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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_{total} = t_{accel} + t_{decel} + t_{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} \\ | ||
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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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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}/2)</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>d_{cruise} = d_{total} - d_{accel} - d_{decel}</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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Time spent cruising is: | Time spent cruising is: | ||
<math>t_{cruise} = \frac{d_{cruise}}{v_{warp}}</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>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_{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}\\ | ||