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{{hatnote|This article details warp travel. For information about sub-warp speeds, see [[Acceleration]].}} | {{hatnote|This article details warp travel. For information about sub-warp speeds, see [[Acceleration]].}} | ||
{{merge|Warp time calculation|Warp}} | |||
'''Warp''' is the primary method of faster-than-light travel utilized by ships in New Eden. Warp travel is limited to transit between locations within the same solar system, and can only be initiated to locations at least 150 km away. The warp exit point is determined when the warp command is given. This is important if you warp to moving objects like fleet members. You also don't exit warp at the exact point but on a 3 km sphere around the point. This means you sometimes land outside of docking range of a station if you warp to it. This is the reason for [[instadock]] bookmarks. | '''Warp''' is the primary method of faster-than-light travel utilized by ships in New Eden. Warp travel is limited to transit between locations within the same solar system, and can only be initiated to locations at least 150 km away. The warp exit point is determined when the warp command is given. This is important if you warp to moving objects like fleet members. You also don't exit warp at the exact point but on a 3 km sphere around the point. This means you sometimes land outside of docking range of a station if you warp to it. This is the reason for [[instadock]] bookmarks. | ||
== Warp Speed == | |||
Ships have a Ship Warp Speed attribute. Different classes of ships have different base speeds, with [[Covert Ops]] and [[Interceptor]] frigates are the fastest at 8.00 AU/s while [[Freighters]] and [[Titans]] are the slowest at 1.5 AU/s. Here is a [[Travel_fits#Increasing_warp_speed|guide on increasing warp speed]]. | |||
== Stages of warp == | == Stages of warp == | ||
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Total time in warp is given by: | Total time in warp is given by: | ||
<math>\ | :<math>t_\text{total} = t_\text{accel} + t_\text{decel} + t_\text{cruise}</math> | ||
==Long warps== | ==Long warps== | ||
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CCP provided formulae for both distance traveled and velocity reached after ''t'' seconds of acceleration. ''d'' is the distance in meters, ''v'' is speed in meters per second, ''k'' is the ship's warp speed (in AU/s) and ''a'' is 149,597,870,700 meters (1 AU). | CCP provided formulae for both distance traveled and velocity reached after ''t'' seconds of acceleration. ''d'' is the distance in meters, ''v'' is speed in meters per second, ''k'' is the ship's warp speed (in AU/s) and ''a'' is 149,597,870,700 meters (1 AU). | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d & = e^{kt} \\ | d & = e^{kt}\\ | ||
v & = k*e^{kt}\\ | v & = k*e^{kt}\\ | ||
v_{warp} & = k * a\\ | v_\text{warp} & = k * a\\ | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
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To calculate distance traveled while accelerating: | To calculate distance traveled while accelerating: | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d & = e^{kt} \\ | d & = e^{kt}\\ | ||
v & = k*e^{kt}\\ | v & = k*e^{kt}\\ | ||
& = k*d\\ | & = k*d\\ | ||
\therefore d & = \frac{v}{k} | \therefore\quad d & = \frac{v}{k} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
The distance covered while accelerating to ''v<sub>warp</sub> | The distance covered while accelerating to ''v''<sub>warp</sub> is: | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d_{accel} & = \frac{v_{warp}}{k} | d_\text{accel} & = \frac{v_\text{warp}}{k}\\ | ||
& = \frac{k*a}{k} | & = \frac{k*a}{k}\\ | ||
& = a | & = a | ||
\end{align} | \end{align} | ||
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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) | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
v & = k*e^{kt}\\ | v & = k*e^{kt}\\ | ||
\frac{v}{k} & = e^{kt}\\ | \frac{v}{k} & = e^{kt}\\ | ||
kt & = \ln{(\frac{v}{k})}\\ | kt & = \ln{\left(\frac{v}{k}\right)}\\ | ||
t & =\frac{\ln{(\frac{v}{k})}}{k} | t & =\frac{\ln{\left(\frac{v}{k}\right)}}{k} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
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We want to find the time taken to maximum warp: | We want to find the time taken to maximum warp: | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
v_{warp} & = k * a\\ | v_\text{warp} & = k * a\\ | ||
t_{accel} & = \frac{\ln{(\frac{v_{warp}}{k})}}{k} | t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{k} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
This formula can be simplified further to <math> | This formula can be simplified further to <math display="inline">\frac{\ln{a}}{k}</math>, although you may choose not to do this for implementation reasons. | ||
===Deceleration=== | ===Deceleration=== | ||
Deceleration is calculated slightly differently. Instead of using ''k'' to calculate distance and velocity, it uses ''j'', which is defined as <math>\ | Deceleration is calculated slightly differently. Instead of using ''k'' to calculate distance and velocity, it uses ''j'', which is defined as <math display="inline">\min\left(\frac{k}{3},2\right)</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. | ||
There is a complication with deceleration calculations. Ships do not drop out of warp at 0 m/s. Instead, they drop out of warp at ''s'' m/s, after which normal sub-warp calculations take over. | There is a complication with deceleration calculations. Ships do not drop out of warp at 0 m/s. Instead, they drop out of warp at ''s'' m/s, after which normal sub-warp calculations take over. | ||
<math> | :<math>s = \min\left(100, \frac{v_\text{subwarp}}{2}\right)</math> | ||
Where v<sub>subwarp</sub> is the maximum subwarp velocity of the ship; this varies greatly depending on the ship hull and pilot skills. | Where ''v''<sub>subwarp</sub> is the maximum subwarp velocity of the ship; this varies greatly depending on the ship hull and pilot skills. | ||
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This changes the formulae used slightly. Remember that distance travelled is the integral of velocity. | This changes the formulae used slightly. Remember that distance travelled is the integral of velocity. | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
v & = k * e^{jt}\\ | v & = k * e^{jt}\\ | ||
d & = \int_{0}^{ | d & = \int_{0}^{t}k*e^{j\cdot dx}\,dx = \frac{k*e^{jt}}{j}\\ | ||
& = \frac{v}{j} | & = \frac{v}{j} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
The distance covered while decelerating from ''v<sub>warp</sub> | The distance covered while decelerating from ''v''<sub>warp</sub> is | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d_{decel} & = \frac{v_{warp}}{j} | d_\text{decel} & = \frac{v_\text{warp}}{j}\\ | ||
= \frac{k*a}{j} | & = \frac{k*a}{j} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Note that for ships that travel at up to 6 AU/s, | Note that for ships that travel at up to 6 AU/s, <math display="inline">\frac{k}{j} = \frac{k}{k/3} = 3</math>, so these ships cover 3 AU while decelerating. The complication of not stopping warp at 0 can be safely ignored for distance calculations, because the distance that would be covered while decelerating from 100 m/s is insignificant compared to the ~450 billion meters it takes to decelerate from warp speed to warp drop speed. | ||
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As with acceleration, time to decelerate from maximum warp velocity is worked out by rearranging the velocity equation. | As with acceleration, time to decelerate from maximum warp velocity is worked out by rearranging the velocity equation. | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
v &= k*e^{jt}\\ | v &= k*e^{jt}\\ | ||
\frac{v}{k} & = e ^ {jt}\\ | \frac{v}{k} & = e ^ {jt}\\ | ||
t & = \frac{\ln{(\frac{v}{k})}}{j} | t & = \frac{\ln{\left(\frac{v}{k}\right)}}{j} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
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While the deceleration from ''s'' to 0 was insignificant in terms of distance, it is significant in terms of time. This means that the time to decelerate is calculated as follows: | While the deceleration from ''s'' to 0 was insignificant in terms of distance, it is significant in terms of time. This means that the time to decelerate is calculated as follows: | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
t_{decel} & = t_{decel\ | t_\text{decel} & = t_{\text{decel}\_\text{warp}} - t_{\text{decel}\_s}\\ | ||
& = \frac{\ln{(\frac{v_{warp}}{k})}}{j} - \frac{\ln{(\frac{s}{k})}}{j}\\ | & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{j} - \frac{\ln{\left(\frac{s}{k}\right)}}{j}\\ | ||
& = \frac{\ln{(\frac{v_{warp}}{k})} - \ln{(\frac{s}{k})}}{j}\\ | & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)} - \ln{\left(\frac{s}{k}\right)}}{j}\\ | ||
& = \frac{\ln{v_{warp}} - \ln | & = \frac{\ln{v_\text{warp}} - \ln k - \ln s + \ln k}{j}\\ | ||
& = \frac{\ln{v_{warp}} - \ln | & = \frac{\ln{v_\text{warp}} - \ln s}{j}\\ | ||
& = \frac{\ln{(\frac{v_{warp}}{s})}}{j} | & = \frac{\ln{\left(\frac{v_\text{warp}}{s}\right)}}{j} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
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The distance covered while cruising is the total warp distance minus any distance covered while accelerating or decelerating. | The distance covered while cruising is the total warp distance minus any distance covered while accelerating or decelerating. | ||
<math>\ | :<math>d_\text{cruise} = d_\text{total} - d_\text{accel} - d_\text{decel}</math> | ||
For all but the fastest ships, this will be ''d<sub>total</sub> | For all but the fastest ships, this will be ''d''<sub>total</sub> − 4 AU''. | ||
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Time spent cruising is: | Time spent cruising is: | ||
<math>\ | :<math>t_\text{cruise} = \frac{d_\text{cruise}}{v_\text{warp}}</math> | ||
==Short Warps== | ==Short Warps== | ||
The above calculations work as long as some time is spent at maximum warp speed; <math>\ | The above calculations work as long as some time is spent at maximum warp speed; <math>d_\text{total} \geq d_\text{accel} + d_\text{decel}</math>. If the warp is short enough that the ship never reaches top speed, a different set of calculations are needed. | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d_{accel} & = \frac{v_{max}}{k}, d_{decel} = \frac{v_{max}}{j}\\ | d_\text{accel} & = \frac{v_\text{max}}{k}, d_\text{decel} = \frac{v_\text{max}}{j}\\ | ||
d_{total} & = d_{accel} + d_{decel} = v_{max}(\frac{1}{k} + \frac{1}{j})\\ | d_\text{total} & = d_\text{accel} + d_\text{decel} = v_\text{max}\left(\frac{1}{k} + \frac{1}{j}\right)\\ | ||
v_{max} & = \frac{d_{total}*k*j}{k + j} | v_\text{max} & = \frac{d_\text{total}*k*j}{k + j} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
This enables the calculation of new acceleration and deceleration times using the formulae described in the previous sections, but substituting in the new ''v<sub>max</sub> | This enables the calculation of new acceleration and deceleration times using the formulae described in the previous sections, but substituting in the new ''v''<sub>max</sub>: | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
t_{accel} & = \frac{\ln{(\frac{v_{max}}{k})}}{k}\\ | t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{max}}{k}\right)}}{k}\\ | ||
t_{decel} & = \frac{\ln{(\frac{v_{max}}{s})}}{j}\\ | t_\text{decel} & = \frac{\ln{\left(\frac{v_\text{max}}{s}\right)}}{j}\\ | ||
t_{total} & = t_{accel} + t_{decel} | t_\text{total} & = t_\text{accel} + t_\text{decel} | ||
\end{align} | \end{align} | ||
</math> | </math> | ||