# Circular pattern sprinkler in a rectangular backyard - Most effective sequence of selected positions

#### atferrari

Joined Jan 6, 2004
4,752
My backyard is rectangular, measuring approximately 8 x 5 meters. The sprinkler used to water the grass, produces a regular/even (circular) pattern of 1,5 m radius.

While I tried several schemes with different positions each, I could not decide yet what is the best combination of positions to get the most even watering effect on most of the surface.

Since nothing of this automated yet I need to attend it personally and I do not want to exceed the required quantity of water. Grass is a delicate variety of dichondra.

Is there a way that I could calculate the positions and optimal sequence to ensure the most even possible distribution?

Wondering if a little of math and some geometric reasoning could help.

Suggestions are welcome.

#### cmartinez

Joined Jan 17, 2007
8,182

#### atferrari

Joined Jan 6, 2004
4,752
It is the most basic; just a circle.

#### bogosort

Joined Sep 24, 2011
696
Is the water from each sprinkler distributed as a 1D circle or as a 2D disk (surface of a circle)? If the latter, then a hexagonal arrangement is provably the most efficient.

See https://en.wikipedia.org/wiki/Circle_packing

#### atferrari

Joined Jan 6, 2004
4,752
Is the water from each sprinkler distributed as a 1D circle or as a 2D disk (surface of a circle)? If the latter, then a hexagonal arrangement is provably the most efficient.

See https://en.wikipedia.org/wiki/Circle_packing
Thanks bogosort. It is a 2D disk and yes, the hexagonal arrangement seems to fit my needs.

Started to also consider tweaking the actual diameter by reducing the pressure somewhat to get an optimal solution.

#### cmartinez

Joined Jan 17, 2007
8,182
Thanks bogosort. It is a 2D disk and yes, the hexagonal arrangement seems to fit my needs.

Started to also consider tweaking the actual diameter by reducing the pressure somewhat to get an optimal solution.
That's what I would actually do. If it were a perfect square, I'd sprinkle from the center with the largest diameter possible, and then the corners adjusting the pressure so as to cover the adequate area.... you're in for an annoying daily task, I'd consider a little more advanced system instead.