8' Aircraft performance

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• 8. Aircraft performance

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Quasi-equilibrium flight
L
V
T
g
Local horizon
D
W
Equilibrium equations T D Wsing L Wcosg
Rate of change of aircraft weight
3
The range equation
Rate of fuel use
dtdx/Vdx/aM
ltlt1, because gltlt1
4
Breguets range equation
For flight in the stratosphere (aconstant) at
constant Mach number, specific fuel consumption,
and L/D
Known from initial weight estimate
But L/DCL/CDCL/(CD,0CL2) constant Therefore
CL must be constant and tang g
(Z2-Z1)CjH/aM(L/D)ltlt1 Find your actual range
performance
Maximum L/D known from drag chapter
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Take-off performance
Find your actual take-off performance
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Climb performance
Rate of Climb, RC in feet per minute (fpm)
pressure ratio p/ps.l.
quasi-equilibrium flight
thrust in cruise
z
dz
dx
g
x
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Atmospheric conditions in climb
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Typical climb profile
Z (kft) 36
M0.86
constant Mach number climb
25
constant equivalent airspeed climb
10
constant equivalent airspeed climb
0
0 150 250 320 500 VE(kts)
Climb carried out mainly at constant equivalent
airspeed
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Time and distance to climb
Time to climb may be obtained by integration of
the RC equation
z z/24,000, a 236.8(L/D)/Vclimb, and b
(L/D)(T/W)to
Xclimb SVclimb,i Dti
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Typical results for time to climb
For (T/W)to0.3, Mcr0.8, and L/D16 (assumed
constant throughout the climb) the climb
performance is S.L.ltzlt10,000 ft Vclimb 250
ktsDt 2.24 min 10,000ltzlt25,000 ft Vclimb
320ktsDt 6.06 min 25,000ltzltcruise altitude
-Vclimb 474 ktsDt 10.9 min
SDt 19.2 min Note L/D during
segments 1 and 2 lt assumed value of 16, and the
time spent will be greater than calculated.
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Typical climb profile
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Typical climb trajectory
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Fuel and distance to climb
Distance to climb Xclimb (250 kts x 0.037
hr)(320 kts x 0.101 hr)(474 kts x 0.182
hr)127.8 nm 147.2 mi.
Fuel to Climb A reasonable approximation to the
fuel used in segment 4 of the mission profile
described in Chapter 2, is given by the equation
WF,used 4CjTDt, using consistent units.
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Descent performance
Rate of Descent, RD, in fpm
dz
g
dx
g the glide angle
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Descent profile
Descent Profile and Performance Cruise
altitudegtzgt10,000 ft - Vdescent250(Vcr-250)(z/
zcr) 10,000 ft gtzgt sea level - Vdescent250
kts Time to Descend airspeed is reduced linearly
with altitude so that V 250fz, where f (Vcr
- 250)/zcr and the cruise speed is Vcr and is
given in kts.
Distance to descend
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Landing performance
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Landing performance in the air run
g
R
T Wsing D mdV/dt L Wcosg
md(Rdg/dt)/dt 0 During the flare dV/dtVdV/ds
along the trajectory. The distance traveled
during the air run from VVa at sa0, and VVl at
s Sa, may be found by integrating the
equation T D Wg mVdV/ds (W/2g)dV2/ds L
W 0
Note gltlt1
g
V
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Landing performance (continued)
dV2/ds 2g(T D)/L g 2g-(D/L)eff g Vl2
Va2 2g(D/L)eff gavg Sa Sa (1/2g)Vl2
Va2 / (D/L)eff gavg Vl1.2Vstall and
Va1.3Vstall but Vstall2(W/S)l/rCL.l,max1/2 The
air run is therefore Sa (W/S)l/(4grslsCL,lmax
)/ (D/L)eff ga
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Landing performance in ground run
The dynamic equation during the ground run
is dV/dt (1/2g)dV2/dx (T/W)l (D/W)l
(Fbrake/W)l (Fbrake/W)l mbrake (1-L/W) mbrake
1 CL,lrslsV2/2(W/S)l a(1/2)dV2/dx
g(T/W)l mbrake g1 mbrake(CL,l/CD,l)
CD,lrslsV2/2(W/S) T reversal (lt0) braking
drag normal force reduction This is of the
form Y AY B 0 and the solution is V2
Vl2 B/A exp(-Ax) B/A Sg A-1 loge1
(A/B)Vl2