An English translation of L. Euler's "Calculations on aerostatic balloons made by the late Mr. Leonhard Euler, as they were found on his blackboard, after his death on 7 September 1783"

TL;DR

This paper presents an English translation of Euler's 18th-century work on aerostatic balloons, including his original formulas for calculating maximum altitude, velocity, and ascent time based on force balance analysis.

Contribution

It provides the first English translation of Euler's original Latin text on balloon calculations, clarifying historical scientific methods.

Findings

Formulas for maximum altitude and velocity derived from force balance.

Closed-form expressions for ascent time.

Historical insight into 18th-century aerostatics.

Abstract

This is an English translation of E579 in which the introductory remarks are in French, while Euler's original text is in Latin. By considering the balance of forces acting on a raising balloon on an isothermal atmosphere, namely the weight of the balloon, the buoyant force, and the aerodynamic drag force, Euler provides closed formulas for the calculation of the maximum altitude reached by the balloon, the altitude for which the velocity is maximum, the maximum velocity attained by the balloon, and the total ascending time.