Farms seek to reduce operating expenses by optimizing mechanized operations, such as traversing fields. Fields are traversed when plowing, planting, harvesting, and mowing. While some of these need to be completed once per season, mowing needs to be performed many times during the season. We sought to quantify costs by modeling mowing through a graphical simulation of the process. We studied how different movement patterns affect efficiency and costs. Mowing is the model, but the results apply to all field operations. Two results from our work that will be presented: a parametrized, functional model for mowing a rectangular field and a graphical computer simulation. We found that a spiral pattern is more efficient than a rectangular method. The spiral is more efficient primarily due to the decreased number of unproductive turns. The simulation is designed to be made available to farmers to design more efficient traversal patterns for their fields.

1. Introduction Existing Research Methodologies Dissemination
The Cutting Edge:
Modeling Mowing
Jason Novinger
Mentor: Dr. Jon Beck
June 13, 2006

2. Introduction Existing Research Methodologies Dissemination
Acknowledgement
A
Also the LTEXsystem for providing such a simple
and powerful way to typeset my proposal and this
presentation.

3. Introduction Existing Research Methodologies Dissemination
Outline of Presentation

4. Introduction Existing Research Methodologies Dissemination
Outline of Presentation
• Why should we study mowing patterns?

5. Introduction Existing Research Methodologies Dissemination
Outline of Presentation
• Why should we study mowing patterns?
• What in the world are we researching?

6. Introduction Existing Research Methodologies Dissemination
Outline of Presentation
• Why should we study mowing patterns?
• What in the world are we researching?
• Who else is researching this?

7. Introduction Existing Research Methodologies Dissemination
Outline of Presentation
• Why should we study mowing patterns?
• What in the world are we researching?
• Who else is researching this?
• How will we conduct the research?

8. Introduction Existing Research Methodologies Dissemination
Outline of Presentation
• Why should we study mowing patterns?
• What in the world are we researching?
• Who else is researching this?
• How will we conduct the research?
• When and where will we report our results?

9. Introduction Existing Research Methodologies Dissemination
Why should we study mowing?
Mowing is important because:

10. Introduction Existing Research Methodologies Dissemination
Why should we study mowing?
Mowing is important because:
• Mowing is a common activity on farms and
large parcels of land

11. Introduction Existing Research Methodologies Dissemination
Why should we study mowing?
Mowing is important because:
• Mowing is a common activity on farms and
large parcels of land
• Mowing has costs that need to be minimized
(time, labor, equipment, etc.)

12. Introduction Existing Research Methodologies Dissemination
Why should we study mowing?
Mowing is important because:
• Mowing is a common activity on farms and
large parcels of land
• Mowing has costs that need to be minimized
(time, labor, equipment, etc.)
• Mowing represents other activities on farms like

13. Introduction Existing Research Methodologies Dissemination
Why should we study mowing?
Mowing is important because:
• Mowing is a common activity on farms and
large parcels of land
• Mowing has costs that need to be minimized
(time, labor, equipment, etc.)
• Mowing represents other activities on farms like
• Planting
• Fertilizing
• Harvesting

14. Introduction Existing Research Methodologies Dissemination
Why else should we study mowing?
Mowing represents a common problem—an area
needs to be covered or swept while optimizing some
variable. Other applications are:
• Computer-assisted search and rescue operations
• CNC machines used to fabricate custom parts
• Coating a product with paint

15. Introduction Existing Research Methodologies Dissemination
What mowing pattern are we analyzing?

16. Introduction Existing Research Methodologies Dissemination
What mowing pattern are we analyzing?
• Comparing square or rectilinear mowing
patterns with spiral patterns

17. Introduction Existing Research Methodologies Dissemination
What mowing pattern are we analyzing?
• Comparing square or rectilinear mowing
patterns with spiral patterns
• Looking at an inside-out spiral. Start at center
and work our way out

18. Introduction Existing Research Methodologies Dissemination
What mowing pattern are we analyzing?
• Comparing square or rectilinear mowing
patterns with spiral patterns
• Looking at an inside-out spiral. Start at center
and work our way out
• Which method is optimal in terms of money or
time?

19. Introduction Existing Research Methodologies Dissemination
Previous Research

20. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University

21. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work

22. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals

23. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class

24. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class
• Provided code to model mowing process

25. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class
• Provided code to model mowing process
• Classic observations study of mowing efficiency

26. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class
• Provided code to model mowing process
• Classic observations study of mowing efficiency
• 1987 - Pandey and Devani detail efficiencies of
two- and four-sided mowing patterns.

27. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class
• Provided code to model mowing process
• Classic observations study of mowing efficiency
• 1987 - Pandey and Devani detail efficiencies of
two- and four-sided mowing patterns.
• Found that use of both methods was most efficient

28. Introduction Existing Research Methodologies Dissemination
Previous Research
• Previous work at Truman State University
• 2005 - Gordon laid foundations for this summer’s
work
• Identified basic questions and goals
• Dr. Beck’s Spring 2006 CS 370 class
• Provided code to model mowing process
• Classic observations study of mowing efficiency
• 1987 - Pandey and Devani detail efficiencies of
two- and four-sided mowing patterns.
• Found that use of both methods was most efficient
• Introduced idea that turns were wasted time

29. Introduction Existing Research Methodologies Dissemination
Previous Research

30. Introduction Existing Research Methodologies Dissemination
Previous Research
• Newer theoretical and simulation studies

31. Introduction Existing Research Methodologies Dissemination
Previous Research
• Newer theoretical and simulation studies
• 2000 - Huang suggests breaking fields into to
smaller units to minimize number of turns

32. Introduction Existing Research Methodologies Dissemination
Previous Research
• Newer theoretical and simulation studies
• 2000 - Huang suggests breaking fields into to
smaller units to minimize number of turns
• 2000 - Arkin, et al. model field sweeping
mathematically and provide approximation
algorithms

33. Introduction Existing Research Methodologies Dissemination
Previous Research
• Newer theoretical and simulation studies
• 2000 - Huang suggests breaking fields into to
smaller units to minimize number of turns
• 2000 - Arkin, et al. model field sweeping
mathematically and provide approximation
algorithms
• Study of wider applications, particularly impact
on wildlife

34. Introduction Existing Research Methodologies Dissemination
Previous Research
• Newer theoretical and simulation studies
• 2000 - Huang suggests breaking fields into to
smaller units to minimize number of turns
• 2000 - Arkin, et al. model field sweeping
mathematically and provide approximation
algorithms
• Study of wider applications, particularly impact
on wildlife
• 1998 - Tyler, et al. find link between mowing
patterns and wildlife survival rate of Crex crex
chicks

35. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process

36. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns

37. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width

38. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments

39. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:

40. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment

41. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment
• Compute time needed to complete work

42. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment
• Compute time needed to complete work
• Determine area covered

43. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment
• Compute time needed to complete work
• Determine area covered
• Build a graphical computer simulation of the
mowing process. To include:

44. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment
• Compute time needed to complete work
• Determine area covered
• Build a graphical computer simulation of the
mowing process. To include:
• A representation of field being mowed

45. Introduction Existing Research Methodologies Dissemination
How will we conduct the research?
Three step process
• Make physical observations about mowing
equipment and patterns
• Equipment speed, turning radius, mowing width
• Time needed to make turns, adjustments
• Mathematically model the process of mowing a
field. Find equations to:
• Plot the path of the mowing equipment
• Compute time needed to complete work
• Determine area covered
• Build a graphical computer simulation of the
mowing process. To include:
• A representation of field being mowed
• Optimized path given field shape

46. Introduction Existing Research Methodologies Dissemination
When and where will we share our results?
Our results will be presented at:
• The 2006 STEP Summer Undergraduate
Research Symposium, August 2-3, 2006
• The 20th Annual Truman State University
Student Research Conference, April 2007
• This research may also be presented at
additional research conferences and submitted
for publication as opportunities allow
• This research will also provide a foundation for
additional research into efficient field
operations at Truman State University