FlightGlobal.com
Home
Premium
Archive
Video
Images
Forum
Atlas
Blogs
Jobs
Shop
RSS
Email Newsletters
You are in:
Home
Aviation History
1913
1913 - 0064.PDF
fijcm JANUARY 18, 1913. NEGATIVE WING By J. TIPS AND LATERAL STABILITY. H. HUME-ROTHERY, M.A., B.Sc. <.e article reached these offices after the printing of Mr. Berriman's article in last week's issue of FLIGHT, but before the Toumal was in the hands of the public. It is an entirely independent treatment of the subject, and it arrives at the same conclusion as to the stability of negative wine tips. The method is of still further interest and importance, in that it provides a quantitative analysis, while as a line of thniehi it semes as a direct link wi'h Prof. Bryan's mathematical treatise, a synopsis of which was recently presented as a paper to the Aeronautical Society by Mr. E. H. Harper, and will be published in FLIGHT shortly.—ED. IN a few types of aeroplanes—notably the Dunne—the tip* of the curve to that on the outside, in just the same way as we assumed wings are 'inclined at a negative angle, i.e., down in front, and the exact effect of this oa stability when carried out in such a way as to produce a downward pressure on the tips, is a very interesting problem. From the practical point of view the word stability has a wider meaning than its strictly mathematical definition. Strictly speaking an aeroplane is stable, if when slightly disturbed out of its normal flying attitude by some force it tend- of itself to return to the proper position. But practically of equal, if not of greater, importance is the question as to whether there is to be any disturbing force, in other words whether gusts will twist it about. And so long as no gust can produce any great disturbing force, a very slight degree of true stabi ity will suffice, for the pilot's control can be operated to bring the aeroplane back to its position. In most cases, unfortunately, any device that improves the stability of the aeroplane renders it moie subject to disturbance by gusts, and the special interest of the negative wing tips is that it seems possible to prove that they can improve the true lateral (or asymmetric) stability while reducing the effect of gusts. la dealing with guits, they may be classified into horizontal and non-hoiizonial ; also into full gusts, which strike the whole machine nearly simultaneously, and partial gusts, which act on one part of the aeroplane for a considerable time, or act much more strongly on one part than another. Full gusts do not greatly affect modern aeroplanes, at any rate in regard to lateral stability. As long as the lateral centre of pressure is but little above the centre of gravity, and neither in front nor behind it, no serious heeling or turning should be caused. But a partial gust striking one extremity causes serious displacement. Whether any device could prevent a pirtial non-horizontal gust from blowing a wing tip or tail up or down is doubtful, but the O A T B Fij. 1. following considerations seem to prove that negative wing tips may prevent any partial horizontal gust from heeling the aeroplane over to one side. Suppose a partial head gust strikes the aeroplane AOB (Fig. 1), so that it is stronger on the wing AO than on BO this will make the lift on AO the greater, and so cause it to rise and B to fall. If ./.-/' and BB* be negative wing tips then the gust will increase the downward force on A A1 more than BBl, causing a counteracting couple. Since the tips are a long way from O their leverage is great, and this counteracting couple may be sufficient to neutral ze the up-letting couple. For the purpose of calculation, we miy reasonably assume the strength of the gust to increase regularly from B1 to ,/', so that the relative velocity of the air at any point x will be F+ ax, thus varying from V— al at B (if OB = OA = /) to V+ al at A. The upsetting couple will then be (assuming the wings do not taper) = A'J*'( V + axfxdx = A"- Va I* and the counteracting couple due to the tips = A'l Va[l™-P),\ OA' = l\ For these to balance /:' = /':t - /' or /' = 1*27 / roughly, or AA1 must be about one-quarter of OA. If the wings were tapered, less area of negative tip would suffice. If instead of the negative tips being continuous with the wings they were joined to it by light spars (Fig. 2), a smaller area would suffice on account of the grea'er leverage. For instance, if the wings were 15 ft. long and the spars projected 3ft., calculation shows that 3 ft. of negative tip would suffice. But in practice much less would be needed on account of the self- warping of the wings, which reduces the upsetting couple greatly, and hence the righting couple may be much less than that shown by the above calculation. So that smaller negative tips quite within the limits of practical construction would be sufficient. Such tips would have a further effect: in turning, the machine would have no tendency lo bank itself. For in turning, the relative velocity of the air increases from the wing tip on the inside of the when dealing with the partial head gust. Now banking is necessary for turning, but as pilots have at present to use the warp to prevent overbanking during a turn, there seems no reason against their having instead to use it to produce sufficient banking. It would be different from the present practice, but that in itself is no real practical objection. For it has this advantage : while a full gust from the side will not cause the aeroplane to turn if the centre of lateral pressure coincides with the centre of gravity, a partial side gust that strikes only the nose or tail will unavoidably do so, and this sudden turn will cause an ordinary aeroplane to heel over. But if provided with negative tips the sudden turn will not cause any heeling. Negative wing tips, therefore, should prevent any partial horizontal gust (whether coming ahead or astern or sideways) from heeling the aeroplane over sideways. Whether by having the negative tips attached to the two main wing spars (as shown in Fig. 2), so that when the wing warps upwards the negative tips dip down in front, whether this would lessen the effect of a partial non-horizontal head gust might be worth considering, but it is outside the scope of this article. So far we have considered the negative tips as lessening the effects of partial gusts, it is now time to turn to their effect on the strict (or mathematical) stability. Prof. Bryan's book, " Stability in Aviation," gives the method of investigation. On p. 32 he gives certain functions denoted by the German letters ?li >$, S, 5), and (S, all of which must be -f " for lateral stability, as well as the function s8GS>- 9135- -a2© which he calls •§. On p. 126 he shows that this is impossible with simple straight wings, even (p. 128) when 3 13' '••• 1 Fig. 2. : ••.-. • .' 1 / — 64 combined with a vertical keel plane or fin, which one may consider as representing the lateral surface of an aeroplane. Now the special interest of the negative tips is that on introducing the terms representing their effect, I have discovered that the above conditions of stability can be easily satisfied. The essence of the effect of the negative tips is that they render the motions of heeling and turning quite independent of each other, and this removes many of the - terms from the above functions, so that they can easily be rendered + m. In Prof. Bryan's language the resistance derivatives L,; and M/ may both be nude. To fully set out this investigation would be too lengthy for this article, but the following summary will enable anyone conversant with Prof. Bryan's book to follow it and check the results. By having the negative tips so that the moment of inertia of their area with respect to the plane of xy equals that of the main planes (I), but set at a negative angle —a equil to the positive angle a of the main planes his formu'w (137) on p. 126 become :— Lp = 2 A77/cos2a Lv = o Mf-=o Mq = 4 KUIAtfa Assuming that the centre of lateral pressure of the vertical fin (for grazing incidence) is neither before no behind the centre of gravity,
Sign up to
Flight Digital Magazine
Flight Print Magazine
Airline Business Magazine
E-newsletters
RSS
Events
