For constant speed level flight in the cruise the forces shown in the diagram below must equalise. THRUST LIFT WEIGHT DRAG LIFT LIFT UPLOAD DOWNLOAD
In the diagram above:
Thrust = Drag
Lift = Weight ± Tailplane force The tailplane force will depend upon the position of the CG:
Forward CG The more forward the CG the greater the download force required for balance, requiring greater lift. This increase in lift required will increase the induced drag which in turn will require a thrust increase.
Variation of Drag
The drag will vary with speed as shown in the diagram below. The minimum drag speed VIMD,
where CL/CD is at a maximum, is plotted on the graph. When plotting drag against IAS the
total drag does not change with pressure and temperature at a given mass. If the aeroplane mass is increased then the drag does increase and hence VIMD increases as well.
Endurance/Range
To begin the discussion on range and endurance it is best to give simple definitions initially: Endurance The time that an aeroplane can fly on a set amount of fuel
Range The distance that an aeroplane can fly on a set amount of fuel Piston Engined Aeroplanes
Maximum Endurance With a piston powered aeroplane the fuel flow can be said to be proportional to the power setting. The lower the fuel flow required the lower the power setting. In the power/speed graph shown below A defines the maximum endurance power and speed – the point where the power is a minimum to hold level flight. Drag Speed High Weight Low Weight VIMD
Maximum Range The maximum range speed is where the tangent from the origin touches the power/speed curve. This is where the ratio between the power and speed required is at a minimum – Point B.
Note that, this point where the ratio between the power and speed is a minimum is also the minimum drag speed.
Jet Engined Aeroplanes
For a jet powered aeroplane the fuel flow is proportional to the thrust setting. Power Speed A B Drag/Thrust Speed A B
Maximum Endurance speed is the point where the thrust required to maintain level flight is a minimum – Point A. This means that unlike the piston powered aeroplane the maximum endurance speed is the same as the minimum drag speed.
Point B represents the maximum range speed.
When the maximum endurance and maximum range speeds are plotted then the following must be noted:
¾ Even though the appearance of the graphs are the same visually:
Piston Aeroplanes The curve is plotted using power against speed Jet Aeroplanes Thrust versus speed is plotted
Range
Range is expressed as the distance traveled with the fuel available. The term Specific Range is used and is normally expressed as a relationship between TAS and fuel flow.
¾ In jet aeroplanes the fuel flow is dependent on the engine thrust ¾ In propeller aeroplanes the fuel flow is dependent on the engine power Both are related by the term Specific Fuel Consumption (SFC).
SFC can be calculated by the following:
Jet Aeroplanes TAS ÷ (SR x Thrust) Propeller Aeroplanes TAS ÷ (SR x Power)
For a jet aeroplane Thrust equals Drag and for a propeller aeroplane the power available must equal the power required. In real terms the SR depends upon the engine efficiency and the airframe efficiency.
Best Range Speed
Maximum range speed is where the tangent from the origin touches the Drag/Thrust against Speed curve for a jet aeroplane and Power against Speed curve for a propeller aeroplane. This occurs at:
¾ 1.32 VIMD for jet aeroplanes
¾ VIMD for propeller aeroplanes
This speed is not used in performance calculations as: ¾ Speed stability is poor
¾ A higher speed will not give a great loss in the range ¾ Higher speeds give a better time profile
Factors Affecting Range
The following affect the range of an aeroplane:
Wind Maximum range speed is affected by the change in groundspeed and the distance flown.
Headwind A higher maximum range speed is required. Thus the ground distance traveled will be less.
Tailwind A lower maximum range speed is required. The ground distance traveled will be more.
Weight Increased weight increases the drag and power. The greater the thrust the greater the fuel flow required which will decrease the SR.
Altitude
Jet Aeroplanes An increase in altitude will increase the range until the aeroplane reaches its optimum altitude. The increase in range with altitude happens because:
¾ Increase in TAS with altitude
¾ Increase in engine efficiency with altitude
The range will then decrease because as the aeroplane flies above the optimum altitude the drag increases and the specific range is reduced because of the increasing effects of compressibility.
As the aeroplane weight reduces so the optimum altitude increases.
Propeller Aeroplanes Altitude does not affect the propeller driven aeroplane as much as the jet aeroplane. The TAS and the power required increase with altitude. This ensures that the ratio TAS/Power Required remains the same. The range is affected by any change of SFC with altitude.
Temperature An increase in temperature will increase the TAS and reduce engine efficiency – both countering each other which means that there is little change in range for a change in temperature.
Endurance
The time that an aeroplane can remain airborne on a given amount of fuel.
Endurance is at a maximum when the fuel flow is at a minimum. Fuel flow depends upon: Jet Aeroplanes Thrust and SFC
Propeller Aeroplanes Power and SFC
Thrust and power are lowest when the drag and power required are least; VIMD and VIMP.
Factors Affecting Endurance The following affect endurance:
Weight The higher the weigh the higher the power required so endurance will decrease.
Altitude
Jet Aeroplanes An increase in altitude does not affect the drag. SFC improves with increasing altitude and thus endurance improves. Above optimum altitude compressibility increases and the drag increases and endurance reduces.
Propeller Aeroplanes As altitude increases, the power required increases but SFC will improve. The increase in power required will reduce the endurance, the SFC will improve it. The balancing out of these two effects means that the endurance is little affected.