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Created page with "{{Work in progress}} The '''acceleration''' of objects in EVE is not based on classical physics. The physics engine is based on a fluid dynamics model, which assumes that spac..." |
Added images of formulas, edited/revised text. |
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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. | 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. | ||
== Mathematics and formulas == | |||
The following formula describes the velocity of a ship accelerating from a standstill after a particular time: | The following formula describes the velocity of a ship accelerating from a standstill after a particular time: | ||
[[Image:Accelformula2.png|center]] | |||
where: | where: | ||
t | <dl> | ||
<dt>''t'' | |||
<dd>Time in seconds | |||
<dt>''V<sub>t</sub>'' | |||
<dd>Velocity after time ''t'' in m/s | |||
<dt>''V<sub>max</sub>'' | |||
I | <dd>Ship's maximum velocity in m/s | ||
<dt>''I'' | |||
M | <dd>Ship's inertia modifier, in s/kg | ||
<dt>''M'' | |||
e | <dd>Ship's mass in kg | ||
<dt>''e'' | |||
<dd>Base of natural logarithms | |||
</dl> | |||
Explanation | === Explanation === | ||
The final term (with the exponent) gives the fraction of maximum velocity that is reached after time ''t''. This is multiplied by the maximum velocity to find the absolute velocity at time ''t''. Note that this only depends on time, inertia modifier and mass (''e'' is a constant). | |||
The 106 term cancels out a factor of one million in the mass term. So to simplify you can ignore the 106 and use the mass of the ship in millions of kg instead of kg. | The 106 term cancels out a factor of one million in the mass term. So to simplify you can ignore the 106 and use the mass of the ship in millions of kg instead of kg. | ||
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Rearranging the formula for t we arrive at the formula for time taken to accelerate from zero to V: | Rearranging the formula for t we arrive at the formula for time taken to accelerate from zero to V: | ||
[[Image:Accelformula1.png|center]] | |||
Where ''t<sub>V</sub>'' is the time to accelerate to velocity ''V'' in seconds. Note that at ''V'' = ''V<sub>max</sub>'', 1 - ''V'' / ''V<sub>max</sub>'' = 0, but ln 0 is undefined, so in theory it takes infinite time to reach maximum speed (technically, the limit of ''t<sub>V</sub>'' as ''V'' approaches ''V<sub>max</sub>'' 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. (Strictly speaking, velocity is a vector, so it has both direction and magnitude, but the game is really only concerned with its absolute value (i.e. the magnitude part) more commonly called 'speed'.) | |||
====Example==== | |||
Pete has just got himself a new freighter, a {{sh|Charon}}. The Charon has a mass of 1,200,000,000 kg and an inertia modifier of 0.02176875 (after adjustment for skills). Pete wants to know how long it takes for his ship to reach the speed needed to enter warp. Since this is 75% of the ship's top speed regardless of what that top speed actually is, he doesn't bother calculating it, but instead simplifies by substituting 0.75 and 1 for ''V'' and ''V<sub>max</sub>'' respectively. | |||
The Charon has a | |||
Time to Warp = 0.02176875 × 1.2 × 109 × 10-6 × -ln (1 - 0.75 / 1) | Time to Warp = 0.02176875 × 1.2 × 109 × 10-6 × -ln (1 - 0.75 / 1) | ||
= 0.02176875 × 1.2 × 103 × -ln (1 - 0.75) | |||
= 0.02176875 × 1200 × -ln 0.25 | |||
= 26.1225 × 1.38629436 | |||
= 36.2134744 seconds. | |||