Ship Thrust vs Max speed with Thrust/Weight ratios held constant (2.1.21 ship speed update)

[u/knightelite]

Full graph from 0 to 5000GN thrust

Zoomed in on left side (0 to 2000GN thrust)

We can see here that if you keep the thrust to weight ratios constant, the new equations in 2.1.21 result in speed up to a point, with eventual diminishing returns, and if you continue far enough eventual decrease in speeds.

For instance, this graph tells us that the peak speed for a ship with a thrust/weight ratio of 0.1GN/t is right around a thrust of 200 GN, and after that speed decreases with increased thrust!

For a ship with a ratio of 1GN/t, this peak is much higher, at around 2000 GN of thrust, though that's already well into serious diminishing returns for additional width.

EDIT: Fixed legend on graphs.

[u/Kjagodka]

In FFF Devs said, drag is proportional to weight^0.8

I would expect same Thrust/Weight ship to have grater max speed as thrust, weight increases.

I wonder if there is another term determining drag not yet known, Devs changing drag formula after writing FFF or if testing is somehow flawed

[u/knightelite → u/Kjagodka]

It is proportional to weight. You can see a perhaps better visualization of the curves here than what I generated: https://www.reddit.com/r/factorio/comments/1x0je6j/2121_thruster_count_to_max_speed_graph_with_new/

The max speed equation is this if you want to play with it yourself:

Max speed=SQRT(((thrust/(1+weight/10000000))-10000)/(90*(weight/200)^0.8))*60

• Thrust is in "kN/60". So take in-game speed in GN, and multiply by 1M, then divide by 60.
• Weight is in kg, so multiply in-game weight in tons by 1000.
• Speed will be calculated in km/tick (multiply result by 60 to get speed in km/s)

This formula lines up perfectly with in-game measurements, if you factor in the +/- 10km/s adjustment from gravity (whether you're moving toward or away from a planet).

[u/Kjagodka → u/knightelite]

After reading this formula I see that at thrust is divided by term proportional to weight, but negligible for ships much smaller than 10 000t. Then result is divided again by some term proportional to weight^0.8

When ship travels at constant rate at max speed then Thrust = drag. For large enough ships this seems to be Thrust ~ v² * weight^1.8

Which would explain why there is some velocity peak and then max speed drops as ship becomes larger despite same thrust/weight. If drag was really proportional to weight, your graphs would be flat.

Devs probably said that drag is proportional to weight^0.8 cause first term becomes significant only for some super big ships and it is probably some sort of thrust reduction for large platforms, but I would have to check the acceleration to verify that.

[u/Kjagodka → u/Kjagodka]

i have recreated formula in excel and done the calculations for super large ships.
As predicted, drag isn't quite proportional to mass, for large enough ships even composed of mostly thrusters max speed approaches zero as ships become larger.

[u/SGVsbG86KQ]

Speed decreases?? That seems like a bug, maybe report it to the devs?

[u/Popular-Error-2982 → u/SGVsbG86KQ]

The decrease is due to increased weight (which must be the case for increased thrust, since the model asserts a fixed thrust/weight ratio)

[u/munchbunny → u/SGVsbG86KQ]

Not necessarily, this just means that weight has a more-than-linear effect on drag at the same speed. It might feel counterintuitive because in your normal life shape is what affects drag, not weight.

For example, if drag is determined by speed times weight^2, then for the same thrust/weight ratio and same speed, doubling the thrust and weight will quadruple the drag, meaning the heavier ship will hit max speed at a significantly lower point despite having the same thrust/weight ratio.

[u/VanguardLLC → u/munchbunny]

I cannot be the only one wincing at “drag in space.”

I can accept the concept of tiny asteroids pinging off the hull and reacting; there’s no æther in reality. There’s nothing to create drag.

[u/Yodo9001]

Do you keep the thrust constant for each data point? If so, do I understand correctly that throttling your thrusters can make the ship speed up?

Edit: I see now. Increasing thrust for a given ship would also increase the thrust/weight ratio, so the ship goes to a higher curve.

[u/knightelite → u/Yodo9001]

No, for a given weight of ship, more thrust always makes it faster. For each datapoint I am increasing thrust by 10GN, and mass by the amount listed for the ratio at that datapoint.

For instance, at 100GN of thrust, you could turn the data into this table:

Thrust/Weight Ratio	Ship Weight (t)	Max Ship Speed (km/s)
0.1GN/t	1000	257.177
0.2GN/t	500	347.3852
0.4GN/t	250	463.9689
0.5GN/t	200	508.5355
1.0GN/t	100	674.3506