Acceleration

Background

EVE's Physics Engine is based on a Fluid Dynamics Engine, assuming that Space has some substance to it and thus if you turn off the Ship Engine you will slowdown from the friction.

How do Ships in EVE Accelerate and Decelerate?

When a ship starts to accelerate it will quickly gain initial speed, but as the speed increase the acceleration decreases. The decrease is exponential which means that in theory the ship will never reach its top speed, but in reality it won't take much time before you get so close to top speed that the difference is truncated.

Deceleration works the same way but opposite. The closer to your top speed you are the faster you will decelerate and again in theory you can never completely stop the ship.

Please note: The use of the term ship in this article also includes all other objects in space that can move around, for example missiles and drones.

[Graph here]

What decides how quickly a Ship Accelerates?

There are 2 attributes that determines how fast a ship accelerates. Mass and Inertial Modifier. These two multiplied together gives the ships Agility which in turn determines both how fast the ship accelerate and how fast it turns. Lower value equals faster acceleration/turning speed.

Two ships with the same Mass and Inertial Modifier but different top speed will take the same time to reach their respective top speeds. This means a faster ship will have a higher acceleration in m^2/s but will take the same time to reach for example the speed needed to enter warp.

Math

The acceleration formula assuming the ship is starting from a standstill:
V(t) = Vmax * (1 - e^-(t / ((I * M) / 1,000,000)))

V(t) = Velocity after time "t" in seconds.
Vmax = Max Velocity
e = Mathematical constant, base of the natural logarithm.
t = Time in seconds.
I = Inertia Modifier.
M = Mass.

It can also be written as:
T = ((I * M) / 1.000.000) * -ln(1 - (Vt / Vmax))

T = Time in seconds to reach velocity Vt.
ln = Natural logarithm
Vt = Target speed.

Example: Pete has just got himself a new Freighter, a Charon.
The Charon has a Mass of 1,200,000,000 kg and an Inertia Modifier of 0.02176875 (after adjusting for his skills). He wants to find out how long it takes for his ship to reach the speed needed to enter warp, this is equal to 75% of the ships top speed.
He inserts the numbers into the formula above which gives him:
Time to Warp = ((0,02176875 * 1,200,000,000) / 1,000,000) * -ln(1 - (0.75/1)) = 36.2 seconds.