CENTER PIVOT ANALYSIS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


We were asked to analyze the statics involved in a real life system.  I chose to evaluate a

center pivot system.  In addition, I examined how the tower’s stability is affected by differing the tower’s height.  The following is a description of the situation I evaluated, the calculations I made, and the results I found.

 

Problem:  The Department of Biological Systems Engineering at the University of Nebraska-Lincoln is planning an experiment to measure the amount of carbon dioxide removed from the air by agricultural crops and the net amount of carbon that can be stored in the soil.  This is part of an effort to mitigate the impact of global warming and the buildup of greenhouse gasses.  Experiments will be conducted in irrigated fields.  The fields that the Department will use contain center-pivot irrigation systems that have nine-feet tall towers.  To conduct experiments researchers must install testing equipment that is up to 25 feet tall.  The equipment will be permanently installed; therefore, the center pivot systems must be modified to provide higher clearance so that the pivot does not interfere with the testing.

 

My project will be to analyze the static forces involved in traditional center pivot systems that are nine-feet tall, and then analyze the change of these forces for a center pivot that is raised to a height of twenty-five feet to accommodate the University's needs.  I will also analyze the stability of the different tower heights

 

 

System:  Center pivots are mechanical irrigation systems that automatically revolve in a field to apply irrigation water through sprinklers (figure 1).  The systems are typically one-quarter mile long and irrigate an area of about 130 acres.  To irrigate tall crops the systems are designed with towers that suspend the pipe above the ground.  The minimum clearance is about nine feet.  Tires and an electric motor are installed on the tower to propel the center pivot around the field.  Steel pipe is connected between the towers to supply water to sprinklers along the lateral.  The pipe is suspended using an under-pipe truss system.  The distance between towers is called a span.  The length of the span can vary between 130 and 200 feet.  The typical pipe on the pivot has an outside diameter of 65/8 inches with a wall thickness of 0.109 inches.  The pipe and the towers are typically galvanized to prevent corrosion. 

 

Calculations:  The first step to be accomplished was to find the system’s dimensions.  Lindsay Manufacturing supplied me with the system’s dimensions.  The needed dimensions are highlighted in the dimension packet attached.  There is also a dimension sheet of only the useful dimensions.  After researching the dimensions, I began the actual calculations by calculating the weight of the total span when the pipe is filled with water.  To find this value, the weight of the water must be found as well as the steel pipes’ weight.  I began with the free body diagram.

The first calculation I made was to find the water weight in the main pipe.  Since, the pipe is 0.109” thick and 6 5/8” in diameter, the water’s diameter is 6 5/8” – 0.109”.  The volume must be found and multiplied by the density to calculate the water’s weight.

 

 

Water Volume =

Vw = [6 5/8 – 2(0.109)]2pl/4,

 where l = length of the main pipe

 

l can be found by using the middle truss’s dimensions.  (Keep in mind, the curve of the pipe is not drawn to scale and in reality is very small.)

 


Y = [(8.48) 2+(5.38) 2]1/2 = 6.55’

 

Tan-1(Y/89.5) = q = 4.19 degrees

 

Therefore, l/2 = 89.5/cos(q) = 89.74’

Using the calculated l value in the water volume equation gives the following results.

Vw = [6 5/8 – 2(0.109)]2p(2)(89.74)/4 = 40.18 ft3

 

Now, the water’s weight can be found by multiplying the volume by the density of water (1 g/cm3).

 

Water weight = Ww = (40.18 ft3)(1 g/cm3)(1000000 cm3/1 m3)(1 m3/(3.28)3 ft3)

 

Ww = 1140 kg

 

The next step is to calculate the weight of the steel members.  The steel members fall into three categories; the main pipe, truss rods, and trusses.  I began by finding the weight for each of these categories and then adding them together.

 

Truss Rods: