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## Acceleration
## BackgroundEVE's physics engine is based on a 'fluid dynamics model' which assumes that 'space' has some substance to it and thus some friction, this means that with the ship engine turned off you will decelerate, ultimately to a standstill. ## How do ships in EVE accelerate and decelerate?When a ship starts to accelerate it will quickly increase its speed but as the speed increases the acceleration decreases exponentially which means that, in theory, the ship will never reach its top speed. In reality however, 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?There are two attributes which determine how quickly a ship accelerates; Mass and Inertial Modifier, the later can be reduced with both skills and modules while mass can never be reduced only increased. The product of Mass and the Inertia Modifier gives the ship's agility which determines how quickly the ship accelerates (and thus how quickly it turns); lower values imply better acceleration and turning speed. 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 term after the multiplication sign is the fraction of maximum velocity which is reached in 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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