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Added basic information about ship warp speed attribute |
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== Warp Speed == | == 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. | 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>t_{total} = t_{accel} + t_{decel} + t_{cruise}</math> | :<math>t_\text{total} = t_\text{accel} + t_\text{decel} + t_\text{cruise}</math> | ||
==Long warps== | ==Long warps== | ||
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:<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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:<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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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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:<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>\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=== | ||
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. | 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>s = \min(100, v_{subwarp} | :<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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\begin{align} | \begin{align} | ||
v & = k * e^{jt}\\ | v & = k * e^{jt}\\ | ||
d & = \int_{0}^{t}k*e^{ | 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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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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:<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>d_{cruise} = d_{total} - d_{accel} - d_{decel}</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>t_{cruise} = \frac{d_{cruise}}{v_{warp}}</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>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. | 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> | ||