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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
This spreadsheet examines:
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
headland (two passes)
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
Notes about radians and degrees
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
the radius.
Excel formula for computing the number of degrees in a radian = 360/2/PI()
1 radian = 57.2957 degrees
1 degree = 0.0174532 radians
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.
Looks like there are two pi radii around the circumference of a circle, or about 2 times 3.14, i.e., about 6.28, radii
around the circumference of a circle. Each one of these radius lengths would designate one radian, so there
are about 6.28 radians in a full circle.
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
