SEMULAWON OF YEMEUNESS AM!) TRACTABIUW
CONDETIQNS FOR CORN PRODUCTEON SYSTEMS

Dissertation for the Degree of Ph. D.
WCHEGAN STATE UNIVERSFW
MEHMET YEN‘ER TULU
1973

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thesis entitled

SIMULATION OF ,TIMELINESS AND TRACTABILITY
" CONDITIONS FOR
CORN PRODUCTION SYSTEMS
presented by

Mehmet Yener Tulu

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in Agricultural Engineering

 

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Major professor

Date 9/7/73

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ABSTRACT

SIMULATION OF TIMELINESS AND TRACTABILITY
CONDITIONS FOR CORN PRODUCTION
SYSTEMS
by

Mehmet Yener Tulu

The necessary models for the components of a corn
production system were developed to investigate timeliness
losses incurred in corn production. Special attention was
focused on tractability conditions of the fields. Simu-
lations were made with 16 years of weather data for nine
different machine capacity combinations on a hypothetical
200 acre farm in Southeast Michigan.

The model for tractability is deterministic and was
developed using only weather and soil property data. Work,
no-work conditions are obtained as model output for each
day as a tractability state. Verification of the model
was made utilizing weather data and work, no-work records
from three Northern Indiana farms. Tractability model
output proved to be in quite good agreement with the farmers'
records of work, no-work conditions. Total work days were
in error by one day for spring and a maximum of three days

for fall operations.

Mehmet Yener Tulu

The yield values (Bushel per acre) were generated
stochastically. Generation was made for five consecutive
planting periods between April 16 and June 11. The yield
value of each planting period was assumed to be distributed
normally and correlated to the previous period's yield
value. Statistics for the stochastic generation were
estimated from Michigan corn yield data.

Two different planting strategies were considered:
1) finishing the ploughing and harrowing for 200 acres and
then planting, 2) finishing ploughing and harrowing for the
first field (each field is 40 acres) and planting it, and
continuing in the same manner for the remaining four fields.

Planting date timeliness losses due to tillage
capacity were dominant to those caused by harvesting capacity
for planting strategy 1. Timeliness losses for planting
strategy 1 due to tillage capacities were 19.76, 13.77, and
8.54 Bu/A for 3-bottom plough and 10 ft disc harrow (55 HP
tractor), 4-bottom plough and 13 ft disc harrow (75 HP
tractor), and 6-bottom plough and 18 ft disc harrow (110 HP
tractor), respectively. Planting strategy 2 caused lower
timeliness losses due to tillage capacity than planting
strategy 1. The losses were 12.06, 6.94, and 5.03 Bu/A
for planting strategy 2 at the same conditions. Harvest
losses were close to each other (lower for planting capacity

2) for each planting strategy and varied from 4.59 to 5.50

Mehmet Yener Tulu

percent of yield before harvest losses for different
tillage and harvesting capacity combinations. Generally,
decreasing drying costs and increasing harvest losses were
observed with decreasing harvest capacities.

A stochastic model of work, no-work days was
developed. Probability densities were assumed for the
number of work, no-work days in successive 15-day periods of
the year. The parameters of the densities were estimated
employing simulation results obtained utilizing the
deterministic tractability model. The stochastic simulation
was satisfactory for the period April 15 - November 25.

The following conclusions were derived from the
results of this study:

1. The tractability model is adequate for corn
production simulation and its use should be extendable to
other crops and other locations.

2. The yield model is sufficient to represent the
real yield values.

3. Planting date timeliness losses dominate those
associated with harvest losses.

4. Stochastic generation of work, no-work days
appear feasible but needs further development to cover the

entire year.

Approved // AJW

jo Professor

   

Approved

 

   

De artman Chairman—

SIMULATION OF TIMELINESS AND TRACTABILITY
‘CONDITIONS FOR CORN PRODUCTION

SYSTEMS

BY

Mehmet Yener Tulu

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1973

,3 ACKNOWLEDGEMENTS

The author wishes to express his sincere gratitude
to the following:

Dr. J. B. Holtman, the author's major professor and
committee chairman, who from the beginning of the study
provided continuing encouragement and guidance with great
patience.

Dr. Leroy K. Pickett, Dr. Gerald L. Park, Dr. Robert
O. Barr, and Dr. R. V. Erickson who served on the author's
guidance committee.

Dr. Robert G. Staudte of Statistics and Probability,
with whom the author consulted about statistical problems.

Turkish Ministry of Education; Agricultural
Engineering Department, Michigan State University; and
Division of Engineering Research, College of Engineering,
Michigan State University for providing financial support

for the study.

ii'

TABLE OF CONTENTS

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . .

LIST OF TABLES . . . . . . . . . . . . . . . .

LIST OF

Chapter
1.

FIGURES O O O O O O O O O O O O O O O 0

INTRODUCTION . . . . . . . . . . . . .

1.1 Need for Simulation . . . . . . .
1.2 Factors Involved in the System .

TRACTABILITY CONDITIONS . . . . . . .

2.1 Soil Moisture Model . . . . . . .
2.2 Modeling of Surface Conditions .

2.3 Verification of the Tractability Model

THE CORN PLANT . . . . a . . . . . . .

3.1 Plant Development . . . . . . . .
3.2 Yields . . . . . . . . . . . . .
3.2.1 Date of Planting (DOP) . . .
3.2.2 Modeling of Yields . . . . .
3.3.3 Frost Penalty . . . . . . .
3.3 Harvest Losses . . . . . . . . .
3.4 Natural Field Drying . . . . . .

FIELD OPERATIONS AND COST EVALUATIONS
TIMELINESS SIMULATION . . . . . . . .
5.1 Simulated Conditions . . . . . .
5.2 Simulation Procedure . . . . . .

5.3 Results . . . . . . . . . . . . .
5.3.1 Yields Before Harvest Losses

5.3.2 Harvest Losses and Drying Costs

iii

Page

ii

vi

14
16
19

31

31
34
38
39
45
45

47
49

51

51
54
56
56
6O

Chapter Page
6. STOCHASTIC GENERATION OF WORK NO—WORK DAYS . . 79

6.1 Procedure . . . . . . . . . . . . . . . . 80
6.1.1 Stochastic Work, No-Work Days
Model . . . . . . . . . . . . . . 83
6.2 Results . . . . . . . . . . . . . . . . . 85
6.2.1 Test of Independence of Work Days
in 15—day Periods . . . . . . . . 86

7. SUMMARY AND CONCLUSIONS . . . . . . . . . . . 92

REFERENCES . . . . . . . . . . . . . . . . . . . . . . 95

APPENDICES . . . . . . . . . . . . . . . . . . . . . . 104
A. VARIABLE STORAGE ALLOCATION FOR CORN PRO-

DUCTION SYSTEMS ANALYSIS . . . . . . . . . . . 105

B. SUBROUTINE NAMES AND THEIR FUNCTIONS . . . . . 118

C. FLOW CHARTS OF SIMULATION MODEL AND SOME OF
THE SUBROUTINES. . . . . . . . . . . . . . . . 121

iv

LIST OF TABLES

Table Page
1. Soil Types of Three Northern Indiana Farms . . 21
2. Verification Results of Tractability Model . . 24
3. Varieties and Heat Unit Requirements . . . . . 34
4. Parameters of Yield Model . . . . . . . . . . 42
5. Field Efficiencies and Speeds . . . . . . . . 50

6. Machine Capacity Combinations and Related
Values . . . . . . . . . . . . . . . . . . 57

7. Outputs of the Model . . . . . . . . . . . . . 58

8. "Average" Planting, Maturity and Harvesting
Dates at Different Machine Capacity
Combinations for Each of the Sixteen Years 62

9. "Extreme" (Latest) Planting, Maturity and
Harvesting Dates at Different Machine
Capacity Combinations for each of the
Sixteen Years . . . . . . . . . . . . . . . 67

10. Estimated Means and Standard Deviations for the
Number of Days in Critical Periods (16
Years of Data) . . . . . . . . . . . . . . 81
11. Means, Standard Deviations, and Correlation
Coefficients of Work Days in 24 15-day
Periods . . . . . . . . . . . . . . . . . . 82
12. Parameters of Stochastic Tractability Model . 87

l3.’ Hotelling-Pabst Test Statistic . . . . . . . . 90

Figure

l.

10.

ll.

12.

LIST OF FIGURES

Soil Triangle of the Basic Soil Textural
Classes . . . . . . . . . . . . . . . . .

Variety Selection and Planting Date . . . .
The Effect of Date of Planting on Corn Yield
Timeliness Function . . . . . . . . . . . .

Yield Before Harvest Losses at Different
Tillage Capacities . . . . . . .

Timeliness Losses Due to Tillage Capacity .
Timeliness Losses Due to Harvest Capacity at
Different Tillage Capacities (Planting

strategy 1) O O I O C O O O O O I O O O O
Timeliness Losses Due to Harvest Capacity at
Different Tillage Capacities (Planting

Strategy 2) O O O O O O O C O O O I O O O

Drying Costs at Different Machine Capacity
Combinations (Planting Strategy 1) . . .

Drying Costs at Different Machine Capacity
Combinations (Planting Strategy 2) . . .

Smoothing Tractability Parameters . . . . .

Histogram of Work Days for the Period
January 25 - February 8 . . . . . . . . .

Vi

Page

12
35
40
52

72

73

75

76

77

78
88

89

CHAPTER I

INTRODUCTION

Corn is raised extensively in Michigan as well as in
other Mid-western states of the U. S. Its main usage is as
an animal feed. Meat consumption in the U. 8., per capita
or as a whole, is the largest in the world, and the demand
for high quality meat and dairy products is increasing
steadily. A high level of agricultural mechanization and
advanced production techniques allow this country to be a
leading producer of agricultural goods in the world, with
less than two percent of its population engaged in
agriculture.

Food is produced in mainly two categories: carbo-
hydrates and proteins. The efficient American agriculture
produces more carbohydrates than the population needs,
resulting in surplus grains. Because the consumption of
proteins, in the form of dairy products and meat, in the
U. S. is so high it is necessary to import animal proteins.
Even if the surplus grains of the U. S. were converted into
animal protein by conventional methods, the demand for

proteins would not be met (Borgstrom, 1965).

Corn is rich in carbohydrates, but poor in proteins.
However, the low cost of feed nutrients compared to other
crops, the possibility of nearly complete mechanization of
harvesting and feeding, and the reduced cost of protein
resulting from feeding low-cost urea as a supplement, make
corn the most favourable animal feed throughout the country.
Technological advances have increased corn yield at a more
rapid rate than that of any other feed crop, making high
yields relatively easy to attain, of course, not without a
limit (Hildebrand, et al., 1971). Thus, corn has played
an important role in the closing of the protein gap, at
least partially.

The efficiency_and profitability of raising field
crops are closely related to the geographical situation of
the fields and the prevailing meteorological conditions;
corn is no exception. In fact, in places like Michigan,
where year to year variability of climatic conditions is so
great, corn crop development in the field is extremely
susceptible to weather inputs.

Every farmer is in the position of optimizing the
utilization of his resources. Extension specialists recommend
some operational dates to the farmers, which are the results
of research done by Agricultural Experiment Stations, as well
as other suggestions on hybrids, field preparation, ferti-
lizer application, storage, etc. The dates suggested for

planting tend to be earlier than they were years ago (to

obtain higher yields). To minimize harvest losses, it is
recommended that harvesting begin when kernel moisture
content reaches 30 - 35%, w.b. (wet basis). Both, the
earlier planting dates, (mid-April to the beginning of May)
and minimum loss harvesting dates (late September to mid-
November) are unfavourable time periods for these operations
meteorologically. As a result of high rates of precipi-
tation in these two periods, working conditions in the

field are very restricted for agricultural operations. The
farmer's situation is a well known dilemma: either give up
the increased income from timely operations or burden himself
economically with extra machine capacity.

The general behaviour of the agricultural production
system is more probabilistic and intricate than the somewhat
deterministic industrial processes. The Agricultural
Engineers Yearbook (1972) defines the probabilistic
behaviour of agricultural processes as "timeliness":
"Ability to perform an activity at such a time that quality
and quantity of a product are optimized". The phrase
" ... at such a time ..." is where the stochasticity arises.
Stochastic processes are defined as the family of random
variables, X (t), t>0, which are often used to describe the
behaviour of phenomena over intervals of time (Brockwell,
1971). Time dependent meteorological variables govern the
agricultural operations, by causing changes in the envir-

onment.

The main objective of this study was to simulate
corn producing farm operations, and develop necessary models
to investigate the timeliness effect of weather inputs on
production with specific attention given to the modeling

of work and no-work days.

1.1 Need for Simulation

 

Model building is the backbone of simulation work.
Models have been constructed for the prototypes of large
and costly engineering designs, such as dams, airplanes and
navigational vessels. With the introduction of hybrid and
digital computers the methods of model building and
similitude engineering became an inevitable tool of many
diversified areas. Today, it is possible to see studies in
economics, education, social and political sciences using
models and simulation. ‘

There is criticism of the extensive use of modeling
and simulation, even from its contributors. In terms of
Operations Research, Saaty (1972) states that "Operations
Research is the subject in which we never know the real
problem we should be talking about nor whether our solution
of it has any relevance to reality. Nevertheless, we do
such research because people have problems and, as scientists,
we believe that any model is better than none, it is all
right to give bad answers to problems if worse answers would

otherwise be given". Although at times this criticism may

be true, the use of simulation and modeling techniques to
study problems in farm management should be of value.

The use of simulation techniques in agriculture has
been stimulated by the advancement of computer usage and
system science in other industries.. Since the early sixties,
computers and simulation techniques have been used to
analyze farm operations. The American Journal of Agricul-
tural Economics is a good guide to this earlier period.
Most of the material deals with mathematical programming
methods (linear, nonlinear, quadratic, etc.), and later
with the stochastic behaviour of agricultural operations.
Zusman and Amiad (1965) see simulation as a tool for farm
planning under conditions of weather uncertainty. A survey
done by Link and Splinter (1968) reviews simulation techniques
and applications to agricultural problems. This survey
shows that with the continuing efforts of agricultural
engineers, simulation may have considerable impact on
agricultural research. The late sixties produced
considerable research using computer simulation techniques
on agricultural production systems. These are in areas as
widely diversified as are agricultural operations.
Machinery selection (Scott, 1970), insect control (Brewer,
1970), sprinkler irrigation (Stegman and Shah, 1971),
environmental features of corn (Jones, et al., 1970), and
harvest operations under stochastic conditions (Sorensen

and Gilheany, 1970) have been studied.

(Holtman, et al., (1970) state that: "The number
of significantly different circumstances under which the
system must function satisfactorily and the number of
alternative courses of action open to the decision-maker
definitely suggest the need for automating the data trans-
formation task. Production system simulation models are
not substitutes for actual measurement. Rather their
purpose is to transform previous observations into new
forms of information which are of value to the decision-

maker".

1.2 Factors Involved in the System

 

For the simulation of a corn production system there
is a necessity to obtain information from other disciplines
in agriculture, as well as from other sciences. This is
almost imperative, since any kind of production system is a
synthesis of physical and economic interactions of the
system's components.

The land on which corn production takes place has a
definite influence on the process. Besides the economic
factors such as value, rent, and taxes, the size of the land
base is important in determining the size of the operation
itself. Partitioning by service roads and other influences
on field shape are also important for machinery movement

patterns, especially if the size of a field is small.

Geographical closeness to markets determine transportation
needs.

Distance from the machiner storage area and
distances from field to field (if the farmer has scattered
portions of land) should be considered since these factors
influence fuel consumption and labour costs, and contribute
to machine depreciation.

The soil moisture status of a field is a function of
meteorological inputs and soil type. Soil is constituted
mainly of three elements: clay, loam and sand. Different
proportions of these components produce different moisture
holding capacities in the soil. The working conditions of
machines on the ground and the available water for the
plant depend upon the moisture holding capacity of the soil.

Of the weather variables, temperature and precipi-
tation are the most significant. Temperature is often
considered to determine the growing period for any kind
of plant. Since the temperature is a direct function of
radiation, which is caused by sunlight, the maturity level
of the plant is a function of daily temperatures. In
Chapter 3 this aspect of maturity is discussed in terms of
"growing degree days". Evaporation is also a result of
daily heat gains caused by sunlight. The tractability of
soil is dependent on it. While it is not a common practice
to irrigate corn in Michigan, irrigation needs due to

evapotranspiration should also be mentioned.

Precipitation is an important source of water to
the corn plant. As it influences soil moisture the
precipitation affects the tractability condition of the
field.

Important crop parameters are, variety, the time
required for maturity, and yield. As a result of research
on corn, there are growing numbers of properties revealed,
which can be included into a system model. However, required
time for maturity and yield values are considered essential.

In addition to the capacity specifications of
individual machines, man-machine, and machine-crop relations
have significance. Labour, fuel needs, machine breakdowns,
repair times, maintenance, harvest losses, list prices of
machines and taxation should also be considered. Fertilizer,
seed, hauling and drying costs of the harvested crop, and
the market value of corn have a definite effect. As we
progress the parameters will be defined and assumptions
about them will be made.

The computations in this study were performed at
the facilities of Michigan State University, East Lansing,
Michigan using a FORTRAN IV language. The list of
variables, routine names, their functions and flow charts

of some of them are given in Appendices A, B, and C.

CHAPTER II

TRACTABILITY CONDITIONS

The tractability state of a given field is a direct
consequence of weather inputs and soil properties. However,
the mechanical features of the work which takes place on
the ground is also important. Equipment to be used differ
in design and in construction material according to their
desired function, which effects their performance on the
soil.

The earlier work on soil mechanics has been associated
with the needs of earthwork construction and foundations
for large structures. With the increasing number of off-
the-road vehicles and traction devices in military,
construction, agriculture, and mining operations, soil
dynamics has gained importance.

The urgent need to be able to predict performance,
particularly for military mobility, has led to the
development of simplified performance equations with limited
but accepted accuracy. Most of these equations have been

empirically developed.

10

The National Tillage Machinery Laboratory, Auburn,
Alabama, The Army Mobility Research Center, Vicksburg,
Mississippi, and The Land Locomotion Laboratory, Warren,
Michigan are research centers, which conduct experiments
in soil dynamics.

The term soil tractability, or as it is sometimes
called, "soil trafficability" (Knight and Freitag, 1962),
was developed in connection with off—the~road vehicles.
Tractability may be defined as the ease with which a
terrain may be traversed. In the broadest sense, it includes
the influence of all features such as vegetation, slopes
and barriers such as chasms or rivers. In tractability,
the primary interest is in the movement of the vehicle
over the soil with little regard for the soil conditions
produced by the movement. In agricultural operations,
however the effect of the vehicle on the soil may be more
important than the maximum tractive capability that can
be develOped. A traction device that develops the desired
pull at high efficiency may not be useful for agricultural
purposes if, in the process, the device compacts the soil or
ruts it so severely that excessive erosion, mechanical
impedence, lack of moisture, or poor aeration drastically
curtail the subsequent growth of plants.

The terms that are used in tractability are often
misleading. For instance, the term "go", "no-go" and

"work", "no-work" imply only that a soil can or cannot be

ll

traversed. When tractability is further characterized
by adverb modifiers such as, easily, or with difficulty,
time and cost considerations are also implied.

Soils have been classified for construction and
tractability purposes. Waterways Experiment Station (1953),
U. S. Department of Interior, Bureau of Reclamation (1960),
and the U. S. Army Corps of Engineers (Waterways Experiment
Station, 1961) have unified these classifications to some
extent. The classifications are based on physical
properties that are determined by standardized methods
and that indicate certain behavioral characteristics. These
properties are graduation of particle size, consistency,
porosity or void ratio, Specific gravity, moisture content,
bulk density, penetration resistance, unconfined compressive
strength, and soluble salts. USDA's textural soil classi-
fication, which is shown in Figure l, is based on the
particle size of the mineral constituents of a soil, and
is used widely by researchers.

Knight and Meyer (1961) used a soil classification
system to estimate the probability of a vehicle being able
to successfully cross a specific soil. The estimation is
based on comprehensive empirical relations that establish
the probability that different soil strengths will
adequately support the passage of different vehicles. The

vehicles were characterized by the vehicle cone index, which

12

     

  

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Figure 1.—-Soil Triangle of the Basic Soil Textural Classes
(Soil Dynamics in Tillage and Traction, 1967).

13

was the minimum rating cone index required by the vehicle
in order to complete 50 passes over the soil. Soil was
also characterized by a rating cone index that was
measured with a cone penetrometer. The rating cone index
of any soil could be determined by direct measurement.
Thus a means was available to predict "go" or "no-go"
conditions for any vehicle whose vehicle cone index was
known.

Since the condition of soil can vary from a fluid
to a rigid mass, Knight and Meyer's (1961) procedure is
applicable only when soil parameter measurements have just
been made. The condition of a soil at any instant in time
depends on its moisture content, soil type, and previous
history.

A procedure similar to Knight and Meyer's (1961)
was developed by the Waterways Experiment Station (1948)
by using specially developed cone parameters to determine
the soil conditions. Their relative success can be
attributed to the limited soil conditions of loose sand
and wet saturated clay with which they experimented. The
Waterways Experiment Station's (1962) publication is a
compilation of research done by the U. S. Army on
tractability. Link (1962), and Link and Bockhop, (1964)
used a probabilistic model employing a first order Markov
chain, to determine the working days on a "typical" Iowa

corn farm. The Markov chain parameters were estimated

.‘rlullllall ‘II‘. I),

 

14

from the work, no-work data of the Ames Agronomy Farm, Ames,
Iowa. Morey, et al., (1969) labeled the days from September
1 through December 31 as "go" or "no-go" days by using the
daily work data provided by the Department of Agricultural
Statistics, Purdue University, Lafayette, Indiana.

Frisby (1970), to predict the good working days for
fall and spring tillage in Missouri also used a first order
Markov chain. Standard weather data were used. He reported
that the Markov chain procedure would be better with more

years of weather data.

2.1 Soil Moisture Model

 

Shaw's (1963) soil moisture budget was programmed
for the computer by Dr. J. B. Holtman of the Agricultural
Engineering Department, Michigan State University. Although
the model was designed for a soil moisture budget for the
top 5 feet of soil under corn, only the top 6 inches were
important for tractability conditions (see Section 2.2).

Shaw's (1963) model estimates evaporation in
determining soil moisture. It was assumed that the actual
evaporation rate is .1 inch/day from the top 6 inches as
long as any available moisture exists in the top 6 inch
layer. While the model gave quite good overall results, it
was noted that because of the assumption made about
evaporation, the estimation of the moisture of the top 6

inch layer could be inadequate, which would be crucial to

15

the accuracy of the state of field. Baier and Robertson

(1966) gave a set of evaporation coefficients for the

top 6 inches of soil, dividing them into the top 1.2,

the next 1.8 and the next 3.0 inch layers. Using Baier

and Robertson's (1966) coefficients (represented by ki’

i = l, 2, 3) evaporation, Ei, was described as:

E.
l

where:

ki PE AMi' for every i = l, 2, 3

layer number corresponding to the 1.2,
1.8, and 3.0 inch layers

evaporation from ith layer for the day
(inches of water)

.55

.40

.05

.36 open pan evaporation for the day
(inches of water)

fractional available moisture in ith
layer

actual available moisture of ith

(inches of water)

layer

 

maximum available moisture of 1th layer
(inches of water)

 

*Maximum available moisture is defined to be field
capacity minus wilting point water content.

16

Precipitation (after runoff) was assumed to first saturate
the top layer, then the second and finally the third. Any
reminaing precipitation was assumed to be infiltrated
instantaneously. Runoff was computed by the method of

Shaw (1963).

2.2 Modeling of Surface Condtions
Rutledge and McHardy (1968) developed a work, no-work
criteriOn based on the soil moisture distribution in the top
6 inches of soil. They divided the top 6 inches of soil
into the top 1.2, the next 1.8, and the next 3.0 inch layers.
A work day was assumed to exist if:

AMi<Ci, for every 1 = l, 2, 3

 

where:
i = layer number corresponding to the 1.2,
1.8, and 3.0 inch thick layers,
respectively
AMi = fractional available moisture of ith layer
actual available moisture of ith layer
= (inches of water)
maximum available moisture of ith layer
(inches of water)
Suggested values of Ci’ 1 = 1,2,3 were:
C1 = .95
C2 = .95
C3 = .95 - .995 (depending on the soil type and

drainage characteristics).

17

Initially it was assumed that C3 might take on one
of four different values depending upon soil characteristics.
These were labeld by the integers l, 2, 3 and 4. Criterion
number 1 (C3 = 1.0) was assumed to be representative of '
light (sandy)soils. Critera numbers 2 (C3 = .985) and
3 (C3 = .97) represent heavy (clay-loam) soils, the first
one on well drained and the second one on poorly drained
fields... Finally, criterion number 4 (C3 = .99 was assigned
to well drained medium textured (fine to very fine sandy
loam) soils. This model was assumed to characterize
tractability conditions during that period of the year in
Which the soil was thawed.

The time period of importance for corn production
may extend from soil thawing in the spring past the date of
Soil freezing in the winter. In some years corn harvesting
may be delayed into January or February. Thus, soil freezing
and thawing dates were required. Finally, Spring soil
temperatures were also required to determine the earliest
Possible corn planting date (soil temperature greater
than SOOF).

Fridley and Holtman (1972), developed a model which
determines soil freezing and soil thawing dates, and also
Cialculates soil temperature in the spring. To determine
SOil freezing and soil thawing dates a heat unit system

'Was used.

18

Beginning March 1 soil heat unit accumulation is

rnade according to the formula:

'7

 

 

 

F Tmax + Tmin
- 32 no snow on the ground
IDaily Soil Heat =$ 2
Units (T + T. )/ 2 - 32
max min
i 6 snow on the ground
where:
Tmax = maximum temperature for the day (OF)
Tmin = minimum temperature for the day (OF)

Tflaese daily soil heat units are accumulated. If on a
Cxertain day the soil heat unit accumulation from March 1 was
-lxass than zero, the heat unit accumulation was set to zero.
Vnaen the heat unit accumulation exceeded 25 the soil was
assumed to be thawed.

Upon the occurrence of soil thawing, actual
Ei‘Vailable soil moistures for each layer are equated to the
“maximum available soil moistures. Work, no—work conditions
Etre then determined as described above by checking the
f'ractional available soil moisture contents of the tOp
three layers.

To determine the earliest planting date, soil
twanperature was computed via exponential averaging of the
lPrevious air temperatures beginning with the date of soil
thawing (Fridley and Holtman, 1972). This was accomplished

by using the DELDT subroutine of the FORDYN simulation

19

language (Llewellyn, 1965). The input to DELDT (first

order delay, magnitude of delay equal to one) routine was:

r
T + T .
max min no snow on the ground

2

 

Input =i
to DELDT

(Tmax + Tmin)/2 - 32

‘ ‘ 6
The output of DELDT is then soil temperature.

 

+ 32 snow on the ground

 

October 1 is the date, from which daily soil heat
unit accumulation begins in determining the soil freezing
date. In the fall, in contrast to Spring, if the soil heat
unit accumulation since October 1 was greater than zero on
a certain day it was defined to be zero. When the soil heat
unit accumulation became less than -110, the soil was
assumed to be frozen.

It should be noted that the days from the soil
freezing date to March 1 were labeled as work days and from
March 1 to the soil thawing date were labeled as no-work
days. This was done so that unharvested corn could be
harvested after soil freezing. The days on which the soil
is frozen are work days only for the harvesting operation of

course.

2.3 Verification of the Tractability

 

Model
Work, no-work data were recorded on three farms
under the supervision of Samuel D. Parsons (1972) of

Purdue University, Lafayette, Indiana. The farms are

.20

located in Northern Indiana.- Work, no-work conditions
were recorded for the following periods:
Farm 1: April 17, 1970 - June 12, 1970
October 1, 1970 - November 24, 1970
Farm 2: April 16, 1970 - May 23, 1970
September 23, 1970 — October 16, 1970
Farm 3: April 16, 1970 - June 6, 1970
September 22, 1970 - November 25, 1970
The fall operations recorded for each farm were corn
harvesting only. Daily rainfall at these farms was recorded
for the period September 1, 1969 - February 28, 1971.
U. S. Weather bureau data which included Open pan evaporation
values were obtained from appropriate stations in Northern
Indiana. The soil type distributions for each farm were
recorded by Parsons (1972). The use of Figure l with these
soil type distributions yielded the soil types for each
farm as can be seen in Table l. The moisture holding
capacities of each soil type were taken from the U. 8. Soil
Service Soil Survey Series (1961) for Indiana.
Simulations were first made using subroutine SURFIS,
which was designed to determine tractability as described
in Section 2.2 (See Appendices B and C), with the afore-
mentioned data. The missing values of evaporation data were
estimated with the computer routine prepared by Dr. J. B.
Holtman of the Agricultural Engineering Department, Michigan

State University. The values of moisture holding capacities

21

listed in Table 1 were used. The results were compared with
the work, no-work records of the farmers. The records of
the farmers and the results obtained by simulation are given

in Table 2.

Table l.--Soil Types of Three Northern Indiana Farms.

 

Farm 1 Farm 2 Farm 3

 

Soil Type Moisture Soil Type Moisture Soil Type Moisture

 

Holding Holding Holding

Capacity Capacity Capac1ty

(inch/ft) (inch/ft) (inch/ft)
Silt Loam 2.1 Silt Loam 2.1 Silt 2.1
Loam 2.0 Silty Clay Silty Clay 2.3

_ Loam 2.4
Silty Clay - Sandy Clay 2.04
Loam 2.4

 

The farmer's records for Farm 3 indicated that he
did not have work days on 110170, 110970, 111270, 111470,
111570, and on 111670. Upon examining the precipitation
records it was decided that the days were misrecorded or
the fields were not ready for harvesting (perhaps due to
high moisture content of kernels). Therefore, these days
were assumed to be work days and are so indicated by
asterisks in Table 2.

The model describes spring thaw very well. Model
output values and actual values (as recorded by the farmer)

of the first work day of the spring were, respectively:

22

1) April 17 and April 17 for Farm 1, 2) April 18 and April 16
for Farm 2, and 3) April 17 and April 16 for Farm 3.
These results were obtained using tractability criterion 2.

One possible index of the measure of the model's
accuracy is the number of days on which the model's result
and the farm record match. This may be misleading as
"partial" work days were not considered. 'Results for the
spring period were (model criterion 2):

Farm 1: 6 out of 57 missed

Farm 2: 5 out of 38 missed

Farm 3: 9 out of 55 missed
Another index of model accuracy is the total number of work
days in the period as computed with the model in comparison
with the farm records. As indicated in Table 2 the maximum
deviation was one day. Recorded and calculated (from the
simulation) values of work, no-work days were judged to be
in good agreement for the spring period.

' The fall period results yielded less agreement when
tractability criterion 2 was used. After October 31 the
agreement was definitely unsatisfactory. However, simulations
made with tractability criterion number 1 gave satisfactory
results for the fall harvesting period. This was attributed
to machine characteristics. In spring tillage operations,
there is a slippage problem. In the fall, the combine works

on a field covered with stalks and remnants of plants, and

23

does not pull equipment behind it. The results for criteria
numbers 1 and 2 were as follows:
CRITERION NUMBER
1 2

Farm 1: 5 out of 55 missed 25 out of 55 missed

Farm 2: 3 out of 24 missed 6 out of 24 missed

Farm 3: 6 out of 64 missed 23 out of 64 missed

Table 2 shows the daily and total work, no-work
results. It was concluded that choices of criterion number
2 for spring tillage and criterion number 1 for fall

harvesting would be appropriate.

24

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29

 

 

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.OODQHDGOUII.N OHOOB

CHAPTER III

THE CORN PLANT

The characteristics of the corn plant were put into
four main categories. There was a need to measure the
development of the plant. The most important variable, yield
had to be determined. The effect of the time between the
physiological death of the plant and harvesting time on the
moisture content of kernels was significant because of its
effect on drying costs. Finally, we needed to know the
losses that occur in the field before and during harvest.

It was our belief that these characteristics are sufficient
to comprehend the behaviour of the corn plant in the context

of this study.

3.1 Plant Development

 

The concept of considering a plant as a heat storage
unit via physiological conversion of heat into carbohydrates
and other plant components led to the idea of heat units or
as sometimes called "growing degree days (GDD)" (Van Den
Brink, et al-; 1971). The term, heat units, does not
denote BTU's or kilocalories. It is the accumulation from

planting date of daily average temperatures above some base

31

32

temperature. This base is usually taken as 50°F. Those
days with average temperature less than 50°F. are ignored.

Newman and Blair (1969) recommended the measure of
degree days to predict 30 percent kernel moisture at maturity
time, given the planting date of corn. Taking SOOF as the
base temperature a sum of daily average degrees above 500F
of 2600-2800 is required in Central Indiana for full season
hybrids. To adjust for extreme conditions Newman and
Blair (1969) proposed the following computations:

o

if T a9OOF and T ;75 F:
max aV

Daily GDD = T -50- (T
v m

a -90), and

ax

if Tav does not exceed 650E but is above 50°F

 

o o
(50 FaTavz65 F).
Daily GDD = Tav - 50 + (Tmax -65),
otherwise:
Daily GDD = Tav -50,
with:
Tmax + Tm' o
Tav = 2 1n (daily average temperature F)
where:
T = daily maximum temperature, 0F
max
Tmin = daily minimum temperature, 0F.

Brown (1969) recommended a new method for use in
Ontario, Canada. It treats day time temperature distinctly

from that at night:

33

Daily GDD 2 (Day + Night)/2
where:
_ _ _ _ 2
Day — 1.85 (Tmax 50) .026 (Tmax 50)
Night = Tmin - 40.
Van Den Brink, et al., (1971) published growing

degree days for Michigan. They used a formula without any

correction factor, i.e.:

 

Tmax + Tmin
Daily GDD = 2 - Tbase
where:
_ o
Tbase — base temperature ( F).

They found the GDD at four different base temperatures for
different stations in Michigan. Marvin, et al., (1971)
made studies of the application of the GDD concept to
classifying corn hybrids with respect to maturity using
six Ohio locations with three hybrids and four planting
dates. Brown's (1969) method gave the least variation in
the Ohio studies.

To determine heat unit requirements and corresponding
varieties the corn planting dates of Hildebrand, et al.,
(1964) were assumed to be the characteristic dates for
Michigan. These dates lie between April 16 and June 11.

For each day of this period heat units were accumulated over
the period from planting date to an assumed maturity date

using:

34

Tmax + Tmin
Daily GDD = 2 - 50

 

The assumed maturity date was October 15. Sixteen years of
Detroit City Airport temperature data were used. The second
lowest heat unit accumulation for the October 15 maturity
date was assumed to be an appropriate heat unit requirement
for corn in Southeast Michigan. As shown in Figure 2 the
planting period was divided into four subperiods and by
linear approximation heat unit values were found for each
subperiod. Varieties were selected according to the
schedule described in Table 3. Yield frost penalties were

determined by the method outlined in Section 3.2.3.

Table 3.--Varieties and Heat Unit Requirements.

 

 

Planting Period. Required Heat Units Variety Number
416 - 430 2592 l
501 - 514 2537 2
515 - 528 2418 3
529 - 611 2254 4

 

3.2 Yields

 

Most Agricultural Experiment Stations keep records
of corn yield as well as other crOps. Due to differences of

weather, soil, regional practices and plant variety these

35

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36

records show considerable variability. Data from the Ohio
Agronomy Guide (1972) show the increase in corn yields in
recent years over earlier periods which could be attributed
to agrotechnological improvements.

Denmead and Shaw (1959, 1960), Fulton (1970), and
Hanks, 8t al., (1969) have all done some research to relate
the effect of climatological factors to corn yield via soil
moisture stress (Moisture Stress Days or Index), evapo—
transpiration, etc. Runge (1968), and Bonnevalli, et al.,
(1970) considered the effect of weather variables on corn
yield. The effects of chemical fertilizers, plant pOpulation,
Arow width, and seeding depth on the development of the corn
plant have been studied (e.g. Nunez and Kamprath, 1969).

The most important soil parameter in influence on
corn yield variability from season to season in Michigan is
the soil moisture (Hildebrand, et al., .1964). One of the
earlier studies of soil moisture, a classic, was conducted
by Thornwaite (1948). This work was the basis for many
later researchers. Thornwaite, et al., (1965) published a
more general water balance method, which dealt with water
loss to the air from the continents' surface. Holmes and
Robertson's (1959) soil moisture budget was intended to
account for soil moisture stress changes in the drying cycle,
which was not handled before. Baier and Robertson (1966)
develOped a new technique for the estimation of daily soil

moisture on a zone by zone basis from standard meteorological

37

data and called it the "versatile soil moisture budget".
Pierce (1966) presented a practical method of estimating
water use by crops and determining the amount of moisture
remaining in the soil at any particular moment. This model
was tested under corn, meadow, and wheat. Monthly
evapotranspiration, runoff, and soil moisture storage were
predicted numerically and agreement with the actual data
was found to be fairly good by Letteau (1969). For
actual evapotranspiration, Eagleman's (1971) statistically
derived method was reported to be satisfactory when used
for estimating moisture changes in the soil. Availability
of soil water to plants, as affected by soil moisture and
climate was investigated by Denmead and Shaw (1962).
Dale andsflnuv (1965) and Dale (1968) reported a method of
considering the interaction of potential evapotranspiration,
soil moisture and non-moisture stress days for corn in Iowa.
In the earlier stages of this study the main
concern was to develop a yield model with climatic variables
as input and produces corn yields as output. To accomplish
this, the works of Shaw (1963) and Dale and Shaw (1965) were
to be used for soil moisture and moisture stress day index
determinations. This model failed to reflect one important
feature of corn yield behaviour. Contrary to the known
general trend of decreasing yields with later planting dates

(see section 3.2.1), the model produced increasing yields.

38

This result is understandable as Dale and Shaw's (1965)

study did not consider variations in date of planting.

3.2.1 'Date of Planting (DOP)

 

Corn crop yields are susceptible to the planting
date. Generally, it is accepted that earlier planting dates
produce higher average yields (Dale, 1968). Most of the
research results from the Mid-West corn area conclude that
planting dates later than May 10, result in approximately
one bushel per acre per day reduction in yield for each
day (Hildebramd, et al., 1964). This means that the corn
producer has a limited time for planting. The May 10 limit
is often exceeded, however, because of practical constraints
of work time and equipment capacity.

Jones (1967) states that, the earlier planted corn
is less likely to lodge or break over, since the height of it
is less than the later planted ones. Earlier planted corn
of the same variety will have a lower moisture content
than the later planted corn at harvest time. Hicks and
Peterson (1971) published results of DOP studies for
Minnesota. Yields, days required for emergence, and ear
moisture content for three different maturity groups were
reported. One of the other publications of the Minnesota
Agricultural Experiment Station is (Hicks, et al., 1970)
more detailed and gives the results of DOP studies for
different nitrogen application rates, populations, and hybrid

maturity combinations.

39

Hildebrand, et al., (1964) stated that early planted
corn usually yields more because it has passed the critical
stage of growth and roots are developed by late July and
early August when a dry period of some duration occurs in
Michigan.

Hehn, et al., (1968) in their experiment with high
amylose corn stated that the later planted corn has a lower
yield, whole kernel nitrogen, and kernel hardness. Pendleton
and Egli (1969) found in their research that the later
planting dates resulted in lower yields and decreasing stalk
resistance. Center and Jones (1970) reported the same kind
of results for Northern Virginia.* They found approximately
one half day delay of silking, for each day's delay in
planting.

Almost all yield - DOP recordings from the Mid-West

area show the general pattern exhibited in Figure 3.

3.2.2 Modeling of Yields

 

The complexity of interactions of different phenoma
which contribute to the yield of corn prevented the
develOpment of a deterministic yield model (Section 3.2.1).
Stochastic generation of yield values was sought to represent
the year to year variations in yields.

It was hypothesized that the yield values in

subperiods of the planting period would have a normal

40

«L

/

Yield

 

 

May' 10
‘ Date of Planting

Figure 3.-—The Effect of Date of Planting on
Corn Yield.

41

distribution over the years, i.e., the probability density
function of yield is:

in (yi) = N (Di, oi), for every i = l, ..., n

i = subperiod number

yi = yield values for planting subperiod
i (Bu/A)

“i = mean of yields for subperiod i (Bu/A)

Oi = standard deviation of yields for subperiod
i (Bu/A).

The first subperiod's yield value was generated:

Y1 = 01x + “1

X = N (0, 1) random variable.
For the remaining (i = 2, ...,n) subperiods the yield values

were generated as:

Y1 = “i + 91—1 (Oi’/Oi-l) (Vi-1 ’ “1-1' +

= correlation coefficient of yield values
for subperiods i-l and i.

The autocorrelated model (Bartlett, 1955) was used to capture

the high degree of correlation of yields in successive periods

of the same year.

42

The ten year data of Hildebrand, et al., (1964)
were utilized to estimate the model parameters. Unfortu-
nately, varieties were not specified. The planting season
was divided into the planting periods of April 16 - April 30,
May 1 — May 11, May 12 - May 20, May 21 - May 31, and
June 1 - June 11. For the stochastic modeling of corn
yeild these five (n = 5) subperiods were assumed to be
sufficient to reflect the effect of DOP on yield. _It was
also accepted that these data would represent Southeast
Michigan corn yields better than any other available data.
Table 4 lists the estimated values of n, O, and p for the

subperiods.

Table 4.--Parameters of Yield Model.

 

 

 

Planting Subperiods u (Bu/A) O (Bu/A) p
April 16-Apri1 30 105.7 17.77 .939
May l-May 11 109.5 18.61 .943
May 12-May 20 99.6 22.97 .981
May 21-May 31 91.1 23.03 .948
June l-June 11 80.50 23.62

The simulation of the normal variate X, with ”x = 0
OX = l. employed the Central Limit Theorem (Cramer, 1946).

If RNl, RN2, ..., RNN are N independent, identically

distributed random variables each having expected value,

43

E (RNi) = u, and variance, V (RNi' = 02, by the Central

Limit Theorem:

 

 

N
iEIRNi—Nu 1 b “F 22
lim P [a < < b] = ———-‘{e dz
N+OO m 0‘ «21]- a
where:
N
E ( 2 RN.) = Nu
. 1
i=1
N 2
V ( 2 RN.) = NO
. 1
1:1
and
2 mi - Nu
Z = 1:1 = a N (0,1) random variable
“N O

The simulation of the normal variate X by computer
employed the sum of K uniformly distributed (0,1) continuous

random variates RN RN RN The application of the

1] 2' 00., K0

Central Limit Theorem and the use of the expected value and

standard deviation of the uniform random variable yield:

 

= 1
U 2
_ 1
O’____.
/12
and
K
2 RN. - K/12
- 1
i=1
2:
/R//12

Any normal random variable can be transformed to the

N (0,1) random variable, 2, by:

44

 

K
X ‘ “x = iél RNi ' K/z
Ox VK712
or 1
2 K
_ 12 _ _K
X — 0x (_R) (iilRNi 12) + “x

It can be seen from the Central Limit Theorem that
for asymptotic convergence to normality K should be taken
as large as possible. However, the value of K selected must
be justified by the cOmputer time spent in generating K
uniform random variates for each normal variate in relation
to the resulting accuracy. In simulation studies it has
been suggested that K can be as small as 10 (Hillier and
Lieberman, 1968; Naylor, et al., 1968; and Abramowitz and
Stegun, 1964). There is a computational advantage if K is
chosen as 12. If 12 is used,

12
X = OX (igl RNi - 6) + OX.

K = 12 truncates the distribution at the i 60 limits. Thus,
it is not extremely reliable for the tail sections of the
distribution.

The YIELD routine was designed with K = 12. Its

flow chart is in appendix C.

45
3.2.3 Frost Penalty
The loss in yields due to an early freeze in the fall

was calculated by the following formula (Newman, 1968):

.02 (RGDD — AGDD)2/104 if RGDD - AGDD < 450

YR =

.4 if RGDD — AGDD 2 450
where:
RGDD = Required GDD (Base SOOF) from planting to

physiological maturity for the variety planted
AGDD = Accumulated GDD (Base 50°F) from planting to
freezing date
YR = Fraction of yield lost due to the deficit of

heat units accumulated before a fall freeze.

 

3.3 Harvest Losses

Harvest losses in yield can be considered in two
categories, preharvest and harvester (corn combine) losses.
Both of these losses depend upon the amount of stalk lodging
which differs according to the corn variety and DOP.

Holtman, et al., (1970) gave some computational
formulae for computing lodging. Fridley, et al., state
that lodging is a function of time, weather, plant population

per acre and corn hybrids:

n 1.7

L = KC P (D - 199)

h
where:
L = percent stalk lodging

K 2.5 x 10_4 (constant of proportionality)

"U
ll

plant population per acre (thousands of plants)

46

D = number of days from March 1

1.5

n

C hybrid constant.

h
Hybrid constants (Ch) were given for four different
hybrid categories as, .7, 1.0, 1.3, and 1.6 reSpectively.

Parsons, et al., (1971) gave formulas for different

kinds of losses. These were:

Lp = .O7L

Lc = .14 (min [max (M, .22), .35] - .22)

L8 = .55M2 - .23M + .038

where:

Lp = preharvest loss, decimal fraction of yield
at maturity

LC = cylinder loss, decimal fraction of gathered
yield

L8 = separation loss, decimal fraction of

gathered yield
L = stalk lodging, decimal
M = grain moisture, decimal wet basis.
Holtman, et al., (1970) suggested a formula for
gathering losses:

L = .01 + Cr (.01 + .17L)

b‘
ll

gathering loss, decimal fraction of

available corn for harvesting

47

C

r row spacing.coefficient

L = stalk lodging, decimal fraction.
In this work values of plant pOpulation of 18000 and
row Spacing coefficient of 1.1 were used. Cr = 1.1
correSponds to 30 inch row spacing and 2.5 mile/hour ground

speed of combine.

3.4 Natural Field Drying

 

Between the date of physiological death, i.e., the
maturity date of the corn plant, and harvest time natural
drying of the kernel occurs. Reduction of kernel moisture
reduces the drying cost for corn.

Schmidt and Hallaner's (1966) field drying model
was used. This model's quality was indicated by correlation
coefficients of .72 to .92 for the various stages as shown

below. Their final least square estimates were:

 

-2.00 + .047T 75%2Mci a 50%

-0.54 + .021T 50%2Mci a 30%
R =4

-0.08 + .119D 30%2MCi 225%

30.432 + .146D 25%2Mci a20%

or:
R = 0., whichever is larger.
Then:
MCi+1 = MCi + R
where:

MCi = moisture content, percent wet basis on

day i

48

R = daily percent wet basis reduction in MC
T = dry bulb temperature (OF)
D = wet bulb temperature (OF)

The output of this model was the basis for drying

cost calculations.

CHAPTER IV

FIELD OPERATIONS

Daily capacity for field Operations was calculated

by:
Effective
Field Capcity== S. W. E H
(Acre/Day) 8.25
where:

S = speed of the machine (miles/hour)
W = effective width of equipment (ft)
E = efficiency (decimal)
H = number of work hours worked per day.
The effective field capaCity values were reduced by five
percent to account for machine breakdowns.
The following equations were used for horsepower

requirements of different operations (Bowers, 1968):

.. ER 850
HPp ‘ NB 12 Vp 375
_ 280

th — WH vh 37g
_ RW 110
pr1— NR IF vpl 37—

49

where:

HP

HPh

HP
NB

WB

RW

Vpl

pl

50

horsepower requirement for ploughing (HP)
horsepower requirement for harrowing (HP)
horsepower requirement for planting (HP)
number of bottoms of plough

width of plough bottOms (inches)
ploughing speed (mile/hour)

width of harrow (ft)

harrowing speed (mile/hour)

planter width (number of rows)

row width of planter (inches)

planting speed (mile/hour)

Horsepower requirements of harvesting were calculated by

the formulae of Parsons, et al., (1971).

The values of field efficiencies and speeds used in

the model for different Operations are given in Table 5.

Table 5.--Field Efficiencies and Speeds.

 

 

Operation Efficiency Speed (mile/hour)
Ploughing .825 - 4.5
Harrowing .825 4.5
Planting .725 4.5
Harvesting .750 . 2.5

 

CHAPTER V

TIMELINESS SIMULATION

Determination of machinery requirements has been a
problem of agricultural production systems for a long
time. The owner of the machine wants to make maximum
possible profit. The timeliness of a certain agricultural
machinery operation is, therefore, a very important factor
in machinery selection. If the machinery cannot perform
the necessary Operation during the climatologically optimum
period, then timeliness cost occurs.

The "timeliness function" as defined by Link and
Barnes, (1959) is shown in Figure 4. This same repre-

sentation was also used by Sowell (1967).

5.1 Simulated Conditions

 

A corn production simulation was made for 16 years
of weather data from the period 1953 through 1968. The
weather data included maximum and minimum daily temperatures
(0F), wet bulb temperature (OF), daily precipitation (inches),
daily open pan evaporation (inches), and a snow indicator

(one or more inches on the ground, snow, otherwise no-snow).

51

Return

 

52

 

Time Range of Specific Agricultural Operation

Figure 4.--Timeliness Function.

53

Open pan evaporation data were from U. 8. Weather Bureau's
Dearborn-Detroit weather station; and data from U. 5.
Weather Bureau's Detroit City Airport weather station were
used for the other values.

A hypothetical corn producing farm of 200 acres was
the basis of our study. These 200 acres were assumed to
consist of five equally sized fields. Distances from the
machinery storage area, and distances from field to field
were neglected. The farm was operated by one worker and
whenever extra labour was needed (for transport), family
labour was assumed to be available. One tractor, one
combine and necessary tillage and planting equipment were
assumed. A work day was assumed to be ten hours. Sundays
and holidays were considered to be work days if working
conditions were technically appropriate.

Field Operations were divided into two parts: Spring
operations (tillage and planting) and the fall harvest
operation. The operations in spring were considered in
the following order: 1) ploughing, 2) harrowing, and
3) planting. There was no fall tillage. This sequencing
of events was assumed to be adequate to reveal the timeliness
effects on corn production. However, the model can depict
a different sequencing of operations with slight modifi-
cations.

Two kinds of planting strategies were considered:

1) finishing the ploughing and harrowing for 200 acres and

54

then planting (planting strategy 1), 2) finishing
ploughing and harrowing for the first field (each field is
40 acres) and planting it, then continuing in the same
manner for the remaining four fields (planting strategy 2).
The first strategy represents the extreme case and is not
preferred by farmers most of the time. In the second
strategy, the 40 acre portions were thought to be typical
for sectionwise completion of spring operations. Upon
completion of each Operation a one hour deduction from the
available working hours was made to account for the time
required to get ready for the next operation.

To compute drying costs 0.005 dollar per point
above 15.5 percent moisture (wet basis) per bushel was
charged for drying of the harvested crOp (Maddex and
White, 1972).

5.2 Simulation Procedure

 

Nine different machine capacity combinations were
considered using the models described in previous chapters.
A simplified flow chart of the simulation model can be seen
in Appendix C for 16 years for planting strategy 1. The
machine capacity combinations were three tillage capacities
with three different harvesting capacities for each tillage
capacity. Variation in planting capacity was not considered.
Table 6 shows the assumed capacities and related values for

these machine capacity combinations. The machine capacities

55

are indicated by T#H# (Tillage system number and Harvesting
system number). Related horsepower values for tractors
were taken to be approximately 1.33 times the required
horsepower values for each operation. The horsepower
requirement for harvesting (H1, H2, and H3) changes from
35 HP to 83 HP because it is affected by variability in
yield (Parsons, et al., 1971). Although 1-row and 2-row
combines are not now manufactured they were used to reveal
the effect of a lower capacity system on harvest losses
(this could also be considered as a reduction of work hours
per day or increased acreage).

Each of the machine capacity combinations shown in
Table 6 was simulated three times over the 16 year period
for both planting strategies. Yield values were
stochastically generated for each planting period as described
in Chapter 3. However, the discontinuities in yield vs.
planting date implied by this procedure gave irregular
results. Yields for all planting dates prior to May 6
were assumed to be the generated value for the second
planting period (May 1 - May 11). Linear interpolation
between adjacent yield values was used to determine yield
values for planting dates after May 6. (The yield value
for a given planting period was assumed to be the actual
yield value for a planting date which was the mid—date

of the planting period). This procedure on the average

56

gives no yield penalty for planting dates prior to May 6
and a one Bu/day penalty for each day after May 6.

Field harvest dates and harvest moisture contents
were assumed to be those values on the day when one half
of the field was harvested. Field planting dates, however,
were set to that date when the planting of the field was

completed.

5.3 Results

 

Results obtained from the computer simulation model
for both planting strategies are listed in Table 7.

Standard deviations of values are given in parenthesis.

5.3.1 Yields Before Harvest Losses

 

Table 4 shows that the climatologically best yield,
109.5 Bu/A with standard deviation 18.61 Bu/A, occurs if
the planting date of corn is between May 1 and May 11.
Yields before harvest losses were calculated over all
observations of tillage capacities (T1, T2, and T3) in both
planting strategies. Each mean and standard deviation of
yield before harvest losses for individual tillage capacities
shown in Table 7 is based on 144 observations. In Figure
5 it can be seen that the timeliness loss in bushels per
acre decreases with increasing tillage capacity in both
planting strategies. The timeliness losses for three

ploughing capacities are: 19.76, 13.77, and 8.54 Bu/A for

57

 

 

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59

 

 

 

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60

T1, T2, and T3 respectively for planting strategy 1.
Planting strategy 2 gave lower losses: 12.06, 6.94, and
5.03 Bu/A for T1, T2, and T3 are recorded reSpectively. It
may be expected that the curves in Figure 5 approach the
109.5 bushel per acre value if the ploughing, harrowing and
planting capacities are increased. However, it will never
exceed the climatologically best yield (109.5 Bu/A).

Variations in yields are lower for planting strategy
2 than for planting strategy 1. In both planting strategies
the highest tillage capacity, T3, gives the lowest variation
in yield (Table 7). In Figure 6 timeliness losses in bushels
per acre are depicted for the total Acre/Day ploughing-
harrowing-planting capacity of each system (T1, T2, and T3)
for both planting strategies.

Table 8 lists the "average" planting, maturity and
harvesting dates for all combinations and planting strategies
for the years between 1953 and 1968. The "average" was
computed as the arithmetic mean of the dates for the five
fields. The "extreme" (latest over the five fields) dates

are given in Table 9.

5.3.2 Harvest Losses and Drying Costs

 

Decreasing harvest losses and increasing drying
costs occur as the harvest capacity increases for planting
strategy 1 (Table 7) except machine capacity combination

T3H3. In this case high harvest moisture contents produce

61

high cylinder and separation losses (See Section 3.3). This
behaviour of harvest losses is dominant in planting strategy
2. The harvest losses which occur with H3 in all the tillage
capacities are higher than caused by H2. A comparison of
planting strategies 1 and 2 reveals that the harvest losses
(with H1 for planting strategy 1 is higher than for planting
strategy 2. The losses associated with H2 are very close

to each other for the two different planting strategies.,
This behaviour is again attributed to the moisture content
of the harvested grain. Figures 7 and 8 show the harvesting
losses for the two different planting strategies.

The highest harvest losses occur with HlHl for both
planting strategies, while the lowest drying costs per
bushel are recorded for T3Hl for planting strategy 1 and,
for T2H1 and T3Hl for planting strategy 2. If the mature
crop stays on the field in the late fall (after October)
rather than in the early fall, the natural field drying rate
is not as high because of cooler temperatures. The decrease
in drying costs islimited by the temperature inputs for
the time duration the mature crop is in the field. The reason
that the machine capacity combination TlHl does not have the
lowest drying cost is due to this limit in both planting
strategies. The T3Hl, T2H1 and T3Hl capacity combinations
produce a long stay on the field in the early fall for the

mature crOp for planting strategy 1, and planting strategy 2

62

 

 

 

 

 

 

 

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63

 

 

 

 

 

 

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HOFNO HOONO HOOHOH HOOHO. HOBNO
OONHOH OOOHOH OONHHH OObOOH OOhOO
,mmOHm mmOHm mmmOOH mmmom mmhom
OmmNOH OmmNOH OOOHHH OONHOH OOOHO
thOOH hmmOOH hmONOH OOONO thOO
mumnmwnflumm>Hmm. m¢ODTmQfl¥mw>Hmm m#mn mcwumm>me mpma muwnsumz mpma mqfluamHm
mm mm .Hm Na

 

 

aflflommmu.umm>umm, muwommmu mOMHHHH

 

 

OmsGHuGOUII.O mHnme

64

 

 

 

OOONO .QOONO OOmooH OOOHm OOOHO
OOOHOH OOOHOH OOONHH OOOHOH mOHmm
OONOOH OOOOOH OOOHOH OOHOO OOONO
OOONO OOHOOH OONHOH OOONO OOOHO
NOOOO NOOOOH OOONOH mOnmm mOmHm
HOmmm Hmem HOOOOH HOmHm HOOmm
OOmOOH OOHHOH OOONOH OOBOOH OOONO
mmmHm OOOHO mmOOOH mmmom mmmom
OOONOH OOONOH OOOHHH OmnHOH OOOHO
hOHHOH hmOHOH hmmHOH anOOH nmmmm
OOOHOH OOOHOH OOONOH OONHOH OOOHO
mmmom mmmom OOONO mmOOO mmmom
OmmOOH OOOHOH OOnOHH OOONO Ommom
OOOHO Othm OOOOO OOOHm OOONO

Om mm Hm He

m mmmvmuum mafluamHa

OOONO OOONO OOHHOH OONHO OOOOO
hONHOH hOOHOH hOOHmH nOHOOH nOnHO
OOONO OOONO OOOOOH OOOHO OOOOO
OOOOOH OOOOOH OOONOH mOnmm OOOHm
OOmOOH OOhOOH OOOHOH OOONO OOONO

 

 

 

 

 

muma quumm>Hmm

mm

muma maHumm>Hmm

mm

mfima maflumm>umm

Hm

 

muflomamu umm>umm

mumo muflnspmz

muma OcHucmHa

OB

 

muHomamU mOmHHHB

 

 

mmsqaugoouu.m magma

65

 

OOONO
bOOHOH
OOONO
mOmOOH
OOONO
OOONO
NOONO
HOONO
OONOOH
OOOHO
OONNOH
hmOOOH
OOOHOH
mmmom,
OmmHOH
OmOHm

mm

OOmHm
hOOHOH

OOONO
bOOHOH
OOONO
mOmOOH
OOOOOH
OONOOH
NOOOOH
HOth
OOOOOH
OOOHO
OthOH
hmOOOH
OthOH
mmOom
OONNOH
OmOHm

mm

OOONO
hOOHOH

OOHHod

hOOHNH
OOOOOH
OOONOH
OOOHOH
OOOHOH
NOONOH
HOOHOH
OOOHOH
mmOOOH
OONNHH
OOOHOH
OOONOH
OONNOH
OOOONH
OmOOm

Hm

OOOOOH
hOOHNH

OOOHO
NOOOOH

.mmmam

mOOOO
OOmHm
OOONO
NOmHm
HOOHm
OOHOOH
mmmom
OOOHOH
hmOOOH
OOHHOH
OOONO
OOONO
OmOHm

OOmHm
hOhOOH

OOmom
NOOHm
OOhOm
mOOHm
OOHNm
OONHO
NOOHm
HONNm
OOONO
OOONO
OmOOm
hmmmm
OmmHm

OOONO
OmHOm

Othm
NB

OONHm

.hOOHm

 

 

 

 

 

muma mqflumm>umm

mm

mamagmfidumm>Hflm

mm

mmmarmnflumm>umm

Hm

 

muwomamo umm>nmm

muma mmHuspmz

mama maHmcmHa

HE

 

muHomamU mmmHHHB

 

 

.mmnchGOUII.O mHamB

66

 

OOONO
hOOHOH
OOONO
mOmOOH
OOONO
OOONO
NOOOm
HOOOO
OOHOOH
OOOHO
OONNOH
bthOH
OOONOH
mmmom
OOOHOH
OmOHm

OOONO
hOOHOH
OOONO
OOOOOH
OOOOO
OOOOOH
NOmOOH
HOOOm
OOOOOH
mmOHm
OthOH
hmOHOH
OONNOH
mmOOO
OthOH
OmOHm

OOOHOH
hOHONH
OOOOOH
OOONOH
OOOHOH
OOOHOH
NOONOH
HOOHOH
OOONOH
mmOOOH
OONNHH
hmmHOH
OOONHH
mmHNm

OmbHHH
Omomm

OOOHO
hOmOOH
OOOHO
OONOOH
OOOHO
OONNO
NOOHO
HOONO
OOONO
mmmom
OONHOH
hmOOOH
OOOHOH
OOONO
Ombmm
OOOHO

OOONO
hOmom
OOOOm
mOmHm
OOOHm
OOOOm
NOmOm
HOhHm
OOOHm
OOONO
Omhom
hmmHm
OmOOm
OOONO
OOONO
OmmHm

 

 

 

 

 

muma OGHumm>Hmm

mm

muma maHumm>Hmm

mm

muma OaHumm>Hmm

Hm

 

MpHomamo.umm>Hmm

mama maHusumz

muma msHuamHa

OB

 

apfiomamu mmmHHHB

 

 

.Omscaugoouu.m «Hams

67

 

 

 

 

 

 

 

OOONOH OmOOOH mmmom OOONO. OOOHO
Omhmm OONOOH OOnHOH OOOHm OOONO
Om mm Hm OB
OOONO OOONO OOOOOH OOmOm OOOOO
nOHNOH hOOOOH OOONO wOmOOH nObmm
OOONO OOOOm OOHOOH OOOHm OOONO
OOOHOH OOONOH OOONHH mOnOOH OOOOO
OOOOOH OONHOH OOHOOH OOOHm OOHOO
OOOOO OOOOOH OOONOH OOnHm OOHOO
OOONOH OOONOH OOONH NOnOOH OOONO
HOmNm HOOOOH HOOOHH HOOHm HOOOO
OOOHHH OOOHHH OOOONH OOnOHH OOHHO
mmmHm OOHOO mmOOHH mmOom mmnmm
OOONOH OOOOHH OOONOH OOHOOH OOHOO
hmHNOH hmHOOH anHm nmmOOH nOOOO
OOOHOH OOOHOH OOwOHH OONOOH OOHOO
mmmHm mmnHm OONOOH mmmom mmHHm
OOONOH OmOOHH mmmom OOONO OOOHO
OOONO Omhmm OOOOOH OOOHm OOOOO

H.mmmumumm.mcfluqum
mumawmnflumm>umm mama.mdflumm>umm mfima mnflumm>umm mpma muHHdpmz muma mchsmHa
Om «O HO H9

 

 

huHomamU umm>umm muHomamU mmmHHHB

 

wummu ammume may no somm uom mQOHpmcflanu MuHomamU
mqflnomz ucmummmao um mwuma mcwumm>umm cam spansumz .mcfluqmam hummumqo =memnuxm=uu.m magma

68

 

 

 

 

 

 

HOOOOH HOOHOH HOmOHH HOOOm HOOOO
OOmOOH OOOHOH OOOHHH OOOOOH OOONO
mmmHm OOHOO mmOOHH mmmom mmmom
OOHOOH OOOOHH OOHOOH OOBHOH OmmHm
hmmmOH hmOOOH nthHH anmOH anOm
OOHOOH OOONOH anHH OOOHOH OOONO
mmmHm OOOHO OOOHOH OOOOO OOOOO
OOONOH OOOOHH mmmom OOONO OOOOO
OOONO OONOOH OOHOOH OOHHO OOONO
mm mm Hm OB
OOONO OOOOOH OONOHH OOOHm OOONO
nOHmOH nOOOOH OOnmm nOOOOH FOONO
OOONO OOHOOH OOONOH OOOHm OOOHm
OOHOOH OOHOHH OOHOO OOONOH OOONO
.OOOOOH OOOHOH OOmoHH OOnmm OOONO
OOOOOH OONHOH OONOHH OOONO OOONO
OONHOH OOOHOH mmeHH OOOOm mOmHO
HOOOOH HOOOOH HONOHH HOHmm HOmmm
OOOHOH OOONOH OOONOH OOOOOH OOmOO
mmmHm mmHmm OOOOHH mmOom mmmom
OOHOHH OmmOHH OmnHmH OOONOH OOOHO
hOhOOH hOOHOH hmHHHH meOOH anOO
OOONOH OOOOHH anNH OOOHOH OOONO
mmmHm mmmHm OOONOH Ommom Omnom
muma OQHumm>Hmm muma OQHumm>umm mpma OcHumm>Hmm muma thHsumz mpma OsHuQmHa

mm mm H3 H8

 

 

muHomamo umm>umm mbHomamo mmmHHHB

 

 

.wmsgflpaoouu.m magma

69

 

 

 

OOHOOH OOHOHH. OOHOO OOONOH OOOOO
OObOOH OOOHOH OOHOHH OOnmm OONOO
OONOOH OOOOOH OOhNOH OOOOm OOHOO
OONHOH OOOHOH NOnNHH NOOOOH OOONO
HOHooH HOOOOH HONOHH HOmmm HOOOO
OOOHHH OOOHHH OOONHH OOnOHH OOHHO
mmmHm OOHOO OOOOHH mmmom OOONO
OOONOH OmOOHH OOOHOH OONOOH OOONO
FOONOH nmmNOH hmnOHH OONOOH hmmOO
OOONOH OmhmOH OOOHHH OOOHOH OOOOO
OOHHO mmnHm OOOHOH OOOOO OONHO
OOOHOH OOONOH mmmmH OOONO OmmHm
OOONO OOONO OOOHOH OmmHm OmmOO

mm mm Ha Ha

m mmmamaam maaacmHa

OOONO (OOOOOH OONOHH OONHO OOOOO
hOHmOH hOOOOH nOhmm hOOOOH hOmHm
OOONO OOHOOH OOONOH OOOHO OOwOO
OOOHOH OOOHOH OOOHHH OOOOm OOOHO
OOOOOH OOOHOH OONOHH OOONO OOONO
OOOOOH OOOOOH OOONOH OOONO OOONO
OONHOH NOOHOH NOBNHH OOONO NOOHO

 

 

 

 

 

mama Oqaamm>nmm

mm

mama.OqHamm>umm

mm

mama maflamm>amm

Hm

 

maHomamU amm>amm

mama maHHSamz

mama mafiaqMHm

OB

 

maHomamU mmmHHHB

 

 

.mmnqapqomun.m magma

70

 

OOONOH
OOHNO

mm

OOONO
bOmNOH
OOONO
OOOHOH
OOmOOH
OOOOOH
NONHOH
HOOOO
OONHOH
mmmHm
OmOOOH
hmHNOH
OOHNOH
mmmom
OOONOH
OmONm

mm
OOONO

hONNOH
OOONO

OOONOH
OOONO

mm

OOOOOH
hOOOOH
OOHOOH
OOOHOH
OOHHOH
OOOOOH
NOOHOH
HOmOOH
OOOHOH
OOHNO

OmmOHH
OONNOH
OOONOH
mmOHm

OmOOHH
Ombmm

mm
OOHOOH

hOOOOH
OOHOOH

mmOOH

.OthOH

Hm

OONOHH
OOBNN

OOmmoH
OONHHH
OOOHOH
OOONOH
NOBNHH
HONOHH
OOOHHH
mmOOHH
OOONOH
hthHH
OOOHHH
OOHHOH
mmmom

OOOHOH

Hm
OOHOHH

OOBNN
OONOOH

OOONO
OOOHO

OOOHm
NOONOH
OOOHO
OOHHOH
OOONO
OOONO
NOOOOH
HOHNO
OOOHOH
mmOom
OOHNOH
hmOHOH
OOOHOH
mmmom
OOONO
OOOHO

OOOHO
hOOOOH
OOmHm

Omhom
OOONO

OB

OOONO
nOONm
OOOHm
OOONO
OOONO
OOth
NOONO
HOOOm
OOmHO
OOOHO
Othm
hmmOO
OOONO
mmOom
OmHHm
OmHOO

NB
OOOOO

hOOmm
OOONO

 

 

 

 

 

mama Onwamm>umm.

mm

mama Ofiflammkam

mm

mama mafiamm>nmm

Hm

 

maaomamu amm>amm

mama hafiasamz

mama maflaamHa

HB

 

maaomamo mmmHHHB

 

 

.wmsgapgooun.m magma

71

 

OOONO

bONNOH
OOONO

mOhHOH
OOOOOH
OOOOOH
NONHOH
HONOOH
OONOOH
mmmHO

OOHOOH
hmONOH
OOONOH
mmmom

OOOOOH
NOOOOH
OOHOOH
OOOHOH
OOOOOH
OOOOOH
NOOHOH
HOOOOH
OONHOH
OOHOO

OmOOHH
hmmNOH
OmOOOH
mmOHm

 

 

mama Oswamm>amm

mm

mama.mnaamm>amm

mm

(OONOHH

OOBNN

OONNOH
OONHHH
OOONOH
OOONOH
NOBNHH
HONNOH
OOONHH
mmOOHH
OOHNNH
hthHH

thNH
OOHHOH

OOOHO
hOhHOH
OOOHO
OOOHOH
OOONO
OOONO
NOhHm
HOONO
OOmOOH
mmmom
OOHNOH
NONNOH
OOOHOH
mmHOO

OOhom
hOONm
OOhOm
mOmHm
OOONO
OOONO
NOOHO
HOONO
OOOOO
OOOOO
OOOHm
bmHOO
Ommmm
mmOOm

 

 

 

mama Oaflamm>amm

Hm

 

maaomamo amm>amm

mama maHasamz

mama OaflaamHa

OB

 

maHomamo mmmHHae

 

 

.Omsaaaaooll.m mHamB

72

i——-‘——~——_——.———~—-—~_—m———_~

...:
O
\D
O
L

Planting Strategy 1

(Bu/A)

100J Planting Strategy 2

 

Yield Before Harvest Losses
\0
C

CD
0
a
L.

 

1 2 T3 Tillage Capacity

Figure 5.——Yield Before Harvest Losses at Different
Tillage Capacities.

Losses (Bu/A)

20“

15L

10

 

73

      

Planting Strategy 1

Planting Strategy 2

l L
V

ml 11 12 T2 3 14 15 16 f 17
Total Acre/Day Capacity for Spring Operations

Figure 6.-—Timeliness Losses Due to Tillage

Capacity.

74

respectively, therefore, the lowest drying costs are
recorded for these combinations (Figures 9 and 10).

As tillage and harvest capacities are varied there
is always a tradeoff between harvest losses and drying costs.
The tradeoff could be found, but we cannot make a definite
statement about the farmer's utility of harvest losses

against drying costs.

75

 

 

 

 

5°50i

U)

0)
UK!)
HO)
(DO
wit-1
>1
.4J
mm
00)

>
JJH
‘3!!!
(DD:
'0
as:
mos.001
V‘H

0)
mm
0.)
U)
U)
0
1—‘l .
4;, %T1
0)
a “‘ '—“'—--—* T2
(U

4050 YL J 1
H1 H2 H3

Harvest Capacity

. Figure 7.——Time1iness Losses Due to Harvest
Capacity at Different Tillage Capacities (Planting
Strategy 1).

76

5.50

Losses)

5.00

 

 

Harvest Losses (Percent of Yield Before Harvest

 

 

___..——--"'"+
f/
./.--—'4‘
5","
4.50 1 V 4.
H1 H2 H3

Harvest Capacity

Figure 8.-—Time1iness Losses Due to Harvest
Capacity at Different Tillage Capacities (Planting
Strategy 2%

77

.0501

.045«

)

2:
as
?

.035

Drying Cost (Dollar/Bushel

 

 

O

L
r/ . ' W

H1 H2 H3
Harvest Capacity

Figure 9.-—Drying Costs at Different Machine
Capacity Combinations (Planting Strategy 1).

78

.050

(Dollar/Bushel)
O
b
UL

.040

Drying Cost

2:
u:
_Ji.

 

 

0030 5

H3

Harvest Capacity

Figure 10.——Drying Costs at Different Machine
Capacity Combinations (Planting Strategy 2).

CHAPTER'VI

STOCHASTIC GENERATION OF WORK NO-WORK DAYS

The procedure for labeling the days as work or no-work
day. which was described in Chapter 3 requires the use of
weather data throughout the simulation period. Machine
storage of the weather inputs and the required soil moisture
budget is costly for computer-calcu1ations.. The purpose of
the stochastic generation of work, no-work days was to reduce
the time spent on data evaluation either manually or by
computer. If the stochastic generation of work, no-work
days could be proven feasible, work, no-work conditions
could be characterized very concisely for different
localities via the values of their stochastic parameters.

The World Meteorological Organization recommends
(Selirio and Brown, 1972) the use of at least 30 years of
data for good estimation of weather related probabilities.
Feyerharm, et al., (1966) published wet and dry day
probabilities in Michigan by using weather records starting
from 1886 for some locations. This climatological model
gives the initial and transition probabilities for a year

determined by a Markov chain probability model. Strommen,

79

80

et al., (1966) prepared a bulletin for farmers' use in

Michigan based on Feyerharm's (1966) work.

6.1 Procedure

 

The following scheme was proposed for the stochastic
generation of work, no-work days:
1. Generate Stochastically:

a. The number of days from March 1 to soil
thawing,

b. The number of days from March 1 to the first
ocgurence of soil temperature exceeding
50 F,

c. The number of days from December 1 to soil
freezing.

2. Generate and distribute the work days between

soil thawing and soil freezing.

Properties of the values in 1. were found utilizing
the tractability model and 16 years of weather data (Dearborn-
Detroit). These values were generated assuming that they
were normally distributed. The means and standard deviations
of the numbers of days for the 16 years of weather data are
shown in Table 10.

For the generation of work days between the dates
of soil thawing and soil freezing 15-day periods were used.
This was done to capture the known persistency in work,
no-work sequences (Holtman, 1973). Panol (1972) reported
that for his weather simulation based on the utilization of

the "rain, no-rain state" on the previous day (first order

81

Table 10.--Estimated Means and Standard Deviations for the
Number of Days in Critical Periods (16 Years of

 

 

Data)
Mean Standard
Deviation

March 1 to
Thawing 13.60 9.36
March 1 to the
First Occurence
of Soil Tempera-
ture Grgater
than 50 F 31.93 9.52
December 1
to freezing 46.50 18.17

 

Markov assumption) some inadequacies in capturing the
persistency of rain, no—rain sequences existed. Starting
from March 1, which is the beginning of the simulated
meteorological year, the year was divided into lS-day
periods. The use of the tractability model for tract-
ability criterion 2 (December 26 to August 27), and
tractability criterion 1 (August 28 to December 25) yielded
the values given in Table 11 for 16 years of data (Dearborn-
Detroit).

The first attempt was to assume a normal distribution
for work days in the 24 15-day periods as was done for the

generation of yield values in Chapter 4.

82

Table 11.--Means, Standard Deviations, and Correlation
Coefficients of Work Days in 24 lS-Day Periods.

 

 

Starting Date Mean Standard Deviation Correlation
of Period Coefficient
301 0.0 0.0 0.0
316 0.0 0.0 0.0
331 1.19 1.91 0.040
415 3.75 3.26 -0.015
430 7.00 4.21 0.285
515 9.75 3.84 -0.466
530 10.81 2.23 -0.081
614 10.13 3.18 0.623
629 11.86 2.36 0.068
714 11.69 2.24 0.236
729 10.25 2.30 '0.093
813 11.06 3.04 0.223
828 12.06 2.14 0.390
912 11.56 2.19 0.150
927 11.31 3.28 0.354
1012 12.18 2.07 0.198
1027 10.75 2.23 0.065
1111 7.43 3.08 0.131
1126 2.50 3.39 -0.203
1211 1.63 4.06 0.860
1226 2.81 6.05 0.899
110 3.94 6.10 0.658
125 7.88 7.46 0.833

209 10.13 6.59

 

The results in terms of means, standard deviations, and
correlation coefficients after 1000 repetitions were
satisfactory. However, due to the large magnitude of the
standard deviations, the number of work days in individual
15-day periods often fell outside the interval (0, 15).
Therefore, the assumption of normality was abandoned.

The Beta was then considered since it is bounded on

the positive real line (0, l). Naylor, et al., (1968)'

83

state that the beta distribution is the distribution of the
ratio of two gamma variables with identical values of a and
parameters k1 and k2 respectively. a and k can be seen in

the following:

r

«k ka1 e-ccx cc>0, k>0, sz

HX) =) (k-l)! '
10 X<0

The beta variable is then given by:

 

(Gamma Distribution).

 

X = 7337' 0““

1 2
where:
x = beta variable
x1 = gamma variable with parameter k1
x2 = gamma variable with parameter k2

(This can be proven by convolution (Feller, 1971)).

Equating means and standard deviations of work days
in the 15-day periods to the beta mean and standard deviation
resulted in kl and k2 values which were non-integers. Since
there is a great deal of difficulty associated with generating
gamma random variables with non-integer parameters, further

work in this direction was terminated.

6.1.1 A Stochastic Work, No-Work Days Model
We made the assumption that the number of working
days in successive lS-day periods were independent random

variables. Results of a test of this assumption are given

 

84

in 6.2.1. The probability distribution of number of work
days was assumed to be characterized by the following

density for each period:

 

r
ai/5 0<NWDi55
fNWDi (NWDi) =( bi/S 5<NWDi510
. Ci/S 10<NWDi<15
where:

i = l,..., 24 period numbers

NWDi number of work days in period i

c. = l - a. - b.

1 1 1
With the aid of the definitions of mean and variance for a
continuous random variable the following relationships must
hold if we require the mean and standard deviation of the

stochastically generated number of days to be equal to the

data of Table 10:

 

 

s a. 10 b- 15 1-(a +b )
1 1 1 l
= —— —— +
“i J 5 xdx + g 5 xdx [o 5 xdx
5 a. 10 b-
2 _ _i _ 2 _£ _ 2
Ci —6f 5 (X pi) dX + 5f 5 (x pi) (3X
15 [l-(a +b )1
1 1 _ 2
where: 1 = 1, ..., 24 period numbers
“1 = mean number of work days in period 1
Ci = variance of work days in period 1

Solving simultaneously the ai's and bi' s can then be computed by:

_ _ 2 2
_ 275 15ui 3“i + 3oi
ai ‘ 3(50 + 20ui)

 

85

 

The computer generation of the random variables was

made using the inverse transformation technique (Naylor,

 

et al., 1968), i.e., the cumulative distribution functionijn
(0 NWD.SO
. 1
ai NWDi r
__ ,9
5 0<NWDiSO
bi NWDi
Fani (an1) = < —'5—_ ‘ bi + a]; 5<NWD1$1°
3(a.+b.) — 2 + NWD. 10<NWD.315
1 1 5 1 1
L1 NWDi>15

 

and NWDi can be computed by:

NWD. =<<
1

shown.

 

,
SR/ai R S ai

(R + bi — ai)5/bi ai < R s ai + bi
L(R _ 3(ai+bi) + 2)5/(l_ai—bi) OtherWise

where:

R is (0,1) uniform random variate.

6.2 Results

 

In Table 12 the computed values of a and b are

To have a valid probability distribution function

the following relationships must hold:

86

Excluding the trivial periods beginning March 1 and March 16,
it was concluded that the lS-day periods outside of the time
interval April 15 to November 25 could not be described by
the assumed probability distribution function. Although
negative a values do occur during the period April 15 to
November 25, they are small in magnitude. Smoothing of the
a values (See Figure 11) would eliminate all of the diffi-
culties. Thus it was concluded that the stochastic model
was adequate for the time period April 15 to November 25.

The histogram for the period beginning January 25 (See
Figure 12) illustrates the difficulty for the periods where
the assumed probability distribution fits poorly. The
histograms for these periods have peaks at zero and fifteen.
A Markov chain model might be appropriate to describe this
situation as the number of working days in successive

periods are not independent for these periods (Section 6.2.1).

6.2.1 Test of Independence of
Work Days in lS-Day Periods

 

 

To test the independence of numbers of work days for
successive in lS-day periods a version<IESpearman's1Hu3test,
the Hotelling-Pabst test (Conover, 1971) was used for the

periods between April 15 and November 25 as well as the

87

Table 12.--Parameters of Stochastic Tractability Model

 

 

Starting Date "Smoothed"
of Period a b Values of a
301 1.833 -1.167 -

316 1.833 -1.167 -

331 1.459 - .656 -

 

 

 

 

 

 

 

16
2 .
T = ‘2 [R(NWDi) -R(NWDi+1)] , 1 = 1,...,13
J=l '
where:
i = corresponds to the periods between April 15

test is given by:

and November 25

415 .826 .097 .826
430 .368 .364 .368
515 .129 .291 .129
530 -.054 .446 .0
614 .036 .403 .036
629 .015 .094 .015
714 -.009 .181 .0
729 -.060 .570 ,.0
813 .041 .205 .041
828 .013 .067 .013
912 -.022 .231 .0
927 .083 .072 .083
1012 .015 .032 .015
1027 -.055 .461 .0
1111 .154 .705 .154
1126 1.187 -.375 —
1211 1.566 -.958 -
1226 1.598 -l.258 -
110 1.314 -.915 -
125 1.035 -1.145 -
209 .703 -.930 —
other periods. The test statistic for the Hotelling-Pabst

88

100‘

 

0.0 v v r v v —‘ v 1' v ‘ j 1 '1‘

415 .Starting Date of Periods

 

Figure 11.--Smoothing Tractability Parameters.

1111

84

 

uh U1

Frequency

HM

 

 

 

 

89

 

 

 

 

A

 

'3 '4 '57 78: 9‘ 170111213 14175“
Number of Work Days

Figure 12.-—Histogram of Work Days for the Period

January 25-February 8.

 

90

R(NWDi) = rank of the number of days in period
1.
j = 1,..., 16 year index (between 1953-

1968).

The hypothesis was:

HO : number of working days in two consecutive
15-day periods are mutually independent
Hl : H0 18 not true,

H0 is rejected if «/2 quantile of T< observation of T.

Table 13 gives the results of this test. It was
concluded that HO should not be rejected for the period
April 15 - November 15.

The test was also applied to the remaining periods

and H0 was rejected in every case (the test is not applicable

 

 

for the periods beginning March 1 and March 16).

Table 13.--Hote11ing-Pabst Test Statistic.

Starting Date 16 2

of Periods T = Z [R(X.) - R(Y.)] a Decision

j=l l l ——

415’430 668 .05 Do not reject HO
430,515 526.50 .05 Do not reject H
515,530 957 .05 Do not reject H
530,614 588 .05 Do not reject Ho
614,629 265 .05 Reject HO
629,714 604 .05 Do not reject HO
714,729 477.25 .05 Do not reject HO
729,813 588 .05 Do not reject HO

 

Table 13.--Continued.

 

91

 

Starting Date 16

 

 

of periods T = jil [R(Xi) - R(Yi)]2 . Decision
813,828 483.50 .05 Do not reject Ho
828,912 341.50 .05 Do not reject HO
912,927 656 .05 Do not reject HO
927,1012 397.50 .05 Do not reject Ho
1012,1027 476 .05 Do not reject Ho
1027,1111 975 .05 Do not reject HO

 

.025 quantile of T

.01 quantile of T

340

250

CHAPTER VII

SUMMARY AND CONCLUSIONS

The necessary models for the components of a corn
production system were developed to investigate timeliness
losses incurred in corn production. Special attention was
focused on tractability conditions of the fields. Simula-
tions were made with 16 years of weather data for nine
different machine capacity combinations on a hypothetical
200 acre farm in Southeast Michigan.

The model for tractability is deterministic and was
developed using only weather and soil property data. Work,
no-work conditions are obtained as model output for each
day as a tractability state. Verification of the model was
made utilizing weather data and work, no—work records from
three Northern Indiana farms. Tractability model output
proved to be in quite good agreement with the farmers'
records of work, no-work conditions. Total work days were
in error by one day for spring and a maximum of three days
for fall operations.

The yield values (Bushel per acre) were generated

stochastically. Generation was made for five consecutive

92

93

planting periods between April 16 and June 11. The yield
value of each planting period was assumed to be distributed
normally and correlated to the previous period's yield value.
Statistics for the stochastic generation were estimated from
Michigan corn yield data.

Two different planting strategies were considered:
1) finishing the ploughing and harrowing for 200 acres and
then planting, 2) finishing ploughing and harrowing for the
first field (each field is 40 acres) and planting it, and
continuing in the same manner for the remaining four fields.

Planting date timeliness losses due to tillage
capacity were dominant to those caused by harvesting
capacity for planting strategy 1. Timeliness losses for
planting strategy 1 due to tillage capacities were 19.76,
13.77, and 8.54 Bu/A for 3-bottom plough and 10 ft disc
harrow (55 HP tractor), 4-bottom plough and 13 ft disc harrow
(75 HP tractor), and 6-bottom plough and 18 ft disc harrow
(110 HP tractor), respectively. Planting strategy 2 caused
lower timeliness losses due to tillage capacity than
Iplanting strategy 1. The losses were 12.06, 6.94, and 5.03
Bu/A for planting strategy 2 at the same conditions.
Harvest losses were close to each other (lower for planting
strategy 2) for each planting strategy and varied from 4.59
to 5.50 percent of yield before harvest losses for different

tillage and harvesting capacity combinations. Generally

94

decreasing drying costs and increasing harvest losses were
observed with decreasing harvest capacities.

A stochastic model of work, no-work days was
developed. Probability densities were assumed for the
number of work, no-work days in successive lS-day periods
of the year. The parameters of the densities were
estimated employing simulation results obtained utilizing
the deterministic tractability model. The stochastic
simulation was satisfactory for the period April 15 -
November 25.

The following conclusions were derived from the
results of this study:

1. The tractability model is adequate for corn
production simulation and its use should be extendable to
other crops and other locations.

2. The yield model is sufficient to represent the
real yield values.

3. Planting date timeliness losses dominate those
associated with harvest losses.

4. Stochastic generation of work, no-work days
appears feasible but needs further development to cover the

entire year.

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95

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APPENDICES

104

APPENDIX A

VARIABLE STORAGE ALLOCATION FOR CORN

PRODUCTION SYSTEMS ANALYSIS

105

106

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APPENDIX B

SUBROUTINE NAMES AND THEIR FUNCTIONS

118

NAME OF SUBROUTINE

 

DATE
KL DIAT

NOPAN

SOILMC

SURFIS

PLOUGH

PLCOST

HARROW

IEWEST‘

PLNTNG

PLN CS T

SETHET

FXCST?

HUP

NAT

CORNT-IC

YIELD

HRVEST

119

FUNCTION
Generates calendar dates
Reads weather data

Estimates missing evaporation
values

Updates soil moisture budget

Finds surface conditions
(Tractability) I
fl

Performs ploughing

Calculates variable cost for
ploughing

 

Performs harrowing (Disc)

Calculates variable costs for
harrowing

Performs planting

Calculates variable costs for
planting

Sets heat units requirements and
variety number

Calculates fixed costs for spring
field operations

Accumulates heat units starting
from planting dates

Determines maturity of fields
(sections)

Determines kernel moisture (wet
basis) of corn at harvest time

Generates yield values (Bu/A)
stochastically

Performs harvesting

120

 

 

NMIE 01“ SU BRQQTINE FUNCTION _

HRCOST Calculates variable costs for
harvesting

LOSSES Calculates pre-harvest and har-
vest losses

FXCSTl Calculates fixed costs for fall
operations

DRYCST Calculates drying costs

TLCOST Calculates overall costs for pro-

duction year.

 

APPENDIX C

FLOW CHARTS OF SIMULATION MODEL AND

SOME OF THE SUBROUTINES

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   
 
 

 

 

 

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CALLDRYCST
CALLFXC 1
CALLTLC
CA LL [ATE
CA LL KLIMAT
CALLSOILMC
_CALLSURFIS

 

 

 

 

 

 

_ General Model

 

123

 

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124

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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125

 

 

 

 

 

 

 

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126

 

GIVE AVG),

 

STU), RTU)
HERE I=I.-S

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AV“ )= AW l V

Avm ..
srm= arm?
sum”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Y(|)==AV(|) +( F3(I—1)*ST(I)/

s11 l-lgfigfig-AW I-1))+ B *-

Yield Model

 

 

 

 

 

 

 

 

 

 

 

 

 

, 2* RA NFH)
YZ=YZ+Z w a
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127

 

 

 

RETURE)

 

 

X(3€-L-)=‘1. CAP
le 'YeS {
J>S
J=d+ No

 

 

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85

Yes

9

 

X(J+3IOO) =Y(1)

 

 

 

X(J+3|OO) =Y(2)

 

 

 

, X(J+3IOO) =YC’>)

 

 

 

 

‘ X(J*3IOO)= W4)

 

 

 

* X(J+3lOO) = Y6)

 

 

 

 

“

 

 

 

 

 

 

 

XL) 3100) =XKJ€CIID
)*X(K+3800)*X(J

 

K= X(J+| 800)
YR=.OZ(X0<+3825)~

 

X(JHOOO))**Z-/100CU

 

 

 

 

@

_‘

 

“

 

 

+3l00)"(l.-YR) ‘

 

 

 

Yield Model (Conto)

 

 

128

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

AYes

 

 

X (320 I) = O.
J K=X (4992)

 

 

 

 

 

 

 

 

Harvet Operations Model

129

(CD—"K4 N° 'KI =x<IK+3soof B=.95 ,
IK>JK Yes AREA=()((K|*4O7OW<III4OO)¢(I<I+4O@*
”a. K X(I<I+4ooo)/12 .)/8.2 Swoosh B
I x(3zoI) = X(320l)+AREA

 

 

 

 

 

 

 

 

 

 

   

X003)=X(3200'X(|*ZOQ ’1

 

 

 

 

 

 

 

 

 

 

   
 

 

   
  

 

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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aneool-Xfifl f
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Xezol), I. xu+woo>=l I

IDATE X(|O|)=I
A=X(320l)
l... -...
XISG=4-
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t“ W >‘ ' v

 

 

 

 

 

 

 

 

 

  

X003)=X(IO§)-—X(I+ZOO) l

 

 

 

 

 

 

 

 

 

Yes
XBZQD=X0 _ ..---.__ -...
, A: x3320)?! @2004003) ]
PRINT
X0004 CALL HRCOST II
Agog) " . X(3201)=O. x(s 7H [
X I+ZOO=X0+200)-XIIO3) r X(4981) =
“"Z- x(4981)+A

 

 

 

 

 

'.._.IA=0.

(RETURN N° @Y“ @

 

 

 

Harvest Operations Model (Cont.)

 

N

1!!!le

IIIIIIIIIIIII

2 215160