SFC or TAS
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SFC or TAS
Doing some study for up coming interviews later in the year and would like some response to the following question which seems all to common but many varied responses.
Q. What is the optimum altitude for a turbofan engine.
Ideas have been height for best TAS whilst others say best Specific Fuel Consumption. What really determines the best altitiude to fly at. Answers greatly appreciated
Q. What is the optimum altitude for a turbofan engine.
Ideas have been height for best TAS whilst others say best Specific Fuel Consumption. What really determines the best altitiude to fly at. Answers greatly appreciated
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Jet engine specific fuel consumption (SFC) is the amount of fuel that is consumed per hour to produce each pound of thrust. SFC is lowest when the engines are operating within the 85% to 95% RPM range. As RPM increases above or decreases below this range SFC increases.
Maximum jet aircraft range in still air is achieved when flying such that the TAS:drag ratio is maximised and the SFC is minimised. The best TAS rag ratio occurs at about 1.32 of the minimum drag speed (VIMD). This is the maximum range cruise speed (MRC). So maximum range cruise in a jet aircraft is achieved by flying at MRC at the altitude at which the drag at this speed is equal to the thrust produced at 85% to 95% RPM.
Because of the shape of the TAS:drag curve it is possible to increase speed within a narrow band, without incurring significant drag increases. At 1.05 VMRC, for example, the range is still close to 99% of its maximum value. Similarly. Within the 85% to 95% RPM band, changes in RPM cause very little change in SFC. So there is a narrow band of speeds around the MRC, in which the range is very close to maximum.
But the total cost of operating an aircraft is not just the fuel costs. It also includes other factors such as equipment running costs and crew costs. Getting passengers to their destinations more quickly than your competitors do, also has a cash value. 1.32 VIMD is a comparatively low speed, so non-fuel costs can be reduced by flying faster and reducing flight duration. For greatest overall efficiency (lowest total costs) it is necessary to fly faster in order to trade off increasing fuel costs against decreasing non-fuel costs
So aircraft usually fly at a speed slightly higher than the MRC to reduce flight time whilst retaining a good level of efficiency. This is achieved by flying at the long range cruise speed (LRC). The actual value of the best speed for a given flight depends upon the distance to be flown and the relationship between fuel costs and non-fuel costs.
The numbers quoted above are all generally recognised approximations. Other factors such as the onset of rapidly increasing shock-induced drag at speeds above MCDR will determine the actual values for each aircraft type.
Maximum jet aircraft range in still air is achieved when flying such that the TAS:drag ratio is maximised and the SFC is minimised. The best TAS rag ratio occurs at about 1.32 of the minimum drag speed (VIMD). This is the maximum range cruise speed (MRC). So maximum range cruise in a jet aircraft is achieved by flying at MRC at the altitude at which the drag at this speed is equal to the thrust produced at 85% to 95% RPM.
Because of the shape of the TAS:drag curve it is possible to increase speed within a narrow band, without incurring significant drag increases. At 1.05 VMRC, for example, the range is still close to 99% of its maximum value. Similarly. Within the 85% to 95% RPM band, changes in RPM cause very little change in SFC. So there is a narrow band of speeds around the MRC, in which the range is very close to maximum.
But the total cost of operating an aircraft is not just the fuel costs. It also includes other factors such as equipment running costs and crew costs. Getting passengers to their destinations more quickly than your competitors do, also has a cash value. 1.32 VIMD is a comparatively low speed, so non-fuel costs can be reduced by flying faster and reducing flight duration. For greatest overall efficiency (lowest total costs) it is necessary to fly faster in order to trade off increasing fuel costs against decreasing non-fuel costs
So aircraft usually fly at a speed slightly higher than the MRC to reduce flight time whilst retaining a good level of efficiency. This is achieved by flying at the long range cruise speed (LRC). The actual value of the best speed for a given flight depends upon the distance to be flown and the relationship between fuel costs and non-fuel costs.
The numbers quoted above are all generally recognised approximations. Other factors such as the onset of rapidly increasing shock-induced drag at speeds above MCDR will determine the actual values for each aircraft type.
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HEALY,
To follow on from Keith.Williams'. excellent answer -
There are a multitude of Optimum Altitudes for the Jet aircraft, it all depends upon the chosen Speed Schedule. Speed Schedules vary considerably, for example -
(1) Minimum Fuel (Maximum Range Cruise),
(2) Minimum Time (High Speed Cruise),
(3) Minimum Cost (Best Time / Fuel compromise), variable on any given flight.
(Long Range Cruise, i.e. 99% of Optimum Maximum Range Cruise, is a simplified version of Minimum Cost operations).
Each of the above will have a different Optimum Altitude, and in the case of Minimum Cost, will have considerable variation depending upon the Cost Index for a specific flight. Periodic checks of the FMC in cruise, examining all of the above options, will indicate differing Optimum Altitudes for each case.
Considering still air conditions, the Optimum Altitude for each of the above speed schedules, excepting Minimum Time, will steadily increase as the aircraft becomes lighter. Minimum Time operations, i.e. Maximum TAS, will be at a fixed Pressure Height, that is the P.H. at which the scheduled High Speed CAS equals the High Speed Mach Number.
Regards,
Old Smokey
To follow on from Keith.Williams'. excellent answer -
There are a multitude of Optimum Altitudes for the Jet aircraft, it all depends upon the chosen Speed Schedule. Speed Schedules vary considerably, for example -
(1) Minimum Fuel (Maximum Range Cruise),
(2) Minimum Time (High Speed Cruise),
(3) Minimum Cost (Best Time / Fuel compromise), variable on any given flight.
(Long Range Cruise, i.e. 99% of Optimum Maximum Range Cruise, is a simplified version of Minimum Cost operations).
Each of the above will have a different Optimum Altitude, and in the case of Minimum Cost, will have considerable variation depending upon the Cost Index for a specific flight. Periodic checks of the FMC in cruise, examining all of the above options, will indicate differing Optimum Altitudes for each case.
Considering still air conditions, the Optimum Altitude for each of the above speed schedules, excepting Minimum Time, will steadily increase as the aircraft becomes lighter. Minimum Time operations, i.e. Maximum TAS, will be at a fixed Pressure Height, that is the P.H. at which the scheduled High Speed CAS equals the High Speed Mach Number.
Regards,
Old Smokey
