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{{merge|Warp time calculation|Warp}} | |||
This page explains the calculations for the amount of time taken to travel while warping. Please note, this does not cover the time spent getting in to warp (accelerating to 75% maximum velocity), or the time spent slowing down after you regain control of your ship. | This page explains the calculations for the amount of time taken to travel while warping. Please note, this does not cover the time spent getting in to warp (accelerating to 75% maximum velocity), or the time spent slowing down after you regain control of your ship. | ||
==Time taken to 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<ref>https:// | 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<ref>https://www.eveonline.com/news/view/warp-drive-active</ref>. | ||
Warp consists of 3 stages: | Warp consists of 3 stages: | ||
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Total time in warp is given by: | Total time in warp is given by: | ||
<math> | :<math> t_{total} = t_{accel} + t_{cruise} + t_{decel} </math> | ||
=Long warps= | =Long warps= | ||
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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). | 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> | :<math> | ||
\begin{align} | \begin{align} | ||
d & = e^{kt} \\ | d & = e^{kt} \\ | ||
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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} \\ | ||
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The distance covered while accelerating to v<sub>warp</sub> is | The distance covered while accelerating to v<sub>warp</sub> is | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d_{accel} & = \frac{v_{warp}}{k} | d_{accel} & = \frac{v_{warp}}{k} | ||
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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}\\ | ||
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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_{warp} & = k * a\\ | ||
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</math> | </math> | ||
This formula can be simplified further to <math> | This formula can be simplified further to <math>\frac{\ln{a}}{k}</math>, although you may choose not to do this for implementation reasons. Because <math>a</math> is a constant, if warp distance is long enough for a ship to reach full speed, the warp acceleration time can be simplified down to | ||
:<math> | |||
t_{accel} \approx \frac{25.7312}{k} | |||
</math> | |||
==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>\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. | ||
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(100, v_{subwarp}/2)</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}\\ | ||
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The distance covered while decelerating from v<sub>warp</sub> is | The distance covered while decelerating from v<sub>warp</sub> is | ||
<math> | :<math> | ||
\begin{align} | \begin{align} | ||
d_{decel} & = \frac{v_{warp}}{j} | d_{decel} & = \frac{v_{warp}}{j} | ||
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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}\\ | ||
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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\_warp} - t_{decel\_s}\\ | t_{decel} & = t_{decel\_warp} - t_{decel\_s}\\ | ||
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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_{cruise} = d_{total} - d_{accel} - d_{decel}</math> | ||
For all but the fastest ships, this will be ''d<sub>total</sub> - 4 AU''. | For all but the fastest ships, this will be ''d<sub>total</sub> - 4 AU''. | ||
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This one is easy. Time spent cruising is simply | This one is easy. Time spent cruising is simply | ||
<math> | :<math>t_{cruise} = \frac{d_{cruise}}{v_{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_{total} \geq d_{accel} + d_{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_{accel} & = \frac{v_{max}}{k}, d_{decel} = \frac{v_{max}}{j}\\ | ||
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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_{accel} & = \frac{\ln{(\frac{v_{max}}{k})}}{k}\\ | ||
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=Implementation= | =Implementation= | ||
The following python code is one possible implementation of the above. It attempts to generate the same data as presented by CCP in the forums. It matches with their numbers, except for 50 AU titan warps, which are one second out. Note that the sub warp speed of the ship is fixed at 200 m/s. This is because the CCP-produced tables assume that every ship drops out of warp at 100 m/s<ref>https://forums.eveonline.com/ | The following python 3 code is one possible implementation of the above. It attempts to generate the same data as presented by CCP in the forums. It matches with their numbers, except for 50 AU titan warps, which are one second out. Note that the sub warp speed of the ship is fixed at 200 m/s. This is because the CCP-produced tables assume that every ship drops out of warp at 100 m/s<ref>https://forums-archive.eveonline.com/message/3902148#post3902148</ref>. If trying to run calculations for actual ships, this value will need to be replaced with a more appropriate one. The output values are also passed through the ceil() function, as this is what seems to match the rounding mode that CCP used.<ref>http://content.eveonline.com/www/newssystem/media/65418/1/numbers_table.png</ref> | ||
<pre> | <pre> | ||
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max_ms_warp_speed = max_warp_speed * AU_IN_M | max_ms_warp_speed = max_warp_speed * AU_IN_M | ||
accel_dist = | accel_dist = AU_IN_M | ||
decel_dist = max_ms_warp_speed / k_decel | decel_dist = max_ms_warp_speed / k_decel | ||
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=References= | =References= | ||
<references /> | <references /> | ||
[[Category:Game mechanics]] | |||