THE QUESTION OF SUSTENTATION
THE CENTRE OF PRESSURE.

§ 1. Passing on now to the study of an aeroplane actually in the air, there are two forces acting on it, the upward lift due to the air (i.e. to the movement of the aeroplane supposed to be continually advancing on to fresh, undisturbed virgin air), and the force due to the weight acting vertically downwards. We can consider the resultant of all the upward sustaining forces as acting at a single point—that point is called the "Centre of Pressure."

Suppose A B a vertical section of a flat aerofoil, inclined at a small angle a to the horizon C, the point of application of the resultant upward 'lift,' D the point through which the weight acts vertically downwards. Omitting for the moment the action of propulsion, if these two forces balance there will be equilibrium; but to do this they must pass through the same point, but as the angle of inclination varies, so does the centre of pressure, and some means must be employed whereby if C and D coincide at a certain angle the aeroplane will come back to the correct angle of balance if the latter be altered.

In a model the means must be automatic. Automatic stability depends for its action upon the movement of the centre of pressure when the angle of incidence varies. When the angle of incidence increases the centre of pressure moves backwards towards the rear of the aerofoil, and vice versa.

Let us take the case when steady flight is in progress and C and D are coincident, suppose the velocity of the wind suddenly to increase—increased lifting effect is at once the result, and the fore part of the machine rises, i.e. the angle of incidence increases and the centre of pressure moves back to some point in the rear of C D. The weight is now clearly trying to pull the nose of the aeroplane down, and the "lift" tending to raise the tail. The result being an alteration of the angle of incidence, or angle of attack as it is called, until it resumes its original position of equilibrium. A drop in the wind causes exactly an opposite effect.

§ 2. The danger lies in "oscillations" being set up in the line of flight due to changes in the position of the centre of pressure. Hence the device of an elevator or horizontal tail for the purpose of damping out such oscillations.

§ 3. But the aerofoil surface is not flat, owing to the increased "lift" given by arched surfaces, and a much more complicated set of phenomena then takes place, the centre of pressure moving forward until a certain critical angle of incidence is reached, and after this a reversal takes place, the centre of pressure then actually moving backwards.

The problem then consists in ascertaining the most efficient aerocurve to give the greatest "lift" with the least "drift," and, having found it, to investigate again experimentally the movements of the centre of pressure at varying angles, and especially to determine at what angle (about) this "reversal" takes place.

§ 4. Natural automatic stability (the only one possible so far as models are concerned) necessitates permanent or a permanently recurring coincidence (to coin a phrase) of the centre of gravity and the centre of pressure: the former is, of course, totally unaffected by the vagaries of the latter, any shifting of which produces a couple tending to destroy equilibrium.

§ 5. As to the best form of camber (for full sized machine) possibly more is known on this point than on any other in the whole of aeronautics.

In Figs. 44 and 45 are given two very efficient forms of cambered surfaces for models.

The next question, after having decided the question of aerocurve, or curvature of the planes, is at what angle to set the cambered surface to the line of flight. This brings us to the question of the—

§ 6. Dipping Front Edge.—The leading or front edge is not tangential to the line of flight, but to a relative upward wind. It is what is known as the "cyclic up-current," which exists in the neighbourhood of the entering edge. Now, as we have stated before, it is of paramount importance that the aerofoil should receive the air with as little shock as possible, and since this up-current does really exist to do this, it must travel through the air with a dipping front edge. The "relative wind" (the only one with which we are concerned) is thereby met tangentially, and as it moves onward through the air the cambered surface (or aerocurve) gradually transforms this upward trend into a downward wake, and since by Newton's law, "Action and reaction are equal and opposite," we have an equal and opposite upward reaction.

We now know that the top (or convex side) of the cambered surface is practically almost as important as the underneath or concave side in bringing this result about.

The exact amount of "dipping edge," and the exact angle at which the chord of the aerocurve, or cambered surface, should be set to the line of flight—whether at a positive angle, at no angle, or at a negative angle—is one best determined by experiment on the model in question.

But if at any angle, that angle either way should be a very small one. If you wish to be very scientific you can give the underside of the front edge a negative angle of 5° to 7° for about one-eighth of the total length of the section, after that a positive angle, gradually increasing until you finally finish up at the trailing edge with one of 4°. Also, the form of cambered surface should be a paraboloid—not arc or arc of circles. The writer does not recommend such an angle, but prefers an attitude similar to that adopted in the Wright machine, as in Fig. 47.

§ 7. Apart from the attitude of the aerocurve: the greatest depth of the camber should be at one-third of the length of the section from the front edge, and the total depth measured from the top surface to the chord at this point should not be more than one-seventeenth of the length of section.

§ 8. It is the greatest mistake in model aeroplanes to make the camber otherwise than very slight (in the case of surfaced aerofoils the resistance is much increased), and aerofoils with anything but a very slight arch are liable to be very unstable, for the aerocurve has always a decided tendency to "follow its own curve."

The nature of the aerocurve, its area, the angle of inclination of its chord to the line of flight, its altitude, etc., are not the only important matters one must consider in the case of the aerofoil, we must also consider—

§ 9. Its Aspect Ratio, i.e. the ratio of the span (length) of the aerofoil to the chord—usually expressed by span/chord. In the Farman machine this ratio is 5·4; BlÉriot, 4·3; Short, 6 to 7·5; Roe triplane, 7·5; a Clark flyer, 9·6.

Now the higher the aspect ratio the greater should be the efficiency. Air escaping by the sides represents loss, and the length of the sides should be kept short. A broader aerofoil means a steeper angle of inclination, less stability, unnecessary waste of power, and is totally unsuited for a model—to say nothing of a full-sized machine.

In models this aspect ratio may with advantage be given a higher value than in full-sized machines, where it is well known a practical safe constructional limit is reached long before theory suggests the limit. The difficulty consists in constructing models having a very high aspect ratio, and yet possessing sufficient strength and lightness for successful flight. It is in such a case as this where the skill and ingenuity of the designer and builder come in.

It is this very question of aspect ratio which has given us the monoplane, the biplane, and the triplane. A biplane has a higher aspect ratio than a monoplane, and a triplane (see above) a higher ratio still.

It will be noticed the Clark model given has a considerably higher aspect ratio, viz. 9·6. And even this can be exceeded.

An aspect ratio of 10:1 or even 12:1 should be used if possible.[37]

§ 10. Constant or Varying Camber.—Some model makers vary the camber of their aerofoils, making them almost flat in some parts, with considerable camber in others; the tendency in some cases being to flatten the central portions of the aerofoil, and with increasing camber towards the tips. In others the opposite is done. The writer has made a number of experiments on this subject, but cannot say he has arrived at any very decisive results, save that the camber should in all cases be (as stated before) very slight, and so far as his experiments do show anything, they incline towards the further flattening of the camber in the end portions of the aerofoil. It must not be forgotten that a flat-surfaced aerofoil, constructed as it is of more or less elastic materials, assumes a natural camber, more or less, when driven horizontally through the air. Reference has been made to a reversal of the—

§ 11. Centre of Pressure on Arched Surfaces.—Wilbur Wright in his explanation of this reversal says: "This phenomenon is due to the fact that at small angles the wind strikes the forward part of the aerofoil surface on the upper side instead of the lower, and thus this part altogether ceases to lift, instead of being the most effective part of all." The whole question hangs on the value of the critical angle at which this reversal takes place; some experiments made by Mr. M.B. Sellers in 1906 (published in "Flight," May 14, 1910) place this angle between 16° and 20°. This angle is much above that used in model aeroplanes, as well as in actual full-sized machines. But the equilibrium of the model might be upset, not by a change of attitude on its part, but on that of the wind, or both combined. By giving (as already advised) the aerofoil a high aspect ratio we limit the travel of the centre of pressure, for a high aspect ratio means, as we have seen, a short chord; and this is an additional reason for making the aspect ratio as high as practically possible. The question is, is the critical angle really as high as Mr. Seller's experiments would show. Further experiments are much needed.