I am looking for a mathematical model to estimate trip fuel required. I have searched the internet but not found any specific mathematical model as such. The question is formulated as follows:

Let $W_0$ be the weight of a particular aircraft with a given fixed set of technical specifications (say Boeing 737-800) without any fuel, passenger or cargo, $W_c$ be combined the weight of the passengers, their baggage and all additional cargo and $x$ be the flying distance (take off to touch down).


  • What are the best known mathematical models or algorithms to predict or estimate the minimum amount of fuel required $W_{f_{min}}$ in terms of $W_0, W_c$ and $x$ for this aircraft?

Assumptions: For simplicity, let us assume that the following conditions are true

  • Weather is perfect i.e. no additional fuel required due to bad weather

  • There is no air traffic due to which additional fuel is burned

  • The pilot is good and flies tries to minimize fuel consumption

  • In case any addition information is required or missing, please assume them in your answer and proceed.

  • $\begingroup$ There is no such formula because the engine efficiency is unknown. E.g. For the same zero-fuel weight and distance, new models of the same family achieve 15% better fuel efficiency. $\endgroup$
    – kevin
    Commented Nov 3, 2017 at 4:46
  • $\begingroup$ For the given aircraft, the model is fixed and so its technical specification including the engine efficiency is fixed. But we can do even better. Since engine efficiency is expected to decrease with time, for a particular aircraft's using its data, engine efficiency can be tracked as a time series to I don't see why this should be considered unknown. $\endgroup$ Commented Nov 3, 2017 at 5:05
  • 2
    $\begingroup$ The best know algorithm is the Breguet equation $\endgroup$
    – Koyovis
    Commented Nov 3, 2017 at 5:35