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I'm wondering what would be a rough rule of thumb for calculating the fuel consumption of a modern airliner like a Boeing 737 - 300.

I am not asking for anything from the plane's manual or even a rule of thumb to be used by pilots, but rather a "general idea", to be able to compare the fuel consumption of different modes of transportation.
I am citing the Boeing 737 - 300 as an example as it is a pretty common type of airplane, but feel free to answer for another type of passenger aircraft.

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Here are some very rough values for the 737-300, that a certain airline uses to compute manual flight plans in case the computer system fails.
Climb - 2950lbs / 15mins
Cruise - 5500lbs/hr
Descent - 600lbs / 20mins
Hold - 2650 / 30mins
Alternate - 1950 / 20mins
Min arrival fuel - 6300lbs
Recomended arrival fuel - 8300lbs
These numbers were based on a 27000lbs payload (approx 130pax plus bags)

source: http://www.airliners.net/forum/viewtopic.php?t=722273

[EDIT: I've edited the answer to remove any mention of the 737-300 being one of the most common 737 variants, thanks for the constructive comments!]

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    $\begingroup$ I would bet my house that the 737-300 is no longer the most common 737! That thread is 16 years old now. Still interesting data though. $\endgroup$ – Ben Dec 26 '16 at 22:38
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    $\begingroup$ @Ben According to Wikipedia, there were 1113 -300s built, delivered between 1984 and 1999. Since the introduction of the Next Generation 737s (-700/800/900) in 1997, nearly four times that many -700s have been built and a good number of the Classics will probably have been retired. So, yeah, the -300 is nothing like the most common today, and Boeing is cranking out new -700s at a rate of more than one a day. $\endgroup$ – David Richerby Dec 26 '16 at 22:45
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For a first approximation, use 55 to 65 g of fuel per Newton-hour or 15 to 18 g per kN of thrust per second with modern jet engines. Please do not use the static thrust at sea level, but the actual thrust at the right flight Mach number and altitude. If you lack this figure: A modern airliner needs thrust equivalent to between 1/15th (6.67%) and 1/20th (5.0%) of its weight. In cruise flight at Mach 0.82 a value of approximately 1/17th (5.9%) should be used.

Thrust-specific fuel consumption nearly doubles between the static case and cruise at Mach 0.82, and the maximum thrust of the engines is roughly proportional to air density, which is a quarter of its sea level value at cruise altitude (approx. 10 km). The best turbofans achieve 9 g per kN and second in static tests!

If you want to calculate the fuel consumed over a longer trip, use the Breguet range equation and reformulate it so you get the mass ratio between take-off ($m_1$) and landing mass ($m_2$) for a given range $R$. For jets this equation is $$\frac{m_1}{m_2} = e^{\frac{R\cdot g\cdot b_f}{v\cdot L/D}}$$

Nomenclature:
$m\:\:\:\:$ mass in [kg]
$R\:\:\:\:$ Range in [m]
$g\:\:\:\:\:$ gravitational acceleration in [m/s²]
$b_f\:\:\:$ thrust-specific fuel consumption in [kg/Ns]
$v\:\:\:\:\:$ ground speed in [m/s]
$L/D\:$ lift-to-drag ratio

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  • $\begingroup$ Great, very detailed answer. A little tough to do without a calculator (or at least pen and paper), though. $\endgroup$ – John D Dec 28 '16 at 22:00

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