18J3-] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



221 



would be rendered attainable, have been observed in the appointment 

 of the propelling apparatus in Mr. Henson's machine, we shall not 

 stop to inquire, (though from a consideration of their apparent di- 

 mensions and the angle of their impact, we should conclude most as- 

 suredly otherwise;)-' but, giving them full credit for their competency 

 to that effect, proceed to show that even so, with a measure of resist- 

 ance the least assignable, and a rate of impact the least under which it 

 could be developed, the power in question would be utterly incompe- 

 tent to enable the machine to maintain its elevation or continue its 

 course, even for a single moment, at any angle of inclination at which 

 it might be disposed. This we shall do by means of a table calcu- 

 lated for several angles of inclination, exhibiting at a view the several 

 rates at which a machine of the proportions of weight and surface 

 assigned to Mr. Henson's, would have to proceed at the corresponding 

 angles of inclination, in order to generate a resistance opposed to 

 gravity equal to the support of its weight, and the amount of hori- 

 zontal resistance it would experience (considered as a mere plane) at 

 each degree of the scale so impelled, expressed in pounds avoirdu- 

 pois. In another column is shown the resistance which the solid parts 

 of the machine would develop at the corresponding rates, supposing 

 them to be so contrived as to expose an extent of surface not more 

 than equivalent to a plane of one square foot perpendicularly im- 

 pinged upon. In the next column are given the products of these 

 last two quantities multiplied by the velocity assigned in miles per 

 hour, representing the actual forces developed, reduced to the same 

 standard, and consequently, the proper measure of the power commen- 

 surate with such results. The last column contains the expression of 

 this force in horse-power, or the number of horses which it would take 

 to answer this demand, according to the conventional mode of calcu- 

 lating the force of steam ; that is, reckoning the power of a horse to 

 be equal to a resistance of 320001b. at the rate of one foot in a mi- 

 nute, or 363 lb. at the rate of one mile per hour. 



Upon reference to this table it will be seen that the conditions of 

 flight which, under the circumstances prescribed, would be attainable 



Supposing the propelling agents to be able by their rotation at a given 

 rate to generate a given amount of resistance, the machine being at rest ; 

 when motion is conferred upon it, the condition of the.medium, as far as 

 the instruments of its propulsion are concerned, being altered bv the conse- 

 quent abstraction of the air, they would no longer operate with the same 

 effect at the same rate of impact, but must either be worked with additional 

 speed to enable them to overtake the retiring particles, or else proportionably 

 increased m magnitude to enable them to take in a larger quautitv of them. 

 It is to this relation between the superficial dimensions of the "propelling 

 agents and that of the effective opposing front of the machine, that we refer 

 as governing the relation of their respective resistances to their respective 

 rates of motion, and by the due appointment of which, (regard being had 

 to their form and direction of impact,) an equality of resistance becomes as- 

 signable to an equality of rate when the machine is in actual progression. 



with the least expenditure of power, are those which attach to an 

 inclination of about 10 degrees ; and for this a force would be requi- 

 site, equal to the power of above 100 horses. At any other angle of 

 inclination, a greater amount of horizontal resistance in the aggregate 

 would be experienced, and the requirements of power be propor- 

 tionately enhanced. 5 



V. Now it is to be observed that the opposition which is here 

 set forth as the measure of the propulsive power of the machine, is 

 not a force only concerned in the initiation of its motion, which might 

 be expected to vanish or become less influential after its first efforts 

 had been subdued, like the passive resistance of mere weight, the 

 ris inertia, or the resistance of adhesion, which when once suspended 

 or overcome ceases to affect, but a force always in operation, always 

 the same under the same conditions, and requiring always the same 

 amount of power to compete with while it endures. And with this 

 observation we might have been content to let the matter rest, as in- 

 controvertibly determined, were it not that a principle has been set 

 up, implied in the proposition of a certain contrivance, which strikes 

 at the very root of our conclusions, and, were it correctly conceived, 

 would equally invalidate any inference that might be deduced in dero- 

 gation of the scheme, from the consideration of any deficiency of 

 power, however extravagant, that might be alleged against it. Sen- 

 sible of the inadequacy of their means, in the abstract, to the whole 

 effect which it is intended to produce, and under the impression 

 that this deficiency might be supplied by the intervention of a force 

 not inherent in the means themselves, a part of their plan, upon 

 which the greatest reliance has been placed, which has been put for- 

 ward with the greatest pretensions, and which has elicited the great- 

 est .share of the public admiration and approval, is to invest the ma- 

 chine at its first starting with a certain amount of velocity or mo- 

 mentum, by means of a preliminary descent down an inclined plane, 

 which, however unable to originate, its inherent power, it is expected, 

 will be sufficient to maintain. And this obliges us to devote a few 

 lines to the consideration of the principle involved in this contri- 

 vance, which is the fifth and last point to which in the outset we pro- 

 posed to direct our inquiries. 



5 This table may be made available to determine the conditions of flight 

 assignable to any machine upon the same principle, whatever the proportion of 

 its weight to the dimensions of its suspending plane, subject to the following 

 considerations. In the first place, the velocity necessary to effectuate its sup- 

 port depending upon the relative and not the actual quantities, any weight 

 may be assumed as a standard, and the modification necessary to maintain, 

 the proportion, referred to the size of the suspending plane. Let the case, 

 therefore, be reduced to the standard of weight ascribed to Mr. Henson's 

 plane, namely 3000 lb., and the surface determined accordingly. Now as the 

 resistance, ceteris paribus, varies in the simple ratio of the areas of the im- 

 pinging surfaces, and the squares of the rates of impact, the rates, ceteris 

 paribus, must vary inversely as the square roots of the areas. If, therefore, 

 the velocity assigned to any augle in the table above be multiplied by the 

 square root of the area of Mr. Henson's plane, the product divided by the 

 square root of the newly assigned surface, will give the rate at which it must 

 be propelled in order to effectuate its support, as by a common rule of three. 

 The horizontal resistances, depending upon the real quantities, may be de- 

 duced in like manner from those ascribed to Mr. Henson's plane at the same 

 angles, by simply substituting the new rate assigned, in the ratio of the 

 squares of the velocities, and the true surface, in the simple ratio of the di- 

 mensions; and thus all the conditions of flight depending upon these data 

 may be ascertained. For example, if we suppose the suspending plane to be 

 magnified to 10 times that of Mr. Henson's, affording an area of 45,000 in- 

 stead of 4500 square feet within the limits of the same weight, the velocity 



67-7 x A /-t500 

 necessary to its support at an angle of 10 would be 



67-7 x 67-082 



^45000 



212-132 



= 21-108 miles an hour. The horizontal resistance in this 



case, the weight being the same, would stand as in the table, at the same 

 angle of inclination ; the rate of development diminishing exactly as the 

 surface is increased. If to this quantity be added the perpendicular resist- 

 ance due to one square foot at the newly assigned rate = 2-254 lb., and the 

 sum be multiplied by the rate in question, we shall have 11271-71.") lb. as 

 the representative of the whole resistance to be encountered; which, divided 

 by 363, the power of a horse in steam at the same rate, gives upwards of 31 

 as the number of horses, or the measure of horse-power, which would be 

 requisite to enable it to accomplish or maintain its elevation in the air.^ 



30* 



