# WORHP Kata of August 2023: Tsiolkovsky rocket equation ⌚ 2023-08-01

A kata (in the context of programming) is a small training unit to practise coding. In this series of**WORHP Katas**we present standard problems of optimization which you can use to get familiar with optimization (and our optimization software WORHP).

**Kata:**The Tsiolkovsky rocket equation computes the maximum change of velocity of a rocket:

This equation also applies for rockets with more stages, for which the velocity gains in all stages are added.

Here is our optimization problem: The stages of an -stage rocket have the masses , where (in arbitrary units) and each consists of 90% of propellant. After burning the first stage (and gaining the velocity) the hull of the first stage is pushed away, and the second stage is ignited, etc. The payload is , and the effective exhaust velocity of all stages is the same.

What is the maximum change of velocity which a 2-stage or 3-stage rocket can gain?

*A solution will be provided with the next WORHP Kata.*

**Solution of last WORHP Kata:**If is a solution to the queens puzzle, these constraints have to be fulfilled:

exactly one queen in each column: | ||

exactly one queen in each row: | ||

not more than one queen on each downward diagonal/subdiagonal: | ||

not more than one queen on each upward diagonal/subdiagonal: | ||