Page 36 - Aerodynamics for Engineering Students

Basic concepts and definitions 19

It is seldom that a camber line can be expressed in simple geometric or algebraic
forms, although a few simple curves, such as circular arcs or parabolas, have been
used.

Thickness distribution
Having found the median, or camber, line, the distances from this line to the upper
and lower surfaces may be measured at any value of x. These are, by the definition of
the camber line, equal. These distances may be measured at all points along the chord
and then plotted against x from a straight line. The result is a symmetrical shape,
called the thickness distribution or symmetrical fairing.
An important parameter of the thickness distribution is the maximum thickness,
or depth, t. This, when expressed as a fraction of the chord, is called the thickness/
chord ratio. It is commonly expressed as a percentage 100t/c%. Current values in use
range from 13% to 18% for subsonic aircraft down to 3% or so for supersonic
aircraft.
The position along the chord at which this maximum thickness occurs is another
important parameter of the thickness distribution. Values usually lie between 30%
and 60% of the chord from the leading edge. Some older sections had the maximum
thickness at about 25% chord, whereas some more extreme sections have the max-
imum thickness more than 60% of the chord behind the leading edge.
It will be realized that any aerofoil section may be regarded as a thickness
distribution plotted round a camber line. American and British conventions differ
in the exact method of derivation of an aerofoil section from a given camber line and
thickness distribution. In the British convention, the camber line is plotted, and the
thickness ordinates are then plotted from this, perpendicular to the chord line. Thus
the thickness distribution is, in effect, sheared until its median line, initially straight,
has been distorted to coincide with the given camber line. The American convention
is that the thickness ordinates are plotted perpendicular to the curved camber line.
The thickness distribution is, therefore, regarded as being bent until its median line
coincides with the given camber line.
Since the camber-line curvature is generally very small the difference in aerofoil
section shape given by these two conventions is very small.

1.4 ' Dimensional analysis
1.4.1 Fundamental principles

The theory of dimensional homogeneity has additional uses to that described above.
By predicting how one variable may depend on a number of others, it may be used to
direct the course of an experiment or the analysis of experimental results. For
example, when fluid flows past a circular cylinder the axis of which is perpendicular
to the stream, eddies are formed behind the cylinder at a frequency that depends on a
number of factors, such as the size of the cylinder, the speed of the stream, etc.
In an experiment to investigate the variation of eddy frequency the obvious
procedure is to take several sizes of cylinder, place them in streams of various fluids
at a number of different speeds and count the frequency of the eddies in each case.
No matter how detailed, the results apply directly only to the cases tested, and it is
necessary to find some pattern underlying the results. A theoretical guide is helpful in
achieving this end, and it is in this direction that dimensional analysis is of use.