Module 7
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Aircraft Performance
Module 7
Where are we? 1 : Introduction to aircraft performance, atmosphere 2 : Aerodynamics, air data measurements 3 : Weights / CG, engine performance, level flight 4 : Turning flight, flight envelope 5 : Climb and descent performance 6 : Cruise and endurance 7 : Payload-range, cost index 8 : Take-off performance 9 : Take-off performance 10 : Enroute and landing performance 11 : Wet and contaminated runways 12 : Impact of performance requirements on aircraft design
Payload-range and Cost Index
2
Payload-range
Payload-range and Cost Index
3
Payload-range - Introduction
Payload-range and Cost Index
4
Payload-range – Mission profile
Payload-range and Cost Index
5
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
6
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
7
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
8
Payload-range – Fuel reserves
Payload-range and Cost Index
9
Payload-range – Fuel reserves (Cont’d)
Payload-range and Cost Index
10
Payload-range – Fuel reserves (Cont’d)
Payload-range and Cost Index
11
Payload-range – Range calculation
Payload-range and Cost Index
12
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
13
Payload-range – Range calculation (Cont’d)
Assume values for OWE, payload, fuel quantity, fuel reserves, and cruise flight level
•
ZFW = OWE + payload
• •
Fuel quantity must not exceed maximum fuel capacity
ZFW must not exceed MZFW If ZFW > MZFW, payload must be reduced
Ramp Weight RW = ZFW + fuel quantity
• •
RW must not exceed MRW If RW > MRW, fuel or payload must be reduced
Payload-range and Cost Index
14
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
15
Payload-range – Range calculation (Cont’d) Climb from 1500 ft to top of climb (initial cruise flight level)
Climb time, distance and fuel are calculated or obtained from manufacturer’s climb data •
Weight at top of climb = WTOC = WETO – climb fuel
•
Verify that r/c at top of climb meets minimum required r/c (reduce cruise flight level if minimum requirement is not met)
•
Determine weight at beginning of approach and landing WBAL
Approach and landing fuel and time are calculated or specified •
WBAL = LW + approach and landing fuel
•
Payload-range and Cost Index
16
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
17
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
18
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
19
Payload-range – Payload-range diagram A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
20
Payload-range – Payload-range diagram (Cont’d) A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
21
Payload-range – Payload-range diagram (Cont’d) A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
22
Payload-range – Payload-range diagram (Cont’d)
Payload-range and Cost Index
23
Cost index
Payload-range and Cost Index
24
Cost index - Introduction We can now calculate the fuel and time required for a given mission using various assumptions regarding operation of the aircraft: • • • •
Climb speed Cruise altitude Cruise speed Descent speed
Operationally, it is desirable to select assumptions such that operating costs will be minimized
The Cost Index concept is used by many airlines as a means to select optimum operating conditions and to minimize operating costs
Payload-range and Cost Index
25
Cost Index - Economy Speed Cost components • Crew - f(time) • Fuel - f(time,L/D,TSFC) • DMC - f(time,rating) • Ldg/Nav - f(weight)
Economy speed is the speed that minimizes total (time+fuel) costs Fuel + Time
Cost
Fuel
Time Max SAR
Economy
VMO / MMO
Block Speed Payload-range and Cost Index
26
Cot Index - Economy Speed Sample Calculation
767-200 at 35,000 feet Weight - 310,000 pounds Time-related costs - $500 per flight-hour Fuel costs - $.10 per pound
100 NM
Mach
0.75
0.77
0.79
0.81
0.83
Knots TAS
432
444
455
467
478
SAR – NM / lb
0.0446
0.0448
0.0447
0.0436
0.0408
Time - hours
0.231
0.225
0.220
0.214
0.209
Fuel - Pounds
2,242
2,230
2,235
2,294
2,451
Time-related cost - $
115
113
110
107
105
Fuel cost - $
224
223
224
229
245
Total cost - $
340
336
334
336
360
Payload-range and Cost Index
27
Cost Index – Derivation of Cost Index Cash or Direct Operating Cost
time related cost component
fixed cost component
III C=C I p f W fu e C l fuel price
block fuel
dW fuel
dC d I dWfuel = C + pf =0 dt dt dt
dt
=− min cos t
differential eqn for min. cost
CI = −
I C pf
One Onenumber numberserves servesto toidentify identifythe theeconomy economy flight flighttechnique techniquefor forall allmissions missions Payload-range and Cost Index
28
C I pf
Cost Index – Derivation of Cost Index (Cont’d)
In practice, Cost Index (CI) is calculated as follows in the American environment:
CI = (Time-related cost) / (Fuel cost) CI = ($ / flight hour) / [ $ / (lb of fuel) * 100 ]
CI is a fixed value for a given airline and a given aircraft type
CI can be calculated for the previous example:
• •
Time-related cost = 500 $ / hour Fuel cost = 0.10 $ / lb of fuel
CI = 50
Payload-range and Cost Index
29
Cost Index - Block Fuel-Time Curve
Block Fuel
• Many flight techniques share the same Cost Index • Flight technique with Distinct flight techniques; minimum fuel for given each denotes a given Cost Index is min. cost climb schedule,
Minimum Time
initial cruise altitude, cruise speed, step profile and descent schedule
Optimum altitude or Maximum service ceiling Increasing Altitude
Minimum Fuel
High speed climb and descent modes combined with Max. Cruise to intermediate cruise speeds
Intermediate to low speed climb and descent modes combined with intermediate to Max (or Long) Range Cruise speeds
Block Time Payload-range and Cost Index
30
Cost Index Values for Various Equipment
COST INDEX
High-speed Prop
COST INDEX
COST INDEX
50-seat Turbofan 70/90-seat Turbofan
COST INDEX
COST INDEX
COST INDEX
MD-80
B757
A300
Payload-range and Cost Index
COST INDEX
B737
COST INDEX
B747 31
50
Co st I nde x=
0
Performance Document Presentation for Climb
0 10
common initial climb
Some observations • Objective is least cost to climb to common cruise point • Max RoC (steeper trajectory) & min. fuel with Cost Index Zero • CLB thrust decrease = slower economy climb speed • Tailwind = slower economy climb speed
Payload-range and Cost Index
32
common cruise point
Performance Document Presentation for Cruise
Fixed Altitude
Some observations • Cost Index promotes less variation in Mach as AUW decreases • Tailwind = slower economy cruise speed Payload-range and Cost Index
33
Performance Document Presentation for Descent
100
50
common Co st cruise point Ind ex
=0
common EoD @ common speed
Some observations • Objective is least cost to descend from common cruise point • Max RoD (steeper trajectory) at high Cost Index Payload-range and Cost Index
34
Identifying Economy Flight Techniques: CRJ700, 1000 nm Sector Example Optimum Altitude
Flight Level
TOC
Trajectory A: Minimum Fuel CLB Mode L, MRC and DES Mode L
Trajectory B: Intermediate CLB Mode L, MCRZ and DES Mode L
BOD
Trajectory C: Minimum Time CLB Mode H, MCRZ and DES Mode H
Cruise Soaking
Origin
Destination
Payload-range and Cost Index
35
Identifying Economy Flight Techniques: CRJ700, 1000 nm Sector Example (Cont’d) 9800 9600
CLB Mode H MCRZ @ FL 310 DES Mode H
9400
Block Fuel (lb)
9200
mean curve
9000 8800
CLB Mode H MCRZ @ FL 390 DES Mode H
8600 8400
CLB Mode L MCRZ @ FL 390 DES Mode N
8200 8000
CLB Mode L Close to MRC @ FL 390 DES Mode L
Cost Index = 22 7800 7600 150
152
154
156
158
160
162
164
166
168
Block Time (min.)
Based on input crew cost, engine/airframe maintenance cost, materials cost, reserves and typical fuel price ==> Cost Index = 22
Optimal technique in ISA, still air corresponds to CLB Mode L / MCRZ @ opt. FL / DES Mode N
Payload-range and Cost Index
36
Module 7
Where are we? 1 : Introduction to aircraft performance, atmosphere 2 : Aerodynamics, air data measurements 3 : Weights / CG, engine performance, level flight 4 : Turning flight, flight envelope 5 : Climb and descent performance 6 : Cruise and endurance 7 : Payload-range, cost index 8 : Take-off performance 9 : Take-off performance 10 : Enroute and landing performance 11 : Wet and contaminated runways 12 : Impact of performance requirements on aircraft design
Payload-range and Cost Index
2
Payload-range
Payload-range and Cost Index
3
Payload-range - Introduction
Payload-range and Cost Index
4
Payload-range – Mission profile
Payload-range and Cost Index
5
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
6
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
7
Payload-range – Mission profile (Cont’d)
Payload-range and Cost Index
8
Payload-range – Fuel reserves
Payload-range and Cost Index
9
Payload-range – Fuel reserves (Cont’d)
Payload-range and Cost Index
10
Payload-range – Fuel reserves (Cont’d)
Payload-range and Cost Index
11
Payload-range – Range calculation
Payload-range and Cost Index
12
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
13
Payload-range – Range calculation (Cont’d)
Assume values for OWE, payload, fuel quantity, fuel reserves, and cruise flight level
•
ZFW = OWE + payload
• •
Fuel quantity must not exceed maximum fuel capacity
ZFW must not exceed MZFW If ZFW > MZFW, payload must be reduced
Ramp Weight RW = ZFW + fuel quantity
• •
RW must not exceed MRW If RW > MRW, fuel or payload must be reduced
Payload-range and Cost Index
14
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
15
Payload-range – Range calculation (Cont’d) Climb from 1500 ft to top of climb (initial cruise flight level)
Climb time, distance and fuel are calculated or obtained from manufacturer’s climb data •
Weight at top of climb = WTOC = WETO – climb fuel
•
Verify that r/c at top of climb meets minimum required r/c (reduce cruise flight level if minimum requirement is not met)
•
Determine weight at beginning of approach and landing WBAL
Approach and landing fuel and time are calculated or specified •
WBAL = LW + approach and landing fuel
•
Payload-range and Cost Index
16
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
17
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
18
Payload-range – Range calculation (Cont’d)
Payload-range and Cost Index
19
Payload-range – Payload-range diagram A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
20
Payload-range – Payload-range diagram (Cont’d) A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
21
Payload-range – Payload-range diagram (Cont’d) A
A
12000
MZFW Limit
B
MTO W
8000
Lim it
C M el Fu . t ax imi L
Payload - lb
16000
4000 0 0
1000
2000
3000
D
Range - nm
Payload-range and Cost Index
22
Payload-range – Payload-range diagram (Cont’d)
Payload-range and Cost Index
23
Cost index
Payload-range and Cost Index
24
Cost index - Introduction We can now calculate the fuel and time required for a given mission using various assumptions regarding operation of the aircraft: • • • •
Climb speed Cruise altitude Cruise speed Descent speed
Operationally, it is desirable to select assumptions such that operating costs will be minimized
The Cost Index concept is used by many airlines as a means to select optimum operating conditions and to minimize operating costs
Payload-range and Cost Index
25
Cost Index - Economy Speed Cost components • Crew - f(time) • Fuel - f(time,L/D,TSFC) • DMC - f(time,rating) • Ldg/Nav - f(weight)
Economy speed is the speed that minimizes total (time+fuel) costs Fuel + Time
Cost
Fuel
Time Max SAR
Economy
VMO / MMO
Block Speed Payload-range and Cost Index
26
Cot Index - Economy Speed Sample Calculation
767-200 at 35,000 feet Weight - 310,000 pounds Time-related costs - $500 per flight-hour Fuel costs - $.10 per pound
100 NM
Mach
0.75
0.77
0.79
0.81
0.83
Knots TAS
432
444
455
467
478
SAR – NM / lb
0.0446
0.0448
0.0447
0.0436
0.0408
Time - hours
0.231
0.225
0.220
0.214
0.209
Fuel - Pounds
2,242
2,230
2,235
2,294
2,451
Time-related cost - $
115
113
110
107
105
Fuel cost - $
224
223
224
229
245
Total cost - $
340
336
334
336
360
Payload-range and Cost Index
27
Cost Index – Derivation of Cost Index Cash or Direct Operating Cost
time related cost component
fixed cost component
III C=C I p f W fu e C l fuel price
block fuel
dW fuel
dC d I dWfuel = C + pf =0 dt dt dt
dt
=− min cos t
differential eqn for min. cost
CI = −
I C pf
One Onenumber numberserves servesto toidentify identifythe theeconomy economy flight flighttechnique techniquefor forall allmissions missions Payload-range and Cost Index
28
C I pf
Cost Index – Derivation of Cost Index (Cont’d)
In practice, Cost Index (CI) is calculated as follows in the American environment:
CI = (Time-related cost) / (Fuel cost) CI = ($ / flight hour) / [ $ / (lb of fuel) * 100 ]
CI is a fixed value for a given airline and a given aircraft type
CI can be calculated for the previous example:
• •
Time-related cost = 500 $ / hour Fuel cost = 0.10 $ / lb of fuel
CI = 50
Payload-range and Cost Index
29
Cost Index - Block Fuel-Time Curve
Block Fuel
• Many flight techniques share the same Cost Index • Flight technique with Distinct flight techniques; minimum fuel for given each denotes a given Cost Index is min. cost climb schedule,
Minimum Time
initial cruise altitude, cruise speed, step profile and descent schedule
Optimum altitude or Maximum service ceiling Increasing Altitude
Minimum Fuel
High speed climb and descent modes combined with Max. Cruise to intermediate cruise speeds
Intermediate to low speed climb and descent modes combined with intermediate to Max (or Long) Range Cruise speeds
Block Time Payload-range and Cost Index
30
Cost Index Values for Various Equipment
COST INDEX
High-speed Prop
COST INDEX
COST INDEX
50-seat Turbofan 70/90-seat Turbofan
COST INDEX
COST INDEX
COST INDEX
MD-80
B757
A300
Payload-range and Cost Index
COST INDEX
B737
COST INDEX
B747 31
50
Co st I nde x=
0
Performance Document Presentation for Climb
0 10
common initial climb
Some observations • Objective is least cost to climb to common cruise point • Max RoC (steeper trajectory) & min. fuel with Cost Index Zero • CLB thrust decrease = slower economy climb speed • Tailwind = slower economy climb speed
Payload-range and Cost Index
32
common cruise point
Performance Document Presentation for Cruise
Fixed Altitude
Some observations • Cost Index promotes less variation in Mach as AUW decreases • Tailwind = slower economy cruise speed Payload-range and Cost Index
33
Performance Document Presentation for Descent
100
50
common Co st cruise point Ind ex
=0
common EoD @ common speed
Some observations • Objective is least cost to descend from common cruise point • Max RoD (steeper trajectory) at high Cost Index Payload-range and Cost Index
34
Identifying Economy Flight Techniques: CRJ700, 1000 nm Sector Example Optimum Altitude
Flight Level
TOC
Trajectory A: Minimum Fuel CLB Mode L, MRC and DES Mode L
Trajectory B: Intermediate CLB Mode L, MCRZ and DES Mode L
BOD
Trajectory C: Minimum Time CLB Mode H, MCRZ and DES Mode H
Cruise Soaking
Origin
Destination
Payload-range and Cost Index
35
Identifying Economy Flight Techniques: CRJ700, 1000 nm Sector Example (Cont’d) 9800 9600
CLB Mode H MCRZ @ FL 310 DES Mode H
9400
Block Fuel (lb)
9200
mean curve
9000 8800
CLB Mode H MCRZ @ FL 390 DES Mode H
8600 8400
CLB Mode L MCRZ @ FL 390 DES Mode N
8200 8000
CLB Mode L Close to MRC @ FL 390 DES Mode L
Cost Index = 22 7800 7600 150
152
154
156
158
160
162
164
166
168
Block Time (min.)
Based on input crew cost, engine/airframe maintenance cost, materials cost, reserves and typical fuel price ==> Cost Index = 22
Optimal technique in ISA, still air corresponds to CLB Mode L / MCRZ @ opt. FL / DES Mode N
Payload-range and Cost Index
36
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