1843.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



151 



a model determines nothing that cannot as well be determined without 

 it — the correctness of the principle, which is the proper subject of 

 mathematical research. With regard to the possibility of its con- 

 struction upon the great scale it would determine nothing, even if it 

 were, which in this case it is absolutely impossible it should be, in the 

 strict sense of the word, a perfect model, observing all the proportions 

 of strength, weight, bulk, power and dimensions as they will appear in 

 the real machine with reference to which they are contrived. The only 

 true and satisfactory mode of arriving at any thing like a correct 

 conclusion respecting the efficiency of the machine in question, or 

 any other of the like character, is by a critical examination of its parts 

 severally and with reference to each other, which is the course we 

 intend to pursue on the present occasion. To enable us to do this the 

 more intelligibly, we will begin by describing in a few words what 

 Mr. Henson's machine is, and what is the principle upon which it 

 is intended to act, so far as they can be collected from the statements 

 in the public press. In general terms, then, Mr. Henson's machine 

 may be described as an horizontally extended plane, 150 feet in length 

 and 30 in breadth, (consequently containing an area of 4,500 square 

 feet) across which, close beneath and in the centre, is suspended a 

 cuneiform car or body accommodated with a pair of circular flying 

 vanes, by the oblique impact of which against the air (upon the 

 principle of the archimedean screw) it is designed to be propelled, 

 and furnished with two caudal appendages like fans, one of a large 

 and the other of small dimensions, by means of which the vertical and 

 horizontal course of the machine is intended to be controlled. The 

 whole is proposed to be set in motion by an accession of extraneous 

 force acquired through the intervention of a preliminary descent 

 down an inclined plane, and maintained by the operation of a steam- 

 engine located in the body or car of the machine. Omitting therefore 

 the consideration of minor details, our attention will be directed, in 

 succession, to the suspending plane — the caudal appendages — the 

 flying vanes — the motive power — and, finally, to the principle upon 

 which the elevation in the first instance is intended to be secured. 



And, first, with regard to the suspending plane. The object of this 

 contrivance, involving, in fact, the essence of Mr. Henson's patent, 3 

 is, simply, to obtain a direction for a certain amount of weight different 

 from what it would assume if left to pursue its course according to 

 the unobstructed force of gravitation. This it accomplishes, or would 

 accomplish if efficiently constructed, by a progressive motion conferred 

 upon it at an angle inclined to the horizon, whereby a part of the force 

 generated by its opposition becomes resolved in a direction opposed 

 to its descent ; and the merit of it consists in this, — that a less degree 

 of force is required to produce this progressive motion than that 

 which the actual weight of the machine would require for its support. 

 A familiar mode of illustrating this has been adopted by Sir George 

 Cayley, in the Mechanic's Magazine for the first of April. It proceeds 

 upon an analogy with the suspension of spherical substances upon an 

 inclined plane, and cannot be better explained, as far as it goes, than 

 in his own words. "Suppose A B to represent an inclined plane, 



rising one foot in ten; it is well known that if the ball F weighed 

 1001b., a force of 101b. applied horizontally would sustain it from 



his life : and the public will not yet have forgotten the pleasing experiments 

 with Mr. Green's model of the balloon at the Polytechnic Institution last 

 year, in «hich the practicability of controlling its course by mechanical re- 

 action was so interestingly illustrated. 



3 It is not our desire to detract from the merits of any individual who 

 seeks by bis ingenuity to extend the limits of our attainments in art or 

 science : but a regard to truth obliges us to observe that the idea of obtaining 

 an ascension by means of the inclined plane is not original or peculiar to 

 Mr. Hensi n's project ; being in fact the mo le to which all those who of late 

 years have thought to etlectuate an aer.al navigation by mere mechanical 

 reaction, have looked for the solution of this interesting question. In the 

 numfcr of the Mechanic's Magazine, for the 25th April, 182U, is a sketch of 

 an apparatus constructed entirely upon the same principle, and many more 

 might be referred to of an earlier as well as a more modern date. 



rolling back. Conceive the same line A B to represent, also, the 

 section of a large surface, like the sail of a ship, and that C G repre- 

 sents a cord by which it is sustained from being driven back by a 

 horizontal wind in the adverse direction. If the sail contains 100 

 square feet of surface, and the wind has sufficient power to press with 

 one pound to the foot, 1001b. weight will be supported, and the ten- 

 sion on the cord will be only 10 lb. It is the same thing whether the 

 wind thus blows against the sail, or the sail be driven with equal ve- 

 locity horizontally in calm air; the 101b. propelling power will still 

 sustain the 1001b. in the air." It only remains to observe in what 

 manner it effects this ; namely, by producing such a rate of motion in 

 the inclined plane as, at the given angle, would generate a pressure of 

 one pound to the square foot. 



Now to apply this to the case of Mr. Henson's machine. In the 

 first place, the area being 4500 square feet, and the weight (taking it 

 according to the statements in the public prints) being 30001b. sup- 

 posing the same angle of inclination to be observed as in the foregoing 

 illustration (that is to say, one in ten) if the wind move at a rate suffi- 

 cient to generate a pressure equal to two-thirds of a pound upon the 

 square foot, the resistance to its horizontal progress, and consequently 

 the force it would require to compete with that resistance, would be 

 one-tenth of its actual weight, or 3001b. If, instead of an angle of 

 inclination of one in ten, be substituted an inclination of one in twenty 

 (which is perhaps more nearly in the ratio observed by birds in their 

 flight, and consequently more consistent with the analogy Mr. Henson 

 appears most desirous of maintaining) the same result will be obtained 

 with half the force, or a resistance of 1501b.; and accordingly it is 

 upon this hypothesis that we shall proceed, in the next place, to in- 

 vestigate the rate at which the machine must be propelled in order to 

 enable it to realize this resistance. 



The proposition which we here have to deal with is simply, "having 

 the pressure upon a plane surface at a given angle of inclination, to 

 find the rate under which that pressure is developed ; " and the so- 

 lution is deduced from a consideration of the rate corresponding to 

 the resistance the same plane would experience if perpendicularly 

 impinged upon. 



We will not trouble our readers with entering into the details of the 

 equations by which the ratio of the forces generated by inclined planes 

 moving in fluid media has been determined ; but, content with refer- 

 ring them for the solution of these interesting problems to Whewell's 

 Treatise upon Dynamics (or indeed any other works of good repute 

 upon the same subject), proceed at once to observe that the resistance 

 experienced by an inclined plane in passing through the air with a 

 given velocity, varies as the cube of the sine of the angle of impact ; 

 and that, consequently, whatever be the ratio which this number bears 

 to the cube of radius (the sine of the angle of 90 degrees), the same 

 will be the ratio of the resistance it will experience at the angle 

 assumed, to that which it would experience at the same rate of motion 

 if perpendicularly encountered. 



Now the velocity under which the plane in question, cont lining an 

 area of 4500 square feet, would develop the prescribed amount of 

 resistance, namely 30001b. by perpendicular impact (being at the rate 

 of two-thirds of a pound per square foot) is, according to the tables 

 of Messrs. Rouse and Smeaton, founded upon actual experiment, about 

 12 miles an hour. The angle of inclination at which we have agreed 

 to dispose the suspending plane, being one in twenty, may be Con- 

 sidered with sufficient accuracy for practical purposes, as an angle of 

 3 degrees, the sine of which (radius being estimated at 1) is -05 

 As therefore 1 J = 1 : -05 3 = -000125 : : 3000 ; .375 = the 

 resistance on the inclined plane at the rate of 12 miles an hour ; and 

 the resistance increasing as the squares of the velocities and conse- 

 quently the velocities following t he ra tio of the square roots of the 

 resistance, as ^/^JE ' = -o : V3000=55 : : 12 ; 1100, the number 

 of miles per hour representing the rate of the inclined plane required 

 to support it, in conformity with the conditions described. 



The consideration of some of these conditions will, however, show 

 that this rate of motion, and, consequently, the amount of force by 

 which we have presumed it to be generated, is far from sufficient to 



