Center for Irrigation Technology
  Irrigation Notes
California State University, Fresno, California 93740-0018

August 1988
A New Way To View Sprinkler Patterns*
By Kenneth H. Solomon

  Denso-grams and the scheduling coefficient offer irrigators a chance to "test drive" their sprinkler system design and solve problems before they are buried.
Denso-grams and the scheduling coefficient are two new tools you can use to obtain a computer preview of how specific sprinkler and spacing combinations will irrigate your turf. Visualizing the coverage makes it easier to select the best equipment for the job.

A denso-gram is a pattern of dots that shows the expected coverage from a particular combination of sprinklers, nozzles, pressure and spacing.

The scheduling coefficient is a number that relates to the uniformity of coverage and how to operate the system to adequately irrigate the en-tire turf area.


Annual Annual Energy Savings
Gross Water per PSI of
Application Pressure Reduction
(inches/year) (BHP-HRS/Acre)


The coefficient of uniformity (CU) is determined from the statistical analysis of the irrigation pattern. The higher the CU, the more uniform the water application. The ideal CU is 100 percent, but that is unattainable - even rainfall isn't 100 percent uniform.

The CU is a widely-recognized pattern evaluation tool, but some turfgrass irrigators criticize it because it treats over-watered and under-watered areas the same. Turfgrass irrigators generally are more interested in combating dry spots than wet spots.

At the Center for Irrigation Technology, we compute the CU on all of our computer-developed sprinkler patterns, but we also use denso-grams and the scheduling coefficient to better evaluate sprinkler and spacing combinations. Most people readily understand the denso-gram's display of irrigation patterns. In contrast, only those who are very familiar with irrigation uniformity analysis have a good comprehension of the significance of CU numbers.


Denso-grams clearly show good and poor irrigation coverage. Both denso-grams shown here are based on the same sprinkler head, but the sprinkler spacing differs. The denso-gram above clearly indicates too much space between sprinklers, which can lead to poor coverage. The denso-gram below shows the coverage when the spacing problem is solved.


The denso-gram visually displays the irrigation wetting pattern between the sprinklers. The sidebar "Using Denso-Grams" shows how denso-grams illustrate irrigation problems. The denso-gram uses dot-matrix shading to clearly show the wet and dry areas in the pattern. The darkest portions receive the most water and the lightest spots receive little or no water.

Both the denso-gram and scheduling coefficient concepts are intended for use with computer-generated irrigation patterns based on tests of single sprinklers (although they could be used with pattern evaluation data gathered in the field).




Unlike CU, the scheduling coefficient does not measure average uniformity. Instead, it is a direct indication of the dryness of the driest turf areas (critical areas). The number is called the scheduling coefficient because it plays a direct role in establishing irrigation times.

The scheduling coefficient is a numerical indicator of irrigation uniformity that was developed with turfgrass irrigation in mind. It is based on the critical turf area because in turfgrass irrigation it is common to irrigate any critical area until it's sufficiently watered.

To calculate the scheduling coefficient, first find the critical area in the water application pattern. This is the area receiving the least amount of water. The amount of water applied to this critical area is divided into the average amount of water applied throughout the irrigated area. The answer is the scheduling coefficient. Scheduling coefficients will be numbers greater than 1, like 1.5, 2.2 and so on. If perfect uniformity were attainable, the scheduling coefficient would be 1.0.

The scheduling coefficient indicates the amount of extra watering needed to adequately irrigate the critical area. For example, suppose your irrigation system's average watering rate would satisfy your turf with a 30-minute irrigation cycle. If the irrigation pattern were perfectly uniform, a 30-minute watering time would give all the turf the necessary amount of water. However, the irrigation system is not perfectly uniform.

Suppose the irrigation pattern has a scheduling coefficient of 1.8. After 30 minutes of irrigation, a critical area of turf would still be under-watered due to non-uniformity. It will take 54 minutes (30 minutes x 1.8) to apply an adequate amount of water to the critical area. Those extra 24 minutes of watering time would adequately water the dry spot but over-water the rest of the area.

Ideally you discovered this problem before you installed your sprinkler system. If so, you can solve the problem by reevaluating your component choices -sprinklers, nozzles, nozzle pressure and sprinkler spacing.


The staff at The Center for Irrigation Technology will run denso-grams on your sprinkler system for a nominal fee. For further information, con-tact: The Center for Irrigation Technology, California State University, Fresno, CA 93740-0018, (209) 278-2066.



An energy conservation measure that would reduce the pressure requirement by 10 PSI on this golf course would save $988.80 per year. If that measure had an economic life of 15 years, the Present Value Factor would be 10.05 (see Table 4), and the present value of the total savings would be $9,937.44. So you see, energy conservation can pay off pretty well.

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