Planning for Foot Traffic Flow in Buildings

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P 8 2 9 4 9 93

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TT75-52054

Planning for Foot Traffic Flow in Buildings [ProektirovanieZhdaniis UchetomOrganizatsii DvizheniyaLyudskikhPotokov]

V.M. Predtechenskii and A.I. Milinskii

StroiizdatPublishers Moscow,1969

TranslatedFromRussian

Publishedfor the NationalBureauof Standards, United States Department of Commerce,and the NationalScienceFoundation,Washington.O.C. by AmerindPublishingCo. Pvt. Ltd., New Delhi 1978

© 1978 Amerind Publishing Co. Pvt. Ltd ., New Delhi

Translated and published for the National Bureau of Standards, United States Department of Commerce, pursuant to an agreement with the National Science Foundation, Washington, D.C., by Amerind Publishing Co. Pvt. Ltd., 66 Janpath, New Delhi 110001

Translator: Dr. M.M. Sivaramakrishnan General Editor: Dr. V.S. Kothekar

Available from the U.S. Departme_ntof Commerce, National Technical Information Service, Springfield, Virginia 22161

Printed at Oxonian Press Pvt. Ltd., Faridabad, India

PREFACE

Construction of public buildings including theat er c:.cultural centers, cinema halls, clubs, concert halls, sports arenas, schools, stores, offices, and transport terminals is proceeding on a large scale in the Soviet Union. All of these buildings are periodically occupied by large numbers of people, often tens of thousands at a time. This fact poses a complex problem for architects, designers and builders and places on them the responsib.ility for providing conditions that will be conducive to efficient productivity and pleasurable environment. In meeting these objectives it is also important to take technical and economic requirements into account. The systematic coordination of the fundamental requirements for flows of foot traffic inside a building is a complex problem. Its solution is dictated by economic and functional considerations, for the size and layout of individual rooms and for the building as a whole. Consequently it also affects costs. Current standards suffer from a number of drawbacks because when they were formulated there were no appropriate scientific principles in this field. As a result , plans for public buildings and the design of buildings often incorporate serious inadequacies. During the last 30 years, experimental and theoretical studies on the movement of people in public buildings have been conducted in the Soviet Union. These studies have been carried out by the Institute of Architecture, All-Russian Academy of the Arts; the All-Union Scientific Research Institute of the Fire Protection Service (VNIIPO); the V.V. Kuybishev Engineering-Construction Institute, Moscow; and the Higher School of the USSR Ministry ofinternal Affairs. This research revealed certain patterns governing the flow of people and led to an understanding of the basic principles involved. The results gave a,rchitects and builders entirely new requirements for the standardization calculation and selection of optimum architectural designs for public buildings with considerable foot traffic. It should be noted that foreign literature mentions no significant research on this subject. This book presents the methodology and results of experimental and theoretical study of the movement of people, the fundamentals of the theory and the calculation of the process, as well as practical recommendations for incorporating the findings in the planning and design of public buildings. Because of space limitations this book covers only the basic concepts. Neverthe-

iv Preface less, the material opens the way for improvement of building designs and for further study of the subject. In writing this book the authors set the following goals: first, to acquaint the technical community with the problem and its present state of develop ment; second, to present the material in such a way that it could serve simultaneously as a text for advanced engineering students and as a practical handbook to aid in the design of large public buildings and connecting passageways for large flows of foot traffic. The second aim influenced the style of presentation of the material, which includes many detailed examples so that complex calculations can be attempted. For this reason some of the calculations will appear ponderous. But when the method of calculating foot traffic flows and determining the dimensions of correcting passageways is mastered, the calculations will become elementary technical problems. The authors gratefully acknowledge the valuable comments and suggestions of the reviewers, Dr. of Architecture Prof. N.I. Sobolov and Kandidat of Architecture ~.E. Poz.barskii, as well as the scientific editor of this book, Kandidat of Technical Sciences V.S. Pchelintsev. The authors also express their gratitude to Kandid. Tech. Sci. V .A. Kalintsev, to Engineers T.A. Tarasova and R.M. Duvidzon, and to Sr. Lab. Asstt. A.S. Zhil'tseva, who participated in the studies and helped to prepare the manuscript. The authors are also grateful to Kand id. Tech. Sci. M.Ya. Roytman for discussions on particular aspects of the problem. The authors will be pleased to receive any comments and advice with respect to the material presented.

CONTENTS

PREFACE............................................................... INTRODUCTION ................

. .......

. .... ... ......

iii

................

.

1. Functional basis of design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Movement of people in buildings and structu res. ............

1 7

Part I. TheoreticalPrinciples and Calculationsof Foot TrafficFlows CHAPTBR I. STUDY OF ANO METHODS OF CALCULATIONS OF FOOT TRAFFIC FLOWS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3. General information on foot traffic.......................... 4. The basic facts, terminology and units..................... . 5. Research at the In stitute of Architecture of the Russian Academy of Arts (VAKh)................................ 6. Research by the All-Union Scientific Research Institute of the Fire Protection Service (VNIIPO). . . . . . . . . . . . . . . . . . . . . . . . . . 7. Studies by the V.V. Kuybishev Engineering Construction Institute, Moscow (MIS!)........... . ................... . .... CHAPTER JI. TYPES OF FOOT TRAFFIC FLOWS AND THEIR CHARACTERISTICS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8. Classification according to type of movement.. . . . . . . . . . . . . . 9. Characteristics of movement under norma l and emergency conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 0. The structure of traffic flows and types of streamlined movement in buildings.................................... .... CHAPTER ill. PARAMETERS OF MOTION OF FOOT TRAFFIC FLOWS..

1I. Size of people and design characteristics of flow paths. . . . . . . . 12. Methodology of actual observation for evaluation of density and speed of movement of foot traffic flows. . . . . . . . . . . . . . . . . . 13. Density of foot traffic flows...... . ....... . .............. . ..

13

13 14 16 17 19

21

21 23 24 26

26 28 30

vi Contents 14. Speed of movement of foot traffic flows and coefficients of the conditions of movement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. Traffic capacity of path and intensity of movement of foot traffic flows...... .. ............ .. ............... ..... .... ... .. 16. Estimation of parameters of movement . . . . . . . . . . . . . . . . . . . . . CHAPTER IV. BASIC CALC ULATIONS FOR CASES OF FOOT TRAFFIC FLOWS....... . ........ . .. . ................ . ....... .. .. . . . ...........

17. 18. 19. 20.

Graphical description of foot traffic flows. . . . . . . . . . . . . . . . . . Foot traffic flow past boundaries of adjoining sections of path.. Merger and branching off of streams . ... .. ....... . ... .. . . . . Variation in parameters of movement during reformation and diffusion of traffic flows. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER V. FORMATION OF HIGH-DENSITY CROWDING.....

.. .....

21. General theoretical assumptions and the movement across boundaries of adjacent sectors in crowding....... . .... . . . . . . 22. Conditions for unimpeded movement .. ........ .. ...... . ... 23. Merger of streams during crowding........... . . . . . . . . . .. . . .

33 42 43

47

47 49 55 61 67

67 74 77

CHAPTER VI. MERGING OF STREAMS OF PEOPLE IN RESTRI CTED PASSAGEWAYS............

. . . ........

. . . .......

. .. . ...........

. .. . . .

83

24. General principles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25. Merging of streams in the corridors of auditoriums without the formation of maximum density. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26. Determination of the time for foot traffic flows in passageways of auditoriums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27. Merging of streams of people in the passageways of auditoriums with development of maximum density. . . . . . . . . . . . . . . . . . . . . 28. Approximate formulas for time of flow in the passages of auditoriums . ...... . ............... . ... . ..... .. ......... .

83

105

CHAPTER VII. SPECIAL CASES IN THE MOVEMENT OF STREAMS OF PEOPLE...... . ... . ... . ......... . . . ...... ... . . ......... . . . . ........ . ..

112

29. Flow along a path of variable width........ .. ........ .. .... 30. Foot traffic flows on an e~alator. . . . . . . . . . . . . . . . . . . . . . . . . . 31. Other cases of movement furough openings with high density of foot traffic flow..... . ..... .. ........... .-. . . . . . . . . . . . . . . . .

85 92 97

112 116 121

Contents

vii

Part II. Basic Design Taking into Account the Motion of Streams of People CHAPTER vm. LIMIT STATES OF PASSAGEWAYS AND THE METHOD OF CALCULATING THE MOTION OF FOOT TRAFFIC FLOWS... . ....

32. Design limit states.. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Prerequisites for the determination oft, and D 1••••••••• . •• • • 34. Procedure for the calculation of foot traffic flows and determination of the dimensions of communication buildings. . . . . . . . 35. Example of calculation of foot traffic flows and dimensions of communication passage... . ....... ... .. .... .. . ........... 36. Features of the computational procedure for the second limit state... ... ... . ..... . .... . ....... .. .... . .. .... ........... CHAPTER IX. COMMUNICATING PASSAGEWAYS.. . .. . . .........

129

129 131 133 135 160

. ... . . .

165

37. Corridors and passages .. ......................... . . .. .. . . 38. Staircases and ramps (glideways).................... .. .... 39. Other forms of communicating passages....................

165 168 171

CHAPTER X. STRUCTURAL ELEMENTS AND SPECIAL FEATURES RELATED TO THE MOVEMENT OF FOOT TRAFFIC FLOWS..........

40. 41. 42. 43.

177

Doors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Floors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emergency staircases.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emergency descents............ . . . . . . . . . .. . . . . . . . . . . . . . . .

CHAPTER XI. DESIGN FEATURES OF PUBLIC BUILDINGS.............

44. 45. 46. 47. 48.

177 180 183 185 189

Commercial buildings..................................... 189 Educationa l buildings..................................... 194 Entertainment centers and structures.. . ........ .. .. .. .. ... . 201 Industria l buildings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Sport complexes .. ...... . ....... . . . . . . . . . . . . . . . . . . . . . . . . . 218

APPENDIX I. DESIGN TABLE FOR PARAMETERS OF FOOT TRAFFIC FLOWS.. . . . ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

225

APPENDIX U. NOMOGRAMS FOR FOOT TRAFFIC PARAMETERS......

234

APPENDIX Ill. FUNDAMENTAL COMPUTATION FORMULAS..........

236

REFERENCES ....................

·........

.. . ......

. . . .. . . ...........

. .. .

239

Introduction

1. FUNCTIONAL BASIS OF DESIGN

A building or any enclosed space as a whole as well as its individual parts and structural components must conform as fully as possible with the social processes of labor, customs and culture for whose realization the building or enclosure has been designed. Thus the basic purpose of any building, premises, structure or group thereof is to satisfy specific functions of the social or private life of people . This holds for places for physical and intellectua l work, study, sport, places for serving food, public toilets, different types of theater, community halls, places of movement, rest and sleep, etc. As a society develops new functions arise, old ones fade away; there occurs differentiation of functions as well as combination of public and private functions. In other words, social functions in the life of people continually change both qualitatively and quantitatively . Realization of each of the above functions is accompanied by the realization of some other or even several other functions playing accessory or subsidiary roles. For instance, teaching is frequently associated with the showing of films, experiments, acquisition of new materials, financial operations, movement, etc. Hence it is necessary to distinguish the principal from the subsidiary functions. It is evident that under different conditions the principal function may become subsidiary and vice versa. In many instances it is very difficult to separate a principal function clearly from a subsidiary one. For some so-called multipurpose premises there may be several principal functions. For example, the sport palace in Moscow is used for different purposes (sport, film shows, social gatherings) and consequently has many principal functions to perform. The auditorium of an institute designed for official functions, students' evenings, meetings, exhibitions, etc . also bas several principal functions. Thus the division of functions into principal and subsidiary is always to some extent arbitrary. Despite this arbitrary nature the identification of principal and subsidiary functions offers a proper approach to the design and construction of buildings and the most rational solution. In places assigned for specific purposes such conditions should be created as will most comple-

2

Foot Traffic Flow in Buildings

tely comply with the working of the social man in the discharge of his assigned duties. The following functional factors determine these conditions: I. Microc/imate of the place. This is characterized by the temperature, humidity and rate of movement of air as also by the content of chemical and mechanical pollutants that are harmful for man. It is necessary that the microclimate indices ensure normal working of the respiratory organs and proper heat and moisture exchange of the organism. Microclimate depends on the total area of the premises, the size and thermal engineering properties of partition walls, on the climate of the locality, location of the particular premises in the building (height from the ground and orientation with respect to natural light), and on the technological and operational qualities ~f internal heating and air circulation systems. Hence the choice of length, width and height of the premises depends on the microclimate as a functional factor. However, the use of central heating and air circulation systems and particularly air conditioning with automatic control reduces to a great extent the importance of the volume of the premises for the provision of conditioned air. 2. Lighting condition. This is characterized by the level of lighting of the work place and uniformity of distribution of light in the premises. It must satisfy the requirement of minimum fatigue to the eyes. Lighting conditions in any premises are created by both natural and artificial sources of light. They depend o~ the size, location and light engineering qualities of lighttransparent partitions, general illumination, the status of the locality, location of the building in relation to the position of the sun, the nature of the surroundings, and on the quality, technical parameters and position of artificial sources of light. The latter, in view of the developments in illumination technology, have been in increasingly in common use. But natural light is most important. The lighting conditions created by natural light govern the choice of all the fundamental geometrical parameters of buildings as well as lighttransparent positions. 3. Acoustic conditions. These are characterized by the loudness level and the_reception quality of the source of sound. It is necessary that loudness and .reception of sound to a great extent correspond to the given functional process (audibility of speeches and music concerts). The acoustic conditions of premises depend on their dimensions and shape and the acoustic qualities of the surface of partitioning structures (capacity to absorb and reflect sound energy falling on them). With the development of electroacoustics the limitation imposed on the selection of size and shape of premises by the acoustic requirements has been greatly reduced. However, from economic and other .con~iderations which restrict the use of electroacoustics, the acoustic conditions remain aniong the factors influencing the choice of parameters of particular premises.

Introduction

3

4. Noise level. This is characterized by the qualitative and quantitative Jevelof sounds emanating in the place or reaching it from outside and disturbing the particular functional process. It is necessary that noise be minimal and in any case not exceed the permissible limits for health and hygiene. Cutting the noise emanating from external sources is done mostly by decreasing the level of noise at the source proper (for example, by replacing noisy motors by silent ones), vibro- and sound insulation, sound absorption by the surfaces of partitioning structures and to a lesser degree by changing the dimensions of the premises: Sound insulation technique is used against external noise, i.e. partitioning structures are given the necessary sound insulating properties. Hence the noise level of premises influences the selection of partitioning structures and can also influence the choice of dimensions. 5. Vision and visibility. This is the most important factor for premises whose functional purpose involves observation of plane or three-dimensional pictures (cinema and theater halls, lecture halls, museums and exhibitions). Visual reception and visibility depend on the nature of the object, its brightness, the position of the observer or the object and other factors determining the normal working conditions of the eyes and the comfort of the observer. Evidently these conditions can be decisive in selecting the dimensions and shape of a structure. 6. Space for persons and equipment for realizing a particular functional process. This is a major factor determining the size and shape of premises. It must be minimum but adequate for efficient organization of the functional process. 7. Space for movement of persons within the premises. (Passage between equipment, etc.). This should also be minimum but adequate for efficient movement and rapid evacuation of people in an emergency. Consideration of all these factors provides an optimal solution for the premises in question and its partitioning__structures in terms of geometric and technological parameters. The enclosed area is the primary, basic functional space-planned component of a building. Depending on its purpose, the main functional process (one or more) and the related subsidiary functional processes are allocated to this area. For example, in the auditorium of an institution the basic functional process is teaching. This entails writing notes, watching experiments, writing on the blackboard, etc. and listening to teachers' lecture. The subsidiary (associated) functional process is movement in the auditorium at the behest of the teacher and during entry into or exit from the auditorium. Once we know the principal and subsidiary functional processes we can identify the functional factors that govern the size of the enclosed place. In relation to auditoriums, at the planning stage it is necessary to make provision for the microclimate, lighting conditions, noise exclusion and acous-

4

Foot Traffic Flow in Buildings

tics, visual reception and visibility, space for accommodating students and equipment and space for movement. For relatively few places it is necessary to consider all these functional factors. For most places the number of factors considered is smaller and for such areas as corridors usually only ·such functional factors as space for movement and lighting conditions are considered. Accordingly, a building of one or another type is planned which conforms to the functional purpose of its main areas. For example, school buildings comprise mostly auditoriums or classrooms, laboratories and study rooms in which the principal function is realized. However, in these areas, besides the principal function of the building, other functions are performed which are subsidiary in nature. For example, in a school such subsidiary functional processes would be office and management, catering, personal hygiene, etc. They are covered by the corresponding premises (administrative, kitchen, buffet, toilet blocks, etc.). Each subsidiary area has its own principal function for the given premises. All the premises of the building conforming to the principal or sbusidiary functional purposes together form sectors in the building which are interconnected as a big group by the so-called communicating space. Here the principal functional process is the movement of people. Such communicating or linking areas are corridors, staircases, lobby, foyer, vestibule, and so on. Figure I is a plan of functional dependences showing the formation of premises and buildings. Systematization of buildings and structures according to their functional features is the basis of their scientific classification. Such a classification allows us to introduce a nomenclature for the most rational type of buildings and structures in large-scale construction. Buildings and structures are normally divided into two basic groups: public and industrial buildings. Public buildings and structures in their turn are divided into residential and community or public buildings. In industrial structures productive and nonproductive structures are distinguished. Each group is divided into subgroups. For example, among residential buildings a distinction is made between apartment blocks, hostels, hotels; community buildings are divided into schools, hospitals, theaters, sport, commercial and trade centers, community kitchens and office blocks; industrial buildings are divided into main production, auxiliary production, power house and stores. · The above subgroups of buildings and structures are further divided into types according to the narrower functional features. For example, educational buildings are divided according to type features into subtypes. Such type features are: for community buildings-capacity (number of seats for the audience. :number of trading places, etc.), form, suitability for construction under various local conditions. The functional validity of buildings and structures is directly linked with

Introduction

5

the question of economy in the widest sense of the word as well as with the economics of construction. The functional factors determining the geometric parameters of sections and the technical characteristics of partitioning structures simultaneously determine the material surroundings in which any functional processes are performed. Evidently these material surroundings greatly influence the occupant's condition. It is known that the temperature of the air in a section where people are engaged in physical work must be lower than in a section meant for intellectual work. If the temperature of the surroundings does not conform to F u -;;;:

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Subsidiary function Premises

FUNCTION

Premises

____ •::~~~:-=--~' l' L. ---_-_

-_ -_ -_ -_. ___

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MAIN

MAIN Passageways

Subsidiary function

Subsidiary function BUILDING

FUNCTION MAIN PREMISES

FUNCTION SUBSIDIARY PREMISES

Fig. I. Plan of functional relationships.

6 Foot Traffic Flow in Buildings working conditions a man may soon feel fatigue, his working efficiency will fall. In many countries with a tropical climate work is suspended during the hottest hours since economic efficiency at this time is extremely low. Work is resumed when the temperature drops to a tolerable level. Lighting and noise levels greatly influence labor productivity. Studies made in communication centers (telephone exchanges, sorting centers of post offices, etc.) have shown that by regulating the above functional factors it is possible to influence labor productivity favorably (by 15% and more). In recent years great attention has been paid to problems of the effect of light on the state of the worker. It has been proved that different illumination ratios in partitioning structures, the color of equipment and the spectrum of electic lighting affect the efficiencyof human labor in different ways. Proper planniug of the work place is of greatest importance. If, for example, proper working conditions are provided for a draftsman: table and stool adjustable for heights, convenient placement of the drawing instruments, proper lighting conditions on the table (no glare)-then his efficiency will definitely increase and there will be no fatigue. On the other hand, if the table and stool do not conform to his height, he has to stretch or bend awkwardly and physical fatigue results. If the drawing instruments are placed at a distance his hand will soon get tired and may start shaking, which evidently will lead to errors in drawing and also to irritation and mental fatigue. Special studies have shown that proper planning of the work place greatly influences working efficiency. If we assume that with proper planning of work the efficiencyof a draftsman increases by 20%, then the work of 50 persons can well be done by 40, i.e. functional comfort in the building can produce direct economic advantage. Besides increasing productivity the functional comforts of premises and buildings are of great importance from the viewpoint oflabor saving by providing necessary sanitary-hygienic conditions. In most cases, during determination of the parameters of premises or buildings based on functional factors minimum permissible values will be obtained. This will eliminate work on superfluous space in buildings and structures which are often permitted in planning if objective methods are not properly employed. Thus the functional validity of l:?!lildingsand structures can produce economic advantage by elimination of excessive one-Jim~- and operational expenditures entailed by any unnecessary volume (excess) of construction. Finally, buildings and structures conforming to conditions of functional validity are economically advantageous even under operational conditions. For example, if the dimensions of light absorbers have been chosen with due regard to the functional process to be performed in the premises, then not only one-time but also operational costs for heating the premises will be considerably lower than with . grandiose. constructions using cutoff partitions,

Introduction

7

which are frequently used without proper justification. Thus the functional validity of buildings and structures has great economic, sanitary-hygienic and technological importance. At the same time, in design and construction practice it must be remembered that the choice of building parameters is also influenced by technical, architectural and aesthetic considerations. Therefore it is in practice impossible to ignore these parameters which are dictated by functional conditions. The effect of these compromises on economic indices can always be evaluated by comparing them with indices obtained from a total consideration of functional requirements . Herein lies one more argument for functional validity as a standard of optimum solution. 2. MOVEMENT OF PEOPLE IN BUILDINGS AND STRUCTURES

The movement of people as a subsidiary function corresponds to each functional process. Hence in premises meant for any purpose it is necessary to allow space for movement-passages on the shop floor between machines for access to the work place, passages between rows of seats in auditoriums. The area occupied by passages often constitutes a considerable part of ihe total area of the premises. On the scale of the building as a whole, independent of its purpose, the movement of people, while retaining its importance as a subsidiary function, becomes the principal function in most communications buildings. In such buildings this accounts for relatively large areas constituting in many cases as much as 30% or more of the working space. Consequently the selection of rational dimensions for passages in communications centers and premises is of great importance since one can achieve economic advantage by proper planning. There is also a large group of buildings and premises that have a functional purpose linked to the movement of people. Here we can include the buildings of depots for different types of transport, their passenger platforms, the above-ground vestibules and underground stations of subways, pedestrian underpasses and exits of pavilions, parks and stadiums, and the passageways of commercial enterprises. Here a rational space-designed solution mainly depends on proper planning of the movement' of people-the principal functional process-and a proper choice of parameters of the premises in which it takes place. Proper planning of the movement of people in buildings and premises is not only economically important but also creates the comfort necessary for this. This refers mainly to prevention of overcrowding offlows of people. We have all been disgusted by jams in theater buildings after the show resulting from bottlenecks at .cloakroom doors and by stampedes in lobbies with inadequate dimensions. It can be confirmed that poorly planned subsidiary

8 Foot Traffic Flow in Buildings functional processes re.duce the efficiency of the principal functional process, in this case relaxation or enjoyment of the show. To avoid delays and stampedes, part of the audience leaves the theater ball a few minutes before the end of the show, causing needless discomfort to the rest of the audience and even to the artistes. One can cite many examples where movement of people is associated with serious discomfort, often verging on actual danger due to excessive crowding. Thus by the term "providing convenience during movement of people" we understand providing optimum for a building with a particular purpose the duration of the process and observing a particular density en route. Restricting the duration of the process of movement within a known limit is essential to ensure the safety of people during emergency situations that may arise. These may crop up in any building during fire or earthquake if the building is situated in a seismic zone or during accidents caused by technical equipment. In such emergency situations passages in the premises and communicating .premises in the buildings become paths for. evacuating people. The time and nature of movements depend on the extent to which the paths of people's movement during an emergency conforms to the conditions of evacuation. If the paths of rno\'ement are comfortable, i.e. are fairly wide and uniform with a nonskid floor surface and simple geometry, people can see the nearest path to the exit; in such a case the movement will be fast ~ithout delays and without untoward happenings. On .the contrary, with improperly planned paths of movements hold-ups in movement_are quite frequent, confusion is common and the nervousness of people increases, some·times to the point of panic, leading, il.-swe know, to _tragic con ·seqitences. To highlight the .seriousness of. this problem we present the following figures reproduced from America11 .data: . During the 33-year period · from 1897 through 1930, of the number of lives lost in fires in theaters 49:8% died not due to fire but due to poor evacuation. Panic is a sudden, unaccountable, irrepressible fear that takes possession of a large crowd. In this state people lose their ability to orient themselves rationally with respect to the ~urrounding~ The following examples illusttate the reasons for_and. consequences of panic: In 1849 in Glasgow, during a theatrical presentation someone threw a .p_ieceof burning paper ..qn the flo.or after lighting his pipe and immediately: e~tinguished it. The ligl}Urom the sm~ll flame alarmed the audience; s9mebody shouted "fire.J J.JFire?'. Inth~ ensuing panic, some 65 persons lost their lives in a stampede. In "I878, in the Coliseum theater, Liverpool, during the show a member of the. audience .ran through the hall to the exit. Immediately everyone else follo.wed him, evi~ dently . out of panic. The result was 37 deaths and many injured. It should be noted that any movement attracts people. Someone seeing the moYement involuntarily .starts t(? copy it. Thus .spectators .accompanying troops _rnecha~ nically: .mar_ch __wit:pthem: . In. 1924.in the .jam-packe.d . hall..oL Leniqgrad'.s

Introduction

9

Molniya movie theater someone shouted during the show. This was enough to induce hundreds of people to make for the exit. Movement, increasing with every second, immediately turned into panic. People surged forward to exits, rushing downstairs, pressing on those in front and causing serious bottlenecks in passages. When someone switched on the lights people saw there was no reason to panic. Congestion at the doors quickly eased. In panic people always exaggerate the danger they are trying to escape. Moreover, in most cases of panic there never was any real danger to life. If people had not lost their ability to grasp the situation in panic many accidents could have been avoided. Unfortunately even the part of the public that did not lose its presence of mind at a critical time was often carried away by the flow of people caught in panic. It follows from the above examples that the tragic consequences of panic in public places are linked with the flow of people from the center of events or supposed danger, with jams and congestion. If movement paths are planned in such a way that jams are not possible and excessively dense crowds are not formed, then apparently it will be possible to avoid any kind of unpleasant situation and its consequences . Thus the proper planning of the movement of people as a functional process is of great importance as a safety measure. Consideration of people's movement as a functional process during the planning of buildings and structures is becoming more and more important. This is explained by the considerable development of the social forms of life, particularly in socialistic countries, and by the tremendous rise in the popu lation of cities and on the global scale as well. The capacity of public buildings and structures of public utility has greatly increased. Open sport arenas can now house more than 100,000 spectators. The capacity of movie theaters has reached 2,000 seats and apparently will increase still further. Closed sport complexes and concert halls .have a capacity of 10,000-12,000 people . If we compare these .figures with the data of 50 years ago we find that the capacity of public utility buildings has risen several-fold. All this compels us to attend to the question of planning the movement of a large body of people and not confine ourselves to approximate consideration of movement in emergency situations. Evidently consideration of the movement of masses of people must become a necessary part of the planning of public buildings.

Part I Theoretical Principles and Calculations of Foot Traffic Flows

'

CHAP TERONE

Study of and Methods of Calculating Foot Traffic Flows 3. GENERAL INFORMATION ON FOOT TRAFFIC

There are two basic phases in the cycle of movement: 'single-support,' when the person makes contact with the surface with one foot; and 'twinsupport,' when the foot which is propelled forward makes contact with the surface while the foot trailing behind has not yet left the surface. With an increase in walking speed the twin-support periods become shorter and shorter and ultimately disappear altogether . From this moment walking changes into running. Consequently running, unlike walking, is a motion in which a person alternately makes contact with the surface with one foot and then is airborne. Walking is the normal mode of motion. Under normal conditions people rarely run. They do so either while engaged in sports; or in emergency or near-emergency situations, provided that the way is clear to allow the change from walking to running. While designing pedestrian routes it must be borne in mind that at the time of walking the pressure on the support, due to the dynamic nature of the process, can exceed the weight of the person by as much as 25 per cent. The speed may vary within wide limits. The maximum speed attained by man is about 600 m/min (in the 100 m sprint event). Walking speed can reach about 220 m/min (achieved in the 20 km walking race). Under norma l conditions the average walking speed is about 60 m/min, although instances have been recorded when the speed attained was as much as 120-140 m/min . The variations in speed depend on many factors wbich are difficult to take into account. The significant factors are age, physical characteristics, type of activity and psychological state at the time. Therefore while evaluating traffic speed it is necessary to depend on mean values, which can be considered reliable if they are established by statistical methods. The traffic speed depends to a considerable extent on the density of traffic. The greater the density, the slower the rate of movement . This law is important since high density traffic movements are of maximum interest. Figure ·2 shows the stream of 13

14 Foot Traffic Flow in Buildings

people near a subway station after the end of a football match in the V.I. Lenin Central Stadium, Moscow. Figure 3 shows the movement of people in the stands of the Bolshoi sport arena approximately half a minute after the end of a football match. High density traffic formed near the exits. Large congregations can also be observed in subway stations during peak hours, in large department stores, in theaters, etc. These photographs (Fig. 2 and 3) indicate a calm foot traffic flow. However, one can imagine the repurcussions if an accident suddenly occurs and traffic dispersion becomes difficult for one reason or another. Data are unavailable on foot traffic flows during emergency situations, for understandable reasons. So for this situation it is necessary either to use the conditions of traffic during near-emergency situations or to extrapolate the data obtained under normal conditions. The highest traffic density observed (under normal conditions) was 7 persons/m2. The density depends on the age, :physical characteristics and attire Fig. 2. Movement of stream of people. of people and hence may vary within wide limits. The density can be even more than 7 persons/m 2 especially under emergency conditions, when there is considerable physical exertion as people attempt to force their way out of the narrow traffic flow. 4. THE BASIC FACTS, TERMINOLOGY AND UNITS

The problem of organizing the movement of a large number of people in public buildings has long attracted the attention of research and development (Rand D) organizations as well as individual specialists. The main objective is to formulate a methodology for the analysis and regulation of the evacuation of people from a building in case of fire-so-called "forced" evacuation. A number of works, well known in this field, serve as. the basis for the analysis and regulation of forced evacuation and for solving specific design

Calculating Foot Traffic Flows

15

problems. Before assessing these works let us define certain general terms and units that characterize foot traffic. When the traffic flow is simultaneous and unidirectional it has a length l and width b.

Fig. 3. Evacuation of people from central sport arena of Lenin Stadium in Moscow.

Entrances to public buildings and specifically assigned space-corridors, staircases,-route the foot traffic flows. The routes are characterized by free length L and width b. They are intersected by doorways and decorative portals, and they narrow down at times due to various projections from the walls. The path length Lo·of the passage or other constrictions is as a rule relatively small and is usually neglected. The width is expressed by ho meters. The pathways are divided into segments identified by their characteristic features (horizontal, inclined, entrance-way) and dimensions L and b. It is important to consider the entrance as an independent segment of the path. Foot traffic is characterized by the number of people N and density D. The latter is defined as the number of people per unit length of the route, or per unit area occupied by the flow. The traffic flow has a specific speed v and is characterized by the traffic capacity Q,-the number of people passing through one section of the flow path in unit time. Let us first consider works of research interest that also have practical significanceas well.

16 Foot Traffic Flow in Buildings 5. RESEARCH AT THE INSTITUTE OF ARCHITECTURE OF THE RUSSIAN ACADEMY OF ARTS (VAKh)

In 1937, the Institute of Architecture of the Russian Academy of Arts became the first organization to place the study of foot traffic flows on a serious scientific basis [2). Nearly 200 series of observations on the flow of traffic were made in public places to study the traffic capacity and speed of foot traffic flows. This work showed that the traffic capacity of an elementary •flow (representing the arbitrarily chosen row of people moving in a file) varies from 25 to 50 persons /min. Here the flow density corresponds to the physical limit of 4-5 persons per meter of path length. On this basis it has been suggested that at maximum density the traffic capacity of the flow is not less than 25 persons/min. Measurements showed that flow speeds along horizontal paths did not fall below 17 m/min. The speed for descending stairs varied from 11 to 16 m/ min. Climbing stairs it was on the average 20 percent slower. It was concluded that the speed was inversely proportional to the density whereas the traffic capacity was directly proportional to it. The results of these counts are shown graphically in Fig. 4. The curves are drawn only through minimum values of the observed parameters since different values of speed and traffic capacity were recorded for the same values of density. The broken lines were obtained by extrapolation. Qn+I the maximum

Formation of High-Density Crowding

69

density at the boundary appears almost instantaneously (as a sudden jump) independent of the magnitudes of Dn and AQ. Consequently, for Qn > Qn+t, i.e. when it so happens during calculation that qn+I >qmax,the density at the next sector should be taken equal to Dmax• Exampl e: To determine the parameters of flow in a doorway (Fig . 38) of width c>o=l.5 m if Dn=0.70; qn= 10.02 m/min, c>n=3m; Qn=30.06 m 2/min. Solution: Determine the intensity .a.,0 of fl.owin the doorway. Qn 30.06 I . qo= c5o= t'T= 20 m mm >qomax

= 10.59 m/min (for doorways).

C Q 11+1 the so-called "expansion flow" occurs. This means that while crowding takes place in front of the boundary with density Dmax,the density in the next sector n + I (Fig. 37) is considerably less than Dmax•Expansion of the flow is to be explained by the fact that for a certain density (for each form of path) two different values of density correspond to the same value of intensity of flow, since while changing from D=O to Dmax, the intensity of fl.owhas an extreme value (Fig. 23). For example, for horizontal paths there are two values of density: Dmax=0.92 and D=0.51 corresponding to q=8.35 m/min (normal conditions of flow). Consequently, if crowding takes place as the flow crosses the boundary of adjacent sectors, then, in the absence of obstacles ahead, movement in sector n + 1 can take place at a lower density than Dmax•

70 Foot Traffic Flow in Buildings The process of expansion is characterized by the fact that the speed of reformation of the flow v' is equal to zero, since q,, =qn+t• Actually v'=q,. + 1- q"= Dn +I - Dn

0 Dn +I - Dn

=0 ·

The phenomenon of expansion is most probable under conditions approaching emergency. In such cases people te nd to accelerate their movement, which for q=constant and two values of D is possible without changing Q, given that people will cross from the denser part of the stream to the sparser part at increased speed. txample: To determine parameters of motion in a sector (Fig. 37) n+ 1 of width n +I = 1.5 m, if D,, =0. 7; q,,= 10.02; qmax= 10. 13 m/ mm 1•5 (for horizontal paths).

Consequently crowding and delay are unavoidable. Theo qn+t = 8.35 m/ min , corresponding to Dmax=0.92 . Parameters D 11+1 =0.51 and Vn+i = 16.38 m/min correspond to this value of q,,+ 1 (Appendix I) and these are the parameters of the flow while moving in sector n+ I. Expansion of flow should be considered for computation only in cases where the next sector (n + 1) has finite length, as shown in Fig. 37. If the next sector is of comparatively small length, for example a doorway, then the effect of expansion is practically negligible. In this case, the front of the stream moving into sector n + I with density Dmax= 0.92 and corresponding to the intensity of motion when there are no obstacles, almost instantaneously reforms and occupies a larger area along the length of the path when the density decreases for a constant intensity of motion. The process of crowding on the boundary between adjacent sectors of path follows certain laws. Crowding takes place as soon as the front of the stream reaches the adjacent sector, since Q,,> Q11+ 1• At this moment the number of people approach ing the boundary between the sectors n and n + 1 ( Q,,c)in unit time is equal to the number of people leaving the boundary along the sector n+ 1 (Q 11+ 1): (35) Simultaneously, in the sector n beyond the boundary a stream composed of two parts seems to be formed: the first part is the crowd of people with density Dmax=0.92 and the second is the approaching stream with density D,,. The latter constantly reinforces the denser mass and as a result the boundary between them moves in the opposite direction at speed C The value of v~C can be found as follows:

v;,.

Formation of High-Density Crowding

71

U sing the expression (35), we write s:

s:

qncC111=qn+ICln+ I Or qnc=qn+I

On+I

Tn ,

where q,.c is the intensity of movement at the point where there is crowding. The development of crowding is similar to the process of variation in flow parameters during movement when v1< v2. Consequently in the expression (30)

Then (36) or, transforming into the usual form:

o,

q,--q2 I

Ve=

D

02 1-

D

I .

2

m mm.

(37)

The speed of movement of the boundary of crowding (v~c or v~) has negative values. As soon as people trailing the stream approach this boundary crowding is halted and the boundary starts moving in the positive direction along the flow, i.e. the density remains constant in sector n, where the .flow speed or the speed of crowd diffusion becomes On+1 qn+I ~ Cln Vc= --=D=---=Vn+J n+ I

-• s: ~+I CII / , =Vi Tm mm. Cln Cl2

~

(38)

Hereq1=q 11+1 and V1=Vn +r correspond to Dmax=0.92. Example: To determine the time of foot traffic flow along a path made up of a corridor of width On= 2 m, doorway Oo= 1 m and On+1= 2 m a corridor (Fig. 39). The stream comprises 100 adults in street dress, i.e. N =f-100= 0.125 x 100= 12.5 m2 • The flow density D,.=0.5. Solution: The stream occupies a length lat the end of the sector, given by N 12.5 I= onDn = 2xo.5=l

2 ·5 m.

Thespeedofmovementoftbe flow in sector n for D,.=0.5 is (Appendix I) the intensity of motion q,.=8.25 m/min.

v,.=16.5 m/min, and Then

Q,.=DnVn On=qn On=8.25 x 2= 16.5 m2/min.

If spread of flow is not taken into account the front reaches the doorway after

72

Foot Traffic Flow in Buildings 1= 3.6 1 (3.65)

n-r 1 = 2.0

0

ci N II

,.._ (")

-,i

ii

..!i

I

Vc = 4.93

--r

-,-

.

1 Crowding I ID = 0 92 I I I I I I

0

ci ..,. II

...,. C:

I 1 .67

I

1

I

I

I

I

I I

I I

I I

r = I1n + 1=

10.62 .

,.._ 2

... II

~

N

st:

3

0 ·57 4 min

N

II

·.: .: 'Fig. 39. Computational graph of formation and dispersion of crowd near opening.

, _ 40-12.5_27.5_167 tn- 165-. Vu •

. mm,

and the rear after 40 . =2.42mm . 16 5 V11 • Let us determine the parameter of motion in the doorwa y:_ 111

t,,=-=

qo=q,t

=8.25 }= 16.5 m/min >qmax= 10.59 m/min.

Consequently a crowd collects in front of the doorway and the density and speed are Do=0.92 and vo= 9.85 m/min; the intensity of movement q0 = 9.06 m/min. Then Qo = Do vo Oo= 0.92 x 9.85 x 1= 9.06 m 2/min. Let us determine the rate of crowding beyond the doorway·, using the expression (37):

Jo

qo--qn - · · _ v·c,.= . 011

_ 9.06x .½-8 .25_ . 3.72_ 885 / . . Do-D11 - 0.92-0.5 - -0.42- - · m mm.

Formation of High-Density Crowding

73

The point a is found in the graph as the boundary of the maximum dispersion of the dense part of the flow. According to the expression (38) the rate of crowd dispersion is determined as:

!:

Vc= Vo = 9.85 x ½=4.93 m/min. Parameter of movement in sector n + I (beyond the doorway):

qn+i=qo/

0

U11 +I

= 9.06x½=4.53 m/ min;

D,.+I =0.13;

Vn+l =35.32 m/min.

The rear of the flow leaves sector n + l after l,.+1 20 0 . tn+1=V,, +1 =35_32= .57 mm,

after negotiating the doorway. The total time of movement along the whole path is (from graph) t = 3.65 min. The time of delay due to crowding can be determined not only graphically, as in the example, but also analytically. It is the difference between the time for the flow to pass through the cross section of adjacent sectors. Since the time for the stream to pass through the section of the path is given by the division of the number of people by the traffic capacity of the path the delay time ('r) is given by 't"=

I 1).

N N ( Qn+I- Qn·=N Qn+I - Q,. mm.

(39)

Returning to the last example, one-obtains

Then the total time of flow along the complete path will be l= ln +-r+

lnH =2.42+0.62+0.57=3.61

min.

(From graph t = 3.65 in1n;the error is in the plotting). Thus the duration of flow movement is made up of the sum of the time of movement along the sectors of the paths and time spent on delay: t=.Et + .E-r.

(40)

The distance (le) through which the crowd spreads can also be determined analytically with the help of the graph (Fig. 40). From the graph we obtain ,;.

74 Foot Traffic Flow in Buildings N/ Or

d

Boundary I between sectors

... ·u

Fig. 40. Determination of boundary of crowding.

, Ve=

ab ab be ; v,,= bd .

Solving both these equations and keeping in mind that ab=le; bd= N Qn - be, we get (41)

(since the absolute value of le is determined it is not necessary to consider the negative sign for the quantity v~). Knowing le, it is easy to determine tbe maximum number of people mak ing up the crowd : (42) Returning again to the example, we determine

le=!!_ ( v~ v,, ) = 12.5 . 8.85 x 16.5 Q11 Vn+v~ 16.5 (16.5+8.85)

4 _37 m,

and the maximum number of people in the crowd

Ne= Dmax8n lc=0.92 X 2 X 4.37 = 8.05 m 2 (::::::65 persons, since/ =0.125 m 2). 22. CONDITIONS FOR UNIMPEDED MOVEMENT

It was established above (see section 18) that for unimpeded crossing of the boundary between adjacent sectors their traffic capacities must be identical:

Formation of High-Density Crowding

75

If this equality is violated, i.e. Qn > Qn+I, then crowding takes place at the boundary of adjacent sectors and consequently the movement is delayed. In this case, if it is necessary to ensure unimpeded movement the width of the next sector of the path '5,.+J should be increased. Using the expression (23) it is possible to write 5:

Vn + 1 =--

q,, qmax= 10.13. U2n 2

qn+I =y-=

Consequently the merger is accompanied by the creation of maximum density and a delay in movement. Then D11+i=0 .92; qn+I =8.35 m/min.

These same parameters are also applicable to the zone of the convergence of streams with one difference, that the quantities q111 and q211 are reduced on account of the convergence of the path of the combined flow '511+1 as compared to Eqmax= 10.13 m/min.

Consequently, in sector 7 crowding starts and the density reaches a maximum. Let us determine the "critical section of the path" (Ocr),i.e. the section where Dmaxis attained. It is possible to use formula (43) for a solution:

qo

Ocr= qmax

3.93 X 5 l O.l3 = I.93 m.

Taking the computational width of the first part of sector 7 equal to Ocr,we obtain q1= 10.13 m/min; D1=0.75; v1= 13.51 m/min; Q1= 19.65 m 2/min• Starting from the critical section, the movement in the second part of sector 7 and in sector 8 (if the decrease in density of flow is not taken into account) will take place with the parameters: q1=8.35 m/min; D1=0.92; v1=9.08 m/min; Q1=q101=8.35x 1.85=15.45 m 2/min; qs=8.35 m/min; Ds=0.92; vs=9 .08 m/min; Qs=qs os=8 .35 x 1.4= 11.7 m 2/min.

At the instant A (Fig. 55) crowding starts. Using expressions (37), we determine the speed of movement of the boundary of crowding in the first part of sector 7: .

08

~s -q1 01 Vc7 = Ds-D1

1.4 . 8.35 rn-10.13 0.92-0.75

. = - 24 m/mm;

The boundary of crowding moves toward the flow, gradually reducing speed as the path widens. Proceeding in an analogous way, we determine

Cases in the Movement of Streams of People

115

8.35 ;:~ -8.54 . 0.92-0.53 = -8.82 m/mm; 8.35 2\~ - 7.13 _ 0.92-0.38 = -5.31 m/mrn; 8.35 ~:~-6.12 . 0.92-0 .25 = -3.65 m/mm; 1

8.35 3.~ - 5.38 . 0.92 - 0.18 = - 2.93 m/mm. At point B crowding ceases because there is a halt in the arrival of people and dispersion starts. The rate of dispersion increases on the decrease in the width of the path and the consequent decrease in the number of people. Using expression (38), we obtain Vc3 =vs

~:=9 .08 3\~=3.48m/min;

!:~ = 3.97 m/min;

Vc 4

= vs !: = 9.08

Vc 5

=vs ~=9.08 3_~=4.62m/min;

Vc6

=vs ~:=9.08 !:~=5.53m/min;

1

7

9 / 8 ~=6.87m

Vc-i=v1::, =9.08 / ~=6 .58 m/min; Vc1 =Vs

Vc 8

~=9.08

/min;

=vs !:=9.08 ~::=9.08 m/min.

According to the graph, the time for emergence of the stream from sector is 0.85 min; during this time, with the traffic capacity of the sector Qs = 11.7 m 2/min, the number of people who go out: t2

N= Qs t2= 11.7 x0.85=9.95 m2 ~IO m2 . As we see, the graphical-analytical computation has been carried out correctly. The time for the front of the stream to begin to leave the sector can be determined graphically or using the formula:

116 Foot Traffic Flow in Buildings

Then the total time t,

where n is the number of computational sectors. !~practice there is no need for such difficult computations . It is sufficient n

to replace the first term in the above expression El/v by a simpler term I

1/vm,in which /=length of the full sector with variable length; vm=mean speed of the stream; Vm

Ven+Vcx

2

• m/ min,

where Ven is the speed on entering the sector; Vex is the speed on leaving the sector. Then the computational formula takes the form

t=l/vm+N/Qex min,

(58)

where Qex is the traffic capacity of the flow on leaving the sector. Let us solve the problem with the help of this relation. At the start of the sector the flow has D=O .l (according to the condition of the problem) . Consequently Ven= 39.27 m/min. At the exit D =0.92 and Vex= 9.08 m/min. Qex=qex X Jex= 8.35 X 1.4 = 11.66. 3.6 10 t (39.27;9.08) + 11.66= I.Ol. The prob lem for a sector of path of variable width is solved in a similar way when the flow enters it at the narrow end and leaves at the wide end. In this case the problem is simplified because a critical density does not arise in such a sector: the density of the stream continuously decreases along the flow, where in the previous case it increased. 30. FOOT TRAFFIC FLOWS ON AN ESCALATOR

Escalators can be considered as sectors of the general path of foot traffic flows. Two basic types of escalators are produced in the country [3]:

Cases in the Movement of Streams of People

117

I) with the width of each step 1 m (two people on each step) and with a speed of movement of the escalator belt 0. 75 m/ sec, or vc=45 m/ min; 2) with a step width of 0.63 m (one person per step) and a speed of 0.5 m/sec, or vc=30 m/min. The theoretical timewise maximum capacity of the escalator ( QT) when all the steps are occupied, ignoring the movement of people relative to the belt, will be (3):

QT= 3,600 -

1

1st

nv passengers/hr,

(59)

where 1/ lst is the number of steps perm of belt; width of the step lst =0.4 m; n is the number of passengers on each step; v is the speed of the escalator belt, m/sec. In the expression (59) a number of factors that affect the capacity of the escalator have been neglected: rate of boarding by people; effect of the speed of the belt on boarding; arrangements that render boarding difficult or easy. Then the rated capacity (Qr) becomes Qr=3,600 -

I

!st

nv q, passenge r s/ hr,

(60)

where q, is the coefficient of occupation of the belt , equal to Qr Qr q,=-= QT 3,600 (1/ tsi) nv

(61)

The mean value of the coefficient of occupation obtained on the basis of experimental data [3] can be taken equal to 0.74. Then the design maximum timewise capac ity of an escalator with a belt width of I m, according to expression (60), will be

I

Qr=3,600 x 0.4 x 2 x 0.75 x 0.74= 10 x 103 passengers/hr.

*

*

*

Hereinafter we will switch to the parameters and symbols adopted in this book and consider escalators with a belt width of I m. In the expression (60) the product (l/ts1) nq, represents the flow density on the escalator De, When/ =0.125 m 2 (adults in winter clothing) I

Do,=-nf tsi

I

q,=o.4 x 2 x 0.125 x 0.74=0.465.

Then the rated maximum traffic capacity is

118 Foot Traffic Flow in Buildings

or 1,250 m2/hr, i.e. 10,000 passengers/hr.

For f =0.113 m2 and f =0.1 m 2 Der are 0.42 and 0.37 and Qer= 18.8 and 16.7 m2/min, i.e. also 10,000 passengers/hr, but at a lower density of people on the escalator on account of lighter dress. The maximum traffic capacity of the escalator, taking Qemax=28.l m 2/ min, i.e. more people approach the escalator than it can accommodate. Consequently a delay in movement is unavoidable and its duration will be

Cases in the Movement of Streams of People

~J=

1:=N ( Q:max-:

125 ( 2

;.J-313)=0.66

121

min;

the density on the escalator for Qemaxwill be Demax=0.625 (two persons per step). 1f the maximum traffic capacity of the escalator is more than 28.1 m2/min, then Qo= Qe=33 m2/min .

Thus the density on the escalator belt is De= Qe/Ve= 33/45 = 0.73

or 2.3 to 2.4 persons per step, which is impossible. To avoid overcrowding of the escalator it is necessary to reduce the number of people approaching it in unit time, i.e. to reduce the traffic capacity of sector n to a value Qemax = 28.1 m2/min. It is poss ible to do this by reducing either the density of the stream or the width of the sector (On), Then for Dn=0.5 we have i'reqd

u,,

= Qcmax= 28.1 = 3 4 q,,

8.25

· m.

The duration of the flow is increased correspondingly. If for Qe= 33 m2/min t=N /Q.= 125/33=3 .8 min, 2

then for Qcmax = 28.1 m /min N 125 . t= Q•max=28 .l =4.45 mm.

The guide barriers used at the entrances of subway stations narrow down sector n and avert overcrowding of the escalator. The presence of excess Qn within the limits of the path bounded by the baniers leads to development of maximum density , causing a delay in movement, and Qn is reduced. However, in certajn public buildings such guide barriers are not used. Therefore under adverse conditions, for example, during forced evacuation, overcrowding of the escalator could occur and lead to accidents. In computing escalators as paths of emergency foot traffic flows they should be considered as stationary stairs, taking into account the possibility of breakdown of the escalator under emergency condition. 31. OTHER CASES OF MOVEMENT THROUGH OPENINGS WITH HCGH DENSITY OF FOOT TRAFFIC FLOW

The other cases include foot traffic flows at turns, along wide and a.long

122 Foot Traffic Flow in Buildings

narrow sectors of paths, along inclined paths with steep gradients and movement through small openings at high density.

Flow at Turns The structure of a foot traffic flow changes at points where the path involves a turn and this can be studied using the diagram in fig. 58. Let the stream of people move at uniform density and speed along a corridor of width & which turns through an angle of 90°. The axis of the flow is shown by the solid line. Observations show that each person on reaching the corner turns along a curve close to the arc of a circle. The farther the person is from the corner 0, the longer is the path along the arc that he negotiates l,/2 6/ 2 to make the turn. Here, in spite of the differences in length of path, the duration of the movement is roughly the same. This is due to people moving around point O at different speeds thanks to Fig. 58. Layout of movement the unequal densities on the inside and outside of at corners. the stream. Obviously, the greater the reduction in density and increase in speed, the broader the arc followed by the person concerned. At the corner the denser part of the stream applies pressure on the thinner part, displacing the latter in the radial direction (arrows in Fig. 58) away from the center 0 . Due to this the stream shifts toward the periphery. The shift continues until a more or less uniform traffic capacity is achieved along the width. Thus a redistribution of flow parameters takes place in the zone of the turn and there is a deformation of the trajectory followed by people. This phenomenon has a negative effect on the conditions of fl.ow, especially in emergency situations. Therefore in designing paths of flow it is good to avoid unnecessary turns. As regards the traffic capacity of the path at the turn, observations show, and it follows from the previous discussion, that it does not alter appreciably. Hence it is possible to neglect turns in computations.

i

Movementin Wide Sectors of Path of LimitedLength If the length of the path appreciably exceeds its width the stream of people usually fills the complete width of the sector. In the opposite case, the stream fills only part of the width of the sector. This covers, for example, movement in auditoriums at the end of a show when the auditorium is surrounded by lobbies or foyers from the other side of which stairs or other

Cases in the Movement of Streams of People

123

structures lead to the exits (Fig. 59). Observations show that in the wide sector of the path the stream disperses, i.e. its density somewhat decreases, until it converges again according to the size of the next sector. The widening takes place as a result of overtaking along the sides of the main stream of people and due to their desire to increase the comfort of movement by reducing the density of flow. The traffic flow along such sectors of path and its parameters should be calculated taking into account the formation of two or three zones: -the first, where the stream expands (Fig. 59); -the second, where the stream, having reached the density correspon ding to free flow, maintains constant width; -the third, where the stream narrows to the size of the exit from the building. If the length of the sector is small the second zone does not appear. Example:Compute the parame ters of flow through a large building if the width of the entrance Oen=1.5 m and the width of the exit Oex= 2.5 m. The total length of the sector / = 8 m. Traffic capacity Fig. 59. Layout of movement in wide and narrow sections of path. Q= 12 m2/min. Solution: Determine the width of the second zone with parameters of free movement: D2 = 0.05; q2= 2.36 m/ min; v2=47. 19 m/min . 02=Q/q2=12/2.36=5. l m. Find the computational width of the first and third zones: .1: _

UI-

Ocn+o2_ 1.5+5 .l _ 3 3 . --- • ID, 2

.I: 02+0ex u3=-2 -

2

5.1 +2.5 2

3.S m.

Determine the length of the first and third zones:

Ii =0 .87 (02-01) =0.87 (5.1- 1.5) = 3.13 m; /3=0 .5 (02-03) =0.5 (5.l -3.8)=0.65 m. The length of the second zone is: li=l-(/1 +h)=8-(3 .13+ 0.65)=4.22 m. The parameters of flow in the first and third zones will be: q1= Q/01 = 12/3.3=3.63 m/min; v1=40.7 m/min; D1 =0 .09;

124 Foot Traffic Flow in Buildings =3.16 m/min; v3=43 m/min; D3=0.075. 8 The duration of the flow along the whole sector will be: 3.13 4.22 0.65 t= I1Ivi+ l2v2+ / l/3V3= 40_7 + 47 _19 + ~; t = 0.182 min . q3= Q/J3=;~

Movement along Inclined Paths with Steep Gradient

Thl laws of movement ascending and descending staircases established earlier (see section 14) cover the gradients widely used in construction, roughly equal to I : 2. As is well known, the steeper the gradient, the lower the speed of movement at the same density of flow. Conversely, the gentler the gradient, the higher the speed of movement, approaching the speed along horizontal paths. Consequently, if the staircase is steep it is necessary to introduce a correction to take into account the reduction in the speed of movement. If the slope is gentle such corrections need not be made because there is a saving of time during movement. Unfortunately there are as yet very little data on the values of speed as a function of density and gradient of path. The speed of movement in the stands of sports stadiums was studied by the research workers of the V. V. Kuibyschev MISI to confirm the standards for their designs. It was established that with increasing gradient up to I : 1.75 under normal conditions of flow the speed falls for the same densities: for descent by 30% and for ascent by 18%, Consequently, for such conditions of movement "coefficients of inclination" I.fl equal to 0. 7 and 0.82, respectively, should be introduced. In these conditions speeds close to the speed of movement along inclined paths in comfortable conditions will be obtained. Until we have the required data for steep staircase we may use values of the parameters of fl.ow (v and q) under normal flow according to the scale of comfortable movement, and under emergency conditions according to the scale for normal flow. For emergency staircase with very steep gradients (I : 1) it is good to take v and q for emergency conditions of movement also according to the scale of comfortable motion. It is worth emphasizing that the recommended allowance for the effect of gradient is not accurate. It approximates the solution to the actual conditions of movement of a stream along an inclined path with a steeper gradient than normal. Movement throughOpenings

Foot traffic flow through an opening, as through any sharply narrowing

Cases in the Movement of Streams of People

125

sector of a path, is a very complex process whose nature has not yet been fully studied. We have seen that movement through an opening is characterized by parameters somewhat differing from the parameters of .flow along other paths (see Appendix I). The special interest in movement through openings results not so much from the difference in parameters as from the possibility of situations developing that can have grave consequences. It has been noticed in a number of studies that as long as the foot traffic flow moving through a small opening is of moderate density and the principle Qn = Qn+t is maintained, all goes smoothly. But as soon as the density of flow in the opening and immediately in front of it starts to approach the maximum (Dmax=0.92) or attains it for any reason, movement through the opening becomes difficult. Its traffic capacity falls and the condition Qn = Qn+t is violated, as a result of which crowding takes place in front of the opening. Under normal conditions the flow through the opening proceeds without special difficulties. In an emergency situation, when people under the influence of danger try to flee the center of the accident, a dangerous situation may arise in the zone of the opening. In this case movement through the opening takes place nonuniformly with lower traffic capacity, right up to development of the so-called jam. The danger of a jam is that quick resolution is difficult and sometimes impossible. Experience and statistics show that in emergency conditions accidents and deaths occur mainly at points where a jam has developed. In such a case obstruction takes place when the people from a kind of "arch" whose abutment presses on the doo1frame, with the curve of the arch in the direction opposite to the direction of movement (Fig. 60). People become a part of this arch and are subjected to strong compression. In such conditions it is difficult for a person to extricate himself and as a result of great compression serious injury can occur. The mutual disposition of different people in the arch may vary widely, which helps to destroy it. The arch is destroyed as soon as it attains a steady state-a phenomenon which is relatively rare. The problem of the probability of a jam at an opening during Fig. 60. Layout of formation movement through it of a foot of arch at opening.

126 Foot Traffic Flow in Buildings traffic flow under emergency conditions has been little studied. This is explained by the impossibility of observing the phenomenon in real life. There are two opinions as to the occurrence of the "jam" in an opening and the formation of the "arch." Some believe the cause of the appearance of the arch is the development of the so-called false opening. The latter is formed by people approaching the streams from the sides at the very entrance to the opening. Having wedged into it they obstruct the opening, as a result of which the width of the opening is reduced for some moments. This phenomenon has been called "the effect Mfalse opening" (Fig. 61). After these people pass through, the opening resumes its normal width until the formation of a new "false opening." Such alternately developing and resolving false openings lend a pulsating character to the process. They also cause the appearance of an arch of people in front of the opening, and here the people who create the false opening form the base of this arch. Others associate the formation of this live arch of people in front of the flow into the opening with the fact ---::: ..., that on approaching the opening people are compelled to change their - --~~~µ trajectory from parallel movement to False opening b 0 1 a radial movement toward the center of the opening. In such a case a Fig. 61. Effect of false opening. strong increase in density takes place. If at this point people accidentally bunch in the form of a continuous curved chain that obstructs the opening, then they are wedged into it and form an arch. ~

Part II Basic Design Taking into Account the Motion of Streams of People

CHAPTEREIGHT

Limit States of Passageways and the Method of Calculating the Motion of Foot Traffic Flows

32. DESIGN LIMIT STATES

Computation of foot traffic flows aims at determining either the time of movement or the nature of the sequence of the process for the correct solution of a building problem (for example, for deciding the number of staircases and exits and the width of corridors, for establishing values of densities attained, points of crowding and delay in movement). The computation is carried out on the basis of the so-called rated limit states . The first design limit state is the state of the paths of movement where they cease to satisfy the working requirements of the time of flow, i.e. where the paths of motion cannot pass the rated number of people in a given time (ti).

The condition of the first design limit state can be expressed by the following formula: (62)

The computation is carried out, according to the first limit state, for example for the forced evacuation of people from the building in case of fire or other emergency conditions. The second design limit state is the state of the paths of flow where they cease to satisfy the requirements of the comfort of movement, i.e. where densities of flow (D) are created in the paths of movement that exceed the established maximum density (D1)for the building on the basis of the requirements of comfort. This limit state is (63)

130 Foot Traffic Flow in Buildings Computation accord ing to the second limit state is carried out for bui ldings and premises where it is necessary to avert the possibility of high densities of foot traffic flows forming (halls for conventions of congresses, conferences, etc.). The quantities t and D are functions of the number of people (N), parameters of the paths of flow(/ and qo max= 13.27 m/ mm. . qo= Q4+ Q3+ Qi =0,9= 606 Crowding takes place in front of the door. D=0.92; v= .11.42 m/ min; qo=I0.5 m/ min; Q = 9.45 m 2/miu. The rate of crowd formation

H

•

. 10.5 ~4.66 vc= 0.92-0.07

i

o.56 = - o.66 mImm. . -0.85

When the front of the stream from the passage· I approaches the rate of crowd formation (point K) changes:•

v= C

10.5 ~:;- 6.35 2.25 0.92-0.12 = - 0.8 =;,

.

2·81 m/mm.

...,,.

When the rear of the stream from passage 4 emerges from the opening (point L) the parameters of flow change: qo=

Q3+ Q2+Q1 14.64 1625 . c>o 6 =0,9 = . >qo max,

crowding will take place at the earlier rate. When the rear of the stream from p~ssage 3 (poiµt M) approaches the rate of crowding becomes

, I0.5~:~-4 .04 0_06 . Ve= 0.92-0.06 = 0.86 =0.0 7 m/mrn, i.e. it starts dispersing slowly. A t tp,e ,n~xtmoment (point N) the rate of dispersion increases to

0.9 . 1~.5 2.3 - 2.35 1.75 . 1 97 VC = 0.92-0.03 = 0.89 = · m/mm. ,

At the end of the approach of people (point P)

. _ = 4.5 mI mm. Vc=Vo6Oo6= l ..42·o.9 23 06 Thus the whole process continues for about 0.4 min; the crowd formed near the door means that the opening is too narrow. Although the crowd is small it could comp]4cate movement under emergency conditions. Hence it is necessary to make the width of the door mqd_

uo

-

Q1+Q2+Q3 + Q4= 18.3 = 137=14 13•.27 · · m. qo max ·

Design Features of Public Buildings

20 1

Or in any case, if very short intervals of time ( < 0.01 min) are not consi dered, when the combined stream from all four passages (see the graph, near pointL) passes through the door, the width of the door should be Q1+Q2+Q3=14.64=1.1 qo max 13.27

m.

Assume that the door is 0.9 m in width as before . The time t for the exit of the stream from the class is 0.38 min. Consequently the average traffic capacity of the opening 06 is

N - 3.6 -- 9 . 5 m 2/ mm. . Q o.v-- T-0.38 Then qoav= 10.5 m/ min, which corresponds to (taking into account the reduction in density after the opening) Do.v=0.2 1. These values can be taken for further computation. The comp utation is continued in the usual sequence: the paths of movement are establishe d depending on discovery of the location of the danger. The points where merger of individual streams from classrooms takes place are determined. The parameters of the latter have been given above. With plotting of the graph the whole process is computed and on the basis of the results and given limiting conditions (t, and D 1) the dimensions of communi cating passages are determined (section 35). The above computation of the movement of streams in a re latively small building is quite complex and is hardly justified by practical necessity. In the majority of cases the mean indicators of movement are sufficient. 46. ENTERTAJNMENT CENTERS AND STRUCTURES

Enter tainment complexes and structures include theaters, movie theaters, circuses, concert halls, indoor sports arenas , multipurpose closed halls and open sports stadiums. The special feature of these bui ldings is the large dimension of the prem ises or structures for accommodating spectators (audi torium , stands) and enclosures designed to serve the spectators before the start of the entertainment show, during the intervals and after the end . Con sidering that modem entertainment centers and structures are built for a large number of spectators (in an outdoor sports stadium it can be more than 100,000), proper organization of foot traffic flows assumes special importance. As in the previous types of buildings , here also we have the followi ng types of movement: (a) occupation of the building or structure before the start of the event; (b) movement during intervals; (c) evacuation of spectators from the building or structure at the end of the event; (d) evacuat ion of spectato rs when accidents occur.

202

Foot Traffic Flow in Buildings

The occupation of the building takes a long time and hence as a rule cannot be the deciding type of movement. Movie theaters fill up quite quickly. The earHer consideration of the working of the cloakroom (see sections 35 and 45) during occupation of the building and evacuation under normal conditions holds for entertainment complexes and structures. But whereas in the first case self-service was considered in the computation, here the area of the cloakroom itself is excluded from computation of the accommodation of people and the area of the vestibule should be computed on the basis of the seconAlimiting state for the given Di so as to create the necessary comfort for collecting coats. Movement during intervals takes place from the auditorium to refreshment rooms, smoking areas and toilets. The formation of streams of people moving in these directions depends on many factors (number of intervals, type of entertainment and its duration, number of spectators, etc.), which are difficuit to account for. In a number of cases such streams are formed and in other cases not. In any case, until special studies are carried out to establish the mean percentage of spectators going to snack bars, smoking rooms and other parts of the entertainment structure during the interval and the distribution in time, it does not seem possible to compute the parameters of the paths of movement from the auditorium to one such room with any reliability. For preliminary computations it is possible: (a) to determine the duration of the movement in the structure on the basis of the parameters of comfortable movement, assuming that during the intervals not more than 75% of the total number of spectators leave their seats; (b) to determine the time of movement through the foyer and lobbies, assuming the anticipated densities in these areas (obviously not more than 0.15) with free streamUned movement, also taking comfortable conditions; (c) to establish the number of people (N) served by the snack bar during the interval; (d) to compute the paths leading directly to the area concerned (snack bar), assuming that people approach the initial part of the path uniformly for a time equal to one-half or one-third of the duration of the interval. Apparently the deciding type of movement in entertainment complexes and structures must be the evacuation of spectators in normal and emergency conditions. The computation is carried out according to the established procedure principally for the first limiting case (t< l1), although there may be buildings where it is necessary to compute even for the second limiting state (D< D 1). Two examples of the computation of evacuation from movie theaters are given below for the first limiting state. The first calculation, where the spectators emerge directly from the building, is the simpler of the two. The second, where the computation is for complete evacuation of the building, is more complex.

Design Features of Public Buildings

-

rr -- - - - -0

203

-

N "'

9 8 7 6 S 4 31l! IZ:21201911~71E15K"11 1111v

0.D75and 0.165 " 0.08 " 0.325 0.525 0.305 0.06

1

0.08 0.305 0.525 0.06 0.06 0.025

2

V1 v 2 v,>v2 Vi t 1, then after analysis of the process an attempt is made to change the parameters of the paths of movement so as to achieve t ~ ti. But if the change in dimensions does not yield the desired results or considerably reduces the production area, then additional exits are tried out and a new check computation is carried out. Modern single-storied industrial buildings often have large dimensions along the width and length . In such cases it may be that there is no way to locate additional exits from the building so that people can reach them within time (