Page 290 - Aerodynamics for Engineering Students

272 Aerodynamics for Engineering Students

8 A straight wing is elliptic and untwisted and is installed symmetrically in a wind-
tunnel with its centre-line along the tunnel axis. If the air in the wind-tunnel has an
axial velocity V and also has a small uniform angular velocity w about its axis, show
that the distribution of circulation along the wing is given by
I? = 4sAz sin(20)

and determine A2 in terms of w and the wing parameters. (The wind-tunnel wall
corrections should be ignored.)
9 The spanwise distribution of circulation along an untwisted rectangular wing of
aspect ratio 5 can be written in the form:
r = 4sva[0.023 40 sin(8) + 0.002 68 sin(30) + 0.000 72 sin(58) + 0.000 10 sin(70)l
Calculate the lift and induced drag coefficients when the incidence a measured to no
lift is 10". (Answer: CL = 0.691, C,i = 0.0317)

10 An aeroplane weighing 250 kN has a span of 34 m and is flying at 40 m/s with its
tailplane level with its wings and at height 6.1 m above the ground. Estimate the
change due to ground effect in the downwash angle at the tailplane which is 18.3 m
behind the centre of pressure of the wing. (Answer: 3.83")
11 Three aeroplanes of the same type, having elliptical wings of an aspect ratio of 6,
fly in vee formation at 67m/s with CL = 1.2. The followers keep a distance of one
span length behind the leader and also the same distance apart from one another.
Estimate the percentage saving in induced drag due to flying in this formation.
(Answer: 22%)

12 An aeroplane weighing 100kN is 24.4m in span. Its tailplane, which has
a symmetrical section and is located 15.2 m behind the centre of pressure of the wing,
is required to exert zero pitching moment at a speed of 67 m/s. Estimate the required
tail-setting angle assuming elliptic loading on the wings. (Answer: 1.97")
13 Show that the downwash angle at the centre span of the tailplane is given to
a good approximation by

CL
,
E = constant x -
AR
where AR is the aspect ratio of the wing. Determine the numerical value of the
constant for a tailplane located at 2s/3 behind the centre of pressure, s being the
semi-span. (Answer: 0.723 for angle in radians)
14 An aero lane weighing lOOkN has a span of 19.5m and a wing-loading of
P
1.925 kN/m . The wings are rather sharply tapered having around the centre of span
a circulation 10% greater than that for elliptic wings of the same span and lift.
Determine the downwash angle one-quarter of the span behind the centre of pres-
sure, which is located at the quarter-chord point. The air speed is 67 m/s. Assume the
trailing vorticity to be completely rolled up just behind the wings.
(Answer: 4.67')