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Comparison of Container Placement Patterns for Maximizing Greenhouse Space Use

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Abstract and Figures

A series of equations were developed to provide a convenient means to calculate the number of containers that can be placed into a specified area using three different placement patterns. The calculations require three pieces of information; the container spacing, i.e., distance between the center of one container and the center of the neighboring container, and the length and width of the greenhouse bench or floor area. The solutions allow comparisons of the total number of containers that will fit into that area using three different placement patterns; square, long-staggered, and short-staggered. In general, the close the container spacing or the larger the production area, the greater the benefit of staggered spacing compared to square spacing. Staggered spacing frequently allows for up to 13% more containers to fit into a given area than square spacing; however, calculations must be made for specific situations to determine the most efficient spacing pattern. Cost analyses were performed on a range of container spacings and greenhouse dimensions. Spacing pattern can affect overhead costs from 0.02to0.02 to 0.20 per container for a 10-week crop. A spreadsheet, Bench Crop Calculator, is available from the authors for providing assistance in performing the calculations.
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July–September 1999 9(3)432
RESEARCH REPORTS
Comparison of
Container
Placement
Patterns for
Maximizing
Greenhouse
Space Use
Elizabeth Will,1 James E. Faust,1
and Benali B. Burgoa2
A
DDITIONAL
INDEX
WORDS
.
efficiency,
bench dimensions, staggered spacing,
square spacing
SUMMARY. A series of equations were
developed to provide a convenient
means to calculate the number of
containers that can be placed into a
specified area using three different
placement patterns. The calculations
require three pieces of information; the
container spacing, i.e., distance
between the center of one container
and the center of the neighboring
container, and the length and width of
the greenhouse bench or floor area.
The solutions allow comparisons of the
total number of containers that will fit
into that area using three different
placement patterns: square, long-
staggered, and short-staggered. In
general, the closer the container
spacing or the larger the production
area, the greater the benefit of stag-
gered spacing compared to square
spacing. Staggered spacing frequently
allows for up to 13% more containers
to fit into a given area than square
spacing; however, calculations must be
made for specific situations to deter-
mine the most efficient spacing pattern.
Cost analyses were performed on a
range of container spacings and
greenhouse dimensions. Spacing
pattern can affect overhead costs from
$0.02 to $0.20 per container for a 10-
week crop. A spreadsheet, Bench Crop
Calculator, is available from the
authors for providing assistance in
performing the calculations.
Overhead costs (including
equipment, taxes, and
utilities) are a significant part
of total greenhouse crop-production
costs. The overhead cost per square foot
per week of bench space has been esti-
mated to be $0.20 (Brumfield, 1995).
Since overhead costs remain constant in
a given location regardless of the crop or
the number of containers produced, the
efficiency with which growing space is
used in order to minimize overhead
costs per plant is important.
Efficient use of greenhouse space
requires knowing how many plants will
fit on a bench or floor so that each plant
has sufficient space to grow. Containers
are spaced by commercial growers on
square or staggered spacing. Square spac-
ing is frequently employed since this
method is considerably easier for work-
ers to perform accurately. Also, growers
usually assume square spacing when
planning for the number of containers
that will fit in a greenhouse, since the
calculation is relatively simple.
We are unaware of an available
process through which growers can de-
termine how to place containers on a
bench or floor in such a way that the
space is used most efficiently. The ob-
jective of this project was to develop a
decision-support tool to calculate the
maximum number of containers that
can be placed in a specified area. The
equations could be entered in a spread-
sheet to allow growers to determine the
most efficient spacing pattern for their
individual situations or a spreadsheet,
named Bench Space Calculator, is avail-
able from the authors.
Materials and methods
There are three commonly used
patterns of container placement (Fig.
1). Square placement involves placing
containers in parallel rows perpendicu-
lar to each other in both directions on
the growing surface so that any four
containers form a square. The other two
patterns involve placing containers in
staggered arrangements in which any
three containers form an equilateral tri-
angle. In the long-staggered pattern,
the rows of containers are parallel to the
long dimension of the bench or floor
space. In the short-staggered pattern,
the rows of containers are parallel to the
short dimension of the bench or floor
space.
We developed a series of equations
to calculate the number of containers
fitting in a given area in each of the three
The cost of publishing this paper was defrayed in part
by payment of page charges. Under postal regulations,
this paper therefore must be hereby marked advertise-
ment solely to indicate this fact.
1Department of Ornamental Horticulture and Land-
scape Design, The University of Tennessee, Knoxville,
TN 37901.
2CDM Federal, Oak Ridge, TN 37830.
433 July–September 1999 9(3)
arrangements. Equation inputs are the
length (feet; 1.0 ft = 0.3048 m) and
width (feet) of usable area and the con-
tainer spacing (inches; 1.0 inch = 2.54
cm), i.e., the distance from the center of
one container to the center of the next
container.
SHORT-STAGGERED PATTERN.
Equa-
tions 1 to 6 are used to calculate the total
number of rows of containers [Eq. 1]
(Fig. 1B), the number of odd-num-
bered [Eq. 2] and even-numbered rows
[Eq. 3], the number of containers fit-
ting in odd-numbered rows [Eq. 4] and
in even-numbered rows [Eq. 5], and
the total number of containers fitting in
the specified area [Eq. 6] using the
short-staggered arrangement pattern.
Number of rows = [long dimension –
(0.01083 × container spacing)]/
(0.0725 × container spacing) [1]
In Eq. [1], the solution is rounded
down to the nearest whole number.
Number of odd-numbered rows = num-
ber of rows/2 [2]
Use the rounded solution for num-
ber of rows in Eq. 1. The solution for
Eq. 2 is rounded up to the nearest whole
number.
Number of even-numbered rows = num-
ber of rows/2 [3]
Use the rounded solution for num-
ber of rows in Eq. 1. The solution for
Eq. 3 is rounded down to the nearest
whole number.
Number of containers in odd-numbered
rows = (short dimension × 12)/con-
tainer spacing [4]
The solution for Eq. 4 is rounded
down to the nearest whole number.
Number of containers in even-num-
bered rows = [short dimension –
0.04167 × container spacing)]/
(0.08333 × container spacing) [5]
The solution for Eq. 5 is rounded
down to the nearest whole number.
Total number of containers = (number
of odd-numbered rows) × (number of
containers in odd-numbered rows +
number of even-numbered rows × num-
ber of containers in even-numbered
rows) [6]
Use rounded answers to Eqs. 2 to
5 when calculating a solution for Eq. 6.
LONG-STAGGERED PATTERN.
Equa-
tions 7 to 12 are used to calculate the
total number of rows of containers [Eq.
7] (Fig. 1A), the number of odd-num-
bered [Eq. 8] and even-numbered rows
[Eq. 9], the number of containers fit-
ting in odd-numbered rows [Eq. 10]
and in even-numbered rows [Eq. 11],
and the total number of containers fit-
ting in the specified area [Eq. 12] using
the long-staggered arrangement pat-
tern.
Number of rows = [short dimension –
(0.01083 × container spacing)]/
(0.0725 × container spacing) [7]
In Eq. [7], the solution is rounded
down to the nearest whole number.
Number of odd-numbered rows = num-
ber of rows/2 [8]
Use the rounded solution for num-
ber of rows in Eq. 7. The solution for
Eq. 8 is rounded up to the nearest whole
number.
Number of even-numbered rows = num-
ber of rows/2 [9]
Use the rounded solution for num-
ber of rows in Eq. 7. The solution for
Eq. 9 is rounded down to the nearest
whole number.
Number of containers in odd-numbered
rows = (long dimension × 12)/con-
tainer spacing [10]
The solution for Eq. 10 is rounded
down to the nearest whole number.
Number of containers in even-num-
bered rows = [long dimension – 0.04167
× container spacing)]/(0.08333 × con-
tainer spacing) [11]
The solution for Eq. 11 is rounded
down to the nearest whole number.
Total number of containers = (number
of odd-numbered rows × number of
containers in odd-numbered rows) +
(number of even-numbered rows × num-
ber of containers in even-numbered
rows) [12]
Use rounded answers to Eqs. 8 to
11 when calculating a solution for Eq.
12.
SQUARE PATTERN.
Equations 13 to
15 are used to calculate the number of
rows of containers using the short di-
mension of the area [Eq. 13] (Fig. 1C),
the number of containers fitting in each
row [Eq. 14] and the total number of
containers fitting into the given area
using the square spacing arrangement
[Eq. 15].
Number of rows = short dimension/
container spacing [13]
The solution for Eq. 13 is rounded
down to the nearest whole number.
Number of containers per row = long
dimension/container [14]
The solution for Eq. 14 is rounded
down to the nearest whole number.
Total number of containers = number of
rows × number of containers per row [15]
Use rounded answers to Eqs. 13 to
14 when calculating a solution for Eq.
15. The number of containers placed
at various spacings that fit in different
sized areas were compared to illustrate
the application of the model for maxi-
mizing space use (Table 1). Cost analy-
ses were also conducted to illustrate
the potential economic impact of the
different spacing patterns.
Results and discussion
The most common means of esti-
mating the number of containers fitting
into a specific area entails calculating the
bench or floor area (length × width) and
dividing this value by the container area,
calculated as the square of the container
spacing. For example, using a 6-ft (1.83-
m) × 10-ft (3.05-m) bench [60 ft2 (5.57
m2)] and 14-inch (35.6-cm) spacing on
the crop [1.36 ft2 (0.126 m2) per con-
tainer], the number of containers calcu-
lated to fit in this area is 44 (60/1.36).
This answer is incorrect. Using a square
spacing pattern, only five rows of con-
tainers placed on 14-inch (35.6 cm)
spacing will fit along the short (6 ft)
Fig. 1. Three possible arrangements of containers: long staggered, short
staggered, and square. Rows are numbered sequentially.
July–September 1999 9(3)434
RESEARCH REPORTS
dimension of the bench resulting in a
loss of two inches [70 inches (177.8 cm)
used while 72 inches (182.9 cm) are
available]. Only eight rows will fit along
the long (10 ft) dimension resulting in
wasting 8 inches [112 inches (2.85 m)
used while 120 inches (3.05 m) are
available]. Thus, only 40 plants can
actually fit on this bench using the square
pattern. The error results from assum-
ing that the plants will occupy every
square inch of space available. There-
fore, the most common means for grow-
ers to estimate container numbers fit-
ting in a given area is inaccurate.
A staggered arrangement fre-
quently allows a significant increase in
the number of containers fitting in a
given area, as compared to square place-
ment (Table 1). For example, the num-
ber of 6-inch (15.2 cm) containers fit-
ting pot-to-pot in a 6 × 20-ft (1.83 ×
6.10-m) area is 7.1% and 7.9% greater
when arranged in long-staggered and
short-staggered patterns compared to
the square pattern. In fact, the only
examples in which the square spacing
was more efficient than the staggered
spacing were when the containers were
placed on relatively small bench or floor
areas at 12-inch (30.5-cm) spacing.
The advantage of a staggered com-
pared to square arrangement frequently
increases with increasing area (Table 1).
For example, when comparing contain-
ers placed at 6-inch (15.2-cm) spacing,
the percent increase in container num-
ber of the short-staggered pattern ver-
sus the square pattern ranges from 3.1%
on the 4 × 10-ft (1.22 × 3.05 m) bench
to 13.1% on the 20 × 100-ft (6.10 × 30.5
m) area. In general, the dimensions used in
Table 1 that reflect typical greenhouse
floor sizes often display greater percentage
increases in container number using stag-
gered versus square spacing compared to
the dimensions typical of benches. Appli-
cation of these calculations to overwin-
tering of containerized perennials and
woody plants calculated 15% to 20%
increases in containers accommodated
in typical cold frame polyhouses using
staggered patterns compared to square
patterns (Will and Faust, 1996).
Relatively small differences in total
container number were observed be-
tween long- and short-staggered pat-
terns. Typically, the difference in con-
tainer number between short-staggered
and long-staggered arrangements was
Table 1. Number of containers fitting on benches or floors of various dimensions in square (S), short-staggered (SS),
and long-staggered (LS) arrangements (Eqs. [6], [12], and [15]). Numbers in parentheses indicate the percentage change
in the number of containers compared to square placement. The cost analyses use overhead costs of $0.20/ft2 per week
and a 10-week crop.z
Total
Bench containers/ Savings
Container or bench ($ loss)/
diam floor (% change Cost/ bench
or dimensions compared to container compared to
spacing (ft) S arrangement) ($) S arrangement)
(inch) Width Length S SS LS S SS LS SS LS
4 4 10 360 391 (8.6) 384 (6.7) 0.22 0.20 0.21 6.89 5.33
4 6 10 540 595 (10.2) 590 (9.3) 0.22 0.20 0.20 12.22 11.11
4 6 20 1080 1190 (10.2) 1190 (10.2) 0.22 0.20 0.20 24.44 24.44
4 6 50 2700 3010 (11.5) 2990 (10.7) 0.22 0.20 0.20 68.89 64.44
4 10 100 9000 10148 (12.8) 10183 (13.1) 0.22 0.20 0.20 255.11 262.89
4 15 100 13500 15308 (13.4) 15275 (13.2) 0.22 0.20 0.20 401.78 394.44
4 20 100 18000 20468 (13.7) 20366 (13.1) 0.22 0.20 0.20 548.44 525.78
6 4 10 160 165 (3.1) 176 (10.0) 0.50 0.48 0.45 2.50 8.00
6 6 10 240 253 (5.4) 254 (5.8) 0.50 0.47 0.47 6.50 7.00
6 6 20 480 518 (7.9) 514 (7.1) 0.50 0.46 0.47 19.00 17.00
6 6 50 1200 1311 (9.3) 1294 (7.8) 0.50 0.46 0.46 55.50 47.00
6 10 100 4000 4466 (11.7) 4389 (9.7) 0.50 0.45 0.46 233.00 194.50
6 15 100 6000 6756 (12.6) 6783 (13.1) 0.50 0.44 0.44 378.00 391.50
6 20 100 8000 9046 (13.1) 8978 (12.2) 0.50 0.44 0.45 523.00 489.00
10 4 10 48 52 (8.3) 58 (20.8) 1.67 1.54 1.38 6.67 16.67
10 6 10 84 85 (1.2) 92 (9.5) 1.43 1.41 1.30 1.43 11.43
10 6 20 168 176 (4.8) 188 (11.9) 1.43 1.36 1.28 11.43 28.57
10 6 50 420 442 (5.2) 476 (13.3) 1.43 1.36 1.26 31.43 80.00
10 10 100 1440 1576 (9.4) 1554 (7.9) 1.39 1.27 1.29 188.89 158.33
10 15 100 2160 2398 (11.0) 2390 (10.7) 1.39 1.25 1.26 330.56 319.44
10 20 100 2880 3220 (11.8) 3227 (12.1) 1.39 1.24 1.24 472.22 481.94
12 4 10 40 39 (–2.5) 38 (–5.0) 2.00 2.05 2.11 (2.00) (4.00)
12 6 10 60 61 (1.7) 57 (–5.0) 2.00 1.97 2.11 2.00 (6.00)
12 6 20 120 121 (0.8) 117 (–2.5) 2.00 1.98 2.05 2.00 (6.00)
12 6 50 300 314 (4.7) 297 (–1.0) 2.00 1.91 2.02 28.00 (6.00)
12 10 100 1000 1083 (8.3) 1095 (9.5) 2.00 1.85 1.83 166.00 190.00
12 15 100 1500 1653 (10.2) 1692 (12.8) 2.00 1.81 1.77 306.00 384.00
12 20 100 2000 2223 (11.2) 2189 (9.5) 2.00 1.80 1.83 446.00 378.00
zThe numbers in this table indicate the final rounded solutions; however, rounding errors can occur if the rounded solutions are inappropriately used for further calculations.
See text for discussion concerning rounding errors.
435 July–September 1999 9(3)
<3%. The most efficient staggered pat-
tern varies with the bench dimensions,
i.e., no consistent pattern was observed.
While performing the calculations,
keep in mind that calculations may not
always reflect reality. For example, if one
extra row of containers can not fit onto
a bench because it is just 1 mm (0.0394
inch) too wide, then dozens of contain-
ers can be lost. While in reality, one
could easily bend a plastic container 1
mm to force an extra row onto a bench.
Therefore, accurate measurements of
container diameters or spacings is im-
portant, since small changes in con-
tainer diameter can have a relatively
large impact on the number of contain-
ers fitting on a specific bench. Similarly,
accuracy can be lost when an insufficient
number of significant figures are used
when converting the length measure-
ment to or from metric units. For ex-
ample, a 10-cm container is often con-
sidered to be a 4-inch container; how-
ever, the unit conversion results in a
calculated 3.937-inch container. Using
4.000 versus 3.937 results in slightly
different solutions. Consequently, four
significant figures are recommended,
although three are acceptable in most
circumstances.
Increase in the number of contain-
ers fitting on a bench in a staggered
arrangement as compared to square
placement results in a 13% reduction in
growing area per plant. This reduction
in area per plant is independent of con-
tainer size. It is based on the ratio of the
polygonal growing space in staggered
placement to the square growing space
in square placement. The area of the
square growing space of a plant placed
pot-to-pot in square placement is equal
to the diameter of the container squared
(A = d2). The area of the hexagonal
growing space of a plant placed pot-to-
pot in staggered placement is equal to
0.87 times the diameter of the container
squared (A = 0.87 d2). Because the
additional space in the square pattern is
in the corners of the growing area of
each plant, losing this space is not im-
portant to the development of a well-
shaped plant. Light interception by
plants in the staggered patterns is more
efficient than in the square pattern where
leaf overlapping would begin before the
corners of the square were filled in.
Cost analyses were performed to
demonstrate the potential savings from
different spacing situations (Table 1).
These analyses examine the effect of the
spacing pattern on three different bench
or floor dimensions where the overhead
square foot cost per week is $0.20 and a
10-week crop is grown at 12-inch (30.5-
cm) spacing. The cost per container at
the 4-inch (10.2-cm) spacing was mostly
affected by the container spacing, not
the bench or floor dimensions. For ex-
ample, cost per container at the 4-inch
(10.2-cm) spacing was typically less than
or equal to $0.02 difference between
spacing patterns regardless on bench
dimensions. While, the cost per con-
tainer for the 12-inch (30.5-cm) spac-
ing was greatly affected by spacing pat-
terns and bench dimensions, ranging
from a $0.02 to $0.23 difference be-
tween the different combinations.
The savings or loss per bench as a
result of the spacing pattern is also dem-
onstrated in Table 1. Savings per bench
was as high as $548 when comparing
short-staggered to square spacing in the
20 × 100 ft (6.10 × 30.5 m) growing
area. These savings estimates indicate
that spacing pattern can have a signifi-
cant economic impact.
Equations 1 to 15 can be entered
into a spreadsheet to allow for compari-
sons between different greenhouse
bench and crop situations. A Microsoft
Excel spreadsheet has been developed
and is available from the authors (Fig.
2). The user must provide three mea-
surements including container spacing
(inches) and the short and long dimen-
sions of the bench or floor area (feet and
inches). The spreadsheet will calculate
the total container number and percent
change comparing the staggered pat-
terns to the square pattern. Cost and
savings analysis can be calculated by
inputting the estimated overhead ex-
penses per square foot per week and the
crop time, i.e., the number of weeks on
the bench. The spreadsheet then calcu-
lates the cost per container and the
savings or loss per bench comparing the
staggered patterns to the square pat-
tern. Space is provided in the spread-
sheet cells for four significant figures to
be entered. Significant rounding errors
can occur if fewer figures are used. This
is especially the case when converting
units from metric measurements.
Literature cited
Brumfield, R.G. 1995. Production costs, p.
197–211. In: W. Banner and M. Klopmeyer
(eds.). New Guinea impatiens: A Ball guide.
Ball Publ., Batavia, Ill.
Will, E. and J.E. Faust. 1996. Maximizing
efficiency of greenhouse space use. Proc. S.
Nursery Assn. Res. Conf. 41:123–127.
Fig. 2. A view of the Bench Crop Calculator spreadsheet developed to assist
users with container-spacing and cost-analysis calculations (1 inch = 2.54 cm, 1
ft = 0.3048 m). This Microsoft Excel spreadsheet is available from the authors.
... Greenhouse production space is a resource growers must optimise (Will et al. 1999;Whipker & McCall 2000). Hence, crops which are quick to reach flowering and have low variation in their time to flower result in greater efficiency. ...
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