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Added basic information about ship warp speed attribute |
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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> | ||
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:<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> | ||
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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} | ||
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:<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> | ||
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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> | ||
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:<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> | ||