October 29, 1908] 



A^A JURE 



669 



Col. Renard (whose early experiences with ha France 

 were greatly in advance of their time), is still to the 

 forefront in aerial navigation by means of airships. 

 He considers, further, that in spite of its interesting 

 details of construction, the Zeppelin aerostat is not to 

 be regarded as a model to be copied. These views we 

 quote, without comment, on the authority of their 

 exponent. The first or theoretical part contains a 

 simple exposition of the elementary principles on which 

 the success or failure of directed aerostats depends. In 

 the first place, the relative velocity of propulsion (vitesse 

 propre) must exceed the velocity of the wind if the 

 aerostat is to be completely under control, otherwise 

 the course will be confined within a limited angle. 

 This fact every student of elementary mechanics ouyht 

 to realise at a glance, but manv who succeed in pass- 

 ing exquninations fail to do so, and thus Captain 

 Rcnard's remarks are not so superfluous as they might 

 seem to be to a person who really understood elemen- 

 tary mathematics. -As the present writer pointed out, 

 it is mainly the difference in speed between air cur- 

 rents and ocean currents which has rendered aerial 

 navigation less successful hitherto than ocean navi- 

 gation.' 



Captain Renard discusses the questions of perman- 

 ence of form and the relative advantages of large and 

 small screws, and then proceeds to the question of 

 stability. He distinguishes three different kinds of 

 stability, namely, stability in altitude, stability of 

 course, and longitudinal stability. .According to the 

 conditions assumed in text-books, when a balloon is 

 in equilibrium at any altitude that equilibrium- is 

 stable, so that " instability in altitude " is not a 

 mechanical effect, but consists in the effects of phy- 

 sical causes in disturbing the vertical equilibrium of ," 

 balloon ; in a dirigible there are many easv methods 

 of maintaining a constant altitude. Instability of 

 course or instability in a horizontal plane occurs when 

 an aerostat tends to turn about a vertical axis so as 

 to set itself at right angles to the direction of motion, 

 like the ellipsoids of our text-books in hvdrodvnamics. 

 !n longitudinal instability the aerostat tends to turn 

 about a horizontal axis, pitching over forwards or 

 backwards. Captain Renard points out (and this is 

 entirely in accordance with the present writer's inves- 

 tigations) that there is a certain limiting or crilical 

 velocity consistent with stability; in the case of the 

 dirigible the critical velocity is a superior limit, which 

 cannot be exceeded without the motion becoming un- 

 stable. He also clearly shows that this fact was 

 known to Col. Renard in 1404, and further that the 

 critical velocity in question in many tvpes of 

 machine, such as the La France, Lebaudy, and Patrie. 

 has fallen considerably below the maximum speed 

 obtainable from suitable motors. For example, " In 

 the Santos Dumont the critical velocity is 8'5o m. (per 

 sec), and a 7 horse-power engine is sufficient to obtain 

 it ; if longitudinal stability were assured, the aerostat 

 could be provided with a 22-horse-power engine and 

 attain a speed of i2"io m. For the Lebaudy the 

 critical velocity is lO'So m. requiring 41 horse-power. 

 If this aerostat w-ere stable it could carry a machine 

 of 95 horse-power, which would give it a proper 

 velocity of 14-20 m." 



Yet we find another writer attempting to compare 

 the stability of the Patrie and Zeppelin in a paper 

 bristling with unnecessary mathematical formulae, 

 which do not even correctly represent the oscillations 

 of the balloons about a statical state of equilibrium. - 

 All that the calculation really does is to treat the 

 balloons as simple pendulums the points of support uf 

 wliich are at the centres of buoyancy, and the masses 



J Corithill Mftgazlnt:, May, 1Q07. 



- C,ipt. Guido Caslagneris in the Aeronautical J tufnal for July, 190S. 



NO. 2035, VOL. 78] 



of which are concentnited in the cars. The use of the 

 word " moment of inertia " tends to conceal the fact 

 that the moment of inertia of the framework about its 

 centre of gravity is completely ignored. 



Passing on to the equilibrium -and stability of aero- 

 plane systems, we find that not only is there a wide- 

 spread neglect of even some of the' most elementary 

 mathematical principles underlying the subject, but 

 the e.xperimental evidence commonly accessible is in- 

 sufficient to enable any very definite conclusions to be 

 drawn as to the best form of a flying-machine or as 

 to how far the types which have admittedlv given suc- 

 cessful results are capable of improvement. The hft 

 and drift of aeroplanes ha\-e been carefully measured, 

 and so far as the problem of flight depends on their 

 numerical magnitudes, the theory of the aeroplane is 

 summed up " in a nutshell " on pp. 40, 41 of M. 

 -Armengaud's paper. 



In the construction of motors the main, if not the 

 only, object to be aimed at is to make the weight as 

 small as possible for a given horse-power, a problem 

 with which engineers have shown themselves suffi- 

 ciently competent to deal. The best system of aero- 

 planes from the point of view of general efficiency is 

 that which requires the least horse-power to sustain a 

 given total load in horizontal flight. The actual 

 arrangement of the planes will not affect the efficiencv 

 except when one plane is placed in the wake of another. 

 But in connection with equilibrium and stability the 

 conditions are very complex, and a great deal of diffi- 

 cult mathematics is required. 



Take the question of propellers. The present critic 

 makes no claim to have examined the literature that 

 has collected around this problem in connection with 

 its more or less closely allied applications to naval 

 architecture, but it is certain that what has been found 

 out regarding the efficiency of a ship's screw should 

 form a starting point for discussions relating to airship 

 propellers, account being taken of necessary modifica- 

 tions. Yet the most crude methods are forming the 

 subject of published papers at the present time. C. M. 

 Woodward's problems ' would make suitable examples 

 for a conventional text-book on " Dogmatics " (as 

 dynamics should be called) if their working were cor- 

 rect, but the expression for the rate of working in 

 driving an airship " thru " the air involves an error 

 closely resembling that made when the oar is treated 

 as a lever of the second class. The succeeding results 

 regarding the horse-power applied to the " scru " 

 would therefore be incorrect even if the fundamental 

 assumptions were justified. W. B. Parsons ^ deals 

 mainly with experiments, but it mav be reasonably 

 doubted whether he has really kept the power of his 

 motor constant when the inclination of his blades has 

 been varied. To do so the torque would have to be 

 inversely proportional to the angular velocity. Neither 

 the stated method of regulating the power nor the 

 statement " The consequent variation in velocity is 

 the expression of the air resistance for that inclination 

 and velocity" (whatever this may mean?) appear re- 

 concilable with this assumption. 



But to come to the important question of stabilitv, 

 of which longitudinal stability, being the most import- 

 ant, shall alone be considered here. .'\ large propor- 

 tion of the contributors to aeronautical journals have 

 the vaguest possible ideas as to what stabilitv means. 

 The successful flights of Farman, Delagrange, and 

 Wright do not enable us to infer without further 

 evidence that their machines are automaticallv stable. 

 The analogous problem of the bicycle illustrates this 

 fact. The lateral stability of the bicvcle, like the 



'■ .Airship PropeHer Pr blems," Trans. Acad. Sc'., St. Loui<, .x'viii., 



No. 



- Acroitaitiical Journal, -Vpril, igoS. 



