supporting surfaces was about 4 metres (13 feet), and the power was furnished by an extremely light engine of approximately one horse-power. There was no one to direct it on board, and the means for keeping it automatically in horizontal flight were not complete. It is important to remark that the small dimensions of the machine did not allow it to include any apparatus for condensing the steam, so that it could only carry water enough for a very brief course—a drawback which would not be encountered in one of a larger construction.It is also to be noted that the speed estimated by Mr. Bell was that obtained in a continuous ascending flight, and much less than would have been attained in a horizontal course.On Mechanical Flight. Letter of Mr. Alexander Graham Bell to Mr. Langley.Washington, May 6, 1896.I am quite aware that you are not desirous of publication until you have attained more complete success in obtaining horizontal flight under an automatic direction, but it seems that what I have been privileged to see to-day marks such a great progress on everything ever before done in this way, that the news of it should be made public, and I am happy to give my own testimony on the results of two trials which I have witnessed to-day by your invitation, hoping that you will kindly consent to making it known.For the first trial, the apparatus, chiefly constructed of steel and driven by a steam engine, was launched from a boat at a height of about 20 feet from the water. Under the impulse of its engines alone, it advanced against the wind and while drifting little, and slowly ascending with a remarkably uniform motion, it described curves of about 100 metres in diameter; till at a height in the air which I estimate at about 25 metres (82 feet), the revolutions of the screws ceased for want of steam, as I understood, and the apparatus descended gently and sank into the water, which it reached in a minute and a half from the start. It was not damaged, and was immediately ready for another flight.In the second trial it repeated in nearly every respect the action of the first, and with an identical result. It rose smoothly in great curves until it approached a prominent wooded promontory, which it crossed at a height of 8 to 10 metres above the tops of the highest trees, upon the exhaustion of the steam descending slowly into the bay, where it settled in a minute and thirty-one seconds from the start. You have an instantaneous photograph of it, which I took just after the launch. [See plates20,21, and22of present work.]From the extent of the curves which it described, which I estimated with other persons, from measurements which I took, and from the number of revolutions of the propellers, as recorded by the automatic counter which I consulted, I estimate the absolute length of each course to be over half an English mile, or, more exactly a little over 900 metres (2953 feet).The duration of flight during the second trial was one minute and thirty-one seconds, and the average velocity between twenty and twenty-five miles an hour, or, let us say 10 metres a second, in a course which was constantly ascending. I was extremely impressed by the easy regular course of each trial, and by the fact that the apparatus descended each time with such smoothness and gentleness as to render any jar or danger out of the question.It seemed to me that no one could have witnessed these experiments without being convinced that the possibility of mechanical flight had been demonstrated.[8]It is desirable that the reader should be acquainted with the contents of this treatise, and of another by me, entitled “The Internal Work of the Wind,” both published by the Smithsonian Institution. A knowledge of these works is not absolutely necessary, but of advantage in connection with what follows.[9]“Experiments in Aerodynamics,” p. 107.[10]Chapter VIII◊.[11]His device for obtaining automatic equilibrium is found in connection with the description of his “Aeroplane Auto Moteur,” in “L’Aeronaute” for January, 1872.[12]I have never obtained so good a result as this with any rubber motor. S. P. Langley.[13]One pound of twisted rubber appears, from my experiments, to be capable of momentarily yielding nearly 600 foot-pounds of energy, but this effect is attained only by twisting it too far. It will be safer to take at most 300 foot-pounds, and as the strain must be taken up by a tube or frame weighing at least as much as the rubber, we have approximately 0.0091 as the horse-power for one minute, or 0.091 horse-power for six seconds as the maximum effect, in continuous work, of a pound oftwistedrubber strands. The longitudinal pull of the rubber is much greater, but it is difficult to employ it in this way for models, owing to the great relative weight of the tube or frame needed to bear the bending strain. In either form, rubber is far more effective for the weight than any steel spring (see later chapter on Available Motors).[14]The aerodrome is sustained by the upward pressure of the air, which must be replaceable by the resultant pressure at some particular point, designated byCP.[15]See Century Magazine, October, 1891.[16]Subsequent observations indicate that the maximum velocity of horizontal flight must have been about 10 metres per second.[17]Observers following de Lucy have long since called attention to the fact that as the scale of Nature’s flying things increases, the size of the sustaining surfaces diminishes relatively to the weight sustained. M. Harting (Aeronautical Society, 1870) has shown that the relation√area/u+221bweightis surprisingly constant when bats varying in weight as much as 250 times are the subject of the experiment, and later observations by Marey have not materially affected the statement. As to the muscular power which Nature has imparted with the greater or lesser weight, this varies, decreasing very rapidly as the weight increases. The same remark may be made apparently with at least approximate truth, with regard to the soaring bird, and the important inference is that if there be any analogy between the bird and the aerodrome, as the scale of the construction of the latter increases, it may be reasonably anticipated that the size of the sustaining surfaces will relatively diminish rather than increase. We may conveniently use M. Harting’s formula in the forma=n2w(2/3)=l2m2wherea= area in sq. cm.,wthe weight in grammes,lthe length of the wing in cm.,nandmconstants derived from observation.[18]A singular fact connected with the stretching of rubber is that the extension is not only not directly proportional to the power producing it, but that up to a certain limit it increases more rapidly than the power, and after this the relation becomes for a time more nearly constant, and after this again the extension becomes less and less in proportion.In other words, if a curve be constructed whose abscissae represent extensions, and ordinates the corresponding weights, it will show a reverse curvature, one portion being concave toward the axis of abscissae, the other convex.[19]The following table taken from “Experiments in Aerodynamics,” p. 107, gives the data for soaring of 30 × 4.8 inch planes, weight 500 grammes.Angle with horizon α.Soaring speedV.Work expended per minute.Weight with planes of like form that 1 horse-power will drive through the air at velocityV.Metres per second.Feet per second.Kilogram-metres.Foot-pounds.Kilogrammes.Pounds.45°11.236.73362,4346.8153010.634.81751,26813.0291511.236.78662326.5581012.440.76547434.877515.249.84129755.5122220.065.62417495.0209The relations shown in the above table hold true only in case of planes supporting about 1.1 pounds to each square foot of sustaining area. For a different proportion of area to weight, other conditions would obtain.[20]This pressure per unit of area varies with the area itself, but in a degree which is negligible for our immediate purpose.[21]See “Internal Work of the Wind”; also Revue de L’Aeronautique, 3eLivraison, 1893.[22]More recent experiments under my direction by Mr. Huffaker give similar results, but confirm my earlier and cruder observations that the curve, used alone, for small angles, is much more unstable than the plane.[23]As stated in the Preface, Part III has not yet been prepared for publication.[24]According to Wellner (“Zeitschrift für Luftschiffahrt,” Beilage, 1893), in a curved surface with 1/12 rise, if the angle of inclination of the chord of the surface be α, and the angle between the direction of resultant air pressure and the normal to the direction of motion be β, then β<α and the soaring speed isV= √(PK×1F(α)×cos β)while the efficiency isWR=WeightResistance= tan βThe following were derived from experiments in the wind:α =−3°0°+3°6°9°12°F(α) =0.200.800.750.901.001.05Tan β =0.010.020.030.040.100.17so that according to him, a curved surface shows finite soaring speeds when the angle of inclination is 0° or even slightly negative.[25]The following formulæ proposed by Mr. Chas. M. Manly show how the center of pressure may be moved any desired distance either forward or backward without in any way affecting the center of gravity, and by merely moving the front and rear wings the same amounts but in opposite directions, the total movement of each wing being in either case five times the amount that is desired to move the meanCP1, and the direction of movement of the front wing determining the direction of movement ofCP1.In Figure 7,CPfwandCPrware the centers of pressure of the front and rear wings respectively; the weights of the wings, which are assumed to be equal and concentrated at their centers of figure, are represented byw,w, andais the distance of the center of pressure in either wing from its center of figure. The original mean center of pressure of the aerodrome isCP1,Wis the weight of the aerodrome, supposed to be concentrated atCG1, whilemis the distance fromCPrwtoCG1.Now, if we have assumed that the rear wing, being of the same size as the front one, has a lifting effect of only 0.66, and on this assumption is calculated the proper relative positions of the front and rear wings to cause theCP1to come directly over theCG1, and upon testing the aerodrome find that it is too heavy in front and, therefore, wish to move the center of pressure forward an amount, sayb, without affecting the center of gravity, we can calculate the proper relative positions of the front and rear wings in the following manner. While the aerodrome as a whole is balanced at the pointCG1, the weight of the wings is not balanced around this point, for the rear wing, owing to its decreased lifting effect, is proportionately farther fromCP1than the front wing. In order, therefore, to avoid moving the center of gravity of the machine as a whole, any movement of the wings must be made in such a way as to cause the difference between the weight of the rear wing multiplied by its distance fromCG1and the weight of the front multiplied by its distance fromCG1to equal a constant: that is,w(m+a)−w(0.66m−a) = constant,and0.33wm+ 2wa= constant.FIG.7.FIG.8.FIG.9.FIGS.7–9. Diagrams Illustrating formulæ for movingC. P.without disturbingC. G.If now the wings be moved so thatCP1is moved forward a distanceb, we may indicate the distance fromCG1to the newCPrwbyz, and equating the difference between the weight of the rear wing multiplied by its new distance fromCG1and the weight of the front wing multiplied by its new distance fromCG1and making this difference equal to the constant difference, we can calculatezin terms ofmandb, as follows:Fig. 8,w(a+z)−w(0.66(z+b) +b−a) = 0.33wm+ 2wa,∴z=m+ 5b.Knowingz, we readily find that the new distance fromCPfwtoCG1equals:0.66(z+b) +b= 0.66m+ 5b.In a similar manner we may calculate the proper relative positions of the front and rear wings when we wish to move the center of pressure backward a distance,b, from the originalCP1without changing the position ofCG1. From Fig. 7, we have as before:w(m+a)−w(0.66m−a) = constant,0.33wm+ 2wa= constant.Fig. 9,w(z1+a)−w(0.66(z1−b)−b−a) = 0.33wm+ 2wa.∴z1=m−5b.Similarly we have for the new distance fromCPfwtoCG1:0.66(z1−b)−b= 0.66m−5b.[26]It is to be remembered that these aerodromes were under incessant modifications, No. 4 for instance, presenting successive changes which made of it in reality a number of different machines, one merging by constant alterations into the other, though it still went under the same name. After 1895 the type of the models remained relatively constant, but during the first five years of the work, constructions equal to the original building of at least eight or ten independent aerodromes were made.[27]Chapter V◊.[28]“Pocketing” is a form of distortion in which the canvas or silk bags locally in numerous places between the cross-ribs.[29]The site of these experiments, which was 30 miles below Washington, has been described. The writer is designated by the initial “L”; Dr. Barus, who several times assisted, by the letter “B”; Mr Reed, carpenter, by “R”; Mr Maltby, machinist, by “M”; and Mr. Gaertner, instrument maker, by “G.”[30]Weights and dimensions are here given in approximate pounds and feet.[31]“Experiments in Aerodynamics.”[32]On the data of “Aerodynamics,” a plane having 1.8 sq. ft. of surface per pound, and advancing at an angle of 20°, would soar at a speed of 24.1 ft. per second.[33]It will be remembered that the purely theoretical conclusions just cited apply to the power delivered in direct thrust, but that of the above actual H. P. an indefinite amount was lost in friction and slip of propellers.[34]It may be observed that at this time the position of theCPwas calculated on the assumption that the pressure for flight surfaces was proportional to the areas, without also allowing for the fact that the following surfaces, like the tail, were under the “lee” of the wind and so far less efficient. It follows, then, that the valueCP−CGwas not really 0, as was assumed, but something considerable.[35]Very exact accuracy in these minute details is indispensable to the efficient working of the engines.[36]The reader who may care to note the evolution of this boiler, by trial and error, will find a portion of the many discarded types shown in Plate13.

[2]“Experiments in Aerodynamics,”Smithsonian Contributions to Knowledge, Vol. 27, 1891.

[3]This chapter was written almost entirely by Mr. Langley in 1897.

[4]1897.

[5]In this statement, of course, no account is taken of the “internal work of the wind.”

[6]Ten years prior to 1897.

[7]Communication to the French Academy. Extract from the Comptes Rendus of the Sessions of the Academy of Sciences, Vol. 122, Session of May 26, 1896.(Translation.)A Description of Mechanical Flight. By S. P. Langley.In a communication which I addressed to the Academy in July, 1891, I remarked that the results of experimental investigation had shown the possibility of constructing machines which could give such a horizontal velocity to bodies resembling in shape inclined planes, and more than a thousand times heavier than air, that these could be sustained on this element.While I have elsewhere remarked that surfaces other than planes might give better results, and that absolutely horizontal flight, which is so desirable in theory, is hardly realizable in practice, so far as I know there has never been constructed, up to the present time, any heavy aerodrome, or so-called flying-machine, which can keep itself freely in the air by its own force more than a few seconds, the difficulties encountered in absolutely free flight being, for many reasons, immeasurably greater than those experienced when the flight is controlled by the body’s pressing upward against a horizontal track, or whirling-arm. No one is unaware that many experimenters have been engaged in trying to execute free mechanical flight, and although the demonstration which I furnished in 1891 [“Experiments in Aerodynamics,” 1891] of its theoretical possibility with means then at our disposition, seemed conclusive, so long a time has elapsed without practical results, that it might be doubted whether these theoretical conditions are to be realized. I have thought it well, then, to occupy myself with the construction of an aerodrome with which I might put my previous conclusions to the test of experiment.The Academy will, perhaps, find it interesting to read the narrative given here by an eye-witness, who is well known to it. I am led to present it not only by the request with which he honors me, but by the apprehension that my administrative duties may put a stop to these researches, so that it seems to me advisable to announce the degree in which I have already succeeded, although this success be not as complete as I should like to make it.The experiments took place on a bay of the Potomac River, some distance below Washington. The aerodrome was built chiefly of steel, though lighter material entered into the construction, so that its density as a whole was a little below unity. No gas whatever entered into the construction of the machine, and the absolute weight, independent of fuel and water, was about 11 kilos (24 pounds). The width of the supporting surfaces was about 4 metres (13 feet), and the power was furnished by an extremely light engine of approximately one horse-power. There was no one to direct it on board, and the means for keeping it automatically in horizontal flight were not complete. It is important to remark that the small dimensions of the machine did not allow it to include any apparatus for condensing the steam, so that it could only carry water enough for a very brief course—a drawback which would not be encountered in one of a larger construction.It is also to be noted that the speed estimated by Mr. Bell was that obtained in a continuous ascending flight, and much less than would have been attained in a horizontal course.On Mechanical Flight. Letter of Mr. Alexander Graham Bell to Mr. Langley.Washington, May 6, 1896.I am quite aware that you are not desirous of publication until you have attained more complete success in obtaining horizontal flight under an automatic direction, but it seems that what I have been privileged to see to-day marks such a great progress on everything ever before done in this way, that the news of it should be made public, and I am happy to give my own testimony on the results of two trials which I have witnessed to-day by your invitation, hoping that you will kindly consent to making it known.For the first trial, the apparatus, chiefly constructed of steel and driven by a steam engine, was launched from a boat at a height of about 20 feet from the water. Under the impulse of its engines alone, it advanced against the wind and while drifting little, and slowly ascending with a remarkably uniform motion, it described curves of about 100 metres in diameter; till at a height in the air which I estimate at about 25 metres (82 feet), the revolutions of the screws ceased for want of steam, as I understood, and the apparatus descended gently and sank into the water, which it reached in a minute and a half from the start. It was not damaged, and was immediately ready for another flight.In the second trial it repeated in nearly every respect the action of the first, and with an identical result. It rose smoothly in great curves until it approached a prominent wooded promontory, which it crossed at a height of 8 to 10 metres above the tops of the highest trees, upon the exhaustion of the steam descending slowly into the bay, where it settled in a minute and thirty-one seconds from the start. You have an instantaneous photograph of it, which I took just after the launch. [See plates20,21, and22of present work.]From the extent of the curves which it described, which I estimated with other persons, from measurements which I took, and from the number of revolutions of the propellers, as recorded by the automatic counter which I consulted, I estimate the absolute length of each course to be over half an English mile, or, more exactly a little over 900 metres (2953 feet).The duration of flight during the second trial was one minute and thirty-one seconds, and the average velocity between twenty and twenty-five miles an hour, or, let us say 10 metres a second, in a course which was constantly ascending. I was extremely impressed by the easy regular course of each trial, and by the fact that the apparatus descended each time with such smoothness and gentleness as to render any jar or danger out of the question.It seemed to me that no one could have witnessed these experiments without being convinced that the possibility of mechanical flight had been demonstrated.

[7]Communication to the French Academy. Extract from the Comptes Rendus of the Sessions of the Academy of Sciences, Vol. 122, Session of May 26, 1896.

(Translation.)

A Description of Mechanical Flight. By S. P. Langley.

In a communication which I addressed to the Academy in July, 1891, I remarked that the results of experimental investigation had shown the possibility of constructing machines which could give such a horizontal velocity to bodies resembling in shape inclined planes, and more than a thousand times heavier than air, that these could be sustained on this element.

While I have elsewhere remarked that surfaces other than planes might give better results, and that absolutely horizontal flight, which is so desirable in theory, is hardly realizable in practice, so far as I know there has never been constructed, up to the present time, any heavy aerodrome, or so-called flying-machine, which can keep itself freely in the air by its own force more than a few seconds, the difficulties encountered in absolutely free flight being, for many reasons, immeasurably greater than those experienced when the flight is controlled by the body’s pressing upward against a horizontal track, or whirling-arm. No one is unaware that many experimenters have been engaged in trying to execute free mechanical flight, and although the demonstration which I furnished in 1891 [“Experiments in Aerodynamics,” 1891] of its theoretical possibility with means then at our disposition, seemed conclusive, so long a time has elapsed without practical results, that it might be doubted whether these theoretical conditions are to be realized. I have thought it well, then, to occupy myself with the construction of an aerodrome with which I might put my previous conclusions to the test of experiment.

The Academy will, perhaps, find it interesting to read the narrative given here by an eye-witness, who is well known to it. I am led to present it not only by the request with which he honors me, but by the apprehension that my administrative duties may put a stop to these researches, so that it seems to me advisable to announce the degree in which I have already succeeded, although this success be not as complete as I should like to make it.

The experiments took place on a bay of the Potomac River, some distance below Washington. The aerodrome was built chiefly of steel, though lighter material entered into the construction, so that its density as a whole was a little below unity. No gas whatever entered into the construction of the machine, and the absolute weight, independent of fuel and water, was about 11 kilos (24 pounds). The width of the supporting surfaces was about 4 metres (13 feet), and the power was furnished by an extremely light engine of approximately one horse-power. There was no one to direct it on board, and the means for keeping it automatically in horizontal flight were not complete. It is important to remark that the small dimensions of the machine did not allow it to include any apparatus for condensing the steam, so that it could only carry water enough for a very brief course—a drawback which would not be encountered in one of a larger construction.

It is also to be noted that the speed estimated by Mr. Bell was that obtained in a continuous ascending flight, and much less than would have been attained in a horizontal course.

On Mechanical Flight. Letter of Mr. Alexander Graham Bell to Mr. Langley.

Washington, May 6, 1896.

I am quite aware that you are not desirous of publication until you have attained more complete success in obtaining horizontal flight under an automatic direction, but it seems that what I have been privileged to see to-day marks such a great progress on everything ever before done in this way, that the news of it should be made public, and I am happy to give my own testimony on the results of two trials which I have witnessed to-day by your invitation, hoping that you will kindly consent to making it known.

For the first trial, the apparatus, chiefly constructed of steel and driven by a steam engine, was launched from a boat at a height of about 20 feet from the water. Under the impulse of its engines alone, it advanced against the wind and while drifting little, and slowly ascending with a remarkably uniform motion, it described curves of about 100 metres in diameter; till at a height in the air which I estimate at about 25 metres (82 feet), the revolutions of the screws ceased for want of steam, as I understood, and the apparatus descended gently and sank into the water, which it reached in a minute and a half from the start. It was not damaged, and was immediately ready for another flight.

In the second trial it repeated in nearly every respect the action of the first, and with an identical result. It rose smoothly in great curves until it approached a prominent wooded promontory, which it crossed at a height of 8 to 10 metres above the tops of the highest trees, upon the exhaustion of the steam descending slowly into the bay, where it settled in a minute and thirty-one seconds from the start. You have an instantaneous photograph of it, which I took just after the launch. [See plates20,21, and22of present work.]

From the extent of the curves which it described, which I estimated with other persons, from measurements which I took, and from the number of revolutions of the propellers, as recorded by the automatic counter which I consulted, I estimate the absolute length of each course to be over half an English mile, or, more exactly a little over 900 metres (2953 feet).

The duration of flight during the second trial was one minute and thirty-one seconds, and the average velocity between twenty and twenty-five miles an hour, or, let us say 10 metres a second, in a course which was constantly ascending. I was extremely impressed by the easy regular course of each trial, and by the fact that the apparatus descended each time with such smoothness and gentleness as to render any jar or danger out of the question.

It seemed to me that no one could have witnessed these experiments without being convinced that the possibility of mechanical flight had been demonstrated.

[8]It is desirable that the reader should be acquainted with the contents of this treatise, and of another by me, entitled “The Internal Work of the Wind,” both published by the Smithsonian Institution. A knowledge of these works is not absolutely necessary, but of advantage in connection with what follows.

[9]“Experiments in Aerodynamics,” p. 107.

[10]Chapter VIII◊.

[11]His device for obtaining automatic equilibrium is found in connection with the description of his “Aeroplane Auto Moteur,” in “L’Aeronaute” for January, 1872.

[12]I have never obtained so good a result as this with any rubber motor. S. P. Langley.

[13]One pound of twisted rubber appears, from my experiments, to be capable of momentarily yielding nearly 600 foot-pounds of energy, but this effect is attained only by twisting it too far. It will be safer to take at most 300 foot-pounds, and as the strain must be taken up by a tube or frame weighing at least as much as the rubber, we have approximately 0.0091 as the horse-power for one minute, or 0.091 horse-power for six seconds as the maximum effect, in continuous work, of a pound oftwistedrubber strands. The longitudinal pull of the rubber is much greater, but it is difficult to employ it in this way for models, owing to the great relative weight of the tube or frame needed to bear the bending strain. In either form, rubber is far more effective for the weight than any steel spring (see later chapter on Available Motors).

[14]The aerodrome is sustained by the upward pressure of the air, which must be replaceable by the resultant pressure at some particular point, designated byCP.

[15]See Century Magazine, October, 1891.

[16]Subsequent observations indicate that the maximum velocity of horizontal flight must have been about 10 metres per second.

[17]Observers following de Lucy have long since called attention to the fact that as the scale of Nature’s flying things increases, the size of the sustaining surfaces diminishes relatively to the weight sustained. M. Harting (Aeronautical Society, 1870) has shown that the relation√area/u+221bweightis surprisingly constant when bats varying in weight as much as 250 times are the subject of the experiment, and later observations by Marey have not materially affected the statement. As to the muscular power which Nature has imparted with the greater or lesser weight, this varies, decreasing very rapidly as the weight increases. The same remark may be made apparently with at least approximate truth, with regard to the soaring bird, and the important inference is that if there be any analogy between the bird and the aerodrome, as the scale of the construction of the latter increases, it may be reasonably anticipated that the size of the sustaining surfaces will relatively diminish rather than increase. We may conveniently use M. Harting’s formula in the forma=n2w(2/3)=l2m2wherea= area in sq. cm.,wthe weight in grammes,lthe length of the wing in cm.,nandmconstants derived from observation.

[18]A singular fact connected with the stretching of rubber is that the extension is not only not directly proportional to the power producing it, but that up to a certain limit it increases more rapidly than the power, and after this the relation becomes for a time more nearly constant, and after this again the extension becomes less and less in proportion.In other words, if a curve be constructed whose abscissae represent extensions, and ordinates the corresponding weights, it will show a reverse curvature, one portion being concave toward the axis of abscissae, the other convex.

In other words, if a curve be constructed whose abscissae represent extensions, and ordinates the corresponding weights, it will show a reverse curvature, one portion being concave toward the axis of abscissae, the other convex.

[19]The following table taken from “Experiments in Aerodynamics,” p. 107, gives the data for soaring of 30 × 4.8 inch planes, weight 500 grammes.Angle with horizon α.Soaring speedV.Work expended per minute.Weight with planes of like form that 1 horse-power will drive through the air at velocityV.Metres per second.Feet per second.Kilogram-metres.Foot-pounds.Kilogrammes.Pounds.45°11.236.73362,4346.8153010.634.81751,26813.0291511.236.78662326.5581012.440.76547434.877515.249.84129755.5122220.065.62417495.0209The relations shown in the above table hold true only in case of planes supporting about 1.1 pounds to each square foot of sustaining area. For a different proportion of area to weight, other conditions would obtain.

[19]The following table taken from “Experiments in Aerodynamics,” p. 107, gives the data for soaring of 30 × 4.8 inch planes, weight 500 grammes.

Angle with horizon α.Soaring speedV.Work expended per minute.Weight with planes of like form that 1 horse-power will drive through the air at velocityV.Metres per second.Feet per second.Kilogram-metres.Foot-pounds.Kilogrammes.Pounds.45°11.236.73362,4346.8153010.634.81751,26813.0291511.236.78662326.5581012.440.76547434.877515.249.84129755.5122220.065.62417495.0209

The relations shown in the above table hold true only in case of planes supporting about 1.1 pounds to each square foot of sustaining area. For a different proportion of area to weight, other conditions would obtain.

[20]This pressure per unit of area varies with the area itself, but in a degree which is negligible for our immediate purpose.

[21]See “Internal Work of the Wind”; also Revue de L’Aeronautique, 3eLivraison, 1893.

[22]More recent experiments under my direction by Mr. Huffaker give similar results, but confirm my earlier and cruder observations that the curve, used alone, for small angles, is much more unstable than the plane.

[23]As stated in the Preface, Part III has not yet been prepared for publication.

[24]According to Wellner (“Zeitschrift für Luftschiffahrt,” Beilage, 1893), in a curved surface with 1/12 rise, if the angle of inclination of the chord of the surface be α, and the angle between the direction of resultant air pressure and the normal to the direction of motion be β, then β<α and the soaring speed isV= √(PK×1F(α)×cos β)while the efficiency isWR=WeightResistance= tan βThe following were derived from experiments in the wind:α =−3°0°+3°6°9°12°F(α) =0.200.800.750.901.001.05Tan β =0.010.020.030.040.100.17so that according to him, a curved surface shows finite soaring speeds when the angle of inclination is 0° or even slightly negative.

V= √(PK×1F(α)×cos β)

while the efficiency is

WR=WeightResistance= tan β

The following were derived from experiments in the wind:

α =−3°0°+3°6°9°12°F(α) =0.200.800.750.901.001.05Tan β =0.010.020.030.040.100.17

so that according to him, a curved surface shows finite soaring speeds when the angle of inclination is 0° or even slightly negative.

[25]The following formulæ proposed by Mr. Chas. M. Manly show how the center of pressure may be moved any desired distance either forward or backward without in any way affecting the center of gravity, and by merely moving the front and rear wings the same amounts but in opposite directions, the total movement of each wing being in either case five times the amount that is desired to move the meanCP1, and the direction of movement of the front wing determining the direction of movement ofCP1.In Figure 7,CPfwandCPrware the centers of pressure of the front and rear wings respectively; the weights of the wings, which are assumed to be equal and concentrated at their centers of figure, are represented byw,w, andais the distance of the center of pressure in either wing from its center of figure. The original mean center of pressure of the aerodrome isCP1,Wis the weight of the aerodrome, supposed to be concentrated atCG1, whilemis the distance fromCPrwtoCG1.Now, if we have assumed that the rear wing, being of the same size as the front one, has a lifting effect of only 0.66, and on this assumption is calculated the proper relative positions of the front and rear wings to cause theCP1to come directly over theCG1, and upon testing the aerodrome find that it is too heavy in front and, therefore, wish to move the center of pressure forward an amount, sayb, without affecting the center of gravity, we can calculate the proper relative positions of the front and rear wings in the following manner. While the aerodrome as a whole is balanced at the pointCG1, the weight of the wings is not balanced around this point, for the rear wing, owing to its decreased lifting effect, is proportionately farther fromCP1than the front wing. In order, therefore, to avoid moving the center of gravity of the machine as a whole, any movement of the wings must be made in such a way as to cause the difference between the weight of the rear wing multiplied by its distance fromCG1and the weight of the front multiplied by its distance fromCG1to equal a constant: that is,w(m+a)−w(0.66m−a) = constant,and0.33wm+ 2wa= constant.FIG.7.FIG.8.FIG.9.FIGS.7–9. Diagrams Illustrating formulæ for movingC. P.without disturbingC. G.If now the wings be moved so thatCP1is moved forward a distanceb, we may indicate the distance fromCG1to the newCPrwbyz, and equating the difference between the weight of the rear wing multiplied by its new distance fromCG1and the weight of the front wing multiplied by its new distance fromCG1and making this difference equal to the constant difference, we can calculatezin terms ofmandb, as follows:Fig. 8,w(a+z)−w(0.66(z+b) +b−a) = 0.33wm+ 2wa,∴z=m+ 5b.Knowingz, we readily find that the new distance fromCPfwtoCG1equals:0.66(z+b) +b= 0.66m+ 5b.In a similar manner we may calculate the proper relative positions of the front and rear wings when we wish to move the center of pressure backward a distance,b, from the originalCP1without changing the position ofCG1. From Fig. 7, we have as before:w(m+a)−w(0.66m−a) = constant,0.33wm+ 2wa= constant.Fig. 9,w(z1+a)−w(0.66(z1−b)−b−a) = 0.33wm+ 2wa.∴z1=m−5b.Similarly we have for the new distance fromCPfwtoCG1:0.66(z1−b)−b= 0.66m−5b.

In Figure 7,CPfwandCPrware the centers of pressure of the front and rear wings respectively; the weights of the wings, which are assumed to be equal and concentrated at their centers of figure, are represented byw,w, andais the distance of the center of pressure in either wing from its center of figure. The original mean center of pressure of the aerodrome isCP1,Wis the weight of the aerodrome, supposed to be concentrated atCG1, whilemis the distance fromCPrwtoCG1.

Now, if we have assumed that the rear wing, being of the same size as the front one, has a lifting effect of only 0.66, and on this assumption is calculated the proper relative positions of the front and rear wings to cause theCP1to come directly over theCG1, and upon testing the aerodrome find that it is too heavy in front and, therefore, wish to move the center of pressure forward an amount, sayb, without affecting the center of gravity, we can calculate the proper relative positions of the front and rear wings in the following manner. While the aerodrome as a whole is balanced at the pointCG1, the weight of the wings is not balanced around this point, for the rear wing, owing to its decreased lifting effect, is proportionately farther fromCP1than the front wing. In order, therefore, to avoid moving the center of gravity of the machine as a whole, any movement of the wings must be made in such a way as to cause the difference between the weight of the rear wing multiplied by its distance fromCG1and the weight of the front multiplied by its distance fromCG1to equal a constant: that is,

w(m+a)−w(0.66m−a) = constant,

and

0.33wm+ 2wa= constant.

FIG.7.FIG.8.FIG.9.FIGS.7–9. Diagrams Illustrating formulæ for movingC. P.without disturbingC. G.

FIG.7.

FIG.8.FIG.9.

FIG.8.

FIG.9.

FIGS.7–9. Diagrams Illustrating formulæ for movingC. P.without disturbingC. G.

If now the wings be moved so thatCP1is moved forward a distanceb, we may indicate the distance fromCG1to the newCPrwbyz, and equating the difference between the weight of the rear wing multiplied by its new distance fromCG1and the weight of the front wing multiplied by its new distance fromCG1and making this difference equal to the constant difference, we can calculatezin terms ofmandb, as follows:

Fig. 8,

w(a+z)−w(0.66(z+b) +b−a) = 0.33wm+ 2wa,

∴z=m+ 5b.

Knowingz, we readily find that the new distance fromCPfwtoCG1equals:

0.66(z+b) +b= 0.66m+ 5b.

In a similar manner we may calculate the proper relative positions of the front and rear wings when we wish to move the center of pressure backward a distance,b, from the originalCP1without changing the position ofCG1. From Fig. 7, we have as before:

w(m+a)−w(0.66m−a) = constant,

0.33wm+ 2wa= constant.

Fig. 9,

w(z1+a)−w(0.66(z1−b)−b−a) = 0.33wm+ 2wa.

∴z1=m−5b.

Similarly we have for the new distance fromCPfwtoCG1:

0.66(z1−b)−b= 0.66m−5b.

[26]It is to be remembered that these aerodromes were under incessant modifications, No. 4 for instance, presenting successive changes which made of it in reality a number of different machines, one merging by constant alterations into the other, though it still went under the same name. After 1895 the type of the models remained relatively constant, but during the first five years of the work, constructions equal to the original building of at least eight or ten independent aerodromes were made.

[27]Chapter V◊.

[28]“Pocketing” is a form of distortion in which the canvas or silk bags locally in numerous places between the cross-ribs.

[29]The site of these experiments, which was 30 miles below Washington, has been described. The writer is designated by the initial “L”; Dr. Barus, who several times assisted, by the letter “B”; Mr Reed, carpenter, by “R”; Mr Maltby, machinist, by “M”; and Mr. Gaertner, instrument maker, by “G.”

[30]Weights and dimensions are here given in approximate pounds and feet.

[31]“Experiments in Aerodynamics.”

[32]On the data of “Aerodynamics,” a plane having 1.8 sq. ft. of surface per pound, and advancing at an angle of 20°, would soar at a speed of 24.1 ft. per second.

[33]It will be remembered that the purely theoretical conclusions just cited apply to the power delivered in direct thrust, but that of the above actual H. P. an indefinite amount was lost in friction and slip of propellers.

[34]It may be observed that at this time the position of theCPwas calculated on the assumption that the pressure for flight surfaces was proportional to the areas, without also allowing for the fact that the following surfaces, like the tail, were under the “lee” of the wind and so far less efficient. It follows, then, that the valueCP−CGwas not really 0, as was assumed, but something considerable.

[35]Very exact accuracy in these minute details is indispensable to the efficient working of the engines.

[36]The reader who may care to note the evolution of this boiler, by trial and error, will find a portion of the many discarded types shown in Plate13.

Although in 1896 Mr. Langley had made the firm resolution not to undertake the construction of a large man-carrying machine, as he realized that his multitudinous administrative duties left him practically no time available for original research, yet the longing to take the final great step of actually transporting a human being through the air, which the successful flights of the models had now for the first time in the history of the world actually proved to be possible, soon became irresistible.

Ten years of almost disheartening difficulties, a full appreciation of which can hardly be gained from the preceding description, had already been spent in demonstrating that mechanical flight was practicable, and Mr. Langley thoroughly realized that the construction of a large aerodrome would involve as great, if not even greater difficulties. Nevertheless, his indomitable will, which balked at no obstacle, however great it might seem, prevailed against the advice of his close friends and associates, and even that of his physician, who had counselled him that a resumption of concentrated thought and vigorous endeavor would materially shorten his life, which had already passed three score years. Only a few were privileged to come into close contact with him in his daily work, and thereby catch the inspiration of his unwavering persistence, his ceaseless perseverance, his plain inability to submit to defeat; but no one who has read the record of his astronomical expedition to Mt. Whitney, or the story of his development of the Bolometer, or the preceding chapters of this history of his years of patient work in the development of the flying machine, can have failed to obtain some appreciation of this most striking feature of his character. Having once determined on the accomplishment of a definite object, no amount of difficulty that might arise deterred him from pushing on until in some way and by some means he had succeeded; and no one appreciated better than he that if the thin edge of the right wedge can be inserted under an obstacle, that obstacle can be removed, no matter how formidable it may seem.

The undertaking of the construction of a large aerodrome was very largely influenced by President McKinley, who had become impressed with the great[p124]possibilities of a flying machine as an engine of war. When he found that Mr. Langley was willing to devote his own time to the development of a machine, provided the Government would furnish the funds for the actual construction and tests of it, he appointed a joint board, consisting of Army and Navy officers, to investigate and report on the plans with which Mr. Langley had achieved success with the models. The report of this joint board of Army and Navy officers being favorable, the Board of Ordnance and Fortification of the War Department, at the direction of President McKinley, requested Mr. Langley to undertake the construction and test of a machine, which, while not expected to be a practical war machine, might finally lead to the development of such an engine of war. In this connection it is interesting to read a letter which Mr. Langley addressed to the Board of Ordnance and Fortification at the time he undertook this work.

SMITHSONIANINSTITUTION, December 12, 1898.The Board of Ordnance and Fortification, War Department.GENTLEMEN: In response to your invitation, I repeat what I had the honor to say to the Board—that I am willing, with the consent of the Regents of this Institution, to undertake for the Government the further investigation of the subject of the construction of a flying machine on a scale capable of carrying a man, the investigation to include the construction, development and test of such a machine under conditions left as far as practicable in my discretion, it being understood that my services are given to the Government in such time as may not be occupied by the business of the Institution, and without charge.I have reason to believe that the cost of the construction will come within the sum of $50,000.00, and that not more than one-half of that will be called for in the coming year.I entirely agree with what I understand to be the wish of the Board that privacy be observed with regard to the work, and only when it reaches a successful completion shall I wish to make public the fact of its success.I attach to this a memorandum of my understanding of some points of detail in order to be sure that it is also the understanding of the Board, and I am, gentlemen,With much respect,Your obedient servant,S. P.LANGLEY.MEMORANDUMATTACHED TO MY LETTER OF THIS DATE TO THE BOARD OF ORDNANCE AND FORTIFICATIONWhile stating that I have, so far as I know, an exclusive right of property in the results of the experiments in aerodromics which I have conducted heretofore and am now conducting, and while understanding that this property and all rights connected with it, whether patentable or otherwise, will remain mine unqualifiedly, I am glad to place these results, without charge, at the service of the Board of Ordnance and Fortification for the special construction at present proposed, which seems to me to be of National utility.[p125]I assume that no public statement will be made by the permission of the Board until the work is terminated, but that I may publish ultimately at my discretion a statement of any scientific work done in this connection.I understand that the exercise of this discretion includes the ordering and purchase of all material by contract or in open market, and the employment of any necessary help, without restriction, and that, while I desire that no money shall pass through my hands, itemized bills for each expenditure, made in proper form and approved by me, will be paid by the Chief Signal Officer.Much has already been spent at the Smithsonian Institution for the purpose in question, in special apparatus, tools and experiments, and in recent constructions now actually going on, which have involved still more time than money, and which are essential for experimental use in building the proposed machine; and since to re-create all this independently would greatly defer progress, I assume that my discretion includes the decision as to how far this shall be used and paid for at the cost of this allotment (it being understood that I have no personal property in any of the material which might be transferred for the purpose of the work); and I also assume that my discretion includes the decision as to where the work shall be conducted—that is, whether in shops already constructed, or in others to be elsewhere erected or rented, with the necessary adjuncts, whether on land or water, and generally whatever is necessary to the earliest attainment of the object desired by the Board.S. P.LANGLEY.SMITHSONIANINSTITUTION,WASHINGTON, D. C.,December 12, 1898.

SMITHSONIANINSTITUTION, December 12, 1898.

The Board of Ordnance and Fortification, War Department.

GENTLEMEN: In response to your invitation, I repeat what I had the honor to say to the Board—that I am willing, with the consent of the Regents of this Institution, to undertake for the Government the further investigation of the subject of the construction of a flying machine on a scale capable of carrying a man, the investigation to include the construction, development and test of such a machine under conditions left as far as practicable in my discretion, it being understood that my services are given to the Government in such time as may not be occupied by the business of the Institution, and without charge.

I have reason to believe that the cost of the construction will come within the sum of $50,000.00, and that not more than one-half of that will be called for in the coming year.

I entirely agree with what I understand to be the wish of the Board that privacy be observed with regard to the work, and only when it reaches a successful completion shall I wish to make public the fact of its success.

I attach to this a memorandum of my understanding of some points of detail in order to be sure that it is also the understanding of the Board, and I am, gentlemen,With much respect,Your obedient servant,S. P.LANGLEY.

I attach to this a memorandum of my understanding of some points of detail in order to be sure that it is also the understanding of the Board, and I am, gentlemen,

With much respect,

Your obedient servant,

S. P.LANGLEY.

MEMORANDUM

ATTACHED TO MY LETTER OF THIS DATE TO THE BOARD OF ORDNANCE AND FORTIFICATION

While stating that I have, so far as I know, an exclusive right of property in the results of the experiments in aerodromics which I have conducted heretofore and am now conducting, and while understanding that this property and all rights connected with it, whether patentable or otherwise, will remain mine unqualifiedly, I am glad to place these results, without charge, at the service of the Board of Ordnance and Fortification for the special construction at present proposed, which seems to me to be of National utility.[p125]

I assume that no public statement will be made by the permission of the Board until the work is terminated, but that I may publish ultimately at my discretion a statement of any scientific work done in this connection.

I understand that the exercise of this discretion includes the ordering and purchase of all material by contract or in open market, and the employment of any necessary help, without restriction, and that, while I desire that no money shall pass through my hands, itemized bills for each expenditure, made in proper form and approved by me, will be paid by the Chief Signal Officer.

Much has already been spent at the Smithsonian Institution for the purpose in question, in special apparatus, tools and experiments, and in recent constructions now actually going on, which have involved still more time than money, and which are essential for experimental use in building the proposed machine; and since to re-create all this independently would greatly defer progress, I assume that my discretion includes the decision as to how far this shall be used and paid for at the cost of this allotment (it being understood that I have no personal property in any of the material which might be transferred for the purpose of the work); and I also assume that my discretion includes the decision as to where the work shall be conducted—that is, whether in shops already constructed, or in others to be elsewhere erected or rented, with the necessary adjuncts, whether on land or water, and generally whatever is necessary to the earliest attainment of the object desired by the Board.

S. P.LANGLEY.SMITHSONIANINSTITUTION,WASHINGTON, D. C.,December 12, 1898.

S. P.LANGLEY.

SMITHSONIANINSTITUTION,WASHINGTON, D. C.,

December 12, 1898.

As is always the case in experimental work, especially in a field so very new as was the field of aerodromics at the time that this larger construction was undertaken, the “plant,” or shops and laboratories required for the constructional and testing work, grew to a size far beyond what seemed even remotely possible at the beginning of the work; and even the mere administration involved in the carrying on of this work proved to be no inconsiderable matter before it had progressed very far.

The years of experiment with the models had demonstrated clearly that the greatest difficulty in the development of the aerodrome was the construction of a suitable power generator, which should combine the elements of extreme lightness and unusual power with a fair degree of durability. Although remarkably good results had been secured in the case of the models through the use of steam, it was realized from the first that not only would the development of a steam-power plant for a large man-carrying aerodrome present difficulties of a constructional nature, but that such a steam plant would necessarily be so fragile and delicate as to make it a constant menace to the machine which it was to propel. The solution of the difficulty, it was believed, was to be found in the use of an internal combustion engine; but Mr. Langley had had very little experience with such engines, and was averse therefore to undertaking the construction of a large aerodrome until he had assurance that a suitable gasoline engine could be secured. Before making an agreement to attempt the work for the War[p126]Department, he had, therefore, made a search for a reliable builder who would undertake to construct a gasoline engine of not less than 12 horse-power to weigh not exceeding 100 pounds, and what then seemed a safe contract had been entered into with such a builder to supply one engine which would meet these requirements.

Almost immediately before the Board of Ordnance and Fortification had officially placed the work in Mr. Langley’s hands and had made an allotment of fifty thousand dollars to meet the expenses thereof, it was found that the engine builder could not be depended on, and that it would, therefore, be necessary to find one who was more reliable and more experienced in the construction of light engines. After a most extended search for the best builder to undertake this work, a contract was entered into on December 12, 1898, with Mr. S. M. Balzer, an engine builder in New York City. He was to furnish a twelve-horse-power engine to weigh not more then 100 pounds, and delivery of it was to be made on or before February 28, 1899. With this great problem of the engine apparently provided for, every facility of the Institution shops was pressed to the utmost limit in order to have the frame, supporting surfaces, launching apparatus, and other accessories ready as soon as possible after the delivery of the engine. It was expected from the first that more power would be necessary than this one engine would furnish, and provision had been made in the contract that a duplicate engine should be constructed immediately after the completion of this first one. From past experience, however, it was not likely that the correct balancing of the aerodrome could be determined froma prioricalculation based on the results obtained with the models, and it was, therefore, expected that the aerodrome would have to be launched several times before a successful flight could be obtained. In view of this it was planned to make a test of the machine as soon as the first engine was ready, with the expectation that, while the aerodrome would not have sufficient power to fly, yet the test would furnish definite data on the all-important question of balancing, and also determine whether or not the launching apparatus would require modification. In fact, Mr. Langley felt so apprehensive that the first, and possibly the second test, would be unsuccessful that, in order to avoid the possibility of a fatal accident, it was planned that a dummy should be used to represent the weight of the man in these preliminary tests.

This plan, however, was not carried out. In 1903, when the large aerodrome was finally completed, so much time had been lost that the writer proposed to assume the risks of such an accident and to guide the machine in its first test, in the hope of avoiding a disaster, with the consequent delay of months for repairs, which the presence of a controlling hand capable of correcting any inaccuracies of balancing rendered far less likely to occur. To this proposal Mr. Langley assented with great reluctance, as he fully realized the danger involved.[p127]

Particular attention is called to the above facts, which clearly show that while a certain degree of success in the initial tests was later hoped for, yet from the beginning it had been felt rather certain that several tests would have to be made before final success would be achieved.

To those experienced in scientific experiments this realization of the probability of several tests being necessary before success could reasonably be expected does not seem strange, for the record of past experience contains very few examples of epoch-making inventions springing full fledged from the hand of their maker and proving a success on the first test.

The two experiments made in the fall of 1903, in which the aerodrome was each time so damaged in the process of launching that its ability to fly was never really tested, should therefore be considered merely as the first of a series which it had been expected would need to be made before success would be achieved. Further tests were made impossible at the time on account of the lack of funds, the expense of such work being unusually heavy.

While the lack of funds, therefore, was the real cause of the temporary suspension of the work, yet an influence which does not often enter into scientific work—the unjust criticism of a hostile press—was directly responsible for the lack of funds. It seems very certain that had it not been for this criticism of the press the funds would have been readily forthcoming for continuing the work to the point of success.

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