Transport belts/Physics

< Transport belts | Physics

The belt transport system in Factorio is among the most detailed simulations in the game. Items in chests and other containers are stored simply as summed totals, and items on uninterrupted stretches of belts are moved in aggregate as an optimization, but in the end items on belts are simulated individually, especially when they get picked up or put down by inserters. This leads to some intricate behaviors, in particular when it comes to inserter throughput.

Belt properties

• Density. How many items fit onto a certain length of belt, measured in items per tile per belt lane. This is 4 on a straight belt, regardless of the type of item and type of belt. The item density on belts can be different from what they take up when just dropped on the ground (using the Z key).

• Speed. The speed of items on a belt is measured for practical reasons in tiles per second. Note that internally it is measured in positions (1/256 tile) per tick (1/60 sec). More on that below. The speed of a basic transport belt is 1.875 tiles per game-second. Fast transport belt is twice as fast, and express transport belt is three times as fast.

• Throughput. How many items per second that are moved from one tile to the next. That is density (items per tile) multiplied by speed (tiles per second), e.g. for a basic belt it is 4 * 1.875 = 7.5 items per second, for one belt lane. For both lanes it is doubled, i.e. 15 items per second.

• Compression. If there is no empty space between items on the belt it is called fully compressed, otherwise its compression is only partial and it does not have optimal throughput. Entities that put items onto belts - inserters, splitters, other belts coming from the side, mining drills, etc - make room for their item by enlarging a small gap until it is exactly big enough for the item. That means belts naturally become fully compressed before items start to back up.

• Lanes. Belts have two parallel lanes, and the density and speed of each lane is constant and independent of the other one, regardless of twists and turns. So items in the inner lane of a turn exit it before those in the outer lane, since their speeds are equal and the inner lane is shorter than the outer one.

Belt speeds

Given the values above we can calculate the speed and throughput of the three types of belts. Measurements confirm these values.

Belt type	Speed		Throughput
	Factor	Tiles/sec	Single lane, items/sec	Single lane, items/min	Both lanes, items/sec	Both lanes, items/min
Transport belt	1	1.875	7.5	450	15	900
Fast transport belt	2	3.75	15	900	30	1800
Express transport belt	3	5.625	22.5	1350	45	2700

Items on belts

As mentioned earlier, items take space on belts in terms of density and compression. However, every item on a belt is logically on exactly one belt tile at any moment in time.

For example, even though in a screenshot it might look like an item is halfway out from one tile and halfway onto the next, it will be accounted to exactly one of the two tiles:

• If you stop the belt tile the item is on, it stops; else it continues moving - there are no in-between states.
• If you connect the two belt tiles to a circuit network and get them to report statistics about the items they carry, you will see the item being accounted to exactly one of them.
• An inserter can only pick up items that are logically on the tile in front of it, not items butting in from the neighboring tiles.

In this sense it is useful to think of items as points with a certain minimum distance between them, rather than things with an area lying next to each other. For belt calculations and circuit networks involving belts it doesn't really matter where those "center points" are within the graphic of the item, but they appear to be in the middle:

In the image above the belts have been started at 1 tick offsets, then all the top row tiles have been stopped at once, causing the front-most stopped items to poke out by varying amounts. The items on the leftmost belt are almost halfway into the next tile, which means their center points are the closest to the edge of the upper stopped tile.

Below is a schematic example showing some items moving over two straight fast transport belt tiles and what their read signals would be at each tick. Their center points are marked with *. (The space between belt tile 1 and 2 is only for visualisation - in the game there are no such gaps between tiles.)

Tick  Belt tile 1                      Belt tile 2                       Read belt tile 1  Read belt tile 2
      |------------------------------| |------------------------------|    Pulse   Hold      Pulse   Hold
  0         <---*-->  <---*--> <---*-- ><---*-->            <---*-->         0       3         0       2
  1           <---*-->  <---*--> <---* --><---*-->            <---*-->       0       3         0       2
  2             <---*-->  <---*--> <-- -*--><---*-->            <---*--      0       2         1       3
  3               <---*-->  <---*--> < ---*--><---*-->            <---*      0       2         0       3
  4   ->            <---*-->  <---*-->  <---*--><---*-->            <--      0       2         0       2
  5   *-->            <---*-->  <---*- -> <---*--><---*-->            <      1       3         0       2
  6   --*-->            <---*-->  <--- *--> <---*--><---*-->                 0       2         1       3
  7   <---*-->            <---*-->  <- --*--> <---*--><---*-->               0       2         0       3
  8     <---*-->            <---*-->   <---*--> <---*--><---*-->             0       2         0       3

Belt positions and lengths

Careful measurement shows that the outer lane of a turn is exactly 1.15234375 times longer than a straight belt, or 295/256 in fractional format. That means each straight belt tile has 256 positions an item can be in, even though measuring the position with that precision can only be done indirectly.

Here are the speeds and lengths of the various types of belt tiles in terms of these positions:

What		Number of positions
Basic transport belt speed, per tick		8
Fast transport belt speed, per tick		16
Express transport belt speed, per tick		24
Length of one lane of a straight belt tile, underground belt, and splitter		256
Length of the inner lane of a turn		106
Length of the outer lane of a turn		295
Length travelled by an item sideloaded late on a straight belt or underground exit		68
Length travelled by an item sideloaded early on a straight belt or underground entrance		188

Given the figures above, we can deduce the speed of a basic belt: 8 (positions per tick) / 256 (positions per straight belt tile) * 60 (ticks per second) = 1.875 tiles per second.

History

This is outdated and should be outsourced from this article but not deleted, because it is an interesting fact.

Kept for historical purposes, expand to view

Theory

Expected results 13.2 or older

belt-type	factor basic belt speed	speed (tiles/tick)	speed (tiles/sec)	speed (tiles/min)	density (single lane) items/tile	throughput (2 lanes) items/sec	throughput items/min
Basic	1	0.03125	1.875	112.5	3.571	13.39125	803.475
Fast	2	0.0625	3.75	225	3.571	26.7825	1606.95
Express	3	0.09375	5.625	337.5	3.571	40.17375	2410.425

Measured Results for v0.11 or Older

With Factorio v0.12 new belt physics was introduced. Before that the items where moved as real objects (which means, they need to look forward, if there is space to move), with 0.12 the items are moved "per lane". Also the physics in curves changed so that curves are now not longer have lower throughput.

This results have been measured with a special designed factory (a complicated setup to guarantee, that only the running items on a belt are measured and a "timer" which stops the measuring exactly) and Factorio v0.6.x, so this has to be redone. See forum article

Simple straight belt

belt-type	throughput items/min	throughput items/sec	percent of awaited	comments
Basic	719	11.98	90%
Fast	1184	19.73	74%	This is NOT double as fast as basic! it's only 1.65 times faster
Express	1775	29.58	74%	About 2.5 times faster than basic

Belt with 4 turns (2 left, 2 right, see down into next chapter)

belt-type	throughput items/min	comments
Basic	477-486	About 1.5 times slower. This is because the inner lane of a belt in a turn has only the half speed.
Fast	786-792
Express	1038-1042

Belt with 4 turns (2 left, 2 right), but faster belt at the edges

belt-type	throughput items/min	comments
Basic with fast edge-belts	674-683
Fast with express edge-belts	1058-1061	The fast belt with express edge seems to be faster, than pure express belt!

Comments to the results

The first surprising result is, that the theoretic throughput differs from real measured. Too much to be just measurement errors.The second result is, that the more speed a belt has, the more ineffective it becomes. That is in the first moment not clearly explainable. The awaited result is, that a fast belt can transport exactly the double amount of items, than a basic, because it is double as fast (1.875 tiles/sec vs. 3.75 tiles/sec).

The reason for this difference is the distance of the items on the belt when running. Items on the belt cannot run completely compressed, they need a small distance. This is the same problem as in a traffic jam: You cannot drive, when the first car drives, you need to wait until the car before you drives and then you have a reaction-time of about 1/2 second before yourself begin to drive. The same is it with the items on the belt and the reaction-time here is 1/60 or one tick [currently not really validated, but not more than 2 ticks; this can be calculated by measuring how fast the standing wave goes through the items (needs to built a very complicated testing factory)]. You can see this reaction time running through your items as a standing wave, when you have a belt, which is completely filled and only sometimes an item is removed. When you compare the speed of this standing waves, you can see clearly, that they are the same speed for all types of belts.

The reaction-distance for items on a basic belt is

 (1.875 tiles/sec) / 1 tick = 1.875 tiles/sec / 1/60 sec = 0.031125 tiles

or in other words: An item on a moving belt is not 0.28 tiles long, it is 0.31125 tiles, which makes it 11.2% longer

Overview for all belts:

 Basic:   0.28 tiles + 0.03125 tiles = 0.31125 tiles => 11.2%
 Fast:    0.28 tiles + 0.0625 tiles  = 0.3425 tiles  => 22.3%
 Express: 0.28 tiles + 0.09375 tiles = 0.37375 tiles => 33.5%

This explains the reduction to 90% of speed for basic belt and the 74% for the fast belt (all inside measuring errors), but doesn't explain the results for express belt. This is part of further research.

This shows clearly, that the faster a belt is, the more distance the items have on a moving belt. More distance means, the density is lighter and this means, there are not so many items transported.

(This may explain the discrepancy in transported items, but don't use the numbers for real calculations, because they need to be redone!) (This is eventually one reason: http://www.factorioforums.com/forum/viewtopic.php?f=8&t=3630 )

A possible reason for this: http://www.factorioforums.com/forum/viewtopic.php?f=16&t=6817

See also

• Belt transport system
• Jan 04 FFF #276: Belt item spacing & Script rendering
• Feb 03 FFF #176: Belts optimization for 0.15
• Accurate belt segment measurements (discusses 0.17)
• Factorio: a quantitative guide (discusses 0.14)