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n
- 2n W
C~ = p SY7.
(2.221)
(2.222)
(2.223)
(2.224)
(2.225)
Here, we assume that theload factor n .< nrm where nnm is the structurallimitload
factor and CL < CL,max.lfeither ofthese two conditions are not satisfied, then the
aircraft cannot generate the maximum sustained turn rate predicted by Eq. (2.222).
Sharpest sustained turn. Here, we consider the case when the aircraft at-
tempts to make a sharpest turn or the turn with minimum radius of curvature. Such
a turn while holding a constant altitude is called the sharpest sustained tum (SST).
We have
For Rnun,
or
. R=_V2
g^ff/-l-
dR 2(r?2_1)/r 212dd~
dV= - g(n2-1)--
-0
(2.226)
(2.227)
V dn2
4 dV - (r12 - 1) = 0 (2.228)
As before, substitution for dn2/d V gives an equation of the same form as that of
Eq. (2.220), which has no analytical solution. We have to use graphical or numerical
methods to solve this equation. Let Vsr be such a solution that mirumizes the radius
of turn. Then,
1 r7ppP'(kW)(W]S)Vsr
n=Wl]S(ktr7o 2k
p2Ck\.)0'5 (2.229)
4k
AIRCRAFT PERFORMANCE
129
co=gV~ 7
Vst (2.230)
Rmm-- Vs9;
= g ~~-=f (2.231)
1
COS,1. - - (2.232)
n
2n,W
C~ = pS~2 (2.233)
Here, we assume that the load factor n <. nrmi and CL < CL,max. If either of these
two conditions are not satisfied, then the aircraft cannot perform the sharpest tum
with Rnun as predicted by Eq. (2.231).
Turn with maximum load factor. Because the bank angle and load factor are
uniquely related by Eq. (2.207), the turn for maximum load factor is same as the
turn for maximum bank angle. From Eq. (2.215), we have
where
k'r7ppP'(kW)(W/S)V p2C,
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PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL1(75)
