In my last game, over the droughts, my canal containing my water wheels provided less and less power for an ever increasing number of wheels.

Upstream of my canal, I could no longer have a suitable CMS flow, because the water was overflowing and I had to open a floodgate to get out the overflow.

This has the effect of having less water flowing and therefore less flow.

The question was why and to what extent an impeller affected the water flow upstream.

Tests and measurements were made on the water wheels of the "Iron Teeth" faction on the Experimental version v0.2.1.0 and verified for the following updates:

• v0.5.01 (Work In Progress)
  
• v0.4.0.1
  
• v0.3.5.0
  
• v0.2.2.0

Below is a small index to list the different objects involved in the guide as well as the particular terms or even defined by me.

• In Game Object :
  
  • Stream Gauge : Pole that measures depth and water flow in CMS.
    
  • Compacte Water Wheel : A compact generator that transforms water flow into energy.
    
  • Large Water Wheel : A larger and more efficient wheel. Side supported.
    
  • Water Source : A unbuildable rock (1x1) that provides water during wet season.
    
  • Badwater Source : A unbuidable large crack (3x3) that spew out the chemicals all the time, no matter the season (Introduced in v0.5.0.1).

• Terms :
  
  • CMS : Unit of measurement of water flow in the game. Supposed Cube Meter Second
    
  • Height: A level of terrain represents 1 in height
    
  • Water height: The water height is measured to two decimal places. Example 0.15 of water level.
    
  • Canal: A channel surrounded on both sides by walls (dam or natural terrain) with a minimum height of 1 forcing water to flow in one direction (from the source to the outlet).
    
  • Brake effect: This is the effect that a wheel produces on the height of the water on the upstream and the downstream flow.

With the help of debugging tools and the development console, I was able to do more meaningful testing on a flat 128x128 board.


To define the reference value of a water source, with the tools you can see its statistics:



A source of strength 1 (STRENGTH) generates a water flow of 1 CMS with a height of 0.15 in a channel of width 1 once the final evacuation is reached (edge of map).


If we modify the strength of the source to 2, we can see that the water flow goes to 2 CMS with a height of 0.30 once the final evacuation is reached (edge of map).

Originally posted by Mechanistry (Developers) - Update 5 - 2023.09.29:

Badwater is the first extra fluid we have on the maps. It uses Timberborn’s water physics system, so it behaves similarly to, um, the good water. It has a varied current’s strength, flows across the land, fills up basins, interacts with dams etc. But when it reaches a regular river, the two water types start to mix, with the good water becoming increasingly polluted. The two fluids are distinct visually, and you can easily see how the pollution spreads.

(...)

First, badwater gradually reduces the irrigation range of polluted water bodies until they no longer irrigate. On top of that, at a certain threshold, it starts contaminating the nearby terrain. Any plant growing in the affected area - be it a regular crop, aquatic crop, or a tree - will quickly wither and die. Fortunately, the contamination disappears rather quickly after you get rid of badwater. We’ll get to that in a moment.

Badwater also affects the beavers and their operations. It reduces the efficiency of water pumps, turns off several extra buildings, and traversing through it is dangerous. Prolonged exposure, especially when in high concentrations, may contaminate your colonists. After a few days, the affected beaver becomes a zombeaver burden - it moves slowly, refuses to work, and continues consuming resources. This applies to kits too. Bots, to no surprise, are not affected - this allowed us to improve their functionality (and also unlock terraforming for beavers, yay!).

The badwater source has a ground print of 3x3 and it default strength setting is set to 3 :



Badwater source of strength 3 surrounded with a canal of width 3 generates a water flow of 1 CMS with a height of 0.15 once the final evacuation is reached (edge of map).



Both water and badwater sources has the same behavior regarding the generated flow for the strength unit (as mentionned by developers in their presentation)

To put the reference on the flow of water from a source versus the channel in which the water flows, I did several tests and I found a formula that seems to work:

Notes: The values ​​are measured when the flowing water has reached the edge of the map (final evacuation).

Manual reading with flow gauges at several places in the channel with the water sources placed a little bit upstream of the start of the canal.

• For 1 source of force 1, the flow is 1.00 CMS and height 0.150 in a channel of width 1.
  
• For 2 sources of force 1, the flow is 2.00 CMS and height 0.300 in a channel of width 1.
  
• For 3 sources of strength 1, the flow is 3.00 CMS and height 0.450 in a channel of width 1.
  
• For 2 sources of force 1, the flow is 1.00 CMS and height 0.150 in a channel of width 2.
  
• For 3 sources of force 1, the flow is (1.4 and 1.6) CMS and height 0.250 in a channel of width 2. The average of the two is 1.5 CMS.
  
• For 4 sources of force 1, the flow is 2.0 CMS and height 0.330 in a channel of width 2.
  
• For 5 sources of force 1, the flow is 2.5 CMS and height 0.420 in a channel of width 2.
  
• For 6 sources of force 1, the flow is 3.0 CMS and height 0.500 in a channel of width 2.

Determinable formula:

That is:
• n the number of water sources
• W the width of the channel in number of boxes

- Water flow in CM : (<TotalWaterSourceStrength> x 1 CMS) / W
- Approximative* water height without water wheel : (<TotalWaterSourceStrength> x 0.15) / W

* It resides some unresolved external factors due to water movements implies by blocks involved in canal reduction (+ angles). The formula works perfectly with even numbers.

The objective of the second test was to determine the effect of the height of the water fall on the water flow.

The reference value is a source of water on the ground of force 1 (1CMS) in a canal of width 1 (1 source of water of square 1 for a water flow of width 1).

• A ground source whose water flows directly to the ground produces a flow of 1 CMS (height 0.15)
  
• A source on the ground whose water rises to a height of 1 to flow to the ground (fall height of 1) produces a flow of 1 CMS (height of 0.15)
  
• A source on the ground whose water rises to a height of 2 to flow to the ground (fall height of 2) produces a flow of 1 CMS (height of 0.15)
  
• A source on the ground whose water rises to a height of 3 to flow to the ground (fall height of 3) produces a flow of 1 CMS (height of 0.15)

On the 4 height tests, no effect is observed on the water flow.
It is the strength of the source and the combination of these that improves the flow of water.

A water wheel installed in a canal generates a braking effect on the watercourse and on the flow.



The readings show that the water flow in CMS is impacted by approximately 0.25% per wheel downstream and the water level upstream rises. For flow, upstream wheels are unaffected by downstream flow loss.

Notes: On an installation of 4 sources on a canal of width 2 and depth 2, I have almost no loss of flow (0.1cms) for 192 wheels.

This braking effect is effective for each wheel installed in the channel, regardless of the distance between the wheels. Control carried out for intervals in number of boxes of 1, 2, 3, 4, 5, 6, 7, 10 and 15.

The measurements were made with gauges placed upstream to measure the source, downstream to measure the flow rate/remaining height, then a gauge before and after a wheel.








A compact water wheel has a braking effect in terms of upstream water depth of 0.03 per wheel.

A canal of 1 sources of flow 1 CMS, depth of 1, water height 0.15 can receive 28 wheels before overflowing on the sides and impacting the water flow for a total power of 1280 HP (40hp/cms)







A wide water wheel has a braking effect in terms of upstream water depth of 0.05 per wheel.

A canal of 2 flow sources 1 CMS (width 2), depth of 1, water height 0.15 can receive 17 wheels before overflowing on the sides and impacting the water flow for a total power of 3060 HP (180hp/cms)

A canal of 2 flow sources 1 CMS (width 2), depth of 2, water height 0.15 can receive 37 wheels before overflowing on the sides and impacting the water flow for a total power of more or less 6660 HP (Theorical). In test, power viewed was 6479 HP with two 90° dam angles (having also a little brake effet 0.01 in term of height).

A canal of 3 flow sources 1 CMS (width 2), depth of 2, water height 0.24 can receive 37 wheels before overflowing on the sides and impacting the water flow for a total power of more or less 9990HP (Theorical). Indeed, 3 sources of strength 1 merge in a canal of 2 width lead to a flow of 1.5CMS. 37 Wheels x (180HP/CMS * 1.5CMS) = 9990HP



When the maximum height of the canal is reached, adding wheels will have the effect of overflowing the sides reducing the amount of water and therefore the flow applied to the wheels.

To stop the brake effect, it simply for the canal to continue at least one floor level below. The waterfall becomes the "source" of the canal. This lower canal can again accommodate as many wheels as permitted by the braking effect.

Notes: The flow loss of 0.25% per impeller applies to each impeller (downstream) and therefore the flow loss applies, regardless of the height level of the channel.

The water pumps seem to offer a flow rate in CMS of 0.5. Indeed, 2 pumps placed end to end which discharge water into a canal of width 1, generates a flow of 1 CMS.
The water source canal with strength of 1 has 0 CMS flow remaining



The pumps consume 700 HP each.

Considering you have 4 sources of strength 1 CMS . Making a circulare loop in a canal of width 4 only require 8 pumps x 700 HP = 5600 HP to be autonomous.

A sample autonomuous canal :

Following these tests, it is found that the most troublesome is the braking effect in terms of height which applies to each wheel installed in the canal. This height rises quickly. This effect can be reset by stepping down a notch to generate a new upstream source.
However, each wheel roughly reduces the strength of the water current by 0.25% in CMS (not prooven with a flow of 2 CMS) and since the height has no effect on the flow, it is not possible (without an additional source) to boost the flow.

My advice is to build your canal as high as possible (depending on the water sources available) in order to play on the levels to eliminate the brake effect. If possible, combine 4 water sources into a channel 2 squares wide for a depth of 2 squares for large wheels. This model allows to put end to end a good hundred wheels for a total of 66000 HP !



Thank you for reading me to the end.

Do not hesitate to correct me if you have different elements or if my analysis approach seems incorrect or incomplete.

Kindly regards,
Neoblaster.

• 2023-04-16 :
  
  • Update section MECHANICAL WATER PUMP :
    
    • Adjust all content due to the change of the power pump efficience :
      
      • Flow produced by one pump : 0.5 CMS
    • Add an example of canal which produce enougth power to be autonomous.

• 2023-01-08 :
  
  • Control done following the updated of the Experimental version to v0.3.5.0 :
    
    • Updating data regarding Compacte Water Wheel :
      
      • Braking Effect changed from 0.026667 to 0.03 in term of water height.
        
      • Adjusting info for a canal of 1 sources of strength 1, depth 1 :
        
        • Maximum Wheel changed from 32 to 28, loosing 4 wheels.
          
        • Maximum Power changed from 1280 to 1120, loosing 160hp.
    
    
    • Updating data regarding Larger Water Wheel :
      
      • Braking Effect changed from 0.044444 to 0.05 in term of water height.
        
      • Adjusting info for a canal of 2 sources of strength 1, depth 1 :
        
        • Maximum Wheel changed from 19 to 17, loosing 2 wheels.
          
        • Maximum Power changed from 3420 to 3060, loosing 360hp.
      • Add calculation & test for a canal of width 2 from 3 sources of strength 1 :

• 2022-07-21 :
  
  • Control done following the updated of the Experimental version to v0.2.2.0.

• 2022-07-21 :
  
  • Guide creation