Difference between revisions of "Warp"
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===The formulae=== | ===The formulae=== | ||
| − | CCP provided formulae for both distance traveled and velocity reached after ''t'' seconds of acceleration. | + | CCP provided formulae for both distance traveled and velocity reached after ''t'' seconds of acceleration. If ''d'' is distance in meters, ''v'' is speed in meters per second, ''k'' is a (sort of) constant defined as the warp speed (in AU/s) and a = 149,597,870,700 meters (1 AU). |
<math>\pagecolor{Black}\color{White} | <math>\pagecolor{Black}\color{White} | ||
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d & = e^{kt} \\ | d & = e^{kt} \\ | ||
v & = k*e^{kt}\\ | v & = k*e^{kt}\\ | ||
| + | v_{max} & = k * a\\ | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
| − | + | ===Distance=== | |
| + | To calculate distance traveled while accelerating | ||
| + | <math>\pagecolor{Black}\color{White} | ||
| + | \begin{align} | ||
| + | d & = e^{kt} \\ | ||
| + | v & = k*e^{kt}\\ | ||
| + | & = k*d\\ | ||
| + | \therefore d & = \frac{v}{k} | ||
| + | \end{align} | ||
| + | </math> | ||
| + | |||
| + | The distance covered while accelerating to v<sub>max</sub> is | ||
| + | |||
| + | <math>\pagecolor{Black}\color{White} | ||
| + | \begin{align} | ||
| + | d & = \frac{v_{max}}{k} | ||
| + | & = \frac{k*a}{k} | ||
| + | & = a | ||
| + | \end{align} | ||
| + | </math> | ||
| + | |||
| + | This means that every ship covers exactly 1 AU while accelerating to its maximum warp speed. | ||
| + | |||
| + | |||
| + | ===Time=== | ||
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) | 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) | ||
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v & = k * a\\ | v & = k * a\\ | ||
\therefore t & = \frac{\ln{(\frac{v}{k})}}{k}\\ | \therefore t & = \frac{\ln{(\frac{v}{k})}}{k}\\ | ||
| − | + | & = \frac{\ln{(a)}}{k}\\ | |
\end{align} | \end{align} | ||
</math> | </math> | ||
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==Deceleration== | ==Deceleration== | ||
Revision as of 00:37, 24 March 2016
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:
- Acceleration
- Cruising
- 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. If d is distance in meters, v is speed in meters per second, k is a (sort of) constant defined as the warp speed (in AU/s) and a = 149,597,870,700 meters (1 AU).
[math]\pagecolor{Black}\color{White} \begin{align} d & = e^{kt} \\ v & = k*e^{kt}\\ v_{max} & = k * a\\ \end{align} [/math]
Distance
To calculate distance traveled while accelerating
[math]\pagecolor{Black}\color{White} \begin{align} d & = e^{kt} \\ v & = k*e^{kt}\\ & = k*d\\ \therefore d & = \frac{v}{k} \end{align} [/math]
The distance covered while accelerating to vmax is
[math]\pagecolor{Black}\color{White} \begin{align} d & = \frac{v_{max}}{k} & = \frac{k*a}{k} & = a \end{align} [/math]
This means that every ship covers exactly 1 AU while accelerating to its maximum warp speed.
Time
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}\\ & = \frac{\ln{(a)}}{k}\\ \end{align} [/math]
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]
