The Breguet range equation - use and abuse

Abstract

Purpose – The background of the Breguet Range Equation is presented to a level of detail usually not discussed. The presentation explains how the equation can be used correctly, producing good results. This is contrasted with examples of wrong usage, leading to wrong results and wrong conclusions. The Breguet Range Equation is abused, when it is applied incorrectly on purpose to manipulate the audience. --- Methodology – The Breguet equation calculates the range (R) of a powered aircraft from a fuel mass used together with cruise speed (V), glide ratio (E=L/D) and specific fuel consumption (c). Fuel mass used is the difference between initial mass (m_1) and final mass (m_2). Aircraft mass changes as fuel is consumed. With changing mass, lift, drag, thrust, and specific fuel consumption change. As such, range follows from integration. For a jet aircraft: R = VE/(cg) ln(m_1/m_2) with earth acceleration (g). For propeller aircraft a similar equation is derived. This and more follows from first principles. Statistics and handbook methods are applied when considering how glide ratio, E(V) and specific fuel consumption, c(V) depend on speed (V). Optimum speed for a jet aircraft is calculated from real world data numerically and analytically. --- Findings – At first glance, it seems as if range would increase proportionally with speed, but this is wrong. The interpretation ignores that glide ratio, E is a function of speed (and of Mach number). Furthermore, also Thrust Specific Fuel Consumption (c=SFC=TSFC) is a function of speed, which already follows from first principles. TSFC and L/D depend on cruise altitude. The optimum speed for a jet is lower than the classical 1.316 minimum drag speed. The factor is closer to 1.1. The inverse of the Breguet equation calculates the fuel used for a given range. This still ignores that aircraft are not optimized for low fuel consumption, but for minimum Direct Operating Costs (DOC). The equation's name is a misattribution. It should be called Devillers-Coffin Equation. --- Research limitations – The presentation shows dependencies based on first principles, statistics, and handbook methods. It shows the need for optimization in overall aircraft design. --- Practical implications – The presentation intends to give a better understanding of the Breguet Range Equation. It also shows that a fuel metric based on range and the Breguet Range Equation is only one of many definitions for a fuel metric. --- Social Implications – A better understanding avoids becoming a victim of an abused interpretation of the Breguet Range Equation. --- Originality – A similar investigation is not known.