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               CD
                                                   = - CL
so that
        1
= -E
75
(2.40)
  Dnun
Ynun - N-
      W
                1
      = - E~                                    (2.41)
Thus, the fiattest glide (y = Ynun) occurs when the glider fiies at that angle of attack
when the drag per unit weight is minimum or E = Em. Because the weight of a
glider is constant, we can say that the fiattest glide occurs when the drag is at
minimum. We know that when E = Em, CL = C7. =.            7k. The fiight velocity
for the fiattest glide is given by
V --
(2.42)
In other words, the velocity for the fiattest glide is equal to the reference velocity
or u ~ 1.
   For a given height, the distance covered with respect to the ground can be
obtained as follows:
dx = V .                           (2.43)
dt
dx dh = v
dh dt
dx   V
dh = Vy
     1
=~
  y
::= -E
(2.44)
(2.45)
76                 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Let R = x f  _ xi denote the range, which is equal to the horizontal distance covered
with respect to the ground. Then,
                                    R = -l,( Edh                           (2.46)
where hi and hf are the initial and ffnal altitudes, respectively. Assuming that the
angle of attack ct is held constant so that E is constant during the glide, we have
                                      R - EAh                             (2.47)
where Ah = h/.- hf  is the height lost during the glide. From Eq. (2.47), we observe
that, for a given height difference, the range is maximum when E - Em, wluch
is also the condition for the fiattest glide. In other words, maximum range occurs
when the glide angle is minimum. Using Eq. (2.20), we get
                                Rmax = 2~~DO                        (2.48)
Here, we have ignored the effect of wind on the range. Actually, the range depends
on wind conditions. A headwind reduces the range, whereas a tailwind increases it.
   In sailplane terminology, glide ratio is the ratio between the ground distance
traversed and the heightlost. The glide ratio is also equal to E. A high-performance
sailplane with a glide ratio of40 can cover 4 km with respect to the ground for every
100 m of height lost.
      Let the rate of sink, the speed with which the glideris heading towards the Earth,
be denoted by hs. Usually, h denotes the rate of climb. Therefore, hs -  -h. With
this, the rate of sink is given by
hs = -Vy
  DV
-W
(2.49)
The term D V in Eq. (2.49) represents the power required PR to sustain the gliding
flight. Thus, we observe that the rate of sink is minimum when the power required
per-unit-weight is minimum, which also corresponds to the case when the param-
eter (CD] C~./2) is a minimum or (C2t2]CD) is a maximrun It can be shown that
　
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