I showed a bit into the videos and for the video Compression & Throughput the throughput in your first example is exactly the same!
I think I need to clarify this a bit.
Speed
Is the speed of the belts. It is measured in tiles per second or tick. See
https://forums.factorio.com/wiki/inde ... elts#Items
Well, sound stupid, but let's just continue.
Distance
This is how much length of tiles you transport something.
I counted in the video a length of 18 tiles for both belts.
Density
is how much items lay on a length of belt (we are speaking here about belts only, right?). This is measured in item per tile.
So when I stopped the video I could compare it: On the express-belt side there are in general 6 pieces of coal, on the right in general 18.
(You see something: 18 / 6 = 3
)
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Density for left side:
6 items / 18 tiles (length of belt) = 1/3 items / tile
Density for right side:
18 items / 18 tiles (length of belt) = 1 items / tile
The items on the left side are 3 time less dense than on the right. But as we all know, the express belts are 3 time faster than the basic. What does that mean?
Throughput
This is
items per time. It has nothing to do with speed! And also nothing with the distance.
See
http://en.wikipedia.org/wiki/Throughput - this defines it as production speed, which is - well - "items per time".
For the belts it is
https://forums.factorio.com/wiki/inde ... ottlenecks
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Throughout for express belt:
5.625 tiles / sec * 1/3 items / tiles = 1,875 items / sec
Throughput for basic belt:
1.875 tiles/sec * 1 item / tiles = 1.875 items / sec
Why? On the left side is the express belt, but the items have a low density. This can be obviously seen, if you compare it to the right side with the basic belt: the items there have a much bigger density.
And when you think about it clearly: The left and right belt
must have the equal throughput, cause they are feed both by basic inserters, with the same speed, this can also be clearly seen in the video.
The only difference is - of course - the speed. The first items on the express belt get faster to the top. But after the belts are filled, there is no difference and you see that also, when you now stop the inserters down, the items on the left and rights side are moved to the top and when you count both chests after the last item on the basic belt, you will see, that there is exactly the same number of items in it.
Edit: ok, there is a small difference in throughput, when we look into the chests! The difference is the amount if items, that are faster in the left side chest, cause the belt is faster. But over time this difference in throughput will get quite small. But when you turn off the lower inserters and wait, till all items are moved into the upper chests, the throughput is again identical.
Compression
Compression is about trying to achieve the
maximum density on a belt. A state where the items are placed one after another. In other words:
The maximum density on a belt.
Well, now you need to know, that the density on a belt depends on, if the items are moving or not. This is explained here:
https://forums.factorio.com/wiki/inde ... he_results
This explains the size of items, when they are laying on the belt in maximum compression and moving. The density is the reciprocal value:
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Basic: 3,212851406 items / tile
Fast: 2,919708029 items / tile
Express: 2,675585284 item / tile
This is, when the items on the belts move. When the items stop (cause the belt jams...) the density is of course 3,571428571 item/tile.
Pfff..... hands hurt...
Ok, I hope this helps to be more clear in your videos, because - on my sight - you mix continuously the terms.
PS: I like this series, you have a talent for bringing down complicated concepts to its essential basics.