AIR P R E S S U R E ON P
By L. BLIN
W E know that aeroplanes rise from the ground only when the
upward vertical component of the pressure of the air on their
" lifting surfaces " is great enough to balance the weight to be
lifted. Since the lifting force, or, as it is often called, the
lift of an aeroplane depends upon the pressure exerted upon
those surfaces as they move through the air, it is, therefore,
important to know how to estimate the pressure which the air
exerts on surfaces moving through it.
The essential facts that we must know in trying to design
rationally an aeroplane are the following :—
Being given a particular type of surface, what will be (a)
its lifting capability, (b) its corresponding resistance to propulsion or its drift, and (c) through what point in the surface
will pass the resultant of the pressures of the air on the
different portions of that surface.
(a) and (b), i.e., the lift and drift of a surface would be
determined if we knew (i) the magnitude of the total airpressure on the surface and (2) the exact direction of that
air-pressure. For then, knowing the magnitude and direction
of the air-pressure, we should be able to resolve that pressure
into two components : a vertical component, and a horizontal
component. The vertical component would give us the lift,
and the horizontal component would give us the drift,
"We thus see that in order to establish, rationally, the project
of an aeroplane we must know :—(1) the magnitude ; (2) the
direction ; (3) the point of application of the pressure which the
air exerts on the different types of surfaces which it is proposed to use, and for the different positions and speeds of those
surfaces.
The point of application of the pressure of the air on a
surface has been called its centre of pressure.
Very many experiments have been made by numerous
experimenters to find out in what manner the pressure which
the air exerts on surfaces moving in it varies with their size,
shape, inclination and speed. We shall, however, especially
study the conclusions arrived at by Prandtl at the laboratory
of Gottingen, and those by Eiffel, based on results which he
obtained in his experiments from the second floor of the
Eiffel Tower or in the laboratory he has installed a t the foot
of the tower bearing his name.
A sub-committee of scientific experts appointed by the
Academie des Sciences, to which body M. Eiffel had submitted
his worc,t has issued a report which contains the following
paragraphs :—
" We can admit that the results obtained by M. Eiffel and
contained in his work represent to-day the most exact values
known to measure the resistance which the air opposes to the
rectilinear motion of surfaces of the dimensions and shapes
which he indicates, and moving at speeds comprised within
the limits of his experiments.
'' We can, therefore, advise all those whose business it is to
know and use those values, to consult the quantities and
results contained in his work and we can consider that the
principal conclusions he arrives at are established with sufficient exactness."
The simplest case that can be imagined for the determination
of the pressure exerted by the air when a surface moves in it,
is t h a t of a plane surface placed at right-angles to its direction
of motion. A plane surface placed at right-angles to its
direction of motion is said to be moving normally.^
Eiffel has determined the pressure which the air exerts on
a plane surface moving normally by means of two distinct and
independent methods —
Firstlv.—By experimenting on surfaces dropped from the
second floor of the Eiffel Tower.
Secondly.—By experimenting on surfaces placed in an artificial air-current.
The results of his experiments lead to the following conclusions :—
1. The pressure of the air on a plane surafce moving normally can be represented by the formula :—
R = K S V'.
n which R = pressure or resistance of the air, S = area of
* Notes on Lecture I on "Aerodynamics," given in connection with the
Aeronautical Course of the Session 1911-12 at the Polytechnic, Regent Street,
London.
t "Recherches experimentales sur la Resistance de l'air executees a la Toor
Eiffel," by G. Eiffel (Librairie Aeronautique, Paris).
I
SURFACES
MOVING N O R M A L L Y . *
DESBLEDS.
surface, V = speed of translation of surface, and
= a coefficient whose value depends on the density of the nir. and
on the shape and area of the surface.
2. Experiments with plane surfaces whose areas varied
from -jV, sq. metre to 1 sq. metre, and the density of the air
being reduced to the normal (15 0 C. and 760 mm.), the mean
value of
is found to be 0-074 (using the metre-kilogrammesecond system of units).
[N.B.—K 1
(foot-pound-second unit) = 0-01902 x
(metre-kilo.-second unit).]
3. The value of K increases with the area of the surface,
but tends towards the limiting value K = o - o8o (metrekilogramme-second u n i t ;
density of air, normal).
This
value of K is reached when the area of the surface is 1 sq.
metre. For surfaces of areas greater than 1 sq. metre K is
constant, and always equal to <ro8o (metre-kilogrammesecond u n i t ; density of air, normal).
This result is confirmed by Dr. Staunton's experiments.
4. For square surfaces whose areas vary from ,,' „th of a
square metre to 1 sq. metre the value of K (metrc-kilogrammesecond u n i t ; density of air, normal) increases continuously
from 0-065 to o - o8o.
The increase of the value of K up to a maximum with the
area of the surface seems to be capable of a simple explanation
in view of certain indisputed experimental results. I t is
now established that when a surface moves in air the total
pressure which the air exerts on that surface is made up of a
positive pressure in front, and of a negative pressure, or
suction, behind the surface. The negative pressure is now
known to be an important part of the total pressure, and it
can be easily realised that certain linear dimensions are
necessary for the establishment of a zone of negative pressure
behind a surface. The total air pressure on very small
surfaces is diminished because no zone of negative* pressure
can exist behind themi
The two methods of experimenting which have been
adopted by Eiffel, and which we have already alluded to, have
given results which are remarkable for their continuity.
This is a most important point to bear in mind, because it
proves that the pressure which the air exerts on a surface
moving in it is the same as the pressure which the air in
motion would exert on the same surface maintained stationary
in it, supposing the speed of the surface in the first case and
the speed of the air in the second case to be the same. It,
therefore, establishes a principle, the correctness of which
was a t various times questioned, namely :—
The pressure of the air on a body depends only on its
relative motion with respect to the fluid, whether t h a t relative
motion is due to the displacement of the body or of the
fluid,
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