Range and Endurance
Dr. Vijay Kumar Patidar
Range:
• Range is the total distance travelled by an airplane on one load of fuel.
• Consider the following weights:
W0 = gross weight of the airplane including everything; full fuel load,
payload, crew, structure, etc..
Wf = weight of fuel; this is an instantaneous value, and it changes as
fuel is consumed during flight.
Wi = weight of the airplane when the fuel tank is empty.
• At any instant during the flight, the weight of the airplane W is:
W = Wi + Wf
• Since Wf is decreasing during flight, W is also decreasing. The time
rate of change of weight is:
• Where dWf/dt is negative numbers because fuel is being consumed,
and hence both W and Wf are decreasing.
• Range is connected with engine performance through the specific fuel
consumption.
• The specific fuel consumption is a technical figure of merit for an
engine which reflects how efficiently the engine is burning fuel and
converting it to power.
• SFC = c = weight of fuel burned per unit power per unit time (N/W.s)
• For a propeller-driven/reciprocating engine combination, the specific
fuel consumption is:
Where P is the shaft power and the minus sign is necessary because
weight of fuel consumed is decreasing.
• For jet propelled aircraft, the thrust specific fuel consumption is:
Where T is thrust available. However c, can be expressed in terms of ct:
Where ηpr is the propeller efficiency.
Calculation for Range:
• Consider an airplane in steady, level flight. Let s denote the horizontal
distance covered over the ground. Assuming a stationary atmosphere,
the airplane velocity is V:
• Also dWf = dW
• The range of the airplane can be calculated between s = 0, where the
fuel tanks are full and hence W = W0, and s = R, where the fuel tanks
are empty and hence W = W1.
• The above equation is called Breguet range equation.
• For largest possible range: highest possible velocity, maximum L/D.
Range for Propeller driven airplane:
• Replace ct with c:
• For an propeller driven airplane, for the largest possible range: fly at
maximum L/D, highest possible propeller efficiency, lowest possible
specific fuel consumptions, highest possible gross weight to empty
weight ratio.
Range for Jet-Propelled Airplanes:
• Maximum range for a jet engine is not ditacted by maximum L/D, but rather the
maximum value of the product V (L/D).
• For straight and level flight:
• For maximum range: fly at maximum CL1/2/CD
• Have the lowest possible TSFC.
• Fly at high altitude.
• Carry a lot of fuel.
Endurance
• Endurance is the amount of time that an airplane can stay in the air on
one load of fuel.
• Since T = D and L= W in steady and level flight:
• Integrating from t = 0, where W = W0 to t = E, where W = W1
• The above is the general equation for endurance
• For preliminary performance analysis, we can assume ct and L/D is
constant:
Endurance for Propeller Driven aircraft
• The specific fuel consumptions for propeller airplane is given in terms
of power rather than thrust.
• Maximum endurance for a propeller driven airplane corresponds to the
following conditions:
• Fly at maximum CL3/2/CD.
• Have a highest possible propeller efficiency.
• Have the lowest possible specific fuel consumptions.
• Have a highest possible difference between W0 and W1 (i.e. carry a lot of fuel).
• Fly at sea level. Where density is largest value.
Endurance for Jet Propelled aircraft
• The below equation expressed in terms of thrust specific fuel
consumption and it gives the endurance for jet propelled airplane:
• For maximum endurance for a jet propelled airplane corresponds to
the following conditions:
• Fly at maximum L/D
• Have a lowest possible thrust specific fuel consumption.
• Have a highest possible ratio of W0 to W1 (i.e. carry a lot of fuel)
