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==Deceleration== | ==Deceleration== | ||
Deceleration is calculated slightly differently. Instead of using 'k' to calculate distance and velocity, it uses 'j', which is defined as <math>\pagecolor{Black}\color{White}\min(\frac{k}{3},2)</math>. A different rate of deceleration is used to prevent ships suddenly transitioning from "many, many AU away" to "on grid and out of warp" more rapidly than other pilots (or the server / client) can keep up with. | |||
This changes the formulae used slightly. Remember that distance travelled is the integral of velocity. | |||
<math>\pagecolor{Black}\color{White} | |||
\begin{align} | |||
v & = k * e^{jt}\\ | |||
d_{decel} & = \int_{0}^{\infty}k*e^{jt}\,dt = \frac{k*e^{jt}}{j}\\ | |||
\therefore d_{decel} & = \frac{v}{j} | |||
\end{align} | |||
</math> | |||