# Thrust to Power

## Description

Thrust is a reaction force described quantitatively by Newton’s second and third laws.

The power needed to generate thrust and the force of the thrust can be related in a non-linear way.

Note that these calculations are only valid for when the incoming air is accelerated from a standstill – for example when hovering.

The inverse of the proportionality constant, the “efficiency” of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid () and the density of the fluid (). This helps to explain why moving through water is easier and why aircraft have much larger propellers than watercraft do.

## Variables

P | power needed to generate thrust (W) |

T | thrust generated (force) (N) |

ρ | density of the fluid (kg/m^{3}) |

A | area of the cross section of the propelled volume of fluid (m^{2}) |