Warp

Time taken to warp

It is possible to work out how long it should take for a ship to complete warp (once it enters warp) based on formulae released by CCP.

Warp consists of 3 stages:

1. Acceleration
2. Cruising
3. Deceleration

Calculating the time taken to warp is done by calculating the time spent in each of these phases and adding them together. This requires calculating acceleration and deceleration time first, followed by cruise time.

Acceleration

The formulae

CCP provided formulae for both distance traveled and velocity reached after t seconds of acceleration.

[math]\pagecolor{Black}\color{White} \begin{align} d & = e^{kt} \\ v & = k*e^{kt}\\ \end{align} [/math]

Where d is distance in meters, v is speed in meters per second and k is defined as the warp speed (in AU/s). a = 149,597,870,700 meters (1 AU).

To calculate the time spent accelerating to warp speed, the equation for v should be rearranged to be in terms of t, and then solved for the case of v being equal to the warp speed (in m/s)

[math]\pagecolor{Black}\color{White} \begin{align} v & = k*e^{kt}\\ \frac{v}{k} & = e^{kt}\\ kt & = \ln{(\frac{v}{k})}\\ t & =\frac{\ln{(\frac{v}{k})}}{k}\\ \end{align} [/math]

We want to find the time taken to maximum warp:

[math]\pagecolor{Black}\color{White} \begin{align} v & = k * a\\ \therefore t & = \frac{\ln{(\frac{v}{k})}}{k}\\ t & = \frac{\ln{(a)}}{k}\\ \end{align} [/math]

Substituting the time taken to reach maximum speed in to the formula for distance gives the distance covered while accelerating:

[math]\pagecolor{Black}\color{White} \begin{align} d & = e^{k*t},t = \frac{\ln{(a)}}{k}\\ \therefore d & = e^{k*\frac{\ln{(a)}}{k}}\\ d & = e^{ln{(a)}}\\ d & = a \end{align} [/math]

This means that every ship covers 1 AU while accelerating to maximum speed.

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]