Warp: Difference between revisions

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@@ Line 13: / Line 13: @@
 ===The formulae===
-CCP provided formulae for both distance traveled and velocity reached after ''t'' seconds of acceleration.
+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>\pagecolor{Black}\color{White}
@@ Line 19: / Line 19: @@
 d & = e^{kt} \\
 v & = k*e^{kt}\\
+v_{max} & = k * a\\
 \end{align}
 </math>
-Where ''d'' is distance in meters, ''v'' is speed in meters per second and ''k'' is defined as the warp speed (in AU/s). a = 149,597,870,700 meters (1 AU).
+===Distance===
+To calculate distance traveled while accelerating
+<math>\pagecolor{Black}\color{White}
+\begin{align}
+d & = e^{kt} \\
+v & = k*e^{kt}\\
+& = k*d\\
+\therefore d & = \frac{v}{k}
+\end{align}
+</math>
+The distance covered while accelerating to v<sub>max</sub> is
+<math>\pagecolor{Black}\color{White}
+\begin{align}
+d & = \frac{v_{max}}{k}
+& = \frac{k*a}{k}
+& = a
+\end{align}
+</math>
+This means that every ship covers exactly 1 AU while accelerating to its maximum warp speed.
+===Time===
 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)
@@ Line 41: / Line 66: @@
 v & = k * a\\
 \therefore t & = \frac{\ln{(\frac{v}{k})}}{k}\\
-t & = \frac{\ln{(a)}}{k}\\
+& = \frac{\ln{(a)}}{k}\\
 \end{align}
 </math>
-Substituting the time taken to reach maximum speed in to the formula for distance gives the distance covered while accelerating:
-<math>\pagecolor{Black}\color{White}
-\begin{align}
-d & = e^{k*t},t = \frac{\ln{(a)}}{k}\\
-\therefore d & = e^{k*\frac{\ln{(a)}}{k}}\\
-d & = e^{ln{(a)}}\\
-d & = a
-\end{align}
-</math>
-This means that every ship covers 1 AU while accelerating to maximum speed.
 ==Deceleration==