Plan Sprinkler System Layout: Minimize # Circles for Max Coverage

In summary, the conversation discusses strategies for planning the layout of a sprinkler system, with the goal of using the least number of sprinklers to cover the entire floor with water. The participants suggest using shapes such as triangles, squares, and hexagons to ensure no gaps in coverage. They also mention the possibility of using an irregular packing for finite size rooms. One person proposes that hexagonal packing may be the best option, and another provides a resource for exploring the best way to cover a square with circles. The conversation ends with a question about proving the effectiveness of hexagonal packing.
  • #1
Firewolffzc
7
0
I have to plan the layout of a sprinkler system. Basically, each sprinkler shoots a radius of 7.5 feet water, and I want every part of the floor covered with water. How can I use the least number of sprinklers?
 
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  • #2
Welcome to PF!

Hi Firewolffzc! Welcome to PF! :wink:

Tell us what you think, and then we'll comment! :smile:
 
  • #3


Well, I think I figured one way to approach. Is it better to imagine not the circle, but a triangle, square or hexagon inscribed within the circle, because these shapes can link without gaps. Then once done with these shapes, I draw a circle circumscribing the shape. I was wondering if this was an effective method. If it is, which shape is best?
 
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  • #4
yup, that seems a good idea!

i'd guess it's the hexagon, but you'd better do the maths! :wink:
 
  • #5


Well, see, I don't know what math to do! I figured out that the reason we can use triangles, squares and hexagons is because the measurement of their angles are multiples of 360. (triangle)60*6=360, (square)90*4=360, (hexagon)120*3= 360. Well, it is not possible to have a shape with a 180 or 360 degrees angle, therefore hexagons are the best shape because they make the smallest area between circles. Wow, I can't believe I figured that out myself. Anyway, is there more to it or is this the final solution?
 
  • #6
no, that seems fine, so long as you actually prove
Firewolffzc said:
… hexagons are the best shape because they make the smallest area between circles.

:wink:
 
  • #7
A hexagonal packing might be the best for covering the entire plane (not sure), but for finite size rooms, an irregular packing can do better

This is a page with the best known results for covering a square with circles

http://www2.stetson.edu/~efriedma/circovsqu/
 
  • #8
cool! :cool:
 
  • #9


Thanks for all your help. Btw, I don't know how to prove something like the area formed between circles circumscribing hexagons is the smallest compared to triangles and squares.
 

1. How do I determine the best layout for my sprinkler system to ensure maximum coverage?

To determine the best layout for your sprinkler system, you will need to consider the size and shape of your yard, the water pressure available, and the type of sprinkler heads you will be using. It is also important to take into account any obstacles such as trees or buildings that may affect the coverage.

2. Can I minimize the number of circles in my sprinkler system layout?

Yes, it is possible to minimize the number of circles in your sprinkler system layout. This can be achieved by strategically placing the sprinkler heads in a way that maximizes coverage while minimizing overlap. Using the right type of sprinkler heads can also help with minimizing the number of circles needed.

3. How many circles do I need for my sprinkler system?

The number of circles needed for a sprinkler system will depend on the size and shape of your yard, as well as the type of sprinkler heads and water pressure available. It is important to carefully plan and measure your yard to determine the optimal number of circles for maximum coverage.

4. Are there any tools or software available to help with planning a sprinkler system layout?

Yes, there are various tools and software available that can assist with planning a sprinkler system layout. These tools can help with measuring and mapping your yard, as well as calculating the best placement for sprinkler heads to minimize the number of circles needed for maximum coverage.

5. What are the benefits of minimizing the number of circles in a sprinkler system layout?

Minimizing the number of circles in a sprinkler system layout can lead to more efficient water usage and lower water bills. It can also help with preventing overwatering in certain areas, leading to healthier plants and a more visually appealing yard. Additionally, a well-designed sprinkler system can save time and effort in maintaining your yard.

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