
Problem Title: Positioning and Moving Sprinkler Systems for Irrigation 




Year: 2006 




Student Level: Undergraduate 




Source: MCM 




Commentary: Yes (1) 




Student Papers: Yes (6) 







Problem 


There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip systems to periodic flooding. One of the systems that is used on smaller ranches is the use of "hand move" irrigation systems. Lightweight aluminum pipes with sprinkler heads are put in place across fields, and they are moved by hand at periodic intervals to insure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain than other systems. It is also flexible, allowing for use on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and set up the equipment at regular intervals.
Given that this type of irrigation system is to be used, how can it be configured to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? For this task you are asked to find an algorithm to determine how to irrigate the rectangular field that minimizes the amount of time required by a rancher to maintain the irrigation system. One pipe set is used in the field. You should determine the number of sprinklers and the spacing between sprinklers, and you should find a schedule to move the pipes, including where to move them.
A pipe set consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter with rotating spray nozzles that have a 0.6 cm inner diameter. When put together the resulting pipe is 20 meters long. At the water source, the pressure is 420 KiloPascal's and has a flow rate of 150 liters per minute. No part of the field should receive more than 0.75 cm per hour of water, and each part of the field should receive at least 2 centimeters of water every 4 days. The total amount of water should be applied as uniformly as possible. 







Commentary 




Judge's Commentary:
The Outstanding Irrigation Problem
Papers
Daniel Zwillinger
Raytheon Company








Student Papers 




Sprinkler Systems for Dummies:
Optimizing a HandMoved Sprinkler
System
Carroll College, MT








Fastidious Farmer Algorithms (FFA)
Duke University, NC








A Schedule for Lazy but Smart
Ranchers
Shanghai Jiaotong University, China








Optimization of Irrigation
University of California, CA








Sprinkle, Sprinkle, Little Yard
University of Colorado, CO










Developing Improved Algorithms for
Irrigation Systems
Zhejiang University of Technology, China






