KSU-GPSguidance

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```							          KSU-GPSguidance.xls --                 A spreadsheet program to analyze the economics of machine
guidance and section control investment.

Version -- 9.16.10

BACKGROUND INFORMATION
1) machine operation cost relative to field size and shape
2) economics of guidance technology in the context of overlap, which impacts:
a) machine usage per land acre (i.e., overlapping of machine operations)
b) crop input usage per land acre (i.e., overlap of inputs applied), which impacts:
i) cost of crop inputs
ii) reduced yield revenue associated with crop input overlap on headlands
3) economics of boom/machine section control

Typical uses would involve crop spraying, planting, tillage, etc. Dollar-valued calculations generally are on a per "applied" acre basis. A 3,000 acre field
sprayed three times in a year results in 9,000 applied acres for the year. Per-applied acre values are brought back to an implied investment per applied
acre via simple amortization (no salvage value of technology is considered). To derive how much you can invest in a given technology you will need to
consider applied acres per year. But, if you use the same technology for different machine operations, you might also need to add results from multiple
runs of this spreadsheet, where a separate machine operation is associated with a separate spreadsheet run. Finally, notice that a "covered" acre is
something different than an applied acre. In particular, an acre that is doubled-up on for inputs or machine coverage results in 2 covered acres; but, it
would still be only 1 applied acre.

The user inputs information for a field of interest, which is compared to four stylized fields. One of the five fields (user field and four stylized fields) must
be used as the custom rate benchmark. All four stylized fields have the same acreage and can be made the same acreage as the user-defined field if
user desires.

INPUTS vs CALCULATED VALUES
In the Analysis sheet all blue numbers are inputs and all other numbers are calculated from these inputs. The spreadsheet automatically recalculates
every time an additional input is entered. Thus, it is important to wait until all data have been entered and reviewed before interpreting any of the calculated
results (i.e., black numbers).

DESCRIPTION OF INPUTS
Several of the input cells (i.e., blue numbers) and calculated values have a red diamond in the upper right hand corner of the cell (if the comments do not
appear go to View / Comments on the Excel menu -- you may need to click and then again). By moving your mouse cursor over this diamond, a brief
description of the input will be displayed on the screen.

DEVELOPED BY:
Terry L. Kastens                                                Kevin C. Dhuyvetter                                          Dietrich L. Kastens
Professor Emeritus                                              Extension Agricultural Economist                             Geographer
Kansas State University                                         Kansas State University                                      Kastens Inc.

voice: (785) 626-9000                                           voice: (785) 532-3527                                        voice: (785) 626-4600
email: terrykastens@agecon.ksu.edu                              email: kcd@ksu.edu                                           email: dietrich@kastensinc.com
website: www.agmanager.info                                     website: www.agmanager.info                                  website: www.kastensinc.com

bc711096-1927-4c46-a917-b2df68ebdd96.xls
Intro
Terry L. Kastens, Kevin D. Dhuyvetter, and Dietrich L. Kastens
Kansas State University
bc711096-1927-4c46-a917-b2df68ebdd96.xls
Intro
Terry L. Kastens, Kevin D. Dhuyvetter, and Dietrich L. Kastens
Kansas State University
bc711096-1927-4c46-a917-b2df68ebdd96.xls
Intro
Terry L. Kastens, Kevin D. Dhuyvetter, and Dietrich L. Kastens
Kansas State University
bc711096-1927-4c46-a917-b2df68ebdd96.xls
Intro
Terry L. Kastens, Kevin D. Dhuyvetter, and Dietrich L. Kastens
Kansas State University
Field shape and headland economics analysis                                                                                            four stylized fields; assume farm left to right

user-defined
field                         equal sized      equal sized       equal sized
units          userfield        square        isos R trian     equil triang         circle             odd1         odd2
Section A: Input and field characteristics section
Size of field                                                                                    acres                 80               75               75               75                  75           167.4        269.9
Size of field                                                                                  square feet      3,484,800        3,267,000       3,267,000        3,267,000         3,267,000          7,291,944   11,756,844
Maximum width of field, perpendicular to direction of swaths (passes)                             feet              2,000            1,807           1,807             2,379               2,040           3,960        5,502
Running distance of headlands to cover for field                                                  feet              6,000            3,615           5,112             5,494               6,407          16,700       30,690
Number of swaths (passes) needed to cover headlands                                              count                  2                2               2                 2                   2               2            2
Turnaround speed is this portion of field speed                                                 percent              67%              67%             67%               67%                67%              67%          67%
Width of machine                                                                                  feet                 90               90              90                90                 90               90           90
Typical swath overlap in percent of machine width (selected below)                              percent            4.25%            4.25%           4.25%             4.25%               4.25%           4.25%        4.25%
Number of machine or boom sections to be controlled (for Section D)                              count                  5                5               5                 5                   5               5            5
Reaction distance (overlap) on manual shutoff of boom                                             feet                 15               15              15                15                  15              15           15
Effective width of equipment allowing for overlap                                                 feet             86.175           86.175          86.175            86.175              86.175          86.175       86.175
Number of passes in field                                                                        count              23.21            20.97           20.97             27.60               23.67           45.95        63.85
Width of headland                                                                                 feet             176.18           176.18          176.18            176.18              176.18          176.18       176.18
Area in headlands                                                                                acres              24.27            14.62           20.68             22.22               25.91           67.54       124.12
Area in field proper (i.e., non-headlands)                                                       acres              55.73            60.38           54.32             52.78               49.09           99.86       145.78
Implied perimeter distance for each pass (i.e., the 2 ends)                                       feet             258.53          172.35           243.74            199.01              270.73          363.41       480.68
Avg length of a pass (distance before must turnaround)                                            feet            1213.88         1455.13          1309.19            966.53             1048.37         1098.44      1154.13
Running distance of headland per acre                                                             feet              75.00            48.20           68.16             73.25               85.43           99.76       113.71
Average angle of approach to headland in degrees (0-90)                                         degrees             41.81            90.00           45.00             60.00               39.54           28.31        21.01
Machine efficiency
Excess area covered due to machine overlap                                                       acres               3.00             3.00            2.86              2.83                2.74            5.90         9.17
Total area covered by machine                                                                    acres              96.86            86.13           89.89             91.58               92.29          207.32       335.31
Machine efficiency (acres in field / area covered)                                              percent           82.60%           87.08%          83.43%            81.89%              81.27%          80.75%       80.49%
Total "area equivalent" covered by machine w/ speed adjustment                                   acres             103.68            90.14           95.82             98.36               99.45          224.07       363.01
Machine efficiency (acres in field / "area equivalent" covered)                                 percent           77.16%           83.21%          78.27%            76.25%              75.41%          74.71%       74.35%
ing anual control of whole boom or m
Crop input efficiency assum m                                    achine
Excess area for crop inputs at turnarounds due to angle and reaction time                        acres               6.26             1.30            5.20              4.67                6.80           18.71        34.87
Doubling-up of inputs on headlands field efficiency                                             percent           92.74%           98.30%          93.52%            94.13%              91.69%          89.95%       88.56%
Total area to which crop inputs are applied                                                      acres              89.26            79.30           83.06             82.50               84.54          192.01       313.93
Crop input efficiency (acres in field / area applied)                                           percent           89.62%           94.58%          90.30%            90.91%              88.72%          87.18%       85.97%

Section B: Economic factors and overlap amounts input section
Custom rate of machine operation, \$/ application acre                            \$5.00
Cost of input (fertilizer, herbicide, etc.), \$/application acre                  \$15.00
Lost yield revenue for doubling up, \$/doubled-up acre                            \$0.00
Interest rate for investment analysis, percent                                  10.00%
Number of years for amortization                                                   5
overlap %       cost \$/acre
Maximum overlap to consider                                     7.00%           \$0.00
Minimum overlap to consider                                     1.50%           \$0.20

Section C: Value of overlap                                                                                     userfield          square          isos R trian   equil triang         circle             odd1        odd2
Insert a 1 in the row below for the field most representative of the assigned custom machine rate
1 for overlap %                         1                0                 0               0                 0
Machinery efficiencies for custom rates:                                      for cust. rate   overlap %     Machine efficiency at various overlap percentages (includes turnaround slowdown), by field
incl. turnaround slowdown                   77.16%                                 0            7.00%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
crop input efficiency                 89.62%                                       0            5.63%        ########### ########### ########### ########### ###########                  ###########             ###########
doubling-up input efficiency          92.74%                                       1            4.25%        ########### ########### ########### ########### ###########                  ###########             ###########
Custom rate and input cost were assigned to:                                        0            2.88%        ########### ########### ########### ########### ###########                  ###########             ###########
userfield field with 4.25% overlap                                                 0            1.50%        ########### ########### ########### ########### ###########                  ###########             ###########
overlap %     Crop input efficiency at various overlap percentages, by field
7.00%        ########### ########### ########### ########### ###########                  ###########             ###########
5.63%        ########### ########### ########### ########### ###########                  ###########             ###########
4.25%        ########### ########### ########### ########### ###########                  ###########             ###########
2.88%        ########### ########### ########### ########### ###########                  ###########             ###########
1.50%        ########### ########### ########### ########### ###########                  ###########             ###########
overlap %     Doubling-up of inputs on headlands field efficiency at various overlap percentages, by field
7.00%        ########### ########### ########### ########### ###########                  ###########             ###########
5.63%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
4.25%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
2.88%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
1.50%        ###########     ###########     ###########       ###########      ###########        ###########    ###########

Sub-section C1: Machine operations                                                             overlap %     Custom rate for machine operations equivalent (uses turnaround slowdown), \$/applied acre
7.00%        ########### ########### ########### ########### ###########               ########### ###########
Compare dfferent fields and different overlaps                                                   5.63%        ########### ########### ########### ########### ###########               ########### ###########
4.25%        ########### ########### ########### ########### ###########                ########### ###########
2.88%        ########### ########### ########### ########### ###########                ########### ###########
1.50%        ########### ########### ########### ########### ###########                ########### ###########
overlap %     Advantage due to reduced overlap for machine operation (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ########### ########### ########### ########### ###########                ########### ###########
2.88%        ########### ########### ########### ########### ###########                ########### ###########
1.50%        ########### ########### ########### ########### ###########                ########### ###########
overlap %     Investment supported by above annual cost savings (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ########### ########### ########### ########### ###########                ########### ###########
2.88%        ########### ########### ########### ########### ###########                ########### ###########
1.50%        ########### ########### ########### ########### ###########                ########### ###########

Sub-section C2: Crop input cost                                                                overlap %     Crop input cost equivalent, \$/applied acre
7.00%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
Compare dfferent fields and different overlaps                                                   5.63%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
4.25%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
2.88%        ########### ########### ########### ########### ###########                ########### ###########
1.50%        ########### ########### ########### ########### ###########                ########### ###########
overlap %     Advantage due to reduced overlap for crop input expense (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ########### ########### ########### ########### ###########                ########### ###########
2.88%        ########### ########### ########### ########### ###########                ########### ###########
1.50%        ########### ########### ########### ########### ###########                ########### ###########
overlap %     Investment supported by above annual cost savings (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
2.88%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
1.50%        ###########     ###########     ###########       ###########      ###########        ###########    ###########

Sub-section C3: Lost yield revenue with doubling up of inputs                                  overlap %     Lost yield revenue with doubling up of inputs, \$/applied acre
7.00%        ########### ########### ########### ########### ###########                           ###########    ###########
Compare dfferent fields and different overlaps                                                   5.63%        ########### ########### ########### ########### ###########                           ###########    ###########
4.25%        ########### ########### ########### ########### ###########                           ###########    ###########
2.88%        ########### ########### ########### ########### ###########                  ########### ###########
1.50%        ########### ########### ########### ########### ###########                  ########### ###########
overlap %     Advantage due to reduced overlap for yield revenue (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                  ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                  ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ########### ########### ########### ########### ###########                  ########### ###########
2.88%        ########### ########### ########### ########### ###########                  ########### ###########
1.50%        ########### ########### ########### ########### ###########                  ########### ###########
overlap %     Investment supported by above annual cost savings (relative to topmost row), \$/applied acre
7.00%        ########### ########### ########### ########### ###########                  ########### ###########
To compare one % overlap with another just subtract one                                          5.63%        ########### ########### ########### ########### ###########                  ########### ###########
row's values from another in same column (i.e., same field)                                      4.25%        ########### ########### ########### ########### ###########                  ########### ###########
2.88%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
1.50%        ###########     ###########     ###########       ###########      ###########        ###########    ###########

Sub-section C4: Non-ownership costs of technology                                              overlap %     Non-ownership costs of technology, \$/applied acre
7.00%        ########### ########### ########### ###########                    ###########        ###########    ###########
5.63%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
4.25%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
2.88%        ###########     ###########     ###########       ###########      ###########        ###########    ###########
1.50%        ###########     ###########     ###########       ###########      ###########        ###########    ###########

Section D: Boom/nozzle/machine section shutoff on headlands analysis (affects applied input amounts and yield loss only, not machine operation cost):                                                 (based on 4.25% overlap)
userfield       square       isos R trian equil triang                              circle              odd1          odd2
Typical overlap in distance traveled before manually shut off boom                  feet      ########### ########### ########### ###########                                    ###########        ########### ###########
Width of whole machine or boom                                                      feet      ########### ########### ########### ###########                                    ###########        ########### ###########
Width of section of machine or boom                                                 feet      ########### ########### ########### ###########                                    ###########        ########### ###########
Distance into headland before whole boom can theoretically be shut off                            feet        ###########     ###########     ###########       ###########      ###########        ###########    ###########
Distance into headland before boom section can theoretically be shut off                          feet        ###########     ###########     ###########       ###########      ###########        ###########    ###########
Area doubled up on for each pass, manual control of whole boom                                 square feet    ###########     ###########     ###########       ###########      ###########        ###########    ###########
Area doubled up on for each pass, automatic control of whole boom                              square feet    ###########     ###########     ###########       ###########      ###########        ###########    ###########
Area doubled up on for each pass, manual control of boom sections                              square feet    ###########     ###########     ###########       ###########      ###########        ###########    ###########
Area doubled up on for each pass, automatic control of boom sections                           square feet    ###########     ###########     ###########       ###########      ###########        ###########    ###########
Portion of field with headland overlap of crop inputs, manual whole boom                        percent       ###########     ###########     ###########       ###########      ###########        ###########    ###########
Portion of field with headland overlap of crop inputs, auto whole boom                          percent       ###########     ###########     ###########       ###########      ###########        ###########    ###########
Portion of field with headland overlap of crop inputs, manual boom section                      percent       ###########     ###########     ###########       ###########      ###########        ###########    ###########
Portion of field with headland overlap of crop inputs, auto boom section                        percent       ###########     ###########     ###########       ###########      ###########        ###########    ###########

Area in semi-circle                                                                                           ###########     ###########     ###########       ###########      ###########        ###########    ###########
Q-adjustment factor for machine coverage (percent increase)                                      100%         ###########     ###########     ###########       ###########      ###########        ###########    ###########

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                       Analysis
KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                       Analysis
Field shape and headland economics analysis                                                                       four stylized fields; assume farm left to right

user-defined
field                     equal sized    equal sized     equal sized
units       userfield      square       isos R trian   equil triang      circle            odd1         odd2
Section A: Input and field characteristics section
Size of field                                                                     acres                80             75             75              75                75         167.4       269.9
Number of swaths (passes) needed to cover headlands                               count                 2              2              2               2                 2             2           2
Width of machine                                                                   feet                90             90             90              90                90            90          90
Area in headlands                                                                 acres             24.27          14.62          20.68           22.22             25.91         67.54      124.12
Average angle of approach to headland in degrees (0-90)                          degrees            41.81          90.00          45.00           60.00             39.54         28.31       21.01
Number of machine or boom sections to be controlled (for Section D)               count                 5              5              5               5                 5             5           5

Sub-section C5: Summed net benefits to overlap-reducing technology               overlap %   Sum of net annual benefits, \$/applied acre (relative to topmost row)
Percent of category to include in net benefits total                               7.00%          \$0.0000      \$0.0000       \$0.0000        \$0.0000      \$0.0000           \$0.0000       \$0.0000
Machine costs                           1                                         5.63%          \$0.2514      \$0.2491       \$0.2527        \$0.2478      \$0.2490           \$0.2467       \$0.2437
Input costs                             1              Sub-section C5.1           4.25%          \$0.4957      \$0.4911       \$0.4983        \$0.4887      \$0.4911           \$0.4866       \$0.4807
Yield revenue                           1                                         2.88%          \$0.7333      \$0.7264       \$0.7371        \$0.7230      \$0.7265           \$0.7200       \$0.7114
Non-ownership costs                     0                                         1.50%          \$0.9645      \$0.9553       \$0.9694        \$0.9509      \$0.9556           \$0.9472       \$0.9359
overlap %   Investment supported by net annual benefits (relative to topmost row), \$/applied acre
Total acres of use annually         10,000                                         7.00%            \$0.00         \$0.00         \$0.00          \$0.00        \$0.00            \$0.00          \$0.00
5.63%            \$0.95         \$0.94         \$0.96          \$0.94        \$0.94            \$0.94          \$0.92
Expected autoguidance investment                              Sub-section C5.2     4.25%            \$1.88         \$1.86         \$1.89          \$1.85        \$1.86            \$1.84          \$1.82
autoguidance (for C5.4)         \$15,000                                           2.88%            \$2.78         \$2.75         \$2.79          \$2.74        \$2.75            \$2.73          \$2.70
boom/section control (D4)       \$10,000                                           1.50%            \$3.66         \$3.62         \$3.67          \$3.60        \$3.62            \$3.59          \$3.55
autoguidance, \$/acre                 \$1.50                                      overlap %   Investment supported by net annual benefits (relative to topmost row), total for 10,000 acres
boom/section control, \$/acre         \$1.00                                        7.00%               \$0            \$0            \$0             \$0           \$0                \$0            \$0
5.63%           \$9,528       \$9,442        \$9,578         \$9,395       \$9,439            \$9,353        \$9,238
Interest rate used throughout:                                Sub-section C5.3     4.25%          \$18,790      \$18,617       \$18,889        \$18,526      \$18,616           \$18,447       \$18,224
interest rate (Analysis page)        10.00%                                      2.88%          \$27,798      \$27,537       \$27,942        \$27,407      \$27,541           \$27,295       \$26,967
1.50%          \$36,561      \$36,213       \$36,749        \$36,045      \$36,226           \$35,905       \$35,478
Amortization years used in sub-sections C5.2, C5.3, D2, D3:                      overlap %   Payback in years for \$15,000 investment
yrs for amort (Analysis page)                5                                    7.00%              N/A           N/A          N/A            N/A           N/A              N/A           N/A
5.63%             9.53          9.67          9.45           9.75         9.68              9.82         10.03
4.25%             3.78          3.82          3.76           3.85         3.82              3.87          3.92
2.88%             2.40          2.43          2.39           2.44         2.43              2.45          2.48
1.50%             1.77          1.79          1.76           1.80         1.79              1.81          1.83
Return on investment (ROI) going from 7.00% overlap to 1.50% overlap                               57.7%         57.0%         58.1%          56.7%        57.0%            56.4%          55.5%

Section D: Boom/nozzle/machine section shutoff on headlands analysis (affects applied input amounts and yield loss only, not machine operation cost):                       (based on 4.25% overlap)
Insert a 1 here to consider input cost savings >                   1
Insert a 1 here to consider reductions in yield losses >           1
Input cost and yield revenue savings relative to manual whole boom control, expressed as \$/applied acre in whole field and associated with:
automatic control of whole boom                                             \$/acre         \$0.2697       \$0.2600       \$0.2600      \$0.3422    \$0.2934                       \$0.2552      \$0.2199
manual control of boom sections                   Sub-section D1            \$/acre         \$0.7238       \$0.0000       \$0.6240      \$0.4742    \$0.8530                       \$1.1371      \$1.3743
automatic control of boom sections                                          \$/acre         \$0.9935       \$0.2600       \$0.8841      \$0.8164    \$1.1464                       \$1.3923      \$1.5942
Investment supported by annual input savings for:

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                                                                       Results
Field shape and headland economics analysis                                                                       four stylized fields; assume farm left to right

user-defined
field                   equal sized     equal sized    equal sized
units          userfield    square       isos R trian    equil triang     circle          odd1      odd2
Section A: Input and field characteristics section
Size of field                                                                    acres                  80            75             75              75                75     167.4     269.9
Number of swaths (passes) needed to cover headlands                              count                   2             2              2               2                 2         2         2
Width of machine                                                                  feet                  90            90             90              90                90        90        90
Area in headlands                                                                acres               24.27         14.62          20.68           22.22             25.91     67.54    124.12
Average angle of approach to headland in degrees (0-90)                         degrees              41.81         90.00          45.00           60.00             39.54     28.31     21.01
Number of machine or boom sections to be controlled (for Section D)              count                   5             5              5               5                 5         5         5
automatic control of whole boom                                                \$/acre            \$1.0225      \$0.9857         \$0.9857        \$1.2972         \$1.1122      \$0.9675   \$0.8337
manual control of boom sections          Sub-section D2                        \$/acre            \$2.7436      \$0.0000         \$2.3656        \$1.7975         \$3.2335      \$4.3105   \$5.2097
automatic control of boom sections                                             \$/acre            \$3.7661      \$0.9857         \$3.3513        \$3.0947         \$4.3457      \$5.2781   \$6.0434
Investment supported by annual input savings for:
automatic control of whole boom                                     total for 10,000 acres       \$10,225        \$9,857         \$9,857        \$12,972         \$11,122       \$9,675    \$8,337
manual control of boom sections          Sub-section D3             total for 10,000 acres       \$27,436            \$0        \$23,656        \$17,975         \$32,335      \$43,105   \$52,097
automatic control of boom sections                                  total for 10,000 acres       \$37,661        \$9,857        \$33,513        \$30,947         \$43,457      \$52,781   \$60,434
Payback in years for \$10,000 investment
automatic control of whole boom                                         payback in years             4.86         5.09            5.09           3.63              4.37      5.22      6.36
manual control of boom sections          Sub-section D4                 payback in years             1.56    won't pay            1.83           2.49              1.31      0.97      0.79
automatic control of boom sections                                      payback in years             1.11         5.09            1.26           1.37              0.96      0.78      0.68

Return on investment (ROI) for automatic control of boom sections                                    95.9%         9.4%          84.2%           76.9%          112.0%       137.4%    158.0%

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                                                                Results
Field shape and headland economics analysis                                                                         four stylized fields; assume farm left to right

user-defined
field                    equal sized    equal sized     equal sized
units           userfield     square       isos R trian   equil triang      circle              odd1      odd2
Section A: Input and field characteristics section
Size of field                                                                     acres                  80             75             75              75                75         167.4     269.9
Number of swaths (passes) needed to cover headlands                               count                   2              2              2               2                 2             2         2
Width of machine                                                                   feet                  90             90             90              90                90            90        90
Area in headlands                                                                 acres               24.27          14.62          20.68           22.22             25.91         67.54    124.12
Average angle of approach to headland in degrees (0-90)                          degrees              41.81          90.00          45.00           60.00             39.54         28.31     21.01
Number of machine or boom sections to be controlled (for Section D)               count                   5              5              5               5                 5             5         5

Calculations for Return on Investment
Overlap table in reverse order for vlookup                                                  1             2             3               4              5               6      7         8         9
1.50%       \$0.9645       \$0.9553         \$0.9694        \$0.9509         \$0.9556          \$0.9472   \$0.9359
2.88%       \$0.7333       \$0.7264         \$0.7371        \$0.7230         \$0.7265          \$0.7200   \$0.7114
4.25%       \$0.4957       \$0.4911         \$0.4983        \$0.4887         \$0.4911          \$0.4866   \$0.4807
5.63%       \$0.2514       \$0.2491         \$0.2527        \$0.2478         \$0.2490          \$0.2467   \$0.2437
7.00%       \$0.0000       \$0.0000         \$0.0000        \$0.0000         \$0.0000          \$0.0000   \$0.0000

Overlap reduction                            from          7.00%       (\$0.40) \$/acre               \$0.9645       \$0.9553         \$0.9694        \$0.9509         \$0.9556          \$0.9472   \$0.9359
to         1.50%      (\$3,957) \$/farm                \$9,645        \$9,553          \$9,694         \$9,509          \$9,556           \$9,472    \$9,359
\$0.57         \$0.56           \$0.57          \$0.56           \$0.56            \$0.55     \$0.54
\$5,688        \$5,596          \$5,737         \$5,552          \$5,599           \$5,515    \$5,402

(\$0.26) \$/acre               \$0.9935       \$0.2600         \$0.8841        \$0.8164         \$1.1464          \$1.3923   \$1.5942
(\$2,638) \$/farm                \$9,935        \$2,600          \$8,841         \$8,164         \$11,464          \$13,923   \$15,942
\$0.73         \$0.00           \$0.62          \$0.55           \$0.88            \$1.13     \$1.33
\$7,297          -\$38          \$6,203         \$5,526          \$8,826          \$11,285   \$13,304

Internal rate of return or Return on investment (IRR or ROI)
Guidance system                                                                                     57.7%         57.0%          58.1%           56.7%           57.0%            56.4%     55.5%
Section control                                                                                     95.9%          9.4%          84.2%           76.9%          112.0%           137.4%    158.0%
Guidance system and section control                                                                 73.3%         39.4%          68.7%           64.9%           79.6%            89.8%     97.9%

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                                                                    Results
Figure 1. Representation of how values in spreadsheet are calculated

d

b                            Q
w
Area A
c
a

w                    b

reaction time area

angle of approach (a)

bounds of swath
(width of machine)

Notes regarding how angle of approach is calculated given perimeter (running feet of headland)
and number of passes
p = perimeter distance per pass = running feet of headland divided by number of passes
c = p/2, or
w = width of swath
c = (w2 + b2)0.5
sine(a) = w/c, where angle a is expressed in radians
a = arcsine(w/c), where angle a is expressed in radians
Note that in Excel the angle must be expressed in radians for formulas to work

Distance machine must travel into headland before whole boom can be shut off = b
tan(a) = w/b, where angle a is expressed in radians
b = w/tan(a), or
2    2 0.5
b = (c - w )
Crop input overlap area per pass = (Area A plus Q) times 2 since each pass has two ends
d = reaction distance of travel before manually shutoff boom
Q = d*w
Input overlap area per pass = (w*b/2 + Q)*2

A radian is defined this way:
If you have a circle with an angle whose vertex is at the center of that circle...
And if that angle is of such a size that the amount of the circumference of the circle which that angle intercepts
has an arc length equal to the length of the radius...
Then that angle has a measurement of one radian.
Here's another way to say it:
A central angle to a circle has a size of one radian if it subtends an arc length on the circle equal in length to
Excel formula for computing the number of degrees in a radian = 360/2/PI()
What is the reasoning behind these values? It works this way:
How many times can you trace an arc length equal to the size of the radius as you move around the
circumference of a circle? Well, here's the formula for the circumference of a circle:
C=2*pi*r
C is the circumference, and r is the radius.
around the circumference of a circle. Each one of these radius lengths would designate one radian, so there

A couple of relevant trigonometric functions:
Sine is the ratio of the length of the side opposite the acute angle to the hypotenuse in a right triangle.
Tangent is the ratio of the length of the side opposite the acute angle to the adjacent side in a right triangle.

Odd1 field (one on left in picture below)
167.4 acres; farmed north-south; 3960 feet west to east at widest point
Headland length is 16700 feet (whole perimeter)

Odd2 field
269.9 acres; farmed north-south; 5502 feet west to east at widest point
Headland length is 30690 feet (whole perimeter)

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                       Notes
Amortization factors

Interest Rate
Years              6.00%           7.00%            8.00%             9.00%
1                1.0600          1.0700           1.0800            1.0900
2                0.5454          0.5531           0.5608            0.5685
3                0.3741          0.3811           0.3880            0.3951
4                0.2886          0.2952           0.3019            0.3087
5                0.2374          0.2439           0.2505            0.2571
6                0.2034          0.2098           0.2163            0.2229
7                0.1791          0.1856           0.1921            0.1987
8                0.1610          0.1675           0.1740            0.1807
9                0.1470          0.1535           0.1601            0.1668
10                0.1359          0.1424           0.1490            0.1558

payment formula>                PMT=PV*int/[1-(1+int)^(-N)]
payback time formula>           N=-ln[1-PV*int/PMT]/ln(1+int)

amortization      investment        payback
mathematics        supported        in years
interest rate (in)>                 8.00%             8.00%            8.00%
number of years (N) >                     4                4          3.4148
payment factor>                     0.3019
investment (PV) >                 \$13,000            \$14,905         \$13,000
annual payment (PMT) >          \$3,924.97          \$4,500.00       \$4,500.00
acres used on annually>             15,000            15,000          15,000
investment per acre>              \$0.8667
annual cost/benefit per acre>     \$0.2617            \$0.3000         \$0.3000

Note: The information contained in this tab is for illustrative purposes
only. Calculated values in the Analysis and Results tabs are based on
information entered in those tabs, but using the concepts shown here.

KSU-GPSguidance.xls
Terry L. Kastens, Kevin C. Dhuyvetter, and Dietrich L. Kastens
Kansas State University                                Ammortization

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