Page 43 - Aerodynamics for Engineering Students

26 Aerodynamics for Engineering Students
giving

p = 1.71 x 1.0246 x = 1.751 x lop5 kgm-’s-l
For dynamic similarity the Reynolds numbers must be equal, Le.

287 x 1 x p = 20.2 x 106
1.75 x 10-5
giving

p = 1.23kgmP3
Thus the static pressure required in the test section is
p = pRT = 1.23 x 287.3 x 282 = 99500Nm-*
The total pressure ps is given by

e= +tM2)3’5= (1.1445)3.5 = 1.605
(1
P
ps = 99 500 x 1.605 = 160 000 N mP2
If the total pressure available in the tunnel is less than this value, it is not possible to achieve
equality of both the Mach and Reynolds numbers. Either the Mach number may be achieved
at a lower value of Re or, alternatively, Re may be made equal at a lower Mach number. In
such a case it is normally preferable to make the Mach number correct since, provided the
Reynolds number in the tunnel is not too low, the effects of compressibility are more important
than the effects of aerodynamic scale at Mach numbers of this order. Moreover, techniques are
available which can alleviate the errors due to unequal aerodynamic scales.
In particular, the position at which laminar-turbulent transition (see Section 7.9) of the
boundary layer occurs at full scale can be fixed on the model by roughening the model surface.
This can be done by gluing on a line of carborundum powder.

1.5 Basic aerodynamics

1.5.1 Aerodynamic force and moment

Air flowing past an aeroplane, or any other body, must be diverted from its original
path, and such deflections lead to changes in the speed of the air. Bernoulli’s equation
shows that the pressure exerted by the air on the aeroplane is altered from that of the
undisturbed stream. Also the viscosity of the air leads to the existence of frictional
forces tending to resist its flow. As a result of these processes, the aeroplane experiences
a resultant aerodynamic force and moment. It is conventional and convenient to
separate this aerodynamic force and moment into three components each, as follows.

Lift, LI-Z)
This is the component of force acting upwards, perpendicular to the direction of
flight or of the undisturbed stream. The word ‘upwards’ is used in the same sense that
the pilot’s head is above his feet. Figure 1.7 illustrates the meaning in various
attitudes of flight. The arrow V represents the direction of flight, the arrow L
represents the lift acting upwards and the arrow W the weight of the aircraft, and
shows the downward vertical. Comparison of (a) and (c) shows that this upwards is
not fixed relative to the aircraft, while (a), (b), and (d) show that the meaning is not
fixed relative to the earth. As a general rule, if it is remembered that the lift is always