Page 68 - Aerodynamics for Engineering Students

Basic concepts and definitions 51

at various speeds. The maximum lift on the model is measured at the various speeds,
with the results as given below:

Speed (ms-') 20 21 22 23 24
Maximumlift (N) 2960 3460 4000 4580 5200

Estimate the minimum flying speed of the aircraft at sea-level, i.e. the speed at which
the maximum lift of the aircraft is equal to its weight. (Answer: 33 m s-')
7 The pressure distribution over a section of a two-dimensional wing at 4" incidence
may be approximated as follows: Upper surface; C, constant at -0.8 from the
leading edge to 60% chord, then increasing linearly to f0.1 at the trailing edge:
Lower surface; C, constant at -0.4 from the LE to 60% chord, then increasing
linearly to +0.1 at the TE. Estimate the lift coefficient and the pitching moment
coefficient about the leading edge due to lift. (Answer: 0.3192; -0.13)

8 The static pressure is measured at a number of points on the surface of a long
circular cylinder of 150mm diameter with its axis perpendicular to a stream of
standard density at 30 m s-I. The pressure points are defined by the angle 8, which
is the angle subtended at the centre by the arc between the pressure point and the
front stagnation point. In the table below values are given of p -PO, where p is the
pressure on the surface of the cylinder and po is the undisturbed pressure of the free
stream, for various angles 8, all pressures being in NmP2. The readings are identical
for the upper and lower halves of the cylinder. Estimate the form pressure drag per
metre run, and the corresponding drag coefficient.

8 (degrees) 0 10 20 30 40 50 60 70 80 90 100 110 120
p-po (Nm-') +569 +502 +301 -57 -392 -597 -721 -726 -707 -660 -626 -588 -569

For values of 0 between 120" and 180", p -PO is constant at -569NmP2.
(Answer: CD = 0.875, D = 7.25Nm-')
9 A sailplane has a wing of 18m span and aspect ratio of 16. The fuselage is 0.6m
wide at the wing root, and the wing taper ratio is 0.3 with square-cut wing-tips. At a
true air speed of 115 km h-' at an altitude where the relative density is 0.7 the lift and
drag are 3500 N and 145 N respectively. The wing pitching moment Coefficient about
the &chord point is -0.03 based on the gross wing area and the aerodynamic mean
chord. Calculate the lift and drag coefficients based on the gross wing area, and the
pitching moment about the $ chord point.
(Answer: CL = 0.396, CD = 0.0169, A4 = -322Nm since CA = 1.245m)
10 Describe qualitatively the results expected from the pressure plotting of a con-
ventional, symmetrical, low-speed, two-dimensional aerofoil. Indicate the changes
expected with incidence and discuss the processes for determining the resultant
forces. Are any further tests needed to complete the determination of the overall
forces of lift and drag? Include in the discussion the order of magnitude expected for
the various distributions and forces described. (U of L)
11 Show that for geometrically similar aerodynamic systems the non-dimensional
force coefficients of lift and drag depend on Reynolds number and Mach number
only. Discuss briefly the importance of this theorem in wind-tunnel testing and
simple performance theory. (U of L)