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.
[Illustration: FIG. 42.]
§ 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.
[Illustration: FIG. 43.]
§ 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.
[Illustration: FIG. 44.--AN EFFICIENT FORM OF CAMBER.
B D Maximum Altitude. A C Chord.
Ratio of B D: A C :: 1:17. A D 1/3 of A C.]
[Illustration: FIG. 45.--ANOTHER EFFICIENT FORM.
Ratio of B D to A C 1 to 17. AD rather more than ¼ of A C.]
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.
[Illustration: FIG. 46.]
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."
[Illustration: FIG. 47.--ATTITUDE OF WRIGHT MACHINE.]
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.
FOOTNOTES:
[37] Nevertheless some models with a very low aspect ratio make good
flyers, owing to their extreme lightness.