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## Acceleration
## BackgroundThe ## How do ships in EVE accelerate and decelerate?In terms of kinematic motion, when the ship starts to accelerate it will quickly increase its speed, but as the speed increases toward the maximum, the acceleration decreases exponentially. (In theory, the ship will never reach its top speed, however in reality, it won't take long to get so close to top speed that the difference is negligible and EVE rounds up the figure on your display.) Deceleration is simply acceleration in a direction opposed to the one you are travelling in, i.e. 'braking'. The closer to your top speed you are the faster you will decelerate.
## What decides how quickly a ship accelerates?The idea of acceleration = force/mass can be thrown away for now, because there are only two basic attributes which determine the relative acceleration (how quickly a ship accelerates to its maximum speed): Mass and Inertial Modifier. The latter can be reduced with both skills and modules while mass can never be reduced (on the other hand, it may be increased by armor plates and active propulsion modules).
The product of Mass and the Inertia Modifier gives the ship's To demonstrate, here's an example of this exponential acceleration: Two ships with identical Mass and Inertial Modifier but different top speeds will reach their respective top speeds in the same period. Thus, a ship with a higher top speed will have a higher acceleration in ms^-2 but will take the same time to reach the speed required to use warp engines.
## The mathematicsThe following formula describes the velocity of a ship accelerating from a standstill after a particular time: where: *t*- Time in seconds
*V*_{t}- Velocity after time
*t*in m/s *V*_{max}- Ship's maximum velocity in m/s
*I*- Ship's inertia modifier, in s/kg
*M*- Ship's mass in kg
*e*- Base of natural logarithms
Explanation: The final term (with the exponent) gives the fraction of maximum velocity that is reached after time The 10 As for acceleration itself, this is just the first derivative of velocity with respect to time. Rearranging the formula for where V in seconds. Note that at V = V_{max}, 1 - V / V_{max} = 0, but ln 0 is undefined, so in theory it takes infinite time to reach maximum speed (technically, the limit of t_{V} as V approaches V_{max} is positive infinity). In practice the game simulation is not perfectly accurate and it actually takes finite time to reach maximum speed to within whatever precision the simulation uses.
Example: Pete has just got himself a new freighter, a Charon. Time to Warp = 0.02176875 × 1.2 × 10 ## Top Contributors For This Page |
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