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., f*.
Minimum
Sirtk Rrte,
t mai
VR
F-I~ttest
GlIde,
R mai
v
mg. 2.6 Optimal rrelocities for gliding flight
The minimum sink rate is given by
hs.nrm = 4
(2.55)
Sailplane pilots fly at V = Vm when they are in the "lift" mode, i.e., when they
encounter an upward gust_ When the "lift ' dies, they accelerate to VR, the velocity
for flattest glide to cover the most ground while searching for another "lift:' An
instrument called "variometet' tells sailplane pilots whether they arein "lift" mode
or not.
The enduranceis the total time the glider remains in the air and can be determined
as follows:
so that
d
.= _l,~r
t = :Lhy
F(-,),h
(2,56)
(2.57)
Assurrung that the angle of attack is held constant during the glide and ignoring
the variations in density because of changes in altitude, we obtain
AIRCRAFT PERFORMANCE
79
If the difference between theinitial and final altitudeis significant, then the variation
in density may have to be considered. In such cases, the following approximate
equation may be used.
p = Poe-0'000114h
(2.59)
whiere Po is the density at sea level and h is the altitude in meters. Usually, Po -
1.225 kg/m3.
For maximum endurar, r has to fiy at that angle of attack or lift coeffi-
cient when the parame{c~n(C,2t/h/~hd) ~. haximum, which occurs when CL = .AcZ
and V -. 0.76 VR. Note that this is also the condition for minimum sink rate. rl'hus,
the endurance is maximum when the sink rate is minimum. Using Eq. (2.53), we
obtain
f-
rmax -
(h4 hf)
(2.60)
The range and endurance are important measures of a glider's performance.
Whereas the maximum range was independent of the weight, the maximum en-
durance depends on the weight. This calls for the designer to make the glider as
light as possible. Furthermore, both the maximum range and endurance improve
if the aerodynamic parameters k and CDO are kept to theirlowest possible values.
Because of this, gliders tend to have an elliptical wing with a high aspect ratio and
an efficient low-drag, laminar-fiow airfoil section.
Example 2.1
A glider having W -2000 N, S = 8.0 fl12, A - 16.0, e - 0.95, and CDO =
0.015 is launched from a height of 300 m. Determine the maximum range, corre-
sponding glide angle, forward velocity, and lift coefficient at sea level.
Solution. At sea level, we have pt, = 1.225 kg/m3. Furthermore,
k- 1
nAe
rr * 16 * 0.95
- 0.02
E,,, -
2~k~
- 28.86
Rmax = (hf - hi)Em
- 28.86 * 300 m
8.658 km
.;
.;~
;!
+
e
k
. .T
;.f
3
3
l,
g
s/
?
b
e
(<
ii
:,
t
r
}.?.
';,
-.
,!
l:{
p
.i.
jt
/
'g
;j,
s'
'/
f-
t
80 PERFORMANCE, STABILITY, DYNAMfCS, AND CONTROL
The maximum range occurs when the glide angle is minimum
1
ynun - En
1
- 28 86
- 0.0346 rad
= 1.985 deg
The velocity and lift coefficient for the fiattest glide are given by
V : VR
.~ If4[F~
\1 .225~8 OV 0.015
- 23.328 m/s
CL = C:
- 0.866
Example 2.2
A glider weighing 5000 N and having an elliptical wing with an area of 10 m2 is
required to maintajn a glide angle of3 deg at a forward speed of 50 m/s. Assuming
CDO - 0.015, find the aspect ratio of the glider.
So/uOon. Because the glider has an elliptical wing, e - 1. Then,
CD
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