Using the steep outfitting discount of the 1.4 beta, I was able to test over 150 combinations of ship hulls, mass, thrusters and ENG pip allocations. From this dataset I can very closely model the maximum straight-line velocity of each ship and thruster under various conditions.

To begin, here is what we already knew or suspected about the thruster speed model:

- Each thruster module has a stated optimum and maximum mass, but the maximum mass is always 1.5x the optimum mass. There is also a hidden minimum mass which is 0.5x optimum.
- Each ship has a base speed value which used to be displayed directly in the in-game shipyard, but isn't any more. Now the in-game shipyard displays a speed value which is close to (but not exactly) the effective top speed (at 4 ENG pips) with its current (or default) loadout.
- Your effective speed is determined by multiplying the ship's base speed by a modifier which depends on the ratio of your total mass (ship hull + outfitting + fuel + cargo) and the thruster's optimum mass. A lower mass ratio yields a higher speed modifier, but the curve varies by thruster rating and is capped at 0.5 on the low end, beyond which your speed will no longer increase. On the high end, if the ratio is above 1.5 (which is the thruster's maximum mass) then you cannot equip the thruster at all.
- Your ENG pip allocation modifies your effective speed linearly, such that each pip alters your maximum speed by the same amount (in m/s, with a given ship outfitting).

Following on from the above, here are my research findings:

- ENG pips do scale linearly, but differently for each ship. In other words, your 2-pip speed will always be exactly halfway between your 0- and 4-pip speeds, but the ratio of your 0-pip to 4-pip speeds is a hidden property of the ship hull. This property varies wildly: for example, a Vulture retains ~90% of its top speed at 0 pips, while a Viper gets ~62% and a Type-9 gets only ~31%.
- The power distributor has no effect on maximum speed, or on the effect of ENG pip allocations. As far as I can tell the only part of the distributor that affects the speed model in any way is its mass, just like anything else.
- Maximum reverse speed is always 60% of the current maximum forward speed.
- Maximum lateral (up/down/left/right) speed is always 80% of the current maximum forward speed.
- The thrust curve for C thrusters is flat, so for every ton added/reduced, your speed will increase/decrease by the same amount in m/s.
- The thrust curve for A and B thrusters is convex (bows downward), so for every ton reduced below the thruster's optimum, the speed bonus gets larger; likewise for every ton added over the thruster's optimum, the speed penalty gets smaller.
- The thrust curve for D and E thrusters is concave (bows upward), so for every ton reduced below the thruster's optimum, the speed bonus gets smaller; likewise for every ton added over the thruster's optimum, the speed penalty gets larger (quite extremely so, as you get very close to the thruster's maximum mass).
- Curiously, all thrust curves meet at (1,1), so if your total mass is exactly equal to your thruster's optimum mass then no matter what rating thruster you have, your speed modifier will always be 1.0 and you will always achieve exactly the base top speed for the ship hull (at 4 ENG pips). Of course, better ratings have higher optimum masses, so in practice you'll (probably) always see a speed increase by upgrading your thruster.

And finally (or TL;DR), the thrust curves are closely approximated by this formula:

where x is the mass ratio (total mass divided by thruster optimum mass), y is the speed modifier (applied to the ship's base speed), and M and P are constants according to the thruster rating:y = (1 - M) + (M * (3 - 2 * x) ^ P)

To get a visual sense of these thrust curves, here is a plot of the data I gathered in the course of this research:Class E: M = 0.17, P = 0.2350

Class D: M = 0.14, P = 0.5145

Class C: M = 0.10, P = 1.0000

Class B: M = 0.07, P = 1.5100

Class A: M = 0.04, P = 2.3300

Attachment 61636

Note that every dot in this plot depicts an actual in-game speed measurement; the jagginess of the curves is due to the in-game display rounding speeds to integer m/s. Also remember that this graph is normalized according to the mass *ratio*, not the actual ship mass. The graph makes it look like E is better than D at high mass, which is misleading because higher rating thrusters have higher optimum masses, so your *ratio* will (probably) always go down when you upgrade from E to D, resulting in a higher actual speed modifier.

has been updated with thruster speed modeling based on these results. Enjoy!www.edshipyard.com

Further notes:

- I have not done any testing of acceleration, deceleration, pitch, yaw or roll rates, because that data is much harder to gather (and more prone to stopwatch errors). However, a very simple assumption might be that it is based on the same modifier curves, which wouldn't be too hard to verify: simply outfit a ship with a total mass exactly equal to its thruster optimum mass and measure all rates. Then change the outfitting to achieve 0.5, 0.75, 1.25 and 1.5x optimum mass, measure the rates again, and see if the ratios compared to the optimum mass case follow this same formula. If that's true, then we'd only need to establish the baseline values for each ship hull at the 1.0x mass ratio.
- After modeling acceleration and deceleration, it should be possible to model sustainable average boost speed (based on capacitor use per boost, distributor recharge rate, ship boost speed and acceleration/deceleration rates). But that's beyond the scope of this work.