energy maneuvering
DESCRIPTION
Energy Maneuvering and ManagementTRANSCRIPT
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G. Leng, ME Dept, NUS
4 : Climb and Turn Performance
or how nimble is the aircraft ?
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G. Leng, ME Dept, NUS
The rate of climb (ROC)
The rate of climb (ROC) is the rate at which an aircraft increases its altitude
Climb records
h (km) time (s) ROC (m/s)
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G. Leng, ME Dept, NUS
Climb model
γ : flight path (climb) angle
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G. Leng, ME Dept, NUS
Resolving forces parallel and perpendicular to flight path (velocity V)
T – D – W sinγ = m dV/dt
L – W cosγ = m V dγ/dt
The climb rate is then
dh/dt = V sinγ
=
or(T – D) V =
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G. Leng, ME Dept, NUS
The climb equation
(T – D) V = dh/dt + d [V2 / (2g) ] / dtW
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G. Leng, ME Dept, NUS
Specific energy
The quantity on the rhs of the climb equation can be written as :
dh/dt + d [V2 / (2g) ] / dt
=
=
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G. Leng, ME Dept, NUS
Energy perspective
Hence the climb equation is actually an ‘energy” equation
Ps = dhe/dt
The time to transit from one energy state to another is given by :
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G. Leng, ME Dept, NUS
Example : F104 Ps curves
How to fly from energy state A to state B as fast as possible ?
A
B
Source : NASA TN D6398
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G. Leng, ME Dept, NUS
Comparison F4H-1 vs F15A
F4H-1 2 x J79-GE-2A turbojets
thrust = 2 x 10,350 lb ( 2 x 4,693 kg)
MTOW = 54,600 lb (24,761 kg)
T/W =
F15A 2 x F100-PW-100 turbofan
thrust = 2 x 25,000 lb (2 x 11,250 kg)
MTOW = 56,000 lb (25,200 kg)
T/W =
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G. Leng, ME Dept, NUS
Energy-Maneuverability Theory
• Developed by USAF Col John Boyd at Georgia Tech in 1962
• Thesis :
• Proved that the F-4 could not out turn a MiG-21 except at low altitude and high speed
• E-M theory was applied to the design of the F15 and F16
USAF Col John Boyd 1927-1997
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G. Leng, ME Dept, NUS
Sustained level turn
Conventional aircraft change heading by banking
i.e. tilt the lift force so that the horizontal component provides the centripedal force for circular motion.
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G. Leng, ME Dept, NUS
Sustained level turn model
φ
L cosφ =
L sinφ =
Resolving forces in the vertical and horizontal directionsL
φ: : bank angle
dχ/dt : turn rateW = mg
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G. Leng, ME Dept, NUS
Define the load factor n = L/W
= 1 / cosφ ( n > 1 )
Dividing the 2 force equations
V/g dχ/dt = tan φ
=
=
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G. Leng, ME Dept, NUS
The turn equation is :
dχ/dt = (g/V) √ ( n2 - 1 )
The turn radius is :
R = V / dχ/dt
= V2/ ( g √ ( n2 - 1 ) )
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G. Leng, ME Dept, NUS
Example : Turn envelope
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G. Leng, ME Dept, NUS
Exercise : Performance
estimation
Assuming A has a corner velocity of 450 kts at a load factor of 8, what’s the turn radius and turn rate ?
Assuming B is flying at the same speed, what’s the load factor and turn rate for B ?
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G. Leng, ME Dept, NUS
Turn at maximum load factor
Question : What’s the bank angle ?
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G. Leng, ME Dept, NUS
load factor n = ⇒ bank angle =
airspeed V = 450 kts = 450*0.5151 = 232 m/s
turn rate =
=
=
=
turn radius = V / turn rate
=
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G. Leng, ME Dept, NUS
RA = V2 / (g √ (nA2 – 1 ) )
RB = V2 / (g √ (nB2 – 1 ) )
load factor nB =
=
turn rate =
=
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G. Leng, ME Dept, NUS
Comparison of turn rates
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G. Leng, ME Dept, NUS
Bottom Line
High turn rates require high load factors
Notes :
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G. Leng, ME Dept, NUS
V-n Diagram