Aerospace propulsion - Simplified laws for sizing, and examples of use

This article establishes and uses simplified design laws for cruise flight, acceleration, and initially propelled ballistic flight in various examples (rockets, missiles, but also aircraft, etc.).

Three formulas are used for unpowered flight (with an initial speed generally obtained by initial propulsion), gliding or ballistic flight. Examples show how important it is to understand the assumptions and verify that they are applicable before making significant errors in applying them. These formulas allow the introduction of aerodynamic finesse and the ballistic coefficient.

The other two formulas correspond to two specific cases of propulsion use: acceleration from one speed to another, or cruise flight (with two expressions whose authors remain famous: the Tsiolkovsky and Breguet formulas). The first allows the mass of propellant to be calculated for a missile booster or the speed reached by a multi-stage rocket. The second allows the range to be calculated based on the propulsion and aerodynamics of a missile or aircraft.

The simplified expressions in this article thus enable reliable but approximate pre-dimensioning, which will then be confirmed during a project using more accurate models and detailed trajectory calculations.

The examples and data provided are taken from the open literature, as the applications of these engines inevitably lead to restrictions on certain specific aspects of these propulsion systems from a commercial or military perspective. These include an anti-tank missile, passenger aircraft of varying speeds, the Saturn V rocket from the Apollo program, and an old intermediate-range ballistic missile.

A glossary of terms used can be found at the end of the article.