◊[p041]CHAPTER VON SUSTAINING SURFACES
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The following general considerations may conveniently precede the particular description of the balancing of the aerodrome.
In “Experiments in Aerodynamics,” I have given the result of trials, showing that the pressure (or total resistance) of a wind on a surface 1 foot square, moving normally at the velocity of 1 foot per second, is 0.00166 pounds, and that this pressure increases directly as the surface of the plane, and (within our experimental condition) as the square of the velocity,20results in general accordance with those of earlier observers.
I have further shown by independent investigations that while the shape of the plane is of secondary importance if its movement be normal, the shape and “aspect” greatly affect the resultant pressure when the plane is inclined at a small angle, and propelled by such a force that its flight is horizontal, that is, under the actual conditions of soaring flight.
I have given on page 60 of “Aerodynamics,” the primary equations,
Pα=P90F(α) =kAV2F(α),W=Pαcos α =kAV2F(α) cos α,R=Pαsin α =kAV2F(α) sin α,
Pα=P90F(α) =kAV2F(α),
W=Pαcos α =kAV2F(α) cos α,
R=Pαsin α =kAV2F(α) sin α,
whereWis the weight of the plane under examination (sometimes called the “lift”);Rthe horizontal component of pressure (sometimes called the “drift”);kis the constant already given;Athe area in square feet;Vthe velocity in feet per second;Fa function of α (to be determined by experiment); α the angle which, under these conditions, gives horizontal flight.
I have also given on page 66 of the same work the following table showing the actual values obtained by experiment on a plane, 30 × 4.8 inches (= 1 sq. ft.), weighing 500 grammes (1.1 pounds):
Anglewithhorizonα.Soaring speedV.Horiz-ontal pres-sureR.Work expendedper minute60RV.Weight with planes of like form that 1 horse-power will drive through the air at velocityV.Metres per sec.Feet per sec.Gm.Kgm-metres.Foot-pounds.Kgm.Pounds.45°11.236.75003362,4346.8153010.634.82751751,26813.0291511.236.71288662326.5581012.440.7886547434.877515.249.8454129755.5122220.065.6202417495.0209
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It cannot be too clearly kept in mind that these values refer tohorizontalflight, and that for this the weight, the work, the area, the angle and the velocity are inseparably connected by the formulæ already given.
It is to be constantly remembered also, that they apply to results obtained under almost perfect theoretical conditions as regards not only the maintenance of equilibrium and horizontality, but also the rigid maintenance of the angle α and the comparative absence of friction, and that these conditions are especially “theoretical” in their exclusion of the internal work of the wind observable in experiments made in the open wind.
I have pointed out21that an indefinite source of power for the maintenance of mechanical flight, lies in what I have called the “internal work” of the wind. It is easy to see that the actual effect of the free wind, which is filled with almost infinitely numerous and incessant changes of velocity and direction, must differ widely from that of a uniform wind such as mathematicians and physicists have almost invariably contemplated in their discussions.
Now the artificial wind produced by the whirling-table differs from the real wind not only in being caused by the advancing object, whose direction is not strictly linear, and in other comparatively negligible particulars, but especially in this, that in spite of little artificial currents the movement on the whole is regular and uniform to a degree strikingly in contrast with that of the open wind in nature.
In a note to the French edition of my work, I have called the attention of the reader to the fact that the figures given in the Smithsonian publication can show only a small part of the virtual work of the wind, while the plane, which is used for simplicity of exposition, is not the most advantageous form for flight; so that, as I go on to state, the realization of the actually successful aerodrome must take account of the more complex conditions actually existing in nature, which were only alluded to in the memoir, whose object was to bring to attention the little considered importance of the then almost unobserved and unstudied minute fluctuations which constitute the internal work of the wind. I added that I might later publish some experimental investigations on the superior efficiency of the real wind over that artificially created. The experiments which were thus alluded to in 1893, were sufficient to indicate the importance of the subject, but the data have not been preserved.
What immediately follows refers, it will be observed, more particularly to the work of the whirling-table.[p043]
In order to get a more precise idea of the character of the alteration introduced into these theoretical conditions by the variation of any of them, let us, still confining ourselves to the use of the whirling-table, suppose that the plane in question while possessing the same weight, shape, and angle of inclination, were to have its area increased, and to fix our ideas, we will suppose that it became 4 square feet instead of 1 as before. Then, from what has already been said,V, the velocity, must vary inversely as the square root of the area; that is, it must, under the given condition, become one-half of what it had been, for ifVdid not alter, the impelling force continuing the same, the plane would rise and its flight no longer be horizontal, unless the weight, now supposed to be constant, were itself increased so as to restore horizontality.
I have repeated Table XIII under the condition that the area be quadrupled, while all the other conditions remain constant, except the soaring speed, which must vary.
αSoaring speed (feet per second)V′.Work.Weight.Work expended per minute.A=4 sq.ft.W=500gr. = 1.1lbs.Weight of like planes which 1 H.P. will drive through the air with velocityV′.Foot-pounds.Pounds.45°18.41,217303017.4634571518.43121161020.4237154524.9148244232.887418Wis the weight of the single plane;Ais the area;Ris the horizontal “drift.”Wtis the weight of like planes which 1 H. P. will drive at velocityV. Work isRV.I. If Work is constant,Rvaries asu+221bA. II. IfRis constant, Work varies as1u+221bA.III. IfWis constant whileAvaries, the weight which 1 H. P. will support varies as √A.
A=4 sq.ft.
W=500gr. = 1.1lbs.
Wis the weight of the single plane;Ais the area;Ris the horizontal “drift.”Wtis the weight of like planes which 1 H. P. will drive at velocityV. Work isRV.
I. If Work is constant,Rvaries asu+221bA. II. IfRis constant, Work varies as1u+221bA.III. IfWis constant whileAvaries, the weight which 1 H. P. will support varies as √A.
The reader is reminded that these are simply deductions from the equations given in “Aerodynamics,” and that these deductions have not been verified by direct trial, such as would show that no new conditions have in fact been introduced in this new application. While, however, these deductions cannot convey any confidence beyond what is warranted by the original experiments, in their general trustworthiness as working formulæ at this stage of the investigations, we may, I think, feel confidence.
I may, in view of its importance, repeat my remark that the relation of area and weight which obtain in practice, will depend upon yet other than these theoretical considerations, for, as the flight of the free aerodrome cannot be expected to be exactly horizontal nor maintained at any constant small angle, the[p044]data of “Aerodynamics” (obtained in constrained horizontal flight with the whirling-table) are here insufficient. They are insufficient also because these values are obtained with small rigid planes, while the surfaces we are now to use cannot be made rigid under the necessary requirements of weight, without the use of guy wires and other adjuncts which introduce head resistance.
Against all these unfavorable conditions we have the favoring one that, other things being equal, somewhat more efficiency can be obtained with suitable curved surfaces than with planes.22
I have made numerous experiments with curves of various forms upon the whirling-table, and constructed many such supporting surfaces, some of which have been tested in actual flight. It might be expected that fuller results from these experiments should be given than those now presented here, but I am not yet prepared to offer any more detailed evidence at present for the performance of curved surfaces than will be found in Part III.23I do not question that curves are in some degree more efficient, but the extreme increase of efficiency in curves over planes understood to be asserted by Lilienthal and by Wellner, appears to have been associated either with some imperfect enunciation of conditions which gave little more than an apparent advantage, or with conditions nearly impossible for us to obtain in actual flight.
All these circumstances considered, we may anticipate that the power required (or the proportion of supporting area to weight) will be very much greater in actual than in theoretical (that is, in constrained horizontal) flight, and the early experiments with rubber-driven models were in fact successful only when there were from three to four feet of sustaining surface to a pound of weight. When such a relatively large area is sought in a large aerodrome, the construction of light, yet rigid, supporting surfaces becomes a nearly insuperable difficulty, and this must be remembered as consequently affecting the question of the construction of boiler, engines and hulls, whose weight cannot be increased without increasing the wing area.