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consume less fuel when flown slower or when flown higher. However there are
limits to these laws. Flying lower than the maximum range speed will increase the
block fuel, as will flying higher than an optimum altitude.
Block Fuel and Time for various Flight Levels and Mach numbers
A330-223 ISA 3000nm Payload 30000kg JAR Reserves
35000
37000
39000
41000
43000
45000
360 380 400 420 440 460 480 500 520 540 560
Block Time - minutes
Block Fuel - kg
Green Dot
Max Speed
Range
Long
Range
M 0.78
M 0.80
M 0.82
Flight
Level
250
270
290
310
330
350
370
Getting to grips with Fuel Economy IN FLIGHT PROCEDURES
- 37 -
5.3.2 CRUISE ALTITUDE OPTIMISATION
In examining SR changes with the altitude at a constant Mach number, it is
apparent that, for each weight, there is an altitude where SR is maximum. This
altitude is referred to as “optimum altitude”.
Optimum Altitude Determination at Constant Mach Number
When the aircraft flies at the optimum altitude, it is operated at
the maximum lift to drag ratio corresponding to the selected Mach number.
High Speed Polar Curve
When the aircraft flies at high speed, the polar curve depends on the indicated Mach
number, and decreases when Mach increases. So, for each Mach number, there is a different
value of (CL/CD)max, that is lower as the Mach number increases.
M=0.84
M = 0.82
M = 0.86
M <0.76
Pressure
Altitude
5 - IN FLIGHT PROCEDURES Getting to grips with Fuel Economy
- 38 -
When the aircraft is cruising at the optimum altitude for a given Mach, CL is
fixed and corresponds to (CL/CD)max of the selected Mach number. As a result,
variable elements are weight and outside static pressure (Ps) of the optimum
altitude. The formula expressing a cruise at optimum altitude is:
constant
P
Weight
s
=
In the FCOM Flight Planning Chapters the optimum altitude is
shown on the Cruise Level chart for 2 or more speeds. This chart also shows the
Maximum Altitudes as limited by performance and buffet. A typical FCOM chart
showing the variation of optimum altitude with weight for one speed is shown
below.
It should be noted that the influence of airspeed on optimum altitude is not
very significant in the range of normal cruise speeds.
In order to minimize fuel burn, the aircraft should therefore be flown at the
optimum altitude. However this is not always possible. Performance limitations
such as rate of climb or available cruise thrust can lead to a maximum altitude
below the optimum, as can buffet limitations. At low weights, the optimum
altitude may be above the maximum certificated altitude. In addition, Air Traffic
Control restrictions can affect the flown flight level.
Getting to grips with Fuel Economy IN FLIGHT PROCEDURES
- 39 -
The following table shows the specific range penalty of not flying at optimum
altitude, assuming a cruise Mach No of 0.8. It should be noted that each
airframe/engine combination has different values. It should be noted that these
are average values and there are slight variations with different weight/optimum
altitude combinations.
Specific Range Penalty for not flying at Optimum Altitude
Aircraft +2000ft -2000ft -4000ft -6000ft
A300B4-605 2.0% 0.9% 3.4% 9.3%
A310-324 1.9% 1.4% 4.4% 9.3%
A318-111 0.7% 1.6% 5.0% 10.0%
A319-132 1.0% 3.0% 7.2% 12.2%
A320-211 ** 1.1% 4.7% 9.5%
A320-232 1.4% 2.1% 6.2% 12.0%
A321-112 2.3% 1.4% 4.6% 15.2%
A330-203 1.8% 1.3% 4.2% 8.4%
A330-343 3.0% 1.0% 3.2% 7.2%
A340-212 1.4% 1.5% 4.0% 8.0%
A340-313E 1.5% 1.6% 5.2% 9.5%
A340-642 1.6% 0.6% 2.2% 5.1%
** Above Maximum Altitude
Generally if one flies within 2000ft of optimum altitude, then the specific
range is within about 2% of the maximum. However fuel burn-off is an important
consideration.
Consider an A340-313E at a weight such that the optimum altitude is
33000ft. If the aircraft flies at FL 310 the SR penalty is 2.1% for the weight
considered. However after a fuel burn of 20800kg, during which the aircraft would
have traveled 1400nm the optimum altitude increases to 35000ft and the penalty
is now 5.2%.
There is also an effect on block time due to the different altitudes. The true
air speed increases/decreases 4kts, or just under 1% for each 2000ft lower/higher
cruise altitude.
5 - IN FLIGHT PROCEDURES Getting to grips with Fuel Economy
- 40 -
5.3.2.1 CROSS-OVER ALTITUDE VERSUS OPTIMUM ALTITUDE
It has been previously shown that the TAS is the maximum at the crossover
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