Sprinkler layout wetting pattern

Layout and wetting pattern

The four sprinklers are placed 20 m apart, i.e. at the centres of the four 20 m x 20 m quarters of the plot, at (10,10), (30,10), (10,30) and (30,30) m. Each wets a circle of radius 10 m.

 40 m +--------------------+
      |  .--.      .--.    |
      | ( S1 )    ( S2 )   |
      |  '--'      '--'    |
      |  .--.      .--.    |
      | ( S3 )    ( S4 )   |
      |  '--'      '--'    |
   0  +--------------------+
      0       20        40 m
   neighbouring circles touch at only one point;
   the 4 corners and the centre are dry

Calculation

$$\begin{aligned} A_{plot} &= 40\times 40 = 1600\ \text{m}^2\\ A_{wetted} &= 4\times\pi (10)^2 = 1256.6\ \text{m}^2\\ \text{Coverage} &= 1256.6/1600 = 78.5\%\\ \text{Dry area} &\approx 343\ \text{m}^2\ (21.5\%) \end{aligned}$$

Comments

• Neighbouring circles only touch; there is no overlap, so the centre of the plot, the four corners and the spaces between the circles stay dry.
• The depth of water is highest near each sprinkler and falls to zero at the 10 m edge, so the distribution is non-uniform (poor uniformity coefficient).
• About 21% of the plot gets no water.

Improvement

1. Reduce the spacing to about 50-60% of the wetted diameter (20 m), i.e. 10-12 m square spacing, so that neighbouring circles overlap. A 3 x 3 layout (13.3 m spacing, 9 sprinklers) just covers the whole plot; a 4 x 4 layout (10 m spacing, 16 sprinklers) gives good overlap and uniformity.
2. Or increase the throw radius to at least $10\sqrt{2} = 14.14$ m (about 14.2 m) with the same four sprinklers, so that the circles meet at the centre and corners of each quarter.
3. Use a triangular layout for better uniformity, and use part-circle sprinklers along the edges so that water is not thrown outside the plot.
4. Avoid operating in high wind.