190 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[June, 



of the sines of the same angles, any alteration in the obliquity of the 

 plane must affect the latter more extensively than the former, and 

 determine a balance in favour of that condition which is mor.t in con- 

 formity with the change ; if it be to diminish the horizontal resistance 

 (which is the result of a diminished angle of inclination), increasing 

 the relative effects of the vertical, which is the medium of support; 

 and if to increase the horizontal resistance, (which is the consequence 

 of augmenting the inclination) to disparage the vertical resistance, 

 and incontinently subtract from the ascensive powers of the machine. 

 Accordingly, therefore, if the machine be progressing with a given 

 force, and it be desired to rite, this result will be accomplished by 

 reducing the inclination of the suspending plane, and on the other 

 hand, if the angle in question be enlarged, it will immediately begin to 

 descend; the rate in the former instance increasing and in the latter 

 diminishing with the alterations in the obliquity of the plane, and the 

 accompanying alterations in the level of its course. 



With regard to the remaining purpose of these controlling appen- 

 dages, corresponding to the horizontal steerage, of the aerial vessel, 

 but little needs to be observed. Having no forces to contend with 

 which operate to favour one direction more than another, except such 

 as may arise from the unequal resistances occasioned by the opposite 

 sides of the machine itself, any amount of artificial resistance beyond 

 what is thus indicated, if properly applied, is sufficient to give a pre- 

 ponderance to any course which may be chosen ; the only advantage 

 of a more liberal supply being in the limitation of the space within 

 •which it enables the aeronaut to effectuate his purpose — an advantage, 

 of no great consideration in the abundant regions of the sky. In this 

 respect the case of the aerial machine is most favourably distinguished 

 from that of the ship at sea, pursuing her course under the influence 

 of the wind; where the force by which she is propelled being fre- 

 quently oblique, and in a sense adverse to the direction of her route, 

 she requires a given power, not only to obtain a course but to hep it, 

 and the conditions of which are governed by those of the force to be 

 opposed. 



It only remains to observe, in answer to the objections of those 

 who imagine that, in the tenuity of the medium, exists an im- 

 pediment to the efficiency of the rudder, that these objections are 

 founded upon an imperfect consideration of the principles of the case 

 involved. The impediments to the efficiency of any instrument are 

 equally dependent upon the obstacles to be overcome as the means of 

 overcoming them. Where these arise out of the same conditions, 

 there can be nothing in the conditions themselves to influence in 

 either way the success of its operations. And this is the case exactly 

 with respect to the guidance of the aerial machine by means of the 

 rudder. The obstacle to be overcome and the means of overcoming 

 it are the same — namely the resistance of the air; in proportion as 

 the weakness of this condition operates to disparage the powers of 

 the rudder, in exactly the same proportion does it operate to dis- 

 parage the forces by which the action of the rudder is opposed. 



III. We now proceed to examine the third subject of investigation 

 which we proposed to ourselves in the outset; namely, the revolving 

 apparatus, by the reaction of which the impetus is to be maintained, 

 which is to determine the progressive motion of the machine. These 

 instruments may be most succinctly described as both in form and 

 operation resembling the rotatory portion of a windmill, only con- 

 sisting of six arms instead of four, about 10 feet long (the breadth not 

 stated) and inclined to the plane of their revolution at an angle of 

 45 degrees. Being two in number (one on each side of the centre of 

 gravity) in the same plane, and facing the direction of the intended 

 route, that part of the resistance they are calculated to generate by 

 their forced rotation which is perpendicular to the plane in which 

 they revolve, becomes available to the propulsion of the machine, and 

 constitutes, in fact, the measure and the means of its success. As it 

 is clear, by the obliquity of the impact a certain quantity of the force 

 which is developed becomes resolved in directions not favourable to 

 the object in view, before any thing can be pronounced with certainty 

 as to the efficiency of the means at command, it must be determined 

 how much of these means is really turned to account— how much is 



realized and how much lost in the process by which it is conveyed 

 from the source to the object upon which it is intended to act. 



In determining the efficiency of any system of impinging planes, 

 there are three elements concerned in the constitution of the force 

 developed, which require to be considered — the angle of inclination, 

 the maAer, and the tize of the impinging surfaces. 



Of these elements there is one only the actual amount of which is 

 independently determinable — we mean, that does not regard the other 

 conditions of the case, but has its maximum effect assignable with re- 

 ference to itself alone — and this is the angle of inclination. Whatever 

 tins be that may be found to be best suited to the purpose, it will still 

 continue to be the best under all modifications of size and number, 

 rate of motion and condition of medium, which may happen to charac- 

 terize the case. Now this angle, (that whereat an inclined plane is 

 calculated to develop the greatest amount of resistance at right angles 

 to the direction of the impinging force,) has been already determined, 

 both by mathematical induction and actual experiment, in a strictly 

 analogous case; namely, that of the windmill, in which the conditions 

 both of the object and of the means are precisely the same : for it will 

 not be considered to constitute any difference, whether the plane be 

 impelled against the air or the air be directed to act against the 

 plane. In both cases the object is to develop the greatest amount of 

 atmospheric resistance at right angles to the direction of the impact; 

 and the angle at which this is complete has been established to be an 

 angle of 54 c 44'. The arguments, both mathematical and experimental 

 by which this conclusion has been sustained, may be found in most 

 works upon pneumatics ; but we abstain from quoting them here, 

 because we have a shorter way, and more open to the comprehension 

 of the general reader, by which the same is ascertainable, and which, 

 moreover, by the almost perfect coincidence it presents with the re- 

 sult deduced from other sources, serves at once to illustrate and con- 

 firm the correctness of the general inference. We have already had 

 occasion to observe that the ratio of the degrees of vertical resistance, 

 developed by inclined planes moving horizontally, (which is exactly 

 analogous to that the conditions of which we are now investigating) 

 follows the ratio of the squares of the sines into the cosines of the 

 angles of inclination. Accordingly whatever be the angle of which 

 the sine squared, multiplied by the cosine, is the greatest, the same 

 must also be the angle most favourable for the production of the re- 

 quired resistance. This actual computation enables us to fix at 

 54 16', differing only by tin minutes from that otherwise assigned; 

 as any one who pleases may verify for himself by consulting a table of 

 natural sines, and applying the test to the corresponding sines and 

 cosines of the angles, differing only by one minute on either side, 

 taking four places of decimals in the estimation of the quantities 

 concerned. 3 By what process of reasoning Mr. Heuson was led to 

 adopt, for his impinging vanes, an angle of 45 Q we cannot presume to 

 conjecture ; unless, observing that in the opposite conditions of perfect 

 parallelism and direct uniformity of plane, answering to the angles 

 of 90 D and 0°, no available resistance at all was generated, he came 

 to the conclusion that the proper resting place was the half way house 

 between. Be this how it may, by assigning an angle of 45° as the 

 inclination of his impinging planes, he has exactly sacrificed one twelfth 

 of the wdiole amount of his resources, as may be seen by comparing 

 the sines squared multiplied by the cosines of the angles of 45" and 

 54" 46' respectively, which are subjoined in the note below. 4 



With regard to the two remaining elements of the case referred to, 

 the number and size of the impinging planes, the amount of their 

 effects in action being not only governed by an indefinite power of 

 arrangement (being themselves unlimited in extent by any specific 

 terms), but moreover, (in theory at least) entirely subject to the influ- 

 ence of another condition — the rate of their operation, it is clearly 



3 The products of the sines squared multiplied by the cosines of the an- 

 gles of bi" 15', 54 c 46' and 54 c 4 7', are respectively -38483, -38488, and 

 •3847"; whence it is apparent that the turning point is the intermediate 

 angle. 



4 The sines squared multiplied by the cosines of the angles of 45° and of 

 54 c 46' are respectively -3534 7 and'38488, which is very nearly in the ratio 

 of 11 to 12. 



