Cruising for Range and Endurance Flashcards
Thrust and Power Required
● Jet engines produce Thrust, and reciprocating engines produce Engine Power.
● If we plotted the Thrust or Power Required to keep these airplanes at a constant altitude in the air, then we would see that there are some differences.
● These differences appear slight at first, but they are significant enough to lead to differing curves.
○ In turn, they lead us to slightly different answers when discussing range and endurance.
○ Jet engines are more efficient at high speeds and high altitudes, while props are more efficient at lower speeds and lower altitudes
Endurance
● Endurance indicates the amount of time one can stay airborne at a given power setting.
● Maximum Endurance would be the LONGEST we could possibly stay in the air.
○ In this case, we desire the lowest power setting that allows us to maintain our altitude.
○ It has a specific speed, and a specific angle of attack.
● Maximum endurance ALWAYS occurs at the lowest point on the power or thrust required curve.
○ Jets and Props are both the same in this respect
● It is important to remember that this does not correspond to an airspeed that is just above the stall.
○ Such a speed would be in the slow flight window, and we need additional power to overcome the induced dragthat flying in slow flight creates.
● Rule of thumb:
○ Best Endurance:
■ Single-engine fixed gear: 1.2 * Vs
■ Single/Twin retractable: 1.3 * Vs
○ NOTE: Vs = the CAS power-off, flaps-up stall speed
● For reciprocating prop driven airplanes, lower altitudes will always result in greater endurance for that engine.
○ Think about the fuel that we waste at full power in the climb.
● This rule does not apply to turbine engines, as they are designed for thinner air at higher altitudes.
○ They end up having a greater endurance when they are high and fast
● Wind does not change our endurance.
● Turbulence is a different story.
○ Frequent changes in power will be required to maintain altitude in these conditions.
● Turns can also result in a loss endurance.
○ We will tend to lose our altitude–need to increase our power, and this will give a corresponding decrease in our endurance
Range
● Range is the distance attainable at a specific cruise setting.
○ There are many variables that will cause our range to change.
○ Fuel Flow, Altitude, Weight, and center of gravity location are but a few
Maximum Range
● Maximum range occurs where the ratio between the thrust required (or power required) and the velocity required to maintain our altitude is at its lowest
● For a prop driven aircraft, this occurs at the maximum Lift/Drag ratio.
○ This value corresponds to a constant angle of attack
● For a jet driven aircraft, the story of maximum range is slightly different.
● Notice, however, the value for maximum range is still a specific angle of attack
It happens where sqrtCL/CD is at max value
● Remember, the speed for maximum range for a jet still occurs at the same point where we find the lowest proportion of thrust in relation to velocity.
○ This will, however, be at a MUCH higher speed than in comparison with piston airplanes
Maximum Range and Weight
● As we fly, both jets and reciprocating planes burn their fuel, and this will lead to a decrease in weight.
● For a prop driven aircraft, this has the effect of changing our best L/D value to a lower airspeed.
● In either the case of thrust or power, take care to note and remember that the angle of attack to achieve our maximum range does not change with our weight
Maximum Range and Altitude
● As we climb, this will mean that we will need a higher true airspeed to maintain this angle of attack.
● However, this also means that the indicated airspeed for maximum range will not change with our altitude.
● As we have seen, with a typical wing design, the angle of attack for best range will be somewhere between 4 - 6
Maximum Range: Rules of Thumb
● Using the calibrated power-off stalling speed (wings level and flaps up), an estimate may be made for the speed to fly for maximum range:
○ Single-engine, fixed-gear
■ 1.5 * Vs
○ Single-engine, retractable
■ 1.8 * Vs
○ Twin-engine, retractable
■ 1.7 * Vs
Range Factors
● Engine efficiency also plays a part in determining range.
● Best range then = (C L / C D ) * Efficiency / bsfc
○ bsfc: brake specific fuel consumption
Range
● Due to this engine efficiency, altitude is a primary factor in determining and extending our range when it comes to turbojets.
● Specific Air Range (SAR):
○ This is the number of Nautical Air Miles flown per pound of fuel burned
○ SAR = True Airspeed (kts) / Fuel Flow
● Specific Ground Range (SGR):
○ This is the number of Nautical Ground Miles flown per pound of fuel burned
○ SGR = Groundspeed (kts) / Fuel Flow
Range: Compensating for Wind
● A headwind will always decrease the range!
● A tailwind–of course–will always increase the range!
● That said, flying round trip will not “balance things out.”
○ This is because we are affected longer by the headwind than the tailwind.
● We do, however, have a few rules of thumb:
○ Increase our airspeed 5% when flying into strong headwinds, and,
○ Decrease our airspeed 5% when flying with a tailwind
Factors Influencing Range / Endurance
● Fuel Available
● Angle of Attack / Airspeed
● Weight
● Center of Gravity
● Altitude
● Engine efficiency
● Wind
Center of Gravity
● Horizontal stabilizer provides a downward force to offset the lift and weight force couple
● Forward CofG requires more downward force on the horizontal stabilizer
○ Results in a reduced range because more lift is required
○ Position of trim tab and elevator increase drag
● Rearward center of gravity improves range but decreases pitch stability
Altitude
● For a piston/recip aircraft the best altitude to fly depends on the length of the trip and the upper winds.
● Range for reciprocating engines may be improved by choosing higher altitudes, allowing the engine to run more efficiently and reducing our air resistance.
● Maximum endurance for reciprocating engines is at sea level or as close as practical to sea level
● Climbing to a higher altitude is not always a good idea as the fuel saved at higher altitudes may not make up for the fuel burned in the climb
Weight
● Range and endurance both improve with a decrease in weight–prop or jet.
● That said, an increase in weight will also require an increase in airspeed to get our max values for these
increased weight = increased induced drag = more lift required
Range: Turboprop Engines
● More fuel efficient at high altitudes where the air is cold.
● More efficient at higher power settings
Range: Turbo-jet Engines
● Engine efficiency improves with altitude
○ Air temperature decreases.
○ A greater RPM is required to generate the speed for best endurance – Jet engines are designed to run at high RPMs
