HX64076288 RA967 At5 The orientation of b RECAP i! I iiiiiiii mSL- P IP HA3C7 A,tJ Columbia (Hnttier^itj> intljfCtipofltogork College of ^tyv&itiam anb burgeons Htbrarp The (Jrientation of iDuildings or Planning for Sunlight by IVilliam Atkinson Fellow of the Boston Society of Architects FIRST EDITION First Thousatid NEW YORK JOHN WILEY & SONS London : CHAPMAN ©•> HALL, Limited IQL2 . Copyright, 191 2, BY WILLIAM ATKINSON Entered at Stationers' Hall, London Stanbopc lPreas F, H. GILSOH COMPANY BOSTON, U.S.A. In Memory of J. Truman Burdick Digitized by the Internet Archive in 2010 with funding from Open Knowledge Commons http://www.archive.org/details/orientationofbuiOOatki PREFACE The purpose of this book is to set forth the principles which ought to govern the planning of buildings with re- spect to sunlight, a subject to which very little attention has been given. Several years ago, in an essay on hospital construction, 1 I wrote as follows: "To study properly the question of sunlight, a sun plan of the buildings must be drawn, and their positions considered with respect to the shadows they cast upon each other and upon the ground." This state- ment describes very well the general method of study which I have followed in my investigations, the results of which are now for the first time presented to the public in a complete form. I had begun my study of orientation with hospitals espe- cially in mind, but I soon realized that the general principle of planning with reference to sunlight was of fundamental importance in the design of all buildings, and especially in the planning and laying out of cities. In this connection I may mention that a series of diagrams made by me, at the request of a committee interested in securing new legisla- tion regulating the height of buildings in Boston in 1904, was of great service in showing the effect of tall buildings 1 "Small Hospitals," by A. Worcester, M.D., and "Suggestions for Hospital Architecture," by William Atkinson, Architect, New York, John Wiley & Sons, 1894. v VI PREFACE in overshadowing and shutting out the sunlight from the streets. Another series of street diagrams, first shown at a lecture given by me before the Society of Arts, at the Mas- sachusetts Institute of Technology, has been reprinted by permission in a recent English book on city planning. Some of my earlier studies in orientation, originally pub- lished in the National Hospital Record, have been twice re- printed in The Brickbuilder magazine, and also embodied, by permission, in a recent American book on hospital con- struction. All of which has encouraged me to believe that a more complete presentation of the subject, in book form, would not be without interest to the public. In my first chapter I have included so much of the ele- ments of astronomy as is necessary to a clear understanding of the apparent motion of the sun, and the variations in the angles of sunlight at the different seasons. I have also described the method of the stereographic projection, by which the angles of sunlight may easily be obtained, for any season of the year, and for any latitude. The second chapter deals with the distribution of sun- light upon the exterior of buildings, and its admission to the interior, through windows. In this chapter I have developed the method of the "shadow curve" and the "area of complete shadow," an application of the principles of descriptive geometry to the recording of transitory occurrences, which, as far as I am aware, is new. General principles for the planning and placing of buildings are given as far as it has seemed desirable. It is, however, to be understood that, for the PREFACE Vll best results, each case must be studied as a separate prob- lem, with reference to local conditions, and especially with reference to the latitude of the place. In connection with the study of windows an account is given of my experi- ments with the "sun box," an apparatus devised by me to test the practical effect of different window exposures. My third chapter is devoted to hospitals. In it I have discussed the vexed question of the best orientation for hospital ward pavilions and have ventured to make recom- mendations in this regard at variance with common prac- tice. I have also presented a plan for a new type of hospital building especially designed to meet the needs of modern medical treatment. The last chapter is concerned with the distribution of sunlight in streets, as affected by their direction and width, and the height of the buildings upon them. In an appendix I have given in full the building law of Paris regulating the height of buildings and a synopsis of the regulations of some American cities in this matter. While the working out of the diagrams and the calcula- tion of the tables has been a matter of pure mathematics, admitting but one result, the conclusions to be drawn from them are to some extent a matter for individual judgment. It is therefore fitting that I should give here a statement of the premises on which my recommendations are based. I have assumed that it is desirable, in our climate, that all buildings in which human beings dwell or work should have all of their exterior walls exposed to direct sunlight at some time during the day throughout the year, and that the surfaces of streets, alleys, areas, courtyards, and other Vlll PREFACE spaces in and around buildings should also be exposed as much as possible to the action of direct sunlight. In regard to windows, I have assumed that as much direct sunlight as possible is desirable through them during that period of the year in which they are customarily kept closed. On the other hand, during the hot season, when windows may be open day and night, and the sun-purified air brought in from outside by natural means, I have assumed that direct sunlight through windows is rather to be avoided than sought after. The function of sunlight in promoting healthy condi- tions, and its use as a therapeutic agent, may only be authoritatively stated by sanitarians and medical men who have given special study to this question, and I can do no more than refer those who may wish to pursue this branch of the subject to the work of the German and Danish investigators, a full account of which may be found in Luft-und Sonnenbdder , by Dr. Julian Marcuse, Stuttgart, 1907. The diagrams for this book have been engraved by the wax process from drawings made by me, and the few which have appeared in former published articles have been care- fully revised and redrawn. Boxford, Mass., October, 191 1. CONTENTS CHAPTER I THE ASTRONOMICAL DATA Sunlight a requisite for healthy buildings. — An elementary knowledge of as- tronomy necessary for intelligent sun-planning. — The angles of sunlight at the different seasons and in different latitudes. — Calculation of the angles of sun- light by the stereographic projection. — By spherical trigonometry. — Table of sunlight angles. CHAPTER II SHADOW DIAGRAMS Shadows of the cube. — Orientation of the Swiss house. — Shadow curves of the cube. — Theory of the area of complete shadow. — The area of complete shadow as applied to the study of fundamental types of building plan. — Sunlight admitted by windows. — The visual angle of windows. — Quantity of sunlight admitted by windows. — Heating effect of sunlight. — The solar constant. — The sun box. — Sun-box records. CHAPTER III HOSPITALS The orientation of ward pavilions. — Different views upon the subject. — Recommendations of the author. — The typical ward pavilion. — Its unsuit- ability to modern conditions. — A new type of ward needed. — Description of the pyramidal type of ward. CHAPTER IV STREETS Angles of sunlight in streets. — Sunlight curves in streets. — The orientation of streets. — Horace Bushnell's theory. — ■ The height of buildings. — European building regulations. — The law of ancient lights. — Building law recommended by the author. — The skyscraper and the street. APPENDIX A Sun tables for London and New Orleans. APPENDIX B Building laws of Paris regulating the height of buildings. APPENDIX C Building laws of American cities regulating the height of buildings. LIST OF ILLUSTRATIONS CHAPTER I Fig. Page i. Cross sections of the visible celestial sphere 3 2. Apparent orbits of the sun at the different seasons 6 3. Paths of the sun at intermediate periods 7 4. Stereographic projection of the visible celestial sphere 9 5. Construction of the stereographic projection. — First step 12 6. Construction of the stereographic projection. — Second step 14 7. Construction of the stereographic projection. — Third step 16 CHAPTER II 8. Shadows of the cube 20 9. Shadows of the cube 21 10. Shadows of the cube 22 11. Plan of typical Swiss dwelling 23 12. Shadow curves of the cube. Winter solstice 25 13. Shadow curves of the cube. Winter solstice 26 14. Shadow curves of the cube. Equinoxes 27 15. Shadow curves of the cube. Equinoxes 28 16. Shadow curves of the cube. Summer solstice 29 17. Shadow curves of the cube. Summer solstice 30 18. Areas of complete shadow: single straight block 32 19. Areas of complete shadow: L plan 33 20. Areas of complete shadow: U plan 34 21. Method of obtaining the area of complete shadow 36 22. Shadow curves of cube and prism at winter solstice 37 23. Maximum areas of complete shadow for the L and U plans 38 24. Effect of increase of height upon the area of complete shadow 39 25. Good and bad arrangement of L 41 26. Application of the test of the area of complete shadow 42 27. Shadows of the single straight block. Axis N. and S 44 xi Xll LIST OF ILLUSTRATIONS Fig. Page 28. Shadows of the single straight block. Axis E. and W 45 29. Shadows of the single straight block. Axis N. E. and S. W 46 30. Visual angle of ordinary window 47 31. Visual angle of mediaeval window 48 32. Wall section with beveled piers 49 33. Window illumination: winter solstice 50 34. Window illumination: equinoxes S 1 35. Window illumination: summer solstice 52 36. Cross sections of sunlight prism 53 37. Change in area of sunlight prism: winter solstice 55 38. Change in area of sunlight prism: equinoxes 56 39. Change in area of sunlight prism: summer solstice 57 40. Windows : obstructed outlook 59 41. Obstructed outlook: stereographic projection 61 42. Change in area of sunlight prism: obstructed outlook 62 43. Cross section of sun box 64 44. Photograph of sun box 65 45. Sun box records 76 46. Sun house 77 CHAPTER III 47. Ward pavilion: open-ended type 80 48. French method of hanging outside blinds 84 49. Economy of two-story type of pavilion 86 50. Section of ward with ridge ventilation 88 51. Types of ward pavilions 89 52. Grouping of ward units: Virchow Hospital 91 53. Grouping of ward units 92 54. Grouping of ward units 93 55. Grouping of ward units 95 56. Elevation of Virchow ward unit 97 57. Pyramidal type of ward construction 98 58. Pyramidal ward unit: first-floor plan 99 59. Pyramidal ward unit: second-floor plan 100 60. Pyramidal ward unit: third-floor plan 101 61. Pyramidal ward unit: shadow diagram 102 LIST OF ILLUSTRATIONS xm Fig. Page 62. Pyramidal ward unit: shadow diagram 103 63. Pyramidal ward unit: shadow diagram 104 64. Pyramidal ward unit: general plan 1 06 65. Pyramidal ward unit: elevation 107 CHAPTER IV 66. Angles of sunlight in streets in 67. Angles of sunlight in streets 112 68. Angles of sunlight in streets 113 69. Method of obtaining sunlight curves 114 70. Sunlight curves: streets 116 71. Building law of Paris 119 72. Typical cornice section 122 73. Proposed building law 123 74. The skyscraper and the street 124 THE ORIENTATION OF BUILDINGS CHAPTER I THE ASTRONOMICAL DATA Unquestionably one of the first requisites for a healthy building is abundance of sunlight. Not only the exterior wall surfaces of buildings, but also the surfaces of the ground around them, should have the direct rays of the sun for as long a time as possible each day. "Second only to air, is light and sunshine essential for growth and health; and it is one of Nature's most power- ful assistants in enabling the body to throw off those conditions which we call disease. Not only daylight, but sunlight; indeed, fresh air must be sun- warmed, sun- penetrated air. The sunshine of a December day has been recently shown to kill the spores of the anthrax bacillus." (Healthy Hospitals, Sir Douglas Gal ton, Oxford, 1893). To secure sunlight in fullest measure requires careful and intelligent planning with this end in view. It is necessary for such a study to have at hand a table, giving the angles of sunlight at the different hours of the day and at the different seasons of the year, for the particular latitude in question. ORIENTATION OF BUILDINGS In this chapter I shall describe one method by which such a table may be prepared. In all of the operations of practical astronomy, as in the calculation of position of ships at sea, or in deter- minations of latitude and longitude upon land, it has been found best to go back to the conceptions of the first astronomers, who imagined the earth to be the cen- ter of the universe, and the celestial bodies to revolve around it. And thus has survived the ancient fiction of the " celestial sphere." Viewing the heavens on a starry night, the whole firma- ment seems slowly to revolve, successively bringing into view, above the eastern horizon, one constellation after another. If, by magic power, the sun's light could be dimmed so that the stars should be visible in the daytime, he would appear, like them, to be fixed in the celestial sphere, and to turn with the constellations in their uniform diurnal motion around the pole. But if we could extend our observations over a period of several weeks, we should observe that the sun was slowly changing his position among the stars, passing in the course of a single year through the successive constella- tions of the zodiac, in summer north of the celestial equator, in winter south. But this change in the apparent position of the sun is so slow that for any single day it may be disregarded, and his position for that day considered as fixed in the celestial sphere. THE ASTRONOMICAL DATA Z S s' o w' NEW ORLEANS Fig. i. — Cross sections of the visible celestial sphere, showing the path of the sun at the solstices, and at the equinoctial periods, for different latitudes. ORIENTATION OF BUILDINGS Fig. I shows in cross section that part of the celestial sphere which is above the horizon, at the latitudes respec- tively of London (Lat. 5i°-3o' N.), Boston (Lat. /\2°-22' N.), and New Orleans (Lat. 3o°-o' N.). In tnese diagrams H'H represents the plane of the horizon; the position of the observer; P the celestial north pole; Z the zenith,- and SS\ EO, and WW the apparent paths of the sun at the periods of the summer solstice, the equinoxes, and the winter solstice, respectively. It is evident that the altitude of the sun, at noon, at the periods of the year referred to, may be obtained directly from the diagrams, being given by the angles HOS, HOE, and HOW, for the summer solstice, the equinoxes, and the winter solstice,. respectively. It will be observed that these angles are less in the more northerly latitudes, and that the path of the sun inclines more and inore toward the horizon. This decrease in the altitude of the sun is accompanied with an increasing divergence between the extreme points of sunrise and sunset, so that the days in summer are much longer, and in winter much shorter, in the countries of the far north, than in those which are near the equator. At latitude \2°-o' N. (approximately the latitude of Boston, Mass.) the sun rises on the longest day of the year about 32I north of east and sets at an equal angle north of west, reaching at noon an altitude of yi°-2y r above the horizon. On the shortest day of the year he rises about 32§° south of east and sets at an equal angle south of west, reaching at noon an altitude of only 24°-33' above the horizon. THE ASTRONOMICAL DATA 5 At the two periods of the year when day and night are of equal length he rises in the east and sets in the west, reaching at noon an altitude of 48°-o / above 'the horizon. The perspective diagrams of Fig. 2 will give the student an easily-remembered mental image of the path of the sun at these periods. The horizontal circle represents the horizon; the inclined circle the path of the sun, and the diverging lines the direc- tion of the sun's rays at the different hours of the day. It will be noted that at the period of the equinoxes the trace of the sun's rays describes a plane; at the period of the summer solstice a hollow cone, and at the period of the winter solstice a convex cone. His path at intermediate periods may be pictured by the aid of the following diagram (Fig. 3) which gives his posi- tion at intervals of one month apart throughout the year. It will be observed from this diagram that the path of the sun during the four months from April 21 to August 21 resembles more nearly his path at the summer solstice than his path at the equinoxes, and similarly his path during the four months from October 21 to February 21 more nearly his path at the winter solstice than his path at the equinoxes. This must be borne in mind in studying the various shadow diagrams which are given later in this book. Those which are drawn for the period of the winter solstice may be taken as typical of the four months from October 21 to February 21; those which are drawn from the period of the summer solstice of the four months from April 21 to ORIENTATION OF BUILDINGS Sunrise ii m t "Sunset Sunrise E XI HI W Sunset 11 Hi Sunset Fig. 2. - Perspective diagrams showing the apparent path of he sun, «dtib andes of sunlight at the different hours of the day, for Lat. 42 -o N. The upper dLtim i^ ra for the summer solstice, the middle diagram for the vernal and autumnal equinox, and the lower diagram for the waiter solstice. THE ASTRONOMICAL DATA August 21 ; and those which are drawn for the period of the equinoxes of the two months from February 21 to April 21, and the two months from August 21 to October 21. The position of the sun with respect to the observer is generally expressed in terms of azimuth and altitude. Fig. 3. — Cross-section of the visible celestial sphere showing the path of the sun at periods one month apart throughout the year. Lat. 42°-o' X. Actually the declination of the sun on May 21 does not exactly coincide with his declina- tion on July 21, although it is so represented in the diagram. A similar observation applies to the other dates which are grouped in pairs. The differences, however, are so slight that it would be difficult to represent them at the scale at which the drawing is made. The latter term requires no explanation, but the mean- ing of "azimuth" may not be so generally understood. It may preferably be explained by an example rather than a definition. Imagine a stick set upright in level ground in the sun- light. The deviation of the shadow cast by the stick ORIENTATION OF BUILDINGS from a true north and south direction is the azimuth of the sun at that moment. Knowing the distance of the sun north or south from the equator (which information may be obtained from the almanac) the azimuth and altitude for any particular day may be calculated by spherical trigonometry. The desired data may also be obtained very simply and easily, and with sufficient accuracy for our purposes, by the stereographic projection. To one who understands perspective, the stereographic projection presents little difficulty, as it is virtually the method of linear perspective applied to the representation of the sphere, but with this difference, that the drawing when completed is viewed from behind the picture plane, instead of in front of it, as in ordinary perspective. It possesses two properties which make it especially useful; the first being that all circles of the sphere are projected as circles or as straight lines, and hence may be drawn with compasses and ruler; 'and the second being that the angle made by the crossing of two circles upon the surface of the sphere is the same as the angle made by their projections. The statement that by the aid of the stereographic pro- jection one may, with a few hours' labor, construct a diagram which will give the position of the sun at each hour of the day for any period of the year desired, and for any latitude, should be sufficient to induce the student to master its principles. Such a diagram, drawn for latitude 42°-o' N., is shown in Fig. 4. TEE ASTRONOMICAL DATA This is a stereographic projection of the celestial sphere, taken upon the plane of the horizon, which is represented by the circle N, E, S, W, these letters being placed at the four cardinal points. N B2, w ¥-\-\-\ y i-X—\ — Bl / / / / \A// -n FlG. 4. — Stereographic projection of the visible celestial sphere, upon the plane of the horizon. The circular arc WE is the projection of the celestial equator, which is the path of the sun at the period of the equinoxes. The arc of considerably greater curvature to the north is the projection of the tropic of Cancer, which is the path IO ORIENTATION OF BUILDINGS of the sun at the summer solstice, while the more flat- tened and shorter arc to the south is the projection of the tropic of Capricorn, which is the path of the sun at the winter solstice. The twelve circles converging toward the upper part of the diagram are the projections of the celestial meridians, or hour circles, 15 apart. These hour circles may be conceived of as a gigantic cage or framework, fixed in position, and serving as a system of celestial verniers, to mark the passage of the heavenly bodies, which are carried past them with the revolution of the sphere. The passage of the sun across the successive hour circles marks the hours of the day as shown by a sundial. Con- sequently the intersection of any hour circle with the circle representing the path of the sun is the stereographic pro- jection of the sun's position for the corresponding hour and period of the year. And from this projection the azimuth and altitude may readily be found. For instance, the dotted line OB drawn through the intersection of the 11-0' clock hour circle and the celestial equator gives the azimuth of the sun at 11 a.m. {solar time) at the period of the equinoxes, and the dotted line OB 1 drawn through the intersection of the 1-0'clock hour circle and the tropic of Capricorn gives the azimuth of the sun at 1 p.m. on December 21st, and the dotted line OB2 drawn through the intersection of the 6-o'clock hour circle and the tropic of Cancer gives the azimuth of the sun at 6 p.m. on June 21st. THE ASTRONOMICAL DATA II The altitude is obtained by a simple construction. For example, the angle EOD is the altitude of the sun at II A.M. at the period of the equinoxes and is found by measuring off on the line OE the distance OC equal to OA and drawing the line SC intersecting the enclosing circle at the point D. To explain more fully the construction of the diagram, an example will be given and worked out. Let it be required to find the position of the sun at 10 a.m., solar time, April 16, Lat. 30°-o' N. Draw a cross section of the visible celestial sphere, as shown in the upper part of Fig. 5. HH is the horizon, the position of the observer, and Z the zenith. Through O draw the line POP' making an angle of 30°-o' with the horizon. P is the celestial north pole, for it is shown in astronomy that the altitude of the pole is equal to the latitude of the place. Draw OE at right angles to POP. It represents the celestial equator. From the point E lay off the arc ES equal to the declination of the sun on the date required. This we find from the almanac (for 19 10) to be 9°-59' for April 16. Draw SM parallel to OE. It represents the path of the sun above the horizon at this period. The projection is made upon the plane of the horizon, and the station point is upon the surface of the sphere vertically below the zenith, at N. Any point upon the surface of the sphere is projected 12 ORIENTATION OF BUILDINGS Fig. 5. — Construction of the stereographic projection, first step. The upper part of the diagram is a cross section of the celestial sphere; the lower part its pro- jection upon the plane of the horizon. THE ASTRONOMICAL DATA 1 3 by joining it to the station point by a straight line and the point in which this line pierces the picture plane HH is the projection required. The enclosing circle is the horizon, which is drawn without change since it lies in the plane of the projection. The circle MS may now be projected. It is evident that M' and M' are the points at which this circle cuts the horizon, and that S' is the projection of the point S. Through these three points draw the arc of a circle. It is the projection required, for it is a theorem of the stereographic projection that all circles of the sphere are projected as circles or portions of circles, with the exception of those which pass through the station point, which are obviously projected as straight lines. An example of the latter is the meridian or 12-o'clock hour circle, which is projected as the straight line H'S'H'. To find the point upon the arc M'S'M' where the sun is at 10 a.m. it is necessary to project the io-o'clock hour circle. (For the sake of clearness the operation is shown in a separate diagram, Fig. 6.) Since all the hour circles pass through the north and south poles, we have at once, in the projections of the poles (at PP and P'P'), two points of our required projec- tion. It remains to find the center. The line LT, equidistant from PP and P'P', contains the centers of all circles passing through those points. 14 ORIENTATION OF BUILDINGS 1 1 Is \ \ \ \ / s \ S S "■--^r- FlG. 6. — Construction of the stereographic projection, second step. THE ASTRONOMICAL DATA 15 To find the point upon this line which is the center of the projected 10-0'clock hour circle, we avail ourselves of the second theorem of the stereographic projection, which is that the angle made by two circles upon the surface of the sphere is the same as the angle made by their projections. Now the 10-0'clock hour circle makes an angle of 30 with the noon circle, or meridian, where it crosses the latter at the poles, one hour being equal to 15 . Consequently a line drawn through PP, the projection of the north pole, and making an angle of 30 with PP P'P', the projection of the meridian, is a tangent to the pro- jection of the 10-0'clock hour circle, and establishes the center of the latter at once, at the point T, upon the line LT. The circle may now be drawn. Superposing the two circles thus obtained in one diagram (Fig. 7), their intersection at A is the projection of the sun's position and the angle H'OX is the true bearing or azimuth of the sun required. The altitude may be found by a secondary construction. (Lower diagram of Fig. 7.) It is evident that the straight line XAO is the projection of a circle, vertical to the plane of the horizon, and passing through the zenith and the sun. The sun's altitude is measured upon this circle, upward from the horizon. Let us imagine this circle to be revolved into the plane of the horizon, thus bringing the station point to the posi- tion N and the zenith to the position Z. :-' ORIENTATION OF BUILDINGS Fig. 7. — Construction of the stereographic projection, third step. (The point P referred to in the test is the projection of the north pole, to the left of 0, on the dotted line E'H'.j THE ASTRONOMICAL DATA 17 The sun lies at some point upon this circle. To find this point draw the line NA cutting the circle at K. It is the point required, and XOK is the altitude of the sun required. By following the above method and making the pro- jection at a large scale the angles may be found with suffi- cient accuracy for the purposes of the architect. To obtain the result by calculation involves the solution of the spherical triangle POA of which the two sides PA (the north polar distance of the sun), PO (the co-latitude of the place), and APO (the assumed hour angle) are known. (Upper diagram of Fig. 7.) Solving for the angle A OP and the third side AO gives us H'OX, and XA the azimuth and altitude respectively. In the following table is given the azimuth and altitude of the sun for 42 north latitude at each hour of the day for the typical periods of the year. TABLE I Hour angle. S-7 105 7 -S It. 1 *5 90 75 c 6o c 45 C Winter solstice. Equinoxes. Azimuth. , Altitude. Azimuth. Altitude. S^ -49 4i°-38' 29 °- o' i4°-58' o°- o' 4-17 I2°-28' i8°-55' 23 °- 6' 24°"33' 90-0 79°-5° 68°-53 56°-i3 40°-47 2i°-49 o°- o " - 5 2i°-49' 3i°-42' 40°- 4' 45°-52' 4S - o' Summer solstice. Azimuth. Altitude. H7°-io' 5°-9' i°7°-52' 98°-46' 89°-i2' 77° _ 5S 6'2°-47' 38°-36' i5°-27' 26°-i7' 37°-23' 4 S°-2 7' 5S°-57' 6 7 °- 3 8' o°- 0' 7 i°-2 7 ' Sunrise and sunset. 4 h. 28 m. 6 h. m. 57 — 37' o°— 0' 90°-o' o°-o' 7 h. 32 m. I22°-2 3 ' ~° «' 1 8 ORIENTATION OF BUILDINGS EXPLANATION OF TABLE. The first column gives the solar time expressed in hour angles, one hour being equal to 15 degrees, reckoning either way from noon. For instance, the hour angle 30 degrees corresponds to 10 a.m. or 2 p.m., the hour angle 45 degrees to 9 a.m. or 3 p.m., and so on. Azimuth is east of south for the forenoon and west of south for the afternoon. No corrections have been made for refraction, the effect of which is to slightly increase the altitude when the sun is near the horizon. This table is the basis on which all of the diagrams in this book have been constructed. Similar tables, computed for the latitudes of London and New Orleans, will be found in the appendix. CHAPTER II Shadow Diagrams As the first example of the application of the data obtained in the preceding chapter, let us consider the shadows cast by two cubes, one of them placed with its four sides facing the cardinal points, and the other with its diagonal upon the meridian. These shadows are shown in Figs. 8, 9, and 10 and are given for each hour of the day at the typical periods of the year. 1 It is evident that in the first position the north face of the cube receives no sunlight during one-half the year, from the autumnal to the vernal equinox, whereas in the second position all four faces receive sunlight at some por- tion of each day, throughout the year. There is another advantage, not inconsiderable, in the latter arrangement, since in this position the cube shades the surface of the ground considerably less than when it is placed squarely facing the cardinal points. A study of the diagrams will make this apparent. It will be noted that in the lower diagrams of each figure the shadows overlap each other to a greater extent than they do in the upper ones and furthermore that in the lower diagram of Fig. 8 there is a triangular area which receives no sunlight at all. 1 These diagrams and all those which follow are drawn for latitude 42°-o' north. 19 Fig. 8. — Shadows of the cube, winter solstice. The shaded area in the lower diagram receives no sunlight. Lat. 42°-o' N. 20 VIII IX X XI XII I II III VIII IX X XI XII I II III Fig. 9. — Shadows of the cube, autumnal and vernal equinox. Lat. 42°-o' N. Fig. io. — Shadows of the cube, summer solstice. Lat. 42°-o' N. 22 SHADOW DIAGRAMS 23 The advantage of placing a square building with its diagonal upon the meridian was long ago recognized by the mountain dwellers of Switzerland. The ground plan of a typical Swiss dwelling is shown in Fig. n. 1 It will be observed that the living room is placed in the sunniest corner of the building, with its windows facing southeast and southwest. -1 kwlllllllll r u 1 oo[ = J^>\ J\ - 3 =-l tf— ■ '— J Fig. 11. — Ground plan of Swiss dwelling, showing the customary orientation. A is the Living Room. Referring again to the shadows of the cube it will be observed that at the equinoctial periods the tips of the shadows move in a straight line from west to east, whereas at all other seasons they describe a curve. A further study of the diagrams will show that other curves are contained in them besides those described by the tips of the shadows, and in one of the diagrams such a curve is shown, passing through certain points of inter- section of the shadows, those points having been selected 1 Taken from Die Holz-Architectur der Schweiz. Gladbach. Zurich and Leipzig, 1885. 24 ORIENTATION OF BUILDINGS which are in shadow for exactly two hours, as, for instance, the point P, which first comes into shadow at 10 A.M., and emerges again at noon. And a study of the diagram (Fig. 8) will show that each of the other points is in shadow for the same length of time. Such a curve may be called a "shadow curve," and the curve of our figure the "two-hour shadow curve." In the same way we might draw the "three- hour" and the "four- hour shadow curve," and so on, until our original drawing should become translated into a new and strange diagram, consisting entirely of curves. , It is in this manner that the following diagrams have been drawn (Figs. 12 to 17). To express more clearly their meaning, the zones between the curves have been shaded in a series of tints, correspond- ing to the following table: 1 — :1 1 ■'■i 4 Area in sunlight between 9 and 8 hours. Area in sunlight between 8 and 7 hours. Area in sunlight between 7 and 6 hours. Area in sunlight between 6 and 5 hours. Area in sunlight between 5 and 4 hours. Area in sunlight between 4 and 3 hours. Area in sunlight between 3 and 2 hours. Area in sunlight between 2 and 1 hours. Area in sunlight for less than 1 hour. Area without sunlight. These diagrams not only illustrate, in a graphic manner, the effect of the object or building, in shading the ground around it, but they also indicate the distribution of sun- SHADOW DIAGRAMS 25 26 ORIENTATION OF BUILDINGS SHADOW DIAGRAMS 27 28 ORIENTATION OF BUILDINGS SHADOW DIAGRAMS 29 3Q ORIENTATION OF BUILDINGS SHADOW DIAGRAMS 31 light upon the vertical surfaces, or walls, of the building itself. In the same manner the shadow curves of any object or building may be obtained. The process affords a useful exercise in descriptive geometry, and the results are interesting and instructive. To reproduce the complete series of shadow curves for each type of object or building which we shall study would, however, require an unduly large number of dia- grams. It becomes desirable therefore to devise a method which will present the subject in a more condensed form. Such a method has been adopted for the diagrams which follow, and the manner of their construction will now be explained. In the discussion of the shadow curves of the cube, it was pointed out that one of the diagrams differed essentially from the others in that it disclosed an area having no sun- light at all during the day. Such an area will be called an area of complete shadow and may be defined as follows: The area of complete shadow of any object reposing upon a horizontal plane surface is that portion of the object, and of the surface upon which it rests, which is continuously in shade at the particular period of the year under consideration, and an area of perpetual shadow is that portion of the surface which receives no direct sunlight at any time during the year. It is evident that by superposing the areas of complete 3 2 ORIENTATION OF BUILDINGS shadow for different seasons, we may, in a single diagram, embrace the phenomena of an entire year. And this has been done in the following diagrams (Figs. 18, 19, and 20) in which the waxing and the wan- ing of the area of complete shadow is shown by indicat- ing its size at periods one month apart • throughout the year. These diagrams show the area of complete shadow for the three fundamental types of building plan: the single straight block (of which the cube is a particular case), N Fig. 18. — Areas of complete shadow; single straight block. Lat. 42°-o' N. two blocks arranged as an L, and three blocks arranged as a U. As almost all buildings are composed, in their elements, of these simple shapes, in various combinations, it follows that a careful study of these diagrams will enable one to criticize intelligently, as far as concerns the orientation, the plan of almost any building. In the single straight block (Fig. 18) it will be seen that there is an area of complete shadow present in two of the positions shown. This area first appears on September 21 and increases in size up to December 21, after which it decreases, until by March 21 it has disappeared altogether. SHADOW DIAGRAMS 33 In the other two positions the absence of an area of complete shadow indicates that each wall of the building and all portions of the ground around it receive sunlight at some period of the day throughout the year. Fig. 19. — Areas of complete shadow; two blocks arranged as an L. The solid black represents the area of complete shadow at the summer solstice, the lightest tint the area of complete shadow at the winter solstice, and the intermediate tints the areas of complete shadow at intervals one month apart for the intervening periods of the year. Lat. 42°-o' N. In the case of the L plan (Fig. 19) there is one position (that in which the reentrant angle faces the north) in which an area of perpetual shadow first appears, and in the U plan. (Fig. 20) there are three such positions, 34 ORIENTATION OF BUILDINGS Fig. 20. — Areas of complete shadow; three blocks arranged as a U. The height of the blocks in these three diagrams (Figs. 18, 19 and 20) is taken as equal to their width. Lat. 42°-o' N. SHADOW DIAGRAMS 35 those in which the U court faces north, northeast, and northwest. The significance of these diagrams will perhaps be better understood by a study of Fig. 21, which illustrates the method of obtaining the area of complete shadow for the L plan. In all of the foregoing diagrams the height of the blocks is assumed to be equal to their width. The effect of an increase in height will now be con- sidered. As the first example we will take the cube and compare its shadow diagram with that of a square prism having a height, let us say, equal to five times the width. We may imagine the one to represent a building 60 feet square and 60 feet high, and the other a tower 60 feet square and 300 feet high. The diagrams (Fig. 22) represent the shadow curves of the two at the winter solstice. It will be noted that the increase in height enlarges the outer series of curves but does not affect those in the immediate vicinity of the building, and, furthermore, that the area of complete shadow is the same in both cases. An increase of height of the single straight block produces a similar effect. In certain positions of the L and U plans, however, an increase of height produces an enlargement of the area of complete shadow up to a certain point, beyond which any further increase produces no further change in the area of complete shadow upon the ground. It must be remembered, however, that the presence of 36 ORIENTATION OF BUILDINGS Fig. 22. — Showing the effect of an increase of height upon the shadow curves. The lower diagram represents a cube, and, at a smaller scale, is identical with Fig. 12. The upper diagram represents a prism of a height equal to five times that of the cube. Winter solstice, Lat. 42°-o' N. 37 38 ORIENTATION OF BUILDINGS an area of complete shadow in plan indicates that it also extends over a portion of the walls of the building. The maximum areas of complete shadow for the L and U plans produced by an increase in height, are shown in Fig. 23, and in Fig. 24 is shown in isometric projection the area of complete shadow of the L plan, in that position of the L in which the reentrant angle faces the north. •s s* Fig. 23. — Showing the maximum areas of complete shadow for the L and U plans. The diagrams at the left represent the winter solstice; at the right, the summer solstice, and between the two, the vernal and autumnal equinox. Lat. 4 2°-o' N. It is of course to be understood that these positions of the L and U plan are undesirable. For example, let us imagine that we are planning a country dwelling of the farm-house type. The main por- tion of the building has been correctly placed at an angle of 45 with the meridian and the question before us is the position of the L or wing, containing the kitchen SHADOW DIAGRAMS 39 Fig. 24. — Areas of complete shadow for the L plan, autumnal and vernal equi- nox, showing the effect of an increase of height. Lat. 42 N. ^ 40 ORIENTATION OF BUILDINGS and shed (Fig. 25). Of the two arrangements shown in the figure the lower is to be preferred, since in the upper there is a reentrant angle facing the north, involv- ing an area of complete shadow at all seasons of the year. The presence or absence of an area of complete shadow is a useful criterion by which to judge of the excellence of any given plan, and it is a test which should always be applied in studying a group of buildings or in planning a building having a number of courts or wings. To determine the area of complete shadow at the equi- noctial periods is a simple matter, since at this time the trace of the sun's rays describes a plane, and the tips of the shadows of any object cast upon level ground move in a straight line from west to east, as we have already seen in the shadows of the cube. As an example let us apply this test to a type of plan which is quite a common one for institutional buildings (Fig. 26). It will be found that, in any position in which this plan may be placed, there is an area of complete shadow always present. 1 In all the cases so far considered, it will be observed that the positions which give the least amount of shaded area are those in which the blocks or buildings are placed at an angle of 45 with the meridian. 1 In making the sun plan of a building care must be taken to distinguish between the magnetic north and the true meridian. It is customary in surveyors' plans to mark the magnetic north by the symbol of a one-sided arrow, while the true north is denoted by a full-fledged arrow. SHADOW DIAGRAMS 41 Fig. 25. — Good and bad arrangement of L. The shaded area in the upper part of the figure shows the area of complete shadow at the autumnal and vernal equi- nox. Lat. 42°-o' N. 42 ORIENTATION OF BUILDINGS The next step in our study will be to consider the group- ing of buildings, such a problem, for instance, as is presented in planning a pavilion hospital. In studying groups of buildings we have not only to con- sider the shadows cast by the buildings upon the ground, ^_H Fig. 26. — This is a common type of plan for hospitals and other institutional buildings. It is given here as an example to be avoided, since it involves an area of complete shadow in any position in which it may be placed. but also the shadows cast by the different buildings upon each other. Figs. 27, 28, and 29 represent, in isometric projection, two of our single straight blocks placed side by side, with the shadows as they would be at the winter solstice, when the interference of one building with another is the greatest. SHADOW DIAGRAMS 43 In Fig. 27 the long axis of the blocks runs north and south; in Fig. 28 east and west, and in Fig. 29 northeast and southwest. The latter figure will also serve for the case in which the axis of the blocks runs northwest and southeast, the forenoon diagrams of the one corresponding to the after- noon diagrams of the other, and vice versa. The blocks are placed at a distance apart equal to twice their height, the arrangement usually recommended for the ward pavilions of a hospital. A study of these diagrams which, as above noted, repre- sent the most unfavorable conditions of the whole year, justifies the conclusion that adequate sunlight may be obtained with a distance between the blocks of considerably less than that shown. Such is the kind of study which the architect must pursue in order to become proficient in the art of sun- planning. How much weight should be given to the question of sunlight must be a matter for judgment in each case, but to wilfully create an area of complete shadow when, by some different arrangement of plan, it might have been avoided, without detriment to more important considerations, can- not be considered good architecture. Just as a building should be planned in all its parts so as to shed water, and not invite the entrance of damp- ness into its exterior walls, so in its general shape and disposition it should be planned so that the sun may dry out its walls quickly after rains, and keep them clean and bright. 44 ORIENTATION OF BUILDINGS en M d°' .« IN W Tf 2+* >> ... u o en tn £ IH o 1) SHADOW DIAGRAMS 45 bO I eo O • ^ IT in ■ r$ s S O a> o3 C en !> 4 6 ORIENTATION OF BUILDINGS ^ u, J ►, ■n o +j u o & O v T) +j nl ij J3 & SHADOW DIAGRAMS 47 So far we have considered only the distribution of sun- light upon the exterior surfaces of buildings and upon the ground. The admission of sunlight to the interior of build- ings through windows will next be considered. It is evident that a window facing the east, and with an unobstructed outlook, will receive its maximum of sunlight at sunrise of the equinoctial periods. As the sun moves toward the south and mounts higher and higher in the heavens, his rays fall more and more obliquely 145' Fig. 30. — Showing the visual angle of an ordinary window, in a building of frame construction. through the opening, and finally cease to come through at all. The angle at which this will occur varies with the width and height of the opening and the depth of the jamb. Fig. 30 is the plan of a window of ordinary width in a wall of frame construction. The angle of 145 shown upon the diagram may be called the visual angle of the window. If the thickness of the wall is increased the visual angle is restricted and consequently the length of time during which the window will admit sunlight is diminished. 4 8 ORIENTATION OF BUILDINGS By increasing the width of the opening the visual angle may be enlarged but will always be less than 180 . Fig. 31. — Chancel window, Great Casterton Church, Rutland; from An Analysis of Gothick Architecture, by R. and J. A. Brandon. London, 1849. The full visual angle of 180 can only be obtained in the oriel or bay window. We are accustomed to think of bay windows as having a southerly exposure, when, as a SHADOW DIAGRAMS 49 matter of fact, their greatest usefulness is found when they are projected from the north side of a building to catch the oblique rays of the morning sun, which would be shut out of a window set in the plane of the wall. Bay windows are of great use also for city buildings upon narrow streets, where the buildings opposite shut out the sunlight except when it falls in an oblique direction from either side. The visual angle of a window may be increased by beveling the jambs, with the advantage that the light is increased without any increase in the glass surface, and consequent loss of heat by radiation. The advantage of the beveled jamb was well understood by the mediaeval builders (Fig. 31). 10 i_j 1 1 1 1 — 1 — i— i— i— 1 FEET Fig. 32. — Wall section of factory building on Swett St., Boston. Fig. 32 illustrates the wall section of a factory building designed by the author, in which the piers between the windows are reduced to a minimum width and are also beveled, affording the maximum of light. For the following series of window diagrams a window has been assumed 3 ft.— 6 in. wide, and 8 ft.-o in. tall, with a wall thickness of 1 ft.-o in., giving a visual angle ORIENTATION OF BUILDINGS of i48 c -6' and a normal area of opening of 28 square feet. The diagrams (Figs. 33 to 35) represent the plan of a room 24 feet square, lighted by a single window of the dimensions given and with the window sill at a height of 2 feet above the floor. * v \ V. 1/ ''' ' \\ \ \ Fig. 11. — Showing the area of floor subject to direct sunlight, for windows of different aspects; winter solstice; Lat. 42°-o' N. SHADOW DIAGRAMS 51 The parallelograms in dotted lines, somewhat resembling a deformed pack of cards spread upon the floor, indicate the areas in sunlight at successive hours, and the curved figures resulting therefrom the whole area subjected to iiiiiiinniin IjTlTffm^iiiii^HtnilTill Fig. 34. — Showing the area of floor subject to direct sunlight, for windows of different aspects; autumnal and vernal equinox; Lat. 42°-o' N. 52 ORIENTATION OF BUILDINGS sunlight, for the various exposures and at the various seasons indicated. If the room of our diagram were carpeted with a dark material having the property of becoming instantly bleached by exposure to direct sunlight, it would present +^-■""""'.--'1 bfl */ y ..,,,'■ i ' 1 \ Fig. 35. — Showing the area of floor subject to direct sunlight, for windows of different aspects; summer solstice; Lat. 42°-o' N. SHADOW DIAGRAMS 53 an appearance at the end of the day corresponding to these diagrams. The rays of sunlight passing through any aperture, as a window, form a prism, the cross section of which changes as the angle of sunlight changes. The area of such a cross section is the normal area of the aperture for the admission of sunlight at the particular instant at which it is taken. The cross section of such a prism may be found by descriptive geometry. vi vii viir ix x xi Fig. 36. — The parallelograms in the lower part represent the cross sections of the sunlight prism of an east window, for the hours indicated, at the autumnal and vernal equinox. The figure in the upper part is a graphic representation of the total quantity of sunlight admitted by the window, and is identical with the corresponding one of Fig. 38, but at a larger scale. Dimensions of window: 3 ft.— 6 in. wide, 8 ft.-o in. tall, and 1 ft.-o in. wall thickness. The parallelograms in the above diagram (Fig. 36) rep- resent the cross sections of the sunlight prism of an east window of the dimensions assumed, taken at intervals of one hour, at the period of the equinoxes. 54 ORIENTATION OF BUILDINGS The areas of these sections are as follows: a.m. Square Feet. 6 28.00 7 25.05 8 20.39 9 14-50 10 7-86 11 1-35 11. 17 o. These areas may be represented by lines of varying length and are so represented by the vertical lines above them. Joining the extremities of these lines by a curve, we obtain a figure the height of which at any point will repre- sent the area of the sunlight prism at the corresponding hour, and the area of the whole figure the total amount or quantity of sunlight admitted by the window during the day. It is in this manner that the figures of the succeeding diagrams (Figs. 37, 38, and 39) have been drawn. 1 In order to compare these areas we will take as a unit the quantity of sunlight which passes through an opening one foot square, in a plane normal to the sun's rays, in one hour. The areas of the figures may then be expressed in terms of this unit, which for convenience we will call a sun hour, as in Table II. The heating effect of the sun hour will, of course, vary with the altitude of the sun and atmospheric condi- 1 Each division of the vertical scale in these figures corresponds to ten square feet. N N E ^ E . >s ■^ >$ E ;:..-■■/'-. ^ ^^v. III ^~~ ! „._ __ -■:■ 1 :■:-::: III; "[r 1 " -~^]fjS S }N J - ■^ z^zi: \ \l Winter Solstice. Equinoxes. Summer Solstice. North Northeast and northwest East and west Southeast and southwest 32.9 108.5 152.9 18.6 82.7 IOS-5 81. 1 6.8 73-2 no. 7 53-4 16. 2 South An average of twelve observations taken at the Astro- physical Observatory in Washington in 1902-3, under the direction of Mr. C. G. Abbot, 1 gives the intensity of the solar rays at the earth's surface in the afternoon, as 1.24 small calories per square centimeter per minute. Trans- posing this value, we obtain for the energy contained in a prism of the sun's rays one foot square in section shining for one hour (the sun hour of our diagrams), the equiva- lent of 274 British thermal units; an amount of energy, which, if it could be entirely converted into heat would be sufficient to raise one gallon of water 33 F., or 150 cubic feet of air ioo° F. in temperature. The determination of the solar constant, or the intensity of the solar rays in space, at the mean distance of the earth, is one of the most difficult problems in physical science, since the amount of heat absorbed by the earth's atmosphere cannot be directly measured, but must be cal- culated theoretically. It may well be that the term solar constant is in it- self an unwarranted assumption and one that has tended 1 Smithsonian Miscellaneous Collections, Volume XLV. SHADOW DIAGRAMS 59 to mislead the experimenter, since recent investigations appear to show that the heat emitted from the sun is not steadily uniform but fluctuates in some degree, in a man- ner not yet satisfactorily accounted for. The foregoing diagrams are calculated for windows with unobstructed outlook. The effect of an obstruction will now be considered. Fig. 40. — Showing the obstructed horizon of city buildings. No sunlight can come into the window until the plane of the sun's rays has reached the altitude AP. As an example of obstructed outlook, frequent in cities and towns, we shall take the case of a lower-story window facing a row of buildings 60 feet away. We shall assume the cornice line of these buildings to be 40 feet above the ground and to extend indefinitely in both directions from the point opposite our window. The assumed conditions are shown in Fig. 40. 60 ORIENTATION OF BUILDINGS It is clear that no sunlight can come into the window until the plane of the sun's rays has reached the altitude AP, but that after the altitude BP has been reached the obstruction will have no further effect. The hour angles corresponding to these altitudes may be calculated. Let it be required to find the time at which the sunlight will first come into a window with an east exposure, under the conditions assumed in the diagram, and at the period of the winter solstice. The angular altitude of the obstruction above the top of the window {i.e. the slope of the line AP) is found by measurement to be 22°-37' and the problem consists in determining the hour angle at which the plane of the sun's rays will reach this elevation. For the purpose of representing the problem it will be convenient to use the stereographic projection (Fig. 41). The enclosing circle is the horizon; NS the meridian; P the celestial north pole; the dotted circle the path of the sun at the winter solstice, and NXS a great circle of the sphere formed by a plane intersecting the plane of the horizon on the north and south line and making an angle of 22°-^' with it. The intersection of this circle with the dotted circle (at the point X) determines the position of the sun required, and the calculation of the spherical triangle SPX gives us the hour angle (at P) which we find to be /\o°-/[Y , corre- sponding to 9 I1.-17 m. a.m. solar time. Similarly the hour angle corresponding to the elevation BP is found to be 35°-32' or 9 I1.-38 m. solar time. In SHADOW DIAGRAMS 61 other words, the effect of the obstruction is to cut off all sunlight from this window until 9 h.-i7 m. a.m. and a portion of the sunlight from 9 I1.-17 m. to 9 I1.-38 m., after which the obstruction ceases to have any further effect. Fig. 41. — Use of the stereographic projection to represent the conditions shown in Fig. 40. In the case of the southeast window the obstruction is complete until 10 I1.-27 m. and partial until 11 h.-20 m. In the case of the south window the obstruction is com- plete before 10 h-24 m. a.m. and after 1 h-36 m. p.m., between which hours the obstruction is partial. 62 ORIENTATION OF BUILDINGS For the southwest and the west windows the effects correspond to those for the southeast and east windows. The results are shown in diagrammatic form in Fig. 42. -^. ^"v.^ 1 Jte Ifesw — -^ "■S. " E /m \^ --+-. ^' .-•^ s 1 -^-^ ■~-^_ r" 1 1 -I 1 1 1 ^^ --> 1 s '^ 1 1 1 ! 1 1 y^ V / ^ ** j ^m \ V [IV. [II I X ) Li I X II II III I 1 V A T Fig. 42. — Showing the quantity and duration of direct sunlight admitted by a window with obstructed outlook, under the conditions shown in Fig. 40, for different exposures; winter solstice; Lat. 42°-o' N. The full areas of the figures are identical with those of Fig. 37; the shaded portions show the quantity of sun- light admitted by the obstructed window. It may be noted from these window diagrams that the unobstructed south window in winter admits more sun- SHADOW DIAGRAMS 63 light than any of the other exposures, at any period of the year, while the same window in summer admits less than any of the other exposures, except the north. The effect of obstruction, however, is serious upon the south window in winter, when sunlight is most to be desired. The southeast and southwest windows partake to some degree of the character of the south window, in that they show a maximum in winter and a minimum in summer, although the variation is not as great as in the south window. The east and west windows on the contrary show a maximum in summer and a minimum in winter, and are consequently less desirable exposures than the south, south- east, or southwest. The results thus theoretically obtained may be confirmed in a striking manner with a sun box. A sun box is essentially a box or chamber of non-heat- conducting material, having on one side a window or light of glass, sealed tight to prevent air leakage. Such a box, when the window is turned toward the sun, will accumulate heat much faster than it is lost by radiation. Fig. 43 illustrates the construction of the sun boxes employed by the author in experiments at Boxford, Mas- sachusetts (Lat. 42°-4o' N.). Two of these boxes were made, as nearly alike as possible. They were constructed of ordinary pine boards § inch thick, nailed together, without grooving or dovetailing. The inner box (1 foot square, inside measurement) 64 ORIENTATION OF BUILDINGS was covered with one thickness of lino-felt (a non-heat- conducting material made of flax fiber quilted between two thicknesses of building paper). Fig. 43. — Cross-section of sun box. A. Hood or cover. B. Outer box. C. Air space. D. Lino-felt. E. Inner box. T. Thermometer. S. Shield. The sash (glazed with |-inch plate glass) was screwed into place and fitted tightly against a felt weather strip all around the edges. The boxes were painted on the outside one coat of white paint and were shielded from the sun's direct rays, except on the window side, by wooden hoods or covers. SHADOW DIAGRAMS 65 The temperature of the air inside the boxes was shown by a thermometer on the rear wall, in front of which was placed a wooden screen, sufficiently tall to shield the bulb from the sun's direct rays, while permitting the scale to be read from the outside. 1 Fig. 44. — View of sun boxes. The boxes were exposed to the sun on a platform about three feet above the ground, in an open field, with free access of sunlight from every quarter (Fig. 44). The platform was marked with a system of lines running north and south, and east and west, with diagonals in both 1 The protecting covers and thermometer shields were omitted in the first few experiments. 66 ORIENTATION OF BUILDINGS directions, so that it was a simple matter to set the boxes facing in any direction desired. In the earlier experiments the boxes were unsealed at the close of each day and allowed to remain until the temperatures were the same in each, when they were again sealed up and set for the next experiment. In the later experiments this was not done, as it was found that the temperatures became equalized by radiation during the night. Notwithstanding the fact that the boxes were of the same shape, size, and construction, it was found that there was a difference between them, as shown by the experi- ments of July 14 and 15, in which both boxes were set for the same exposure and yet showed a difference of several degrees in temperature under apparently the same con- ditions. For this reason the experiments do not afford an absolute basis of comparison between different exposures, such as might be obtained with apparatus more carefully made and experiments more carefully conducted. By comparing the records for the same box, however, the relative efficiency of the same exposure at different periods of the year is shown with sufficient exactness, and follows quite closely the theoretical conclusions deduced from the diagrams. SUN BOX RECORDS The following is a record of experiments made with these boxes during the season of iqio. All of them (except as noted) were made on clear, bright days, with few or no clouds. All temperatures are in degrees Fahrenheit and all hours in solar time. 67 68 ORIENTATION OF BUILDINGS JUNE 26 Time. Air. Box A, East. BoxB, South. A.M. I 1 5-48 63 72 54 2 6.36 66 80 57 3 7.08 74 IOO 62 4 8. 73 124 68 5 . 9-38 P.M. So 122 -85 6 12.33 85 I05 no 7 i-33 85 I05 112 8 2.23 85 I03 108 9 3-53 85 IOO 104 10 6.58 72 85 85 11 7.18 70 83 83 Remarks. — No hoods on boxes. No shield for thermometers in boxes. 1. Both boxes wet with dew. Glass wet on B. Sun partially obscured by haze. Later on the haze wore off and it was a fine day, with flying clouds. JUNE 29 Time. Air. Box A , East. Box B, Southeast. A.M. I 5.28 62 90 54 2 6.20 69 114 67 3 7-33 71 138 92 4 8.28 71 137 97 5 9.28 72 123 114 6 10.28 75 117 117 7 11.28 P.M. 76 107 114 8 1 -13 77 IOO 103 9 3-i3 77 93 95 10 4-43 77 • 90 9i n 6.28 78 85 86 12 9-13 52 66 65 Remarks. — No hoods on boxes. Remarkably clear day. 1. Glass of B covered with dew. 2. Dew has disappeared. 5. Glass on A misty. 7. Glass on A clear. No shields for thermometers in boxes. SHADOW DIAGRAMS 69 JUNE 30 Time. Air. Box A , West. Box B, South. A.M. I 7-7 78 62 64 2 9.17 82 78 88 3 10.42 82 88 102 4 11.42 P.M. 84 94 no 5 I. 12 84 102 112 6 2. 17 86 118 no 7 3-i7 84 138 IOzl 8 4.27 84 144 100 9 5-27 80 98 10 6.27 72 112 88 11 6-57 67 102 85 Remarks. — No hoods on boxes. No shields for thermometers in boxes. 8. The temperature of 144 recorded in Box A is the highest which the thermometer registers. 9. Glass in A misty so that thermometer cannot be seen. JULY s Time. Air. Box A , South. Box B, Northeast. A.M. I 6.06 72 47 80 2 7.06 72 54 98 3 8. 11 80 70 108 4 9. 11 84 82 no 5 10. 11 84 99 108 6 11. 41 B.M. 84 no 106 7 12.41 86 116 106 8 1. 41 87 117 104 9 2.26 88 ■ 116 102 10 4. II 86 106 100 n 5-H 86 102 96 12 7-5i 64 84 82 Remarks. — No hoods on boxes. Clear day. 1. Glass of A covered with dew. 7° ORIENTATION OF BUILDINGS JULY 7 Time. Air. Box A , South. Box B, East. A.M. I 6. ii 55 48 85 2 7.00 63 55 108 3 7-31 68 60 115 4 9-36 82 84 132 5 10.41 86 96 122 6 11. 41 P.M. 86 106 112 7 12.41 88 112 I06 8 I . 26 90 112 I02 9 3.0I 88 108 98 IO 3-51 84 100 94 ii 4.46 98 98 96 12 5-41 92 94 92 Remarks. — No hoods on boxes. Perfectly clear day. 11. Air thermometer in direct sunlight.., 12. Air thermometer in direct sunlight. JULY ro Time. Air. Box A , South. Box B, East. A.M. I 5-36 62 62 68 2 7-5i 80 72 no 3 8.26 84 77 117 4 9.26 91 87 124 5 10. 26 96 99 124 6 11 .41 P.M. IOO no 118 7 12.41 102 116 114 8 I .06 IOO 117 112 9 i-5i IOO 118 109 10 2.41 95 114 106 11 3-4i 94 no 104 12 4-51 91 i°5 IOO Remarks: — 1. Slight haze: humidity high. 7. Floating clouds. 8. Floating clouds. 9. Thunder clouds. 12. Clear: good breeze. SHADOW DIAGRAMS 71 JULY 14 Time. Air. Box A , East. Box B, East. A.M. I 6. 10 61 98 100 2 6.50 71 118 121 3 7.40 74 126 131 4 8.10 78 132 136 5 g.io 80 136 138 6 10.10 88 138 138 Remarks. — Clear day. Boxes placed side by side, B being to the north of A . JULY 15 Time. Air. Box A , East. Box B, East. A.M. 6-55 68 102 I02 7-35 70 "5 117 8.10 76 124 126 0. 10 80 132 130 10. 10 82 128 128 Remarks. — Somewhat cloudy in early morning placed side by side, A being to the north of B. clear later. Boxes JULY 20 Time. Air. Box A, East. Box B, Southeast. A.M. 5- 5° 60 52 6.40 59 105 76 7- °5 62 114 84 7-35 65 120 94 7-55 68 126 102 8.25 70 122 IO4 8. 55 76 Il8 I06 9- 2 5 76 Il8 I08 9-55 78 I20 no 10.25 78 no 112 11 . 10 76 106 no n-55 78 I02 108 P.M. 12.25 78 96 100 2.25 78 86 86 3-55 78 82 82 Remarks. — Clear day. 72 ORIENTATION OF BUILDINGS JULY 21 Time. Air. Box A , Southeast. Bos B, East. A.M. I 5- 56 54 56 2 ) 6.40 64 74 96 3 7-05 66 82 105 4 7-35 68 9 1 116 5 8. 72 98 129 6 9- 76 no 128 7 10.45 86 120 118 8 11.45 P.M. 90 118 112 9 12-35 94 112 108 IO 2-15 90 102 102 ii 3-3° 86 98 98 12 5.20 80 90 90 Remarks: 1. Sun rising through cloud bank. 3. Perfectly clear. JULY 24 Time. Air. Box A, Southwest. Box B, Southeast. A.M. 8.04 78 67 86 8.44 84 72 98 9-34 88 78 108 10. 19 9° 85 116 10.54 94 92 118 n-54 99 104 120 P.M. i-39 98 III 112 2.49 96 114 107 4-39 94 122 102 5- 94 121 IOI 5-24 92 116 100 Remarks. — Somewhat cloudy day. SHADOW DIAGRAMS 73 AUGUST 7 Time. Air. Box A , South, BoxjB, East. A.M. I 7-45 68 61 121 2 8-35 72 68 I30 3 9- 71 73 I30 4 9-35 P.M. 76 81 129 5 12. IO 8l 105 108 6 i-45 ■ 83 104 102 7 4.40 77 96 90 8 6-35 68 84 80 Remarks: 3. Sun behind thin clouds. 6. Sun behind clouds. AUGUST 21 Time. Air. Box A , West. Box B , Southeast. A.M. 8.28 72 56 104 9-!3 75 60 114 10.13 80 67 123 11.08 80 72 125 P.M. 1 -13 81 88 no 1-53 79 97 104 2.08 76 118 94 3-33 76 123 9i 4-i3 76 132 6.48 67 103 76 Remarks. — Clear day. 74 ORIENTATION OF BUILDINGS AUGUST 28 Time. Air. Box A , South. Box B , Southeast. A.M. I ■> 7 14 65 46 76 2 8 29 7° 61 102 3 8 59 72 68 no 4 9 29 74 77 116 5 - 11 14 78 114 123 6 11 50 78 112 119 P.M. 7 12 . 20 80 117 118 8 12 .40 80 117 114 9 i-5° 82 120 107 10 2.30 S3 11S 103 11 5- 70 95 86 12 7-14 63 75 72 Remarks: 6. Slightly cloudy. 7. Clear again. 8. Slightly cloudy. 9. Slightly cloudy. 10. Clear. SEPTEMBER 18 Time. Air. Box A , South. Box B, East. A.M. 6.31 47 44 57 7.40 60 5i 97 8.46 68 68 112 9. II 69 75 114 936 72 85 114 IO.51 76 104 106 II . 26 77 113 102 P.M. 12.51 82 127 95 2. l6 81 127 93 3.06 82 122 92 4.l6 80 no 89 5.06 76 100 85 7.l6 70 82 76 Remarks. — Clear day. SHADOW DIAGRAMS 75 OCTOBER 24 Time. Air. Box A , South. Box B, East. A.M. 6.19 32 32 32 7- 36 33 45 7-46 39 42 70 8. 11 4i 50 80 8.31 42 58 87 9.04 44 70 92 9-3 1 45 79 93 10.46 5° IOI 85 11. 51 5 2 116 74 P.M. 12. II 55 119 72 I. II 57 123 68 1-33 58 125 67 i-5S 59 125 67 2. 11 59 124 66 3-03 58 107 64 4.41 53 84 60 6.31 46 63 52 Remarks. — Remarkably clear day. DECEMBER 22 Time. Air. Box A , South. Box B, East. A.M. I 9-47 16 56 45 2 10.57 P.M. 20 88 46 3 12.52 24 114 38 4 I .42 25 "5 44 5 3.22 24 94 33 Remarks. — Clear day. . 4. The reading in Box B is probably an error. 7 6 ORIENTATION OF BUILDINGS 6789 10 11 12 123456 100 JUL. 7 100 ^-— ~"">> > o o-'g oj a § J T3 >-, tn . a 5 - ? 8 to £ J I T3 •--a. tn O to -a •£ q rt "C "S 5 "5 '3 P P to tn *j - "3 ,S - A a3 i- to to 3 5 .£ £ -^ CJ 43 - tn O « . _~ 2 toQ a to 3^ C 3 u . ra H 112 ORIENTATION OF BUILDINGS / / ^e i/i .3 o h-3 o £ x r| *sD +j c 3 bO tn C E g 5 & -3 STREETS 113 IO 6 c3 1 M * y bO \ y 1 / «* 73 \ / _rt S 1 o """? fe ii4 ORIENTATION OF BUILDINGS sunlight curves. The method of obtaining these curves is shown in Fig. 69. This is a cross section of a street running southeast- northwest, taken looking northwest. (. t fre_Sun ^ Fig. 69. — Cross section of street running southeast and northwest, looking northwest. The angles of sunlight are shown as they would be at the summer solstice. Lat. 42°-o' N. The dotted lines represent the plane of the sun's rays at the hours noted. It is clear that the point of inter- section of these lines first comes into sunlight at 9 a.m., remaining in sunlight until 5 P.M., a period of eight hours. STREETS 115 By finding a series of such points and connecting them, we shall obtain the curve shown, each point of which is in sunlight for eight hours, and may, therefore, be called the "eight-hour curve." It is in this way that the following series of diagrams have been drawn (Fig. 70). These diagrams give the complete series of sunlight curves at the typical seasons of the year, for streets run- ning north-south, east-west, and at an angle of 45 with the meridian. In these diagrams the height of the buildings is rep- resented as one and one-half times the width of the street. The diagrams show a great difference in the amount of sunlight received. In the north-south street the distribution is symmetrical, the buildings on either side receiving an equal amount. In the. east-west street the surface of the street receives no sunlight at all during six months of the year, and the buildings on the south side of the street are in perpetual shadow during the same period. In city planning the east-west street should be avoided as far as possible, and where unavoidable the buildings, especially on the south side, should be of moderate height, and built in detached blocks, so as to admit the sunlight between them. When streets are laid out at right angles to each other according to the "checkerboard" plan, the best distribution of sunlight is obtained when one series of streets runs north- east-southwest and the other riorthwest-southeast. n6 ORIENTATION OF BUILDINGS ^ Fig. 70. — Sunlight curves in streets. Ihe three upper diagrams are for a street running north and south, the three middle diagrams for a street running east and west, and the three lower diagrams for a street running at an angle of 45 degrees with the meridian. The diagrams of the left-hand column are drawn for the winter solstice; of the center column for the vernal and autumnal equinox; and of the right-hand column for the summer solstice. , The zones between the curves are shaded in a series of tints, the lightest zone being in sunlight between eight and nine hours, and the solid black being without sunlight. STREETS 117 This arrangement was recommended many years ago by Horace Bushnell. In his essay on City Plans 1 occurs the following passage: "It is also a great question, as respects the health of the city, in what direction, or according to what points of the compass, the streets are to be laid. To most persons it will appear to be a kind of law that the city should stand square with the cardinal points of the compass, — north and south, east and west. And where this law appears not to have been regarded, how many will deplore so great an oversight, and even have it as the standing regret of their criticism. Whereas, in the true economy of health and comfort, no single house or city should ever stand thus, squared by the four cardinal points, if it can be avoided. On the contrary, it should have its lines of frontage northeast and southwest, northwest and south- east, where such a disposition can be made without injury in some other respect; that so the sun may strike every side of exposure every day in the year, to dry it when wet by storms, to keep off the mould and moss that are likely to collect on it, and remove the dank sepulchral smell that so often makes the tenements of cities both uncomfortable and poisonous to health." It is unfortunate that in so many cases where the "checkerboard" plan has been adopted, the streets have been laid out north-south and east-west, which is the worst arrangement possible. The effect of tall buildings in cutting off sunlight and sky light from buildings on the opposite side of the street, 1 Work and Play, Horace Bushnell, N.Y., Charles Scribner, 1864. Il8 ORIENTATION OF BUILDINGS and from the street itself, is considerable, and in the building laws of most European cities a definite relation has been established between the width of the streets and the height of the buildings which may be built upon them. An admirable example of such a regulation is found in the building laws of Paris, in which the matter is worked out with a precision and completeness well worthy of study. 1 The accompanying diagram (Fig. 7.1) illustrates its appli- cation to a street 16 meters (52.48 feet) in width. The main structure of the building must be built within the limits of the heavy enclosing line, which is determined as follows: The height of the vertical AA is taken at 6 meters plus the width of the street, for streets less than 12 meters in width, and for streets over that width it is taken at 18 meters, plus one-quarter of the amount by which the width of the street exceeds 12 meters, but must not exceed 20 meters (65.60 feet) in any event. For a street of 16 meters the height AA will, therefore, be 19 meters (63.32 feet). From the top of this line a circular arc is drawn, and tangent to it a line of 45 inclination. This tangent is extended until it meets a vertical halfway back in the building or until it meets a similar tangent determined by the frontage of the rear portion of the building. The radius of this arc is taken at one-half the width of the street, but may not exceed 10 meters (32.80 feet) in any event. A similar regulation governs the rear facade of the build- 1 The Paris law is given in full in Appendix B, STREETS IIQ ing and also all frontages on light courts and areas, the result being an abundance of light and air throughout the structure. Fig. 71. — Diagram illustrating the building regulations of Paris, applying to the height of buildings. The vertical A-A and the radius of the circular arc vary with the width of the street. The horizontal B-B marks the limit of height for party walls, and the vertical line above the curve and just back of the front wall line, marks the setback for chimneys. The lighter enclosing lines beyond the heavy line mark the limit of projection for balconies, cornices, and other projec- tions from the main structure. In England the matter is regulated in two ways: directly, by building by-laws limiting height, varying in different cities and for different classes of buildings; and indirectly, 120 ORIENTATION OF BUILDINGS by the statute law of ancient lights. Under this law an owner or tenant of a building may acquire a right to light coming across the property of another, just as in this country a right of way across the land of another may be acquired by prescription. "Cujus est solum ejus est usque ad ccelum" is an ancient maxim of our common law, and in the words of an English writer, "An interference with the space superincumbent on a man's land is an injury for which the law provides a remedy." In England the deprivation of light is regarded as such an interference, actionable at law, but in this country the individual owner, where not restrained by specific statutes, is allowed to build as high as he pleases, regardless of the injury done to his neighbors and to the public, and even the right of a municipality to impose a limit to the height of buildings has been contested. A recent decision (May 17, 1909) of the Supreme Court, 1 however, upholds the constitutionality of such building laws, and even that city which has taken a mistaken pride in having originated the "skyscraper" type of architecture has recently imposed a maximum limit of 210 feet to the height of its buildings. In my own city of Boston a law has been in force since 1892 limiting the height of buildings generally to two and one-half times the width of the street, with a maximum limit of 125 feet; and subsequent legislation has reduced this limit in certain districts of the city. 1 Welch vs. Board of Appeal of the City of Boston. U. S. Reports, Vol. CCXIV, page 91. STREETS 121 The regulations of some other American cities in this regard are given in Appendix C. The method of limiting the height of buildings by a horizontal plane, either at a fixed height, or at a height proportional to the width of the street, is simple in appli- cation but is not scientific, since it assumes that what is the proper height for the front wall or facade is also the proper height for the rear portions of the building; whereas, as a matter of fact, the rear portions may well be allowed to rise to a greater height, in proportion to their distance back from the street line. This method also results in an uninteresting and hard type of architecture. The land owner, intent on securing every foot of rentable space, duplicates one story on top of another, with the usual result that the cornice is forced above the level of the real roof as shown in Fig. 72, cutting off the sunlight and darkening the street unnecessarily. This false position of the cornice constitutes the dis- tinguishing mark of ordinary American civic architecture, and is the direct result of unscientific building laws. Although a building law designed solely for the purpose of securing an aesthetic effect would probably be decided to be unconstitutional in this country, it fortunately hap- pens that in the matter of regulating the height of build- ings, that method which naturally results from a scientific study of the question of sunlight also tends to produce the best type of architecture. A method which has been proposed by several architects, and which has also been advocated by the writer, is illus- trated in Fig. 73. 122 ORIENTATION OF BUILDINGS Under this plan the height of the building is limited by a slanting line drawn from the opposite side of the street at a certain angle. This angle should be, in the opinion Fig. 72. — This type of cornice is typical of x\merican commercial architecture. It is not really a cornice but a distorted parapet wall, and is also bad from the practical point of view because it cuts off the sunlight unnecessarily. It is the direct result of unscientific building laws, which apply the limit of height to the highest point of the roof, often several feet below the top of the exterior walls of the building. of the writer, such that the height of the front wall of the building should not exceed one and one-quarter times the width of the street, and it is so shown in the diagram. STREETS 123 H - & > 2 S x: r9 - S rt *2 c3 K >>x! 2 -?. a

< _c^ T3 ■^ B -*-> O ol M X C a -n T3 'm s C , ^ /= fs >> — cj rU ^3 c "^ M "^ *S XT' •— <-> ^ C " CJ O O .£P .S S o3 3 S h ,J3 > XI >> ^3 c Tl — 1/ d HI r > E UJ O rt 60 en bl I) bo CJ — *fi 3 C 1- ._ X '/, J3 4-> -= c3 to -4-> XI c rl Xi to -S *J > W Xj £ « to-= •S x xi 72 "33 x -g •53 g •5 g X T3 g rf a « ' g H X CJ +-> 124 ORIENTATION OF BUILDINGS In addition to the slanting line the extreme height of the roof is limited by a horizontal plane at a height uniform for all buildings, irrespective of the width of the street. Fig. 74. — The skyscraper and the street. The left-hand diagram is a cross section of a street bordered by buildings of reasonable height; the right-hand diagram a street with a wall of sky scrapers on either side. The street is supposed to run east and west and the shadows show the angle of sunlight throughout the day, at the vernal and autumnal equinox. Lat. 42°-o' N. A similar method may well be adopted to regulate the walls of the building fronting on light courts and areas, and for this purpose an angle of less inclination from the vertical may be justified. In discussing the question as to what should be the limit of height of buildings in cities it is proper to assume that both sides of the street will in time be built up to whatever limit is decided upon. The effect of a few scattered tall STREETS 125 buildings in darkening the streets is not serious, but the effect of a solid wall of skyscrapers would be extremely so. In the accompanying diagrams (Fig. 74) is shown the section of a street 60 feet wide, in the one case bordered with buildings 250 feet high and in the other with buildings regulated in accordance with the building law proposed by the author. Which of the two should be typical of the American city planning of the twentieth century is left to the judgment of the reader. APPENDIX A Sun Tables Winter Solstice. Equinoxes. Summer Solstice. Hour angle. Az. Alt. Az. Alt. Az. Alt. 120° 127 42' i° 21' I05 ° Il6° 4' 9° 3o' 90° 90 0' o° 0' 105° 7' 18 7' 75° 78 10' 9° 23' 94° 0' 27 20' 6o° 65° 4l' 18 5' 82 2' 36 ° 40' 45° 40 40' 5° 14' 51° 57' 26 6' 68° 10' 45° 39' 3°° 27° 59' io° 25' 36° 25' 32° 36' So° 48' 53° 43' iS° 14 9' 13° 48' 18° 54' 36° 58' 28 2' 59° 4o' o° o° 0' 15° 3' o° 0' 38° 30' o° 0' 6i° 57' Sunrise and Sunset 3h. 48 m. 5o° 16' o° 0' 6h. m. 90 0' o° 0' 8h. 12 m. 129° 44' o° 0' London. Lat. 51 30' N. 126 APPENDIX A 127 Winter Solstice. Equinoxes. Summer Solstice. Hour angle. Az. Alt. Az. Alt. Az. Alt. 90° 9 o° 0' o° 0' «o° 35' 11° 27' 75° 62 ° 24' o° 22' 82 22' 12° 57' 104 18' 23° 52' 6o° 54° 9' ii° 20' 73° 54' 25° 39' 98 16' 36 36' 45° 44° 7' 21° 16' 63 ° 26' 37° 46' 9i° 47' 49° 32' 3o° 3i° 44' 29° 3' 49° 6' 48 ° 36' 83° 27' 62 30' 15° 16° 47' 34° 4i' 28 11' 56° 47' 67° 29' 75° 6' o° o° 0' 36° 33' o° 0' 60° 0' o° 0' 83° 27' Sunrise and Sunset 5 h. 2m. 6 h. o m. 6 h. 58 m. 62 38' 90 117" 22' New Orleans. Lat. 30 o' N. APPENDIX B DECREE REGULATING THE HEIGHT OF BUILDINGS AND PROJECTIONS FROM THE SAME IN THE CITY OF PARIS. August 13, 1902 Article i. The limits beyond which buildings upon the public ways of Paris are not allowed to project is fixed: first: by two "limiting cross sections" established, one for the structure proper, and the other for pro- jections forming an integral part of the structure; second: by special rules set forth under Title II, Sections III and IV of this decree, for projections not forming an integral part of the structure. TITLE I HEIGHTS OF BUILDINGS First Section. Buildings on Public Ways Art. 2. The "limiting cross section" of the structure proper is deter- mined by a vertical line erected on the front line of the lot. The height of this line, measured from the sidewalk level or the level of the pavement at the foot of the facade and taken at the middle point of this facade, is calculated thus. For streets less than 12 meters (39.36 feet) in width, the height must not exceed 6 meters (19.68 feet) plus the width of the street. For streets of 12 meters and over this height must not exceed iS meters (58.64 feet) plus one-quarter of the amount by which the width of the street exceeds 12 meters, but must not in any case exceed 20 meters (65.60 feet). In calculating this height a fraction of a meter in the width of the street is taken at one meter. On sloping streets the facade of the buildings is divided into sections not exceeding 30 meters (98.40 feet) and the height of each section is taken in the middle. 128 APPENDIX B 129 In the case of several distinct buildings the height of each is taken sepa- rately according to the above rules. Art. 3. The "limiting cross section" referred to in the preceding article is completed by a circular arc, tangent to the vertical line, at its highest point, and by another line tangent to this circular arc. The radius of the circular arc is taken at half the width of the street but must not exceed 10 meters (32.80 feet). However, for streets less than 12 meters (39.36 feet) it need not be reduced to less than 6 meters (19.68 feet). The other line referred to, tangent to this circular arc, is drawn with an inclination of 45 degrees until it meets a vertical erected in the middle of the depth of the building, taken at the ground floor level. However, it is allowed, if desired, to prolong this inclined line until it meets the tangent of another such circular arc established as described above on the highest point of the vertical line referred to in Article 10. The inclination of this second tangent must also be 45 degrees. In any case, excepting for chimney stacks, the highest point of party walls between two buildings must not be built more than one meter (3.28 feet) above the horizontal tangent of the circular arc, excepting as provided in Article 6. Art. 4. At street intersections the "limiting cross section" is deter- mined according to the open space between the facades at such inter- sections, taken at right angles, and considered as the width of the street according to Article 2. But such additional height is allowed only for that portion of the facade which is opposite such open space. Nevertheless, every building built upon a corner of two streets of unequal width, whatever may be their level or slope, may be built upon the narrower street up to the height allowed for the wider of the two, provided that such additional height does not extend back on the narrower street for a distance greater than one and a half times its width. For buildings built upon a corner formed by two streets of equal width but of different slopes, the height is taken as the average for the middle points of each frontage. But frontages on which the height is taken con- formably to the level of the street on which such frontages face, as for separate buildings, need not be reckoned in determining such middle point. 130 APPENDIX B Art. 5. For buildings comprised between streets of different widths or of different levels the "limiting cross section" for each facade must be determined by the street upon which it faces. However, if the extreme distance between two such facades does not exceed 15 meters (49.20 feet) the facade upon the narrower or lower street may be built up to the "limiting cross section" fixed for the facade upon the wider or higher street. Art. 6. Chimney stacks may not be built more than one meter (3.28 feet) above the highest point of the "limiting cross section" and their front face must be at least one meter back of the front line. Art. 7. For portions of a building projecting beyond or built back of the general building line the "limiting cross section" referred to in Article 2 is based upon a street width equal to the distance between the extreme projection of the facade and the street line opposite. In such calculations, fractions of a meter are taken as equal to a meter. Buildings or sections of buildings built at the ground story or on the stories above, back of the street fine, may be built within the "limiting cross section" permitted for a street the width of which is equal to the distance between the street line opposite such building or section of build- ing, provided that there is built on the street line a solid and substantial wall at least one meter high. Art. 8. Buildings which are not built up to the "limiting cross sec- tion" permitted may be constructed in all parts as the builder desires, provided they do not project beyond such "limiting cross section." Second Section. Buildings on Areas and Courts Art. 9. Courts which furnish light and air to rooms capable of being used for purposes of habitation, either in the daytime or at night, must have an area of 30 meters (322.80 square feet) at the least. For courts which only light such rooms as kitchens the minimum area may be reduced to 15 meters (161.40 square feet). Small courts or "light shafts" serving to give light and air to rooms which cannot be used for purposes of habitation must have an area of 8 meters (86.08 square feet) at the least. APPENDIX B 131 Art. 10. The clear space opposite each window of a room serving for day or night habitation must not be less than is provided in the following table. Minimum Area of Court. Clear Space. Minimum Area of Court. Clear Space. Square Feet. 322.80 358.63 394.46 430.40 466. 23 Feet. 13.12 14. 20 15.28 16.40 17.48 Square Feet. 502 . 06 538.00 573.83 609.66 Feet. 18.56 19.68 20.76 21 .84 For buildings opposite party walls the minimum clear space opposite windows of habitable rooms is 5 meters (16.40 feet). The "limiting cross section" of buildings or parts of buildings situated on courts, composed of the same elements as indicated in Articles 2 and 3, is determined by the following table. Minimum Clear Space. Maximum Height of Vertical. Maximum Radius of Arc. Square Feet. Feet. Feet. 13.12 39 36 19.68 14. 20 42.64 21.32 15.28 45-92 22 .96 16.40 49. 20 24.60 17.48 52.48 26. 24 18.56 55-76 27.88 19.68 59-04 29.52 20.76 62.32 31.16 21 .84 65.60 32.28 Buildings or parts of buildings built in retreating stories may be built in each story according to the "limiting cross section" determined sepa- rately for that story according to the clear space opposite that story. The ground level of every court is considered independently of that of the public street or of another court. Stairway towers or bays arranged in such courts may project beyond the "limiting cross section" as above determined up to the ceiling level of the highest story served by such stairway. 132 APPENDIX B Art. ii. In the case of courts which only furnish light and air to such habitable rooms as kitchens, the dimensions of the "limiting cross section" may be modified as per the following table. Minimum Area of Minimum Clear Maximum Height of Maximum Radius Court. Space. Vertical. of Arc. Square Feet. Feet. Feet. Feet. . 161 .40 6.56 39 -3 6 19.68 179. 26 7.08 42.64 21.32 197.23 7.64 45-92 22 .96 215 . 20 8.20 49.20 24.60 233.06 8.76 52.48 26.24 251-03 9.28 55-76 27.88 269 . OO 9.84 59-04 29.52 286.86 IO.36 62 .32 31.16 3 4.83 IO.92 65.60 32.28 Art. 12. The vertical walls of "light shafts" may be built to the height determined for the building in general. The clear space opposite windows in "light shafts" must not be less than 1 m. 90 (5.33 feet). Kitchens of the concierge on the ground floor may take their light and air from "light shafts." On the top story of buildings habitable rooms may take their light and air from "light shafts." Art. 13. In any case the minimum area of light courts and shafts as determined by Article 9 may not be diminished by new construction or selling of property. Art. 14. Glass roofs may not be built over light courts or shafts above the rooms which take their light and air from them, whether rooms of habi- tation, kitchens or water closets, unless such glass roofs have monitor ventilating sash with a clear opening of at least one-third the area of the court and of a minimum height of 40 centimeters (15.72 inches), and unless also there are arranged at the bottom of such court or shaft openings com- municating with the cellar or basement having at least 8 decimeters (8.56 square feet) of area. The monitor ventilation is not required for light wells and shafts unless they serve habitable rooms, kitchens, or water closets; but light shafts, the lower part of which does not communicate with the outer air, must be ventilated. APPENDIX B 133 Art. 15. All measurements of light courts and shafts must be taken on the work. Art. 16. Owners of adjoining buildings who may have made an agree- ment to have light courts and shafts in common may build them of the dimensions prescribed in Articles 9, 10, 11, and 12 for light courts and shafts belonging to a single building. They must, in such case, notify the prefect of the Seine of their agree- ment and execute with the City of Paris, before commencing the work, an agreement to maintain such courts and shafts for their common use. Such courts and shafts may be divided by walls of a height in accordance with article 663 of the civil code. Third Section. Story Heights Art. 17. In all buildings bordering on public ways, private ways or courts, the height of the ground story and that of the next above must never be less than 2 m. 80 (9.18 feet) in the clear. The height of basements and other stories must never be less than 2 m. 60 (8.53 feet) in the clear. For the top story of a building this last height applies to the highest part of a sloping ceiling, and every room with a sloping ceiling in part must have at least 2 square meters (21.52 square feet) of level ceiling. TITLE n PROJECTIONS FROM BUILDINGS First Section. In General Art. 18. No projection may be built from any building in Paris, whether on the street line or not, so as to project over a public way, other than those authorized below. Art. 19. For buildings on the street line, the front face of party walls must always mark the street line: for this purpose there must be reserved, at a height of a meter and a half above the ground, a level surface at least 20 centimeters square. Art. 20. Dimensions of projections are fixed (saving the exceptions given below) according to the width of the street opposite the building if 134 APPENDIX B on the street line, and according to the effective width for buildings set back. All projections are measured from the street line for buildings upon the street line and from the ashlar line for buildings not on the street line. In Reckoning such width, fractions of a meter are taken as one meter. Second Section. Projections of Constructions Forming a Part of the Building Proper Art. 21. The limit of projections from the facade, for decorative features, foundations, balconies and built-out constructions, is determined by a "limiting cross section" established as follows: This "limiting cross section" is composed of two vertical lines, one relating to the upper part of the facade from a point taken at the estab- lished height as determined in Article 2, and the other relating to the lower part of the facade. The line separating these two parts, for streets of 30 meters (98.40 feet) and over is placed at a minimum height above the sidewalk of 3 meters (9.84 feet), and for streets less than 30 meters, at a height of 6 meters (19.68 feet) less one-tenth of the width of the street, above the sidewalk. The projection of the "limiting cross section" from the street line is for the upper part of the facade 8 centimeters for every meter in the width of the streets up to streets of 10 meters in width, and 60 centimeters plus ihs of the width of the street, with a maximum of 1 m. 20 (3.94 feet) for streets of 10 meters and over. The projection of the "limiting cross section" for the lower part of the facade must not exceed one-quarter of the projection of the upper part, but need not be less than 20 centimeters (7.8 inches) in any event. For the upper part of the facade, the plane of the street line must serve as the basis of all decoration and occupy, at each story, one-tenth at least of the surface of the facade of that story, after deducting bays. Art. 22. There may be established upon the upper part of facades, constructions corbeled out, whose gross area, projected on a vertical plane parallel to the facade, may not occupy in any case, more than one-third of the total upper part of said facade. For buildings having several facades upon the street, each facade shall be considered separately in such calculation. APPENDIX B *35 Each dividing section counts with either one of the facades which it separates, at the choice of the constructor. Laterally, and at the ends of buildings, the projections of the construc- tions are limited by a vertical plane forming an angle of 45 degrees with the front wall and intersecting it at 25 centimeters (9.8 inches) from the party line. Art. 23. In streets of 16 meters (52.48 feet) of width and over, the established projection of every balcony may be increased one-quarter, provided that in horizontal projection the total of all balconies does not cover more than a quarter of the surface permitted at each story. Art. 24. Notwithstanding Article 21, the decoration of the principal entrances of a building and that of the cornices of the ground story may descend to a height of 2 m. 50 (8.20 feet) above the sidewalk, with a projection equal to twice that permitted for the lower part of the facade. In streets of 20 meters and over, the decoration of the principal entrances may descend to the ground, with a projection not over twice that per- mitted for the lower part of the facade. Art. 25. Iron guards and other similar objects of iron- work intended to serve as defences on balconies may have 25 centimeters (9.8 inches) in excess of the projection allowed for the cornices, balconies and entablatures upon which they are fixed. Art. 26. Roof ornaments, such as finials on dormers, open crestings and galleries, may not project beyond the arc of a circle concentric with that of the "limiting cross section" and of which the radius exceeds that of the latter by the permitted projection of the upper part of the facade. In their total, the size of the crowning members of dormers may not exceed two-thirds of the frontage of the facade of the building, after de- ducting the crowning members of the corbeled-out structures projecting over the public way, as provided for in this decree. For the crowning members of the corbeled-out constructions, the in- crease of radius referred to above, may equal twice the maximum projec- tion permitted for the upper part of the facades, provided that spaces of habitable rooms do not exceed the limits of the concentric arc referred to above. In the three above cases, the circular arcs are prolonged by their tangents at 45 degrees. 136 APPENDIX B For corbeled-out constructions those portions of the crowning members which project above the established line of the roof may not exceed in width one-third of the portion on the facade proper. ■y Third Section. Projection of Objects not Forming an Integral Part of the Structure (This section consists of ten articles and deals with store fronts, grilles, signs, marquises, lights, rain-water conductors, etc.) Fourth Section (This contains one article, dealing with temporary structures.) TITLE HI SPECIAL REQUIREMENTS (This contains seven articles, dealing with special cases, two of which are of sufficient interest to be given in full.) Art. 38. Existing projections beyond the limits fixed by the present decree may not be repaired even in part, or restored, except within the limits established herein. Except that in certain cases, ancient objects of archeological or artistic interest, may be repaired by permission of the prefect of Seine. Art. 42. The prefect of the Seine may, in the case of private con- structions having a monumental character, or for purposes of art, science, or industry and with the approval of the "conseil general des batiments civils" and the minister of the Interior, authorize exceptions from the present decree relative to the height of buildings. He may also, following the same procedure, authorize exceptional pro- jections for buildings having a monumental character. Art. 44. The decrees of July 22, 1882, and July 23, 1884, are repealed. APPENDIX C REGULATIONS OF SOME OF THE PRINCIPAL CITIES OF THE UNITED STATES AND CANADA GOVERNING THE HEIGHT OF BUILDINGS Note. — The regulations given are those which apply to buildings of fireproof construction. Limitations of height for non-fireproof buildings primarily imposed to decrease the fire hazard, rather than to prevent en- croachments upon the light and air of the public streets, are not included in this list. All of the regulations given are those in force in 1911. Boston. — Since 1891 the height of buildings in all cities of Massachu- setts has been limited to 125 feet. Grain elevators, coal elevators, and sugar refineries are excepted, and steeples, domes, towers and cupolas are not included within the 125 feet limit. In Boston this limit of height is subject to a further restriction of 2§ times the width of the street, so that on streets of less than fifty feet in width the height must be less than 125 feet. The maximum height of 125 feet is furthermore only permitted in those portions of the city in which the greater part of the buildings are used for business or commercial purposes. The boundaries of these portions have been determined by a commission appointed for the purpose and the areas within them are known as "District A." The remainder of the city, comprising much the larger part of its area, is known as "District B" and within this district the limitations of height are as follows: On streets of 64 feet in width, or less, the limit is 80 feet. On streets exceeding 64 feet in width the height may be equal to 1 \ times the width of the street but may not exceed 100 feet. Furthermore a 137 138 APPEXDIX C height of 80 feet may not be exceeded unless the width of the building on each and every public street on which it stands is at least one-half its height. In addition to these general regulations there are other special restric- tions, as follows: On certain streets in the vicinity of the state capitol the limit of height is 70 feet. Upon a portion of Commonwealth Avenue (one of the prin- cipal parkways of the city) the limit of height is 70 feet. This latter restriction is imposed by the Park Commissioners, who have the power to impose such restrictions on any parkway, boulevard or public way bordering on a park, within the city. Winnipeg. — Xot exceeding 120 feet. Montreal. — Xot exceeding 130 feet nor over ten stories. Portland. — Xot exceeding 160 feet nor over ten stories. Baltimore. — Xot exceeding 175 feet, except by special permission of the City Council. Cleveland. — Xot exceeding 200 feet, nor more than i\ times the width of the street nor more than five times the width of the base. Chicago. — Xot exceeding 260 feet. (After July n, 1911, not exceeding 210 feet.) St. Louis. — The limit of height for all buildings other than hotels and office buildings is 2§ times the width of the street, with a maximum limit of 150 feet. The limit of height for hotels is 206 feet. The maximum limit of height for office buildings is 250 feet, but this height is not permitted unless the building covers at least one-half of the city block in which it is built, has frontages on at least three different streets, and fulfills certain stringent requirements in regard to fire protec- tion. Otherwise the limit of height for office buildings is the same as that for hotels, viz., 206 feet. St. Paul. — Xot exceeding 250 feet nor over twenty stories. Toronto. — Xot over five times the least horizontal dimension of the building. Seattle. — Xot over five times the least dimension of the base. Indianapolis. — Xo limit, except in the neighborhood of the city monu- ment, where a limit of 86 feet is imposed. APPENDIX C 139 Cincinnati. — No limit. Detroit. — No limit. Hartford. — No limit. Milwaukee. — No limit. Minneapolis. — No limit. New York. — No limit. Philadelphia. — No limit. COLUMBIA UNIVERSITY LIBRARY This book is due on the date indicated below, or at the expiration of a definite period after the date of borrowing, as provided by the rules of the Library or by special ar- rangement with the Librarian in charge. •* DATE BORROWED DATE DUE DATE BORROWED DATE DUE JUN 3 1 '40 ?m % 4 i@#- FEB 2 8 1947 '■■—. i: :*. JUL f\\V 0CT1 71949 C28'Z39)M100 ^ RA9 67 At5 Atkinson