Page 71 - Aerodynamics for Engineering Students

54 Aerodynamics for Engineering Students

viewpoints are mathematically and physically correct. Both observers may use the
same equations to study the mutual effects of the air and the aeroplane and they will
both arrive at the same answers for, say, the forces exerted by the air on the aero-
plane. However, the pilot will find that certain terms in the equations become, from
his viewpoint, zero. He will, therefore, find that his equations are easier to solve than
will the ground-based observer. Because of this it is convenient to regard most
problems in aerodynamics as cases of air flowing past a body at rest, with consequent
simplification of the mathematics.

Types of flow
The flow round a body may be steady or unsteady. A steady flow is one in which the
flow parameters, e.g. speed, direction, pressure, may vary from point to point in the
flow but at any point are constant with respect to time, i.e. measurements of the flow
parameters at a given point in the flow at various times remain the same. In an
unsteady flow the flow parameters at any point vary with time.

2.1.2 A comparison of steady and unsteady flow

Figure 2. la shows a section of a stationary wing with air flowing past. The velocity of
the air a long way from the wing is constant at V, as shown. The flow parameters are
measured at some point fixed relative to the wing, e.g. at P(x, y). The flow perturb-
ations produced at P by the body will be the same at all times, Le. the flow is steady
relative to a set of axes fixed in the body.
Figure 2.lb represents the same wing moving at the same speed Vthrough air which,
a long way from the body, is at rest. The flow parameters are measured at a point
P’(x‘, y‘) fixed relative to the stationary air. The wing thus moves past P’. At times tl ,
when the wing is at AI, P’ is a fairly large distance ahead of the wing, and the
perturbations at P’ are small. Later, at time tz, the wing is at Az, directly beneath P’,
and the perturbations are much larger. Later still, at time t3, P‘ is far behind the wing,
which is now at A3, and the perturbations are again small. Thus, the perturbation at P’
has started from a small value, increased to a maximum, and finally decreased back to a
small value. The perturbation at the fmed point P’ is, therefore, not constant with
respect to time, and so the flow, referred to axes fmed in the fluid, is not steady. Thus,
changing the axes of reference from a set fixed relative to the air flow, to a different set
fixed relative to the body, changes the flow from unsteady to steady. This produces the

ty

I-
I“

Fig. 2.la Air moves at speed Vpast axes fixed relative to aerofoil