Warp: Difference between revisions

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== 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 1.37 AU/s. Here is a [[Travel_fits#Increasing_warp_speed|guide on increasing 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 ==

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</math>

The distance covered while accelerating to ''vwarp'' is:

The distance covered while accelerating to ''v''warp is:

:<math>

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\frac{v}{k} & = e^{kt}\\

kt & = \ln{\left(\frac{v}{k}\right)}\\

t & =\frac{\ln{\left(\frac{v}{k}\right)}}{k}\\

t & =\frac{\ln{\left(\frac{v}{k}\right)}}{k}

\end{align}

</math>

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\begin{align}

v_\text{warp} & = k * a\\

t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{k}\\

t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{k}

\end{align}

</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.

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 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.

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.

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</math>

The distance covered while decelerating from ''vwarp'' is

The distance covered while decelerating from ''v''warp is

:<math>

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</math>

Note that for ships that travel at up to 6 AU/s, ''k~~'' / ''~~j'' = ''k~~'' / (''~~k''/3) = 3, 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.

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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</math>

This enables the calculation of new acceleration and deceleration times using the formulae described in the previous sections, but substituting in the new ''vmax'':

This enables the calculation of new acceleration and deceleration times using the formulae described in the previous sections, but substituting in the new ''v''max:

:<math>

@@ Line 5: / Line 5: @@
 == 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 1.37 AU/s. Here is a [[Travel_fits#Increasing_warp_speed|guide on increasing 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 ==
@@ Line 49: / Line 49: @@
 </math>
-The distance covered while accelerating to ''v<sub>warp</sub>'' is:
+The distance covered while accelerating to ''v''<sub>warp</sub> is:
 :<math>
@@ Line 70: / Line 70: @@
 \frac{v}{k} & = e^{kt}\\
 kt & = \ln{\left(\frac{v}{k}\right)}\\
-t & =\frac{\ln{\left(\frac{v}{k}\right)}}{k}\\
+t & =\frac{\ln{\left(\frac{v}{k}\right)}}{k}
 \end{align}
 </math>
@@ Line 79: / Line 79: @@
 \begin{align}
 v_\text{warp} & = k * a\\
-t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{k}\\
+t_\text{accel} & = \frac{\ln{\left(\frac{v_\text{warp}}{k}\right)}}{k}
 \end{align}
 </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.
+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 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.
+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.
@@ Line 106: / Line 106: @@
 </math>
-The distance covered while decelerating from ''v<sub>warp</sub>'' is
+The distance covered while decelerating from ''v''<sub>warp</sub> is
 :<math>
@@ Line 115: / Line 115: @@
 </math>
-Note that for ships that travel at up to 6 AU/s, ''k'' / ''j''  = ''k'' / (''k''/3) = 3, 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.
+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.
@@ Line 168: / Line 168: @@
 </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>