Question

Using the Breguet range and endurance equation, estimate the amount of kerosene
fuel needed for an aircraft weighing 10 metric tons (this is the dry weight that
includes passengers and cargo) to fly from Boston to Los Angeles, assuming a
distance of 5,000 [km], flying at 300 [m/s].
Assume a lift-to-drag ratio of 15 - this is the ratio of lift force over drag force during
the cruise, the overall efficiency of 0.3, and about half of the standard air density at
an altitude of approximately 6,000 [m]. You can neglect the climb and descent
phases of the flight. The energy density of kerosene is provided in Module 9, section
3: "The Breguet range and endurance equation". Why is this a tricky calculation?

Answer 1

The amount of kerosene fuel needed for an aircraft weighing 10 metric tons to fly from Boston to Los Angeles, assuming a distance of 5,000 [km] is 10000 kg.

What is Breguet equation?

Breguet equation is used to determine the range of airplane fly in some specified set of parameters.

$R=\dfrac{h_f}{g}\dfrac{L}{D}\times \eta \ln \left(\dfrac{W_{initial}}{W_{final}}\right)$

Here, (L/D) is lift to drag ratio, g is gravitation acceleration, h is height and W is weight.

The weight of aircraft is 10 metric tons (this is the dry weight that includes passengers and cargo)  The distance of 5,000 [km], with velocity at 300 [m/s]  from Boston to Los Angeles has to be cover by the airplane.

The initial weight is 10 metric tons or 10000 kg. Thus, the final weight with total fuel burn is,

$W_{final}=W_{initial}-W_{fuel}\\W_{final}=1-\dfrac{W_{fule}}{W_{initial}}$

The lift-to-drag ratio is 15 and the overall efficiency is 0.3,  The standard air density at an altitude of approximately 6,000 [m] is half.

Thus, put the values, in above formula,

$5000=\dfrac{6000}{9.81}(15)\times(0.3) \ln \left(\dfrac{10000}{1-\dfrac{W_{fuel}}{10000}}}\right)$

$\ln \left(\dfrac{10000}{1-\dfrac{W_{fuel}}{10000}}}\right)=1.8167\\\ln \left(\dfrac{1}{10000-W_{fuel}}}\right)=1.8167$

Solving this equation, we get,

$W_{fuel}=10000\rm\; kg$

Thus, the amount of kerosene fuel needed for an aircraft weighing 10 metric tons to fly from Boston to Los Angeles, assuming a distance of 5,000 [km] is 10000 kg.

Learn more about the Breguet equation here:

https://brainly.com/question/15218094

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