Joined: 11 Dec 2005
|Posted: Mon Apr 09, 2012 3:43 am Post subject: Optimum Range, Altitude and Endurance for Propeller Aircraft
| Specific Fuel Consumption:
Prop SFC = Fuel Flow / Power.
Turboprop SFC (like jets) decreases with altitude.
Piston SFC decreaes to full throttle height. After this fuel consumption increases.
Best SAR for a propeller is when maximum distance is covered for a unit of fuel.
SAR = TAS / Fuel Flow
For a propeller:
SFC = Fuel Flow / Power
Fuel Flow = SFC x Power
Combining the two:
SAR = TAS / (SFC x Power)
Power Available = Thrust x TAS
Power Required = Drag x TAS
In an unaccelerating flight, power available must be equal to power required.
SAR = TAS / SFC x (Drag x TAS)
According to the above formula we can observe two things:
1) Best SAR will be found at the best ratio of TAS/Power Required i.e. a tangent on the propeller power required curve (point of min drag).
2) SAR is inversely proportional to SFC (i.e. less SFC will give a better SAR).
Piston engines give their best SFC with:
- High Intake pressure.
- Low RPM.
- Throttle wide open.
These conditions will give too much power at low levels.
So at higher level there wil be a point where the power required to fly the best range speed is achieved with full throttle, weak mixture and cruise RPM selected.
This is full throttle height, the point of best SFC and maximum SAR.
Range initially decreases with altitude but starts to increase again at level where full throttle is reached.
Greater ranges are possible with low power settings.
Best SAR will be at medium altitude at the recommended Flight Manual speed for range flying (10 to 20% above VMD).
Turboprops run at a constant maximum continuous RPM (MCRPM).
Their thermal efficiency improves with lower intake temperatures.
Engine efficiency increases slightly with increasing speed.
Best SAR will be obtained by flying at medium altitude.
From this point on best SAR will be maintained, as weight decreases, in a cruise climb while holding MCRPM.
Best endurance is the minimum power required to maintain level flight.
Best endurance speed is the minimum power speed, VMP.
It is the point where the product of speed and drag are at a minimum.
VMP is always less than VMD and therefore speed unstable.