Research on a Furniture Layout Assessment Methodfrom the Perspective of Preserving Personal Space
Hiroyuki Otake
Tokyo University of Science

Maiko Hatano
Tokyo University of ScienceChihiro Suzuki
Tokyo University of ScienceKazuhiro Kubota
Tokyo University of Science

Hideo Naoi
Tokyo University of ScienceAbstract
The aim of this research is to propose an assessment method on furniture layout from the perspective ofpreserving personal space. To this aim, we made an experiment first to gain the measurement of change
in personal space when some partition is installed within it. Then, using this data, we proposed severalindicators to assess furniture layout, and through assessment and analysis of furniture layout examples, weverified that the proposed method is available enough.

Keywords: personal space, partition installed within personal space, furniture layout

1. THE PURPOSE OF THIS RESEARCH
Personal space (P.S.) is the area surrounding an individual which they do not want others to invade.Wallsand furniture construct architectural space that determines to a certain extent individual stands and his or her
surrounding environment. And the issues concerning the preservation and invasion of P.S. have a significant
impact on the psychology of multiple individuals sharing the same space.
This research first aims to gain the basic data through experiments how P.S. is affected when the height ofpartitions such as various partition walls or back of chairs, installed within P.S. is changed. Using this data,
the research proposes several indicators to assess furniture layout, and through assessment and analysis offurniture layout examples, intends to propose finally a quantitative method for assessment of appropriate
furniture layouts in various spaces from the perspective of preserving P.S.

2. EXPERIMENT ON THE IMPACT OF PARTITION ON P.S.
2.1. Purpose of Experiment
Although many researchers have measured P.S.(e.g. reference 3.), this experiment re-measures P.S. bystudying and organizing past methods and standards. Additionally, by changing the height of partition

installed within P.S., it quantitatively examines the resulting change in the shape of P.S. in both cases ofstanding and seated position.

2.2. Outline of Experiment(1) Method of Experiment
The experiment was conducted in a space that was large enough so that objects other than the partition
used in the experiment had no effect on the P.S. measurement. As Figure 1 shows, the individual who served
as part of the experimental setup stood still or sat on a chair in the center of the room. The chair was of thesmallest possible size, so that no part of it protruded from the position of the seated individual.
The partitions were 100mm in thickness and 800mm in width. Their height was 800mm, 1100mm,1400mm, and 1700mm in the cases when the experimental-setup individual was standing, and 400mm,700mm, 1000mm, and 1300mm when the individual was sitting on a chair. The partitions, which were madeof foamed polystyrene, were set behind and to the side of the individual. For the seated experiments, thesubjects who invaded the P.S. of the individual used a chair with wheels for practical purposes. Additionally,
a 1mm-thick paper was used in the experiment that measured the effect of the thickness of the partitions.
(2) Subjects
Partition
Partition
Standing Positionin the Back to the Side
Twelve male students of the Department of
1700
Architecture at the Tokyo University of Science
1400
1100
(3) Measured Items
800
The following measurements regarding P.S. weretaken:
01. P.S. for both standing and seated positions
Thickness:
1008002. Partition installed in the back / to the side: fourPartition
Partition
Seated Position
intheBacktothe Sidepatterns each, 16 patterns in total
1300
3. Effect of multiple partitions: eight patterns
1000
4. Effect of the thickness of a partition: four patterns
700400(4) Method of Measuring
0The subjects were asked to walk (in the standing
Thickness:
100800experiment) or to move sitting on a chair (in(Unit:㎜)
the seated experiment) one by one towards theFigure 1. P.S. Measurement Method with Partitionexperimental-device individual and to stop whenreaching a position where they did not want to get any closer to the individual. The subjects were instructedin advance that the build, facial expression, clothing, and other personal characteristics of the experimentaldevice individual should not be considered in determining when to stop moving toward him. With theexperiment using partition, P.S. was measured in four directions: forward, backward, left, and right. But
when symmetry was observed, we omitted one of the measurements (Figure 1).
2.3. Result and Discussion(1) Difference in P.S. in Seated and Standing Positions
As Figure 2 shows, P.S. in the seated position was larger than P.S. in the standing position, especially tothe front. However, when P.S. in the seated position was measured from the tip of the toe, instead of from thecenter of the body, it had approximately the same shape as P.S. in the standing position. In other words, P.S.
in the seated position was affected by the length of the part of the legs that protruded from the body.
(2) Change in P.S. due to Partition
After conducting experiments both in seated and standing positions using four different partition heights, itwas found that the higher the partition was, the smaller the P.S. became in the direction to the partition (Figure2). Furthermore, when the partition was as high as the eye level, the subject did not pay any attention to
the presence of the experimental-device individual and was able to approach the partition to a distance fromwhich he could touch them. This means that both to the back and to the side, a partition of sufficient height
could cancel out P.S.
(3) Comparison of effects by one on two partitionsComparing an overlap of P.S. measured separately to the side and to the back, and P.S. measured withpartitions installed both to the back and to the side, little difference was observed. It is possible to conclude
that a simple overlapping of P.S. shape is possible.
(4) Effect of Thickness of Partition on P.S.
When two partitions that were identical except for their thicknesses were used, the P.S. in the directionof the partition set expanded in all experimental patterns by almost 100mm with the case of a 100mm-thickpartition compared to a 1mm-thick partition. Since there was almost no difference in the shape of P.S. in thedirections in which no partitions were installed, the thickness of the partition can be ignored.
Standing Up Position
Seated Position

400 ㎜

700 ㎜

10000 ㎜1300 ㎜

1300×1300 ㎜

No Partition

400 ㎜

700 ㎜

1000 ㎜1300 ㎜Figure 2. Changes in P.S. Shape by Partition (numerical values are heights of partitions)2.4. Summary
This research demonstrated that a partition installed within P.S. affects the shape of P.S. The higher
the partition was, the smaller the P.S. measurement values became in the direction of the partition. Thisquantitatively confirmed that P.S. external to the partition can be canceled out depending on the partition ofsufficent height.

3. EXAMINATION OF A FURNITURE LAYOUT ASSESSMENT METHODFROM THE PERSPECTIVE OF PRESERVING PERSONAL SPACE
3.1. Purpose of Study
Using examples of furniture layout patterns in various spaces, P.S. of a furniture user was mapped out
and the characteristics of each space were analyzed using assessment indicators set in this examination.
Additionally, based on the result of these examinations, the characteristics of furniture layout patterns
suggested by each indicator and the effectiveness of the indicators were analyzed to propose an aimed
assessment method.

3.2. Setting Assessment Indicators(1) Basic Concept of P.S. Preservation

The overlap of multiple P.S. was considered as
an “invasion” from the perspective of preserving
P.S. Of course an invasion happens with a bodyof an invader entering into the P.S., but also may
happen without such a body. In this experiment, bothpatterns were considered as an overlap of P.S. andused for analysis.
(2) Definition of Assessment Indicators
Table.1 shows the definitions of floor areas usedfor assessment indicators of this study. Figure3
shows one of furniture placement example plans
to explain the floor areas defined in Table1. Table2
shows the definitions of assessment indicators set
based on the floor area measurements as described inTable.1.
(3) Setting of P.S. Size used in the Examination
The P.S. size used in this examination was set byreassessing various P.S. measured in past research
projects, and adjusting them to the aforementioned
experimental result (Figure 4).

Room

RoomKitchenWC

Subject room area

Table 1. Definitions of Floor Areas for Assessment Indicators
Subject room area
Total P.S. area
Subject P.S. area
Canceled P.S. area

The floor area of the room that is subjectof assessment
The total area enclosed within the outermost
borderlines of multiple P.S. borders
The total P.S. area excluding the canceled P.S.
area, that may be invaded
The P.S. area that will not be invaded due tofurniture placement

Overlapping P.S. area Overlapping P.S. area in the subject P.S. area

Table 2. Definition of Assessment Indicators
Cp.s.

Cr.s.

Lp.s.

Lr.s.

Or

Canceled
P.S. area

Canceled
P.S. area

Overlapping
P.S. area

Overlapping
P.S. area

Subject
P.S. area

Total
P.S. area

Subject
room area

Subject
P.S. area

Subject
room area

Subject
room area

1300
130
1300
00
850
0850
8650
Unit： mmFigure 4. P.S. Size used in This Study

Room

KitchenWC

Total P.S. area

Room

Kitchen

KitchenWC

Subject P.S. area

WC

Canceled P.S. area

Kitchen

WC

Overlapping P.S. area

Figure 3. Explanation of Each Floor Area Used in Assessment Indicators

3.3. Assessment and Analysis of Furniture Layout Examples(1) Outline of the Assessment
The aforementioned indicators were used to assess all 192 examples collected from architectural reference
documents.
(2) Analysis by Architectural Purpose
Since architectural purposes affect furniture layout, it is presumed that each purpose will show different
indicator values. Using the categories in architectural reference documents as the base, architectural purposes
were classified into ten categories and the average values and standard deviation for each category weremeasured. As a result, restaurants that vary in space design showed avarage deviation in all values. Theater
halls where seats are laid out unidirectionally, presented high Lp.s. and Lr.s. values with a small deviation.
Different characteristics were present to some degree for each architectural purpose. Naturally, large standard
deviations were observed among all examples (Figure 5).

(3) Analysis Focusing on the Similarities in Assessment Indicator Values
Some examples showed similar indicator values despite their different purpose categories. This factsuggests that even though the purpose or the characteristics of spaces may differ, categorization not based on
purposes, as well as categorization of spaces with similar P.S. preservation traits may be possible.
Using the five assessment indicators as variables, a cluster analysis was conducted. The result suggested
that there are two clusters concerning Cp.s., Cr.s., and Lp.s. One is a group of restaurants, classrooms andoffices, and the other one is a group of trains and theaters. In deeper level of clustering, there are five clusters
somewhat corresponded to the categorized purposes. Therefore, the analysis was able to quantitatively
demonstrate that furniture layout is affected by architectural purposes (Figure 6).

3.4. Examination for Improvement of the Assessment Method based on Assessment Results(1) Examination by Results of Cluster Analysis and Correlation of Each Indicator
A large deviation was observed in the bimodality that represents the size of impact that each indicator had
over the cluster analysis results. Cp.s., Cr.s., and Lp.s. in particular affected clustering. The comparison ofcorrelation coefficient of each indicator reveals that seven groups out of ten had strong correlation of 0.6 orabove (Figure 7). This suggests that each of the five indicators does not effectively assess furniture layout.
(2) Setting Assessment Indicators Focusing on the Level of Invasion
Indicators that considered all cases of overlapping P.S. to be identical were not examined the level ofinvasion sufficiently. As Figure 8 shows, a new assessment indicator Rv (Real Violation) was set to label
overlapping P.S. without an invasion by a human body as Invasion 1 and overlapping P.S. with an invasion
by a human body as Invasion 2 (Table 3).
1.0

0.0

0.1

0.80.2

0.3

0.4

0.5

Semi Partial R Squa r

Cluster 1

0.6
0.4

Cluster 1

Cluster 2

0.2

Cluster 3

0-0.2

Cluster 4
Cp.s. Cr.s. Lp.s. Lr.s. Or Cp.s. Cr.s. Lp.s. Lr.s. Or

all examples

restaurant

Cp.s. Cr.s. Lp.s. Lr.s. Or

Cluster 2

Cluster 5theater

Figure 5. Average Values and Standard Deviation of Each
Indicator by Purpose Category

Figure 6. Cluster Tree Diagram (All Examples)

Cr.s.

Lp.s.

Lr.s.

Or

Lp.s.

1

1

1

1

1

0.5

0.5

0.5

0.5

0.5

R =0.97

000.5

Lr.s.

R =0.42

01

Cp.s.

00.5

Or

Cp.s.

R =0.70

01

00.5

Lr.s.

R =0.69

001

Cp.s.

0.5

Or1
Cp.s.

11

1

1

0.5

0.5

0.5

0.5

0.5

R =0.7200.5

1Cr.s.

R =0.73000.5

1Cr.s.

R =0.80

000.5

1

Lp.s.

R =0.55

000.5

1

Lp.s.

Figure 7. Correlations of Each Indicator Value in 192 Assessed Examples

00.5

00.5

Or10

R =0.4101Cr. sR =0.9201

Lr. s

(3) Improvement Based on the Examination Results
In addition to Cr.s. and Lp.s., which wereproven to be effective based on the correlation ofeach indicator and the bimodality of the cluster
analysis, the Rv that takes the level of invasion into
consideration served as a new assessment indicator.

No invasion

invades P.S.

invades
human bodyInvasion 1

Invasion 2

Figure 8. Categories of P.S. Invasion Degree

3.5. Examination of the Effectiveness of Im-

Table 3. Definition of New Assessment Indicators

proved Assessment Indicators

Definition of Invasion 2 area

Invasion 2 area
Overlapping P.S. areawarehouse

1.0
reception
seatkitchen

0.8
pond

0.6

Minimum Rv Example
0.4
shelfkitchen

0.2

0Cr.s .

Lp.s.

Rv

Maximum Rv Example

Figure 9. Examples of Furniture Layouts with a Large Variance in Rv
1.25

1.20
Semi Partial Squared(1) Method of Examination
Cr.s., Lp.s., and Rv were the three indicators used
to reassess furniture layout in subject areas. Subject
areas were 33 restaurants with various furniturelayouts that served the same purpose.
(2) Correlation between Furniture Layout andAssessment Indicators
The characteristics of furniture layout as indicatedby the new assessment indicator Rv were analyzed.
Comparing the furniture layout with the highest Rv
and the furniture layout with the lowest Rv (Figure9) reveals that the former example was a small space
only with a bar counter and chairs in close proximity,
and the latter example was a regular restaurant withchairs around a table with space in between. In otherexamples, many layouts showed similar characteristics.
(3) Examination Using Cluster Analysis
Figure.10 and 11 shows the results of cluster
analysis of 33 examples using three indicators.
Cluster 1 included many spacious restaurants withenough distance between chairs and walls. Cluster
2 included bars and private dining rooms in whichP.S. is affected by the walls. Cluster 3 included
establishments with mixed layouts, which caused avariation in the assessment values among different
cases.
(4) Examination of Assessment Indicators based on
Correlation Coefficient
The correlation coefficient derived by combining
the assessment indicators was extremely low inall combinations (Figure 12). This is because
each assessment indicator represents differentcharacteristics of furniture layouts. From this it canbe concluded that the indicators are effective.

Rv

The overlapping P.S. area in the eventthat a human body invades P.S.

cluster1

1.15

cluster2

cluster3

1.10

1.05

1.00

Figure 10. Cluster Tree Diagram (Restaurant)
1.0
0.8
0.6
0.4
0.2
0-0.2

Lp.s. Rv
cluster1

Cr.s.

Lp.s. Rv
cluster2

Lp.s. Rv
cluster3

Cr.s.

Cr.s.

Figure 11. Confidence Intervals of Assessment Indicator
Values for Each Cluster
Lp.s.

Rv

Rv

111

0.5

0.5

0.5

R =0.006

000.5

1Cr.s.

R =0.10000.5

1Cr.s.

R =0.07

000.5

1

Lp. s

Figure 12. Correlation of the Three Assessment Indicator Values

(5) Characteristics Represented by Assessment Indicators
Because Cr.s. tends to be high when a chair is placed close to a wall and low when there is some distance
between them, the seat placement, not the seating style, is the influential factor. Lp.s. tends tobe high when seats are in line with equal distance from each other. Rv is high when seats are very close
together as in a bar or a private dining room, and it can be deduced that the seating style rather than the seatplacement is the influential factor. Therefore, Cr.s. and Lp.s. can be used to classify examples with similararchitectural purposes to some extent. Rv. represents the characteristics of specific furniture layout.

4. SUMMARY
This research proposed a method to quantitatively assess furniture layout from the perspective of P.S.
preservation and verified its practicality. Since acronyms may cause confusion, the following terms are
preferable to be used when applying this method in the future: “P.S. Preservation Rate” for Cr.s., “P.S.
Overlapping Rate” for Lp.s., and “P.S. Invasion Rate” for Rv.

REFERENCES
1. Hall, Edward ; The Hidden Dimension, Doubleday ＆ Company Inc., 1966
2. Sommer, Robert ; Personal Space, Printice-Hall Inc., 1969
3. Takahashi, Takashi et al ; Seating Patterns of Human Gathering, Summaries of technical papers of Annual
Meeting Architectural Institute of Japan 1980-1987