US3700882A

US3700882A - Faceted reflector

Info

Publication number: US3700882A
Application number: US68951A
Authority: US
Inventors: Jean Planchon
Original assignee: Individual
Current assignee: Individual
Priority date: 1970-09-02
Filing date: 1970-09-02
Publication date: 1972-10-24
Anticipated expiration: 1989-10-24

Abstract

The present invention provides a reflector, e.g. for a desk lamp, which is designed to provide an unusual predetermined pattern of illumination on a surface, for instance a pattern having non-concentric isolux curves around a point of strongest illumination, and which results in a more even distribution of light over the surface illuminated. The reflector is particularly designed for uniformly illuminating a predetermined area, even at a comparatively large distance from the vertical projection of the light source on the said area. For that purpose, the reflector is built in the form of a complex surface comprising a plurality of elementary reflecting surfaces each of which has a distinct shape. The elementary reflecting surfaces are linked to one another at their upper and lower edges through continuous surfaces portions and at their lateral edges through stepped surfaces portions called redans. The horizontal and vertical traces of the tangent planes to the various points of said individual elementary reflecting surfaces are so located respectively on horizontal planes containing said various points and on vertical planes containing both said points and a predetermined point of the source of radiation which cooperates with the reflector so as to provide, on a horizontal area to be illuminated, a plurality of images of the source, said images cooperating for giving a continuous predetermined level of illumination of the said area.

Description

United States Patent Planchon 5] Oct. 24, 1972 [54] FACETED REFLECTOR Jean Planchon, 9, rue Chaptal, Paris 9eme, France [22] Filed: Sept. 2, 1970 [21] Appl. No.: 68,951

Related US. Application Data [63] Continuation-in-part of Ser. No. 695,522, Jan.

3, 1968, abandoned.

[72] Inventor:

[52] US. Cl. .240/41.36, 24.0/ 103 R [51] Int. Cl ..F2lv 7/09 [58] Field of Search ..240/103 R, 8.3, 41.36

[56] References Cited UNITED STATES PATENTS 1,535,985 4/ 1925 Clark ..240/41.36 X 1,566,906 12/ 1925 Matisse et al ..240/41 .36

Primary Examiner-Jerry W. Myracle Attorney-Cushman, Darby & Cushman ABSTRACT The present invention provides a reflector, e.g. for a desk lamp, which is designed to provide an unusual The elementary reflecting surfaces are linked to one another at their upper and lower edges through continuous surfaces portions and at their lateral edges through stepped surfaces portions called redans. The horizontal and vertical traces of the tangent planes to the various points of said individual elementary reflecting surfaces are so located respectively on horizontal planes containing said various points and on vertical planes containing both said points and a predetermined point of the source of radiation which cooperates with the reflector so as to provide, on a horizontal area to be illuminated, a plurality of images of the source, said images cooperating for giving a continuous predetermined level of illumination of the said area.

3 Claims, 27 Drawing Figures PATENTEDHBT24 I912 3 700882 sum 1 0F 7 PATENTED I97? I 3.700 882 SHEET 2 0F 7 PATENTEDUEI 24 I972 SHEET 7 [IF 7 FACETED REFLECTOR This application is a continuation-in-part of Ser. No. 695,522 filed Jan. 3, 1968 and now abandoned.

BACKGROUND OF THE INVENTION The present invention relates to reflectors for reflecting light or heat. It will be more particularly disclosed hereinafter with reference to lighting devices, though it may be also applied to other types of radiation.

Standard lighting devices comprise a light source, consisting either of a bright or frosted bulb, or of a fluorescent tube, placed inside a diffusing reflector, the entire assembly providing for the lighting of certain area. In the special case of an individual lighting device, to be placed, for example, on a desk or a table, the light source-diffusing reflector assembly provides for'the illumination of a work plane and the diffusing reflector, acting as a lampshade, provides in addition, for the concealment of the bulb with respect to the eye of the user so as not to dazzle him. The diffusing reflectors commonly used to obtain such illuminating means, whether general or individual, have, for reasons of convenience of manufacture, simple geometrical forms such as a frustrum, a portion of a right cylinder with a circular elliptical, rectangular or parabolic base, a paraboloid, a portion of an ellipsoid or a form resulting from the association of two or more of the previously mentioned simple geometrical forms.

The devices thus constructed have the disadvantage of not providing the illumination of the area to be illuminated in a manner which is systematically adapted to needs and, in particular, in the case of' individual lighting devices, of not producing an illumination allowing for good vision. Certain known reflectors provide a concentration of energy in one or more preferential directions, but do not, in a systematic fashion, allow for the distribution of energy from the source on a predetermined area and, in accordance with a predetermined level of illumination, which may consist, as a specific example of particular interest, in an uniform illumination over the entire range of said predetermined area.

In the particular case of individual lighting devices, it is observed, with standard devices, that the isolux curves measurable on the work plane are generally concentric and that the illumination decreases rapidly from the point benefiting form the strongest illumination, said point being, most often, located vertically with respect to the light source. For example, with a 75 watt bulb placed approximately 30 cm above the work plane and laid out along the axis of a reflector whose opening is parallel to the work plane, the entire assembly giving an illumination of 2,600 Lux at a'central point located vertically with respect to the bulb, an illumination of 1,000 Lux at a distance of 25 cm from the central point was noted, of 600 Lux at a distance of 33 cm from the central point and finally of 200 Lux-only at a distance of 52 cm from the central point. It follows that, if a work item 40 cm wide is placed in the illuminated area so that its center is located at an illumination point of 400 Lux, one of its edges will be located at an illumination point of approximately 1,000 Lux and the other one of its edges at an illumination point of the order of 100 Lux; one of the halves of the work item will therefore have an average illumination of the order jection of the light source on the said area. For thatv of 700 to 800 Lux while the other half of the work item will have an average illumination of approximately 200 Lux, and when the user views any point in the work item, one of his eyes will have in its visual field, a surface whose average illumination will be very much stronger than the average illumination of the surface located in the visual field of his other eye, which leads to a different accommodation for each eye, thus causing visual fatigue. Moreover, if an effort is made, by increasing the power of the light source, to increase the illumination of that half of the work item receiving the least illumination, an illumination so intense of the other half is liable to be obtained, that the latter, even weakly brilliant, will act as a mirror and create a dazzling effect, thus increasing visual fatigue still further. In order to diminish the intensity of this defect, a diffusing bowl is sometimes placed beneath the bulb, but the effect of the latter, in fact, is to level out the illumination of the work plane by lowering it considerably, which leads to either insufficient illumination or to needlessly high power consumption, and this subsequently limits usage of individual illuminating devices, taking into account high illumination levels generally considered necessary.

Similarly, certain reflectors provide for the concentration of light energy from the source in one or several preferential directions, but if the isolux curves are considered in the regions comprising and in the vicinity of said preferential directions, it is observed that, here again, the illumination decreases vary rapidly from the point at which this illumination is a maximum.

SUMMARY OF THE INVENTION The present invention provides a reflector, eg for a desk lamp, which is designed to provide an unusual predetermined pattern of illumination on a surface, for instance a pattern having non-concentric isolux curves around a point of strongest illumination, and which results in a more even distribution of light over the surface illuminated. The reflector is particularly designed for uniformly illuminating a predetermined area, even at a comparatively large distance from the vertical propurpose, the reflector is built in the form of a complex surface comprising a plurality of elementary reflecting surfaces each of which has a distinct shape.

The elementary reflecting surfaces are linked to one another at their upper and lower edges through continuous surfaces portions and at their lateral edges through stepped surfaces portions called redans. The horizontal and vertical traces of the tangent planes to the various points of said individual elementary reflecting surfaces are so located respectively on horizontal planes containing said various points and on vertical planes containing both said points and a predetermined point of the source of radiation which cooperates with the reflector so as to provide, on a horizontal area to be illuminated, a plurality of images of the source, said images cooperating for giving a continuous predetermined level of illumination of the said area.

In a preferred embodiment, the reflector has a top wall and a generally cylindrical sidewall divided into a front portion extending throughout about l0-l30, two opposing side portions each extending throughout about 30-60 and a rear portion extending throughout about 130-l80. One portion of the top wall of the reflector is designed to reflect light generally axially toward the surface to be illuminated. Another portion of the top wall, near the front 'of the reflector, is angled to substantially prevent direct incidences of light thereon from the source.

The inventor has also devised and described herein a method for determining what orientation of the individual mirrors will result in providing the overall pattern of illumination desiredThis method comprises the steps of selecting a plurality of points on a surface approximating the final reflecting surface of the reflector, of determining, for each of the said points, the horizontal intersection of an infinitesimal reflecting surface located at said point on an horizontal plane containing said point and the vertical intersection of the said infinitesimal reflecting surface with a vertical plane containing both said point and a predetermined point the source of radiation; of locating, at each of said points, a concave mirror tangent to the infinitesimal reflecting surface thus determined, and .of joining the said concave mirrors to one another through curved reflecting surfaces adapted for providing, with the said concave mirrors, a continuous and smooth reflecting surface.

Preferably, the determination of the horizontal and vertical intersection is respectively carried, for each of the infinitesimal reflecting surfaces, through a determination of the angle defined, on one hand, by the bisectrix of the angle between the line which joins the said predetermined point of the source to the selected point on the reflector and the line which joins the said selected point to a predetermined point on the work plane and, on the other hand, by the line which joins the said selected point to the middle point between the orthogonal projections,'on the said horizontral plane, of the said predetermined point of the source and of a further point located on the line which joins the said selected point to the said predetermined point of the source, and through a determination of the angle defined, on one hand by the said bisectriX and, on the other hand, by the line which joins the said selected point on the reflector to the middle point between the said predetermined point of the source and the orthogonal projection of the said further point on the said vertical plane.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagrammatic view showing a plane mirror, an area to be illuminated, and the path of a light ray originating from a light source and, after reflection on the mirror, converging on the said area;

FIG. 2 illustrates a vectorial representation of the intensity of radiation around a point on a perfectly diffusing surface;

FIG. 3 is a diagrammatic view showing the useful solid angle below which, in practice, a point can see a light source consisting of a frosted bulb;.

FIG. 4 shows diagrammatically the form of the image of a frosted bulb produced on a work plane through reflection, at a point on a plane mirror, of rays emitted by said frosted bulb;

FIG. 5 illustrates diagrammatically the method of determination of the intersection of one of the elementary mirrors, which makes up a reflector in accordance with the invention, with a ground plane passing through the central point of this elementary mirror;

FIG. 6 shows diagrammatically the method of determination of the intersection of such an elementary mirror with a vertical plane passing through the central point of this elementary mirror and through the light source;

FIGS. 7a and 7b are diagrams illustrating the construction of a reflector according to the method set forth in FIGS. 5 and 6, FIG. 7a showing the horizontal projection of the traces of the reflector sections by ground planes of various levels and FIG. 7b showing, brought down on a same plane, the traces of the reflector sections through vertical planes passing through the center of the source and making various angles with the plane of symmetry of the reflector;

FIG. 8 is a sectional view of a projector constructed in accordance with the result of the method explained in connection with FIGS. 7a and 7b;

FIGS. 9a and 9b show diagrammatically the illumination area obtained using the reflector shown in FIG. 8;

FIGS. 9c, 9d and 9e are diagrammatic views illustrating a particular application of the method for reflector design to the embodiment of FIGS. 7a-9b.

FIG. 10 shows another construction of a reflector built using the same method as above, which is also adapted for lateral illumination and cooperates with a frosted bulb;

FIGS. 1la-1 1b and 12a-12b show embodiments of a reflector according to the invention, said reflector partially surrounding alight source consisting of a bulb;

FIG. 13 shows, as a section, an arrangement of decorative glassware, part of which was molded so as to show a structure according to the invention and thus act as a reflector;-

FIGS. 14a and 14b illustrate the manner according to which a fluorescent tube illuminates a given point;

FIGS. l5a-l5b and l6a-16b-16c show embodiments of a reflector according to the invention, said reflector providing for the distribution of light energy produced by a fluorescent tube.

DETAILS OF PRESENTLY PREFERRED EMBODIMENTS OF THE INVENTION OPTICAL AND MATHEMATICAL CONSIDERATIONS In order that the basic concept of the invention may be more readily understood, a theoretical analysis of the process of illumination of a plane area from a complex reflecting surface will now be given. FIG. 1 shows a light source consisting of filament 1 of an incandescent lamp, a plane mirror 2 and a work plane 3 to be illuminated.

If any point P on mirror 2 and perpendicular line PN at P to said mirror is considered and if any point S of filament l is considered, it is known that light ray SP will be reflected at P along PR so that straight li ngs SP, PN andPR are in a same plane and that angles SPN and P are equal. It follows that point R is the image of point S on plane 3, given by the infinitesimal element surrounding point P in plane mirror 2. Since mirror 2 is assumed to be perfectly reflecting, i.e., non-diffusing, ray PR is the only reflected ray corresponding to incident ray SP. If, now, all the points of filament l emitting light rays in all directions are considered, there is, for each of said points, one and only one light ray reaching P and it is reflected along a single direction, so that a well-defined image 4 of filament 1 will be obtained on plane 3 formed of a plurality of juxtaposed infinitesimal plane mirrors such as mirror 2. It will give on plane 3, an illuminated area obtained by placing side by side an infinite number of well-defined and controllable images from the source, and it follows that the light intensity at each point of said illuminated area will be accurately controllable.

FIG. 2 illustrates a well-known vectorial representation designed to show the distribution of light in various directions around a point Q of a nonreflecting and perfectly diffusing surface. According to this representation, if the value of l is assigned to the vector showing the light intensity along the perpendicular line at Q to said surface; the light intensity along any direction will be represented by a vector whose extremity is on a sphere of diameter 1 tangent at Q to said diffusing surface. It follows, in accordance with the well-known relationship in right triangles, that the light intensity emitted in a 45 direction with respect to the perpendicular is only 0.707 times that emitted along this perpendicular, that the light intensity emitted in a 60 direction with respect to the perpendicular is only 0.5 times that emitted along this perpendicular and that the intensity decreases very rapidly as the angles increase beyond'60. This means, as shown in FIG. 3, that it is possible in practice, when a frosted light source is viewed from a point P, to take into account only the points of this source such that a straight line joining them to point P makes an angle below 60 with the perpendicular at the source surface to the point under consideration. Under these conditions, it can be seen on FIG. 4 that the image of a light source such as 5, consisting of a frosted bulb, and produced on a work plane 6 be reflection at a point P from a plane mirror 7 of various rays originating from various points of said bulb, will be a well-defined surface. If the bulb is spherical, the total sum of the rays originating from its different points and leading up to P will make up a cone having a right circular section with apex P, the total sum of the reflected rays will make up a cone of apex P and of perfectly well-defined generatrices whose intersection with the work plane will be an ellipse. This ellipse will present a central area with strong illumination corresponding to rays originating from points on the bulb emitting towards point P along a small angle with respect to the perpendicular to the surface of the bulb, said central area being surrounded by areas of decreasing illumination corresponding to points in the bulb emitting towards point P along progressively larger angles.

In accordance with the basic concept of this invention, a reflector adapted for providing for a predetermined distribution of light intensity from a source on a given area will consist of a large number of small elementary mirrors placed side by side with different orientations.

POSTULATE From the above considerations, it clearly results that, taking into account the nature and the position of the light source, the intensity of illumination produced by each elementary mirror on said area and the respective orientations of the elementary mirrors maybe determined so that the illuminated areas produced by them are placed side by side or are superimposed so as to provide the desired predetermined illumination on the total area to be illuminated.

' THE METHOD, IN GENERAL A practical method for effecting said determination will consist in determining, at various points of the area to be illuminated, the form and dimensions of the imageof the source seen by reflection on various elementary mirrors located at points chosen a priori on the surface of a reflector having the desired dimensions and in determining the inclinations required for said elementary mirrors so that the images given by them of the source on the work plane will be suitably placed P of the reflector and striking work plane 8 at R.

FIG. 5 also shows plane 10 passing through point-P and parallel to plane 8, which is therefore horizontal as well as vertical plane 11 containing points S and P; this plane makes an angle H with vertical plane 12 going through point 8 and constitutes a reference plane; finally, a point B was marked on ray PR such that PB will be equal to the distance PS and points B and S were joined by a straight line. According to Descartes laws, perpendicular PN at P, to the infinitesimal plane mirror surrounding this point and causing the reflection of the incident ray SP along PR, is within the plane defined by the three points S,.P and R and is the median relative to apex P of isoceles triangle SPB; this median intersects side SB at a point M. At points 5,, M, and B, on FIG. 5, can be seen the orthogonal projections of points S, M and B on plane 10 and it is evident that point M, is the midpoint of segments 3,, S, i. e. PM, is the median relative to apex P of triangle S,PB,.

If the intersection of the infinitesimal plane mirror, surrounding point P, with plane 10, is represented by a segment of a straight line 13, it is evident that said segment 13 is orthogonal to PM,. It follows, if it is possible to determine, through calculation, the direction of the half straight line PM, in plane 10, that the trace of this plane of the infinitesimal plane mirror surrounding point P will be immediately deduced. Now, since the relative positions of points S, P and R are defined, the distances PS and PR are known, aswell as angle H of the dihedron formed by

vertical planes

11 and 12, angle SPS,, that is d which, by the way, is equal to the angle formed by segment SP with the ground plane passing through S, angle S,,P,,R with S and P being termed the orthogonal projections of S and P on plane 8, angle PR P and finally angle S P R which is equal to angle I-I, increased or reduced, depending on the case, by an angle B which defines the angular position of point R with respect to the vertical plane passing through P and which is parallel to plane 12. If angle PR P is termed r, which is equal to angle B P B,, it can be seen that the following relation exists at B, in right triangle P B 8,:

v sr= ol o and the value of side P S, can be calculated at S, in right triangle PS ,8 using the relation PS =PScosd FIG. 6 shows, at M, and E5, the orthogonal projections of points M and Bon plane 11, and, as for the case in FIG. 5, it can be seen that the half straight line P M is the median originating at P in triangle P B S. Now,

since side PS, in this triangle, is'known, it is possible to calculate side PB which, in triangle PB: B, is given by:

I P B =PBcosy orPB =PScos7 by terming angle R P R, as 7, point R, being the orthogonal projection of R on plane 11. Now it is possi-- ble to demonstrate that angle 7 can be calculated using the formula:

sine'y=cosrsin(H+D) 1 indeed, let 7 be angle P P R,,; considering P in right triangle P P, R the following relation can be written:

P R,,=PP,,tga 2) Furthermore, considering R in right triangle P,,R,R, the following relation can be written P,,R,,=P,,Rcos(H+D) 3) Finally, considering P, in right triangle PP R, the following relation can be written P,,R=PP,, cotgr These relations (2), (3) and (4) give tg'y=cos (H+D) cotgr 5 Now, in right triangle PR R, the following relation can be written R R=PRsiny 6 Similarly, at R inright triangle R,,P,,R, the following relation can be written v R,,R=R,,P tg (H+ D) 7 Furthermore, at -P,, in right triangle R P P, the following relation can bewritten I P R =PP tga it (8) Finally, at P in right triangle PP R, the following relation can be written Equations(6),(7),(8) and(9)lead to sin'y=zg(H+D)tgasinr By replacing tg a by its value given in 5), one can write:

sin 'y tg (H+D) sin r cos (H+ D) cotg 'r *or'by replacing the tangents and cotangents by their I sin 'y=cos rsin (H+ D) which is actually expression 1 It is therefore possible, knowing the relative positions of points S P and R, i.e. the values of angles r, H and D, tocalculate the value of P B, and carry it on half straight line P R, which may be constructed geometrically knowing angle or using formula (5 It is therefore possible to determine the position of point M and subsequently half straight line P M It is therefore known to construct segment 14 which is perpendicular at P to said half straight line P M said segment being the intersection of plane 11 with the infinitesimal plane mirror surrounding point P, causing the reflection along ,PR of ray SP. Under these conditions, given a point S in the source, a point R in the area to be illuminated and a point P on the surface of the reflector, it is possible to determine the plane mirror which must be placed at P for ray SP to be reflected along PR, this determination being made by constructing straight line segments corresponding to the intersections of said mirror with the ground plane passing through point P and with the vertical plane passing through points P and S. Furthermore, knowing the angle at which point P sees filament 9, it is possible to calculate the shape of the image of said filament on the area to be illuminated and toevaluate its relative contribution to the illumination of the area to be illuminated.

HOW TO APPLY THE METHOD The general shape and size of the reflector is first decided upon. For instance, the general shape may be that of an inverted bowl (for an incandescent bulb) or that of an inverted trough (for a fluorescent light). The reflecting areas of the roughed-out reflecting surface are then divided into a plurality of individual sites or points. Using the method, it is possible to determine the spatial orientations or positions required for infinitesimal plane mirrors placed at these points so that the images provided by them will be distributed on the area to be illuminated so as to give a predetermined level of illumination. The entire surface of the reflector can then be obtained by providing a complex reflecting surface set up by placing edge to edge plane mirrors constructed along the horizontal and vertical traces detemiined as indicated above and joined to one another through obtuse angles or through more or less emphasized bends, thus giving a continuous illumination of the work plane due to the spread of the infinite number of images produced by the infinite number of infinitesimal mirrors comprising each one of said plane mirrors. In practice, the size of the bends is decreased and the precision of the distribution of illumination on the area to be illuminated is increased by replacing such plane mirrors by concave mirrors tangent at each point, such as P, to the plane mirror determined as in-' dicated above. The determination of the curvatures of said concave mirrors" is carried out graphically or through calculation according to methods well-known to those skilled in the art.

FIGS. 7a and 7b show the result of a determination conducted according'to this method. The result is expressed in the forrr'i of curvesrepresenting, in FIG. 7a, the intersection of the internal face of a reflector built in accordance with the invention, with the ground planes of different levels and, in FIG. 7b, the intersection of the internal face of the reflector with the vertical planes passing through the center of the source and forming, with a vertical plane of reference, which in this particular case, is the plane of symmetry of the projector, angles of increasing size, said intersections being brought down on said plane of symmetry. The curves of FIG. 7a are shown as a succession of curve segments determined according to the method described and linked to one another through step-shaped connections corresponding to bends between the corresponding surfaces. The curves in FIG. 7b are shown as continuous curves obtained by connecting together curve segments obtained according to the method described. FIG. 7a shows only the curves relating to half of the projector, the second half being obtained through symmetry with respect to axis AA. FIG. 7a shows trace of the intersection of the internal surface of the reflector with the ground plane passing through center S of the source. This trace takes the form of a succession of curve segments, connected to one another through curvilinear links, so that said curve 15 actually takes the form of a continuous concave curve except at point 16 which corresponds to the junction of the front part and back part of the reflector, of different dimensions. This junction takes the form of a large bend practically perpendicular to the parts of said curve 15 enclosing it. FIG. 7a also shows the intersections of the internal surface of the reflector with the ground planes located at different levels above and below the preceding plane, i.e. curve 17 corresponding to the level 8 centimeters, curve 18 corresponding to the level 16 centimeters, curve 19 corresponding to the level 8 centimeters and curve 20 corresponding to the level 19 cen timeters.

These curves show, at the level of bend 16 of curve 15, similar bends 21, 22, 23 and 24. Furthermore, curves l7, l8, l9 and 20 take the form of a succession of curve segments which, instead of forming a connected series as in the case of curve 15, are linked to one another through a slight dent forming a step such as 25 or 26.

The curves in FIG. 7b take the form of a succession of curve segments forming a connected series with one another. Curve 27 corresponds to the intersection of the back part of the reflector with the vertical plane passing through the center of the source and forming a null angle with the plane of symmetry. Furthermore, curve 27 ends up downwards as an oblique part 28 and a circle 29 corresponding to a rolled edge of the projector whose purpose is to increase rigidity, and upwards as a hair-pin-shaped part corresponding to the upper edge of the reflector conveniently shaped so as to provide sufficient rigidity to the assembly. Curve 31 corresponds to the intersection of the forward part of the reflector with a vertical plane passing through the center of the source and forming an angle of 20 with the plane of symmetry of the reflector. The said curve is similar to curve 27. This is similarly true for

curves

32, 33, 34, 35 and 36 corresponding respectively to angles of 65, 75, 90 and 115, with more 'or less sizable oblique parts at the base and re-entering parts at the apex, depending on the case.

Finally, curve 37 gives the intersection of the for ward part of the reflector with the plane of symmetry. The drawing, as a whole, constitutes the diagram of the reflector and perfectly defines in space the elementary mirrors comprising the internal surface of said reflec- I01.

FIG. 8 represents a section of the reflector obtained according to the diagram of FIGS. 7a and 7b; it shows the source of light energy consisting of a bulb 38 whose axis makes an angle of the order of approximately I5 with the vertical axis of the reflector, the back face 39 of the projector with its lower rolled edge 40 and its upper edge 41 folded back in the form of a hair-pin, the

forward face 42 with its lower rolled edge 43, its upper hollow back 44 and its upper edge 45 folded back in the form of a hair-pin. The light rays originating from the light source and striking the back face 39 are reflected in the direction of the work plane. Most light rays originating from the light source and striking the forward face 42, are reflected in the direction of the back face, which, mainly through the area surrounding point 46, reflects them again in the direction of the work plane. A small number of light rays striking forward face 42, particularly those striking the area surrounding point 47, are reflected towards the back but outside the surface of the reflector, and are designed to create an environmental illumination. Similarly, certain rays striking the lateral areasof the reflector are used to create an environmental illumination around the actual work plane.

FIGS. 9a and 9b show the way illumination is distributed on the plane by a reflector of the type described in FIGS. 7a, 7b and 8.

Reflector 48, shown as a front view of FIG. 9a and as a plane view in FIG. 9b, located at a height H above a ground plane, concentrates a considerable quantity of light energy in a beam 49, bound by two end rays, one 50, marking an angle of the order of 30 to 40 with the ground plane, and the other 51, making an angle of the order of 15 to 20 with said ground plane. This light energy is distributed uniformly on a work plane 52 of almost rectangular shape. This work plane is surrounded, on the one hand, by an area 53 located between said work plane and the reflector, also possibly containing the parts of the ground plane located below the reflector and in which illumination is weaker than, or at most equal to that of the work plane 52, and on the other hand, by three areas 54, 55 and 56 in which illumination rapidly decreases starting with the zone in the vicinity of area 52. Furthermore, an area 57 is also created at the back of the projector and provides environmental illumination. For a height of the reflector above the ground plane of the order of 30 cm, the left edge of work plane 52 is approximately 35 cm away from the stand of the projector, its right edge is approximately cm away from said stand and has a width of the order of 45 cm, and inside this entire surface, the illumination is practically uniform.

SPECIFIC APPLICATION OF THE METHOD TO THE EMBODIMENT OF FIGS. 7a-9b The following discussion relates particularly to the specific embodiment of FIGS. 7a-7b or 8, in the case of an incandescent transparent bulb, and when it is desired to illuminate a work plane on a writing table with the particular light distribution which is illustrated on FIG. 9a.

The dimensions and respective light intensities for each of the portions 52 to 57 in FIG. 9a are first calculated, starting from a consideration of the optimum physiological conditions which are desirable for the observer, and from a consideration of the light flux generated by a transparent bulb located at normal height above the work plane. I

They are, in fact, the initial data from which the reflector shape will be determined through application of the method.

The general shape of the reflector is next decided upon. As illustrated in FIGS. 7a-7b and 8, the projector has a pseudo-trapezoidal axial section and two (one upper, one lower) circular baseapertures, the center (S, 1 FIG. 7a) of the upper aperture being offset (of about 20-30 mm) with respect to the center of the lower aperture.

The lateral surface of the reflector comprises a rear face, two side faces and a forward face. The light rays originating from the bulb and striking the back face are reflected on the work plane, and more precisely, they will illuminate portion 52, FIG. 9a. The light rays striking the forward face will mainly illuminate the back face (in the area surrounding point 46, FIG. 8) and be reflected back to the work plane (In other words, the forward face plays the part of a relay). The light rays striking the two side faces will illuminate portion 54 and 55, FIG. 9a. By preference, in the general design of the particular reflector the back face is located as near as possible to the light source and adapted for illuminating the laterally offset area 52. The forward face of the reflector is generally oriented such a way that the light will not be substantially deflected thereon, thus coming back through the bulb and striking again the forward face of the reflector before being finally reflected on area 56. For obtaining as small reflection angles as possible on the said forward face, it has been given cross-sections having the form of circles centered at S (S also being the center of the bulb). These circles are shown on FIG. 7a.

The illumination pattern is completed by light reflected from the two sides face of the reflectors, which provided crossed light beams illuminating the areas 54 and 55. An upper conical face (44,'FIG. 8) is provided, with an inclination with respect to the horizontal plane such that it will extend substantially in the direction of points S, thus avoiding any reflection of light thereon.

The direct illumination from the source covers the area 53 (FIG. 9a).

Once the general shape has been decided, each of the surface portions of the projector will be accurately calculated through application of the method set forth above for the general case.

This method for the specific case, includes four steps:

A. The determination of a small number of points of the sections of the projector in the median vertical plane containing S and in the horizontal plane containing S and of the tangent planes to the reflector at these points.

B. The detemiination of a large number of intermediate points of the projector surface and of the tangent planes to the projector at these points.

C. The determination of elementary fskew mirrors centered on these various points.

D. The determination of the accurate. shape of templates which will be used in the effective manufacture of the reflector.

Step A is carried out as follows:

Very briefly, in the median verticalplane containing S, one firstly determines three points of the profile of the rear face of the projector, namely: the point 0 which belongs to the horizontal line passing through S and the two end points A and A (see FIG.

Point O is taken at about 8 mm from the bulb surface. Unmolding of the projector can be easily effected when the minimum taper angle is at least 1. Therefore, at lower point A, the inclination of the profile with respect to the vertical should equal 1. Then, as the ray 8A should be reflected on the right side of area 52, FIG. 9a, the reflected ray A R will be inclined by 16 with respect to the horizontal. (This is calculated starting from the known position and dimensions of area 52).

It results that 8A should make an angle of about 14 with the horizontal.

Now, it is decided to take, for instance, A such that the line SA will make an angle of about 25 with respect to the horizontal. As R should be on the left side of area 52, it may be shown that A R will be inclined by 60 and it results that the mirror in A, should be inclined by 3730 with respect to the vertical. Finally, the inclination of the profile in 0 will be calculated for obtaining 0R making an angle of about 20 with respect to the horizontal. Then, one may calculate that the mirror at 0 should be inclined by 10. This enables one to roughly determine (by three points and tangents) the profile A,OA which is tangent to the three mirrors A 0 and A The same type of reasoning and calculation enables one to roughly determine (by a few points and the corresponding tangents) the section of the projector in the horizontal plane containingS.

The first determination is a mixture of calculation and general common sense considerations. However, it does not lead to something arbitrary and doesnot involve any trial and error.

The calculation of the inclinations of the tangent in A and O are carried out through the application of the method disclosed above for the general case. Among the common sense considerations are the following:

a. choice of the position of point 0 b. choice of the angle OA S 0. choice of the minimum taper angle at A d. the decision that horizontal sections of the back' face of the reflector (only one of these half-sections is shown at FIG. 7a) should reflect'light rays on all the area of portion 52in FIG. 9a.

The practical reasons for these choices are reasonably imposed by considerations of convenience of manufacture and natural distribution of the flux of the bulb in space. I

Step B is carried out as follows:

Once the general envelope of the projector has thus been roughly determined, one takes a plurality of intermediate points P obtained as follows: one will consider, on one hand 36 vertical planes containing the axis of the projector and 16 conical surfaces having as their common axis the axis of the projector and apex angles increasing by 10 from one conical surface to the following. Finally 16 X 36 576 solid angles are thus determined. Each of said solid angles delimits a pseudo-trapezoidal area on the projector envelope and the central point of the said area will give the approximate position of one point P.

Now, each of the said areas receives a certain light flux from the source, and, as we know the photometric curves of the source, this flux may be exactly calculated, (without any supposition that the source is pinpoint light source).

After that, the method is carried out as illustrated by FIG. 9d.

For the few points P determined in step A, the corresponding points R are exactly known and, also, the orientation of the tangent planes. Therefore, the images of the filament obtained by reflection on these points may be exactly calculated, in size and light intensity.

For the other points P, the points R will be first positioned in regularly distributed intermediate portions and this will enable one to calculate the tangent planes at the corresponding points P and the resulting images. If the resulting light distribution, as apparent from FIG. 90, is not quite perfect, small corrections will be done through slightly modifying the positions of some of the points R and the new orientations of the tangent planes will be calculated.

It is to be emphasized that this is not a trial-and-error matter, but rather a calculus of optimization. This calculus supposes that the reflector surface is made of a patchwork of plane small mirrors each centered at one of the points P and receiving a known light flux. In fact, in the final reflector, the elementary mirrors will not be plane. A small variation of the position of P only results in a very small displacement of the image on the work plane, and a slightly imperfect light distribution will not, anyway, be perceptible to the eye. When, however, it appears on the sketch that two many images concentrate in some regions and two few in others, it will be easy to select another position for some points R and to again calculate the corresponding orientations of the small mirrors.

At the end of step B, one finally has, for instance, 576 points and the corresponding tangent planes, which provides one with a very fine definition of the reflector surface.

Step C is carried out as follows:

Then there are provided around each of the points P, an elementary concave skew" or warped mirror delimited by four arcs of circles, these mirrors being determined in such a way that the tangent planes thereto at each point will exactly have the orientations calculated in step B.

The intersections of these elementary mirrors with the horizontal and vertical planes already defined are determined as illustrated in FIG. 9e for an horizontal intersection.

It is seen that the tangent at P intersects at m and n the lines sm and m inclined by 5 with respect to SP The tangent at m and n are then determined in such a way that the corresponding points R which respectively correspond to P and P and to P and P respectively. Now, the arc of circle which is tangent to the three tangents at m P and n will be determined and only the portion m n' of it which will be retained. The same method will then be applied at P but now, a parallel to the tangent at n should be drawn at m This is why a small redan n m will be formed. If this redan is not small enough, one may divide each 5 angle by two and separately determine the skew mirror curvatures for the two half-mirrors thus defined.

The are of circles m; n and m';, n are obviously not centered at s, their respective centers are accurately calculated.

The same method is applied in the vertical planes.

Finally, one obtains a complete definition of the surface of the projector through an assembly of skew mirrors each of which very closely approximates, as far as its reflection properties are concerned, the plane mirrors described in step B and yet enable one to obtain a smoother projector surface and, therefore, a smoother light distribution.

Step D is carried out as follows:

The mirrors defined in step C are not very easy to build because they are delimited by conical surfaces above-defined. This is why the calculations are made again for finally defining skew mirrors delimited by equidistant horizontal planes, as illustrated in FIG. 7a. The curvatures of the new mirrors are already known in the vertical planes, which remain the same in step D. Calculation of the curvatures in the horizontal planes is made by interpolation. Templates are then built manually with the exact shape determined for these new skew mirrors. These templates are used for manufacturing the mold or stamping die. The molding process is conventional.

In fact, these mirrors are skew only in the rear and side faces of the projector of the preferred embodiment. Their vertical sides are connected to one another through steps or redans, as clearly apparent from FIG. 7a. Some of these redans are very small and practically unapparent. In fact, step C is carried out in such a way that the redans are as small as possible on the rear face, which leads to have a much more important redan 24, FIG. 7a) at the junction between the rear face and each of the side faces.

SOME REFLECTIONS ON THE METHOD AS APPLIED TO THE PREFERRED EMBODIMENT As explained above in step B, the real photometric curves of the source are taken into account when the images of the filament are calculated.

Only the points of the source such that a straight line joining them to P makes an angle below with the been determined by the above method, the calculation of the image is within the reach of those skilled in the art.

The manner according to which the surface of the reflector is divided in small areas is not arbitrary. Of course, one could take a or a 15 division instead of the division described in step B. This is a question of accurateness of the definition which is desired. A l0 division is found sufficient in practice.

The method does not assume that each of the reflector areas is flat. It merely consists in calculating the orientation that the tangent plane to the mirror should have at a finite number of points P for obtaining reflection at a corresponding number of points R. What is assumed is only that the intermediate points P will provide reflection at intermediate points R which will be regularly distributed between the points R for which the calculations are effectively made. This assumption is perfectly correct, provided that the reflector surface does not comprise important discontinuities between the points P for which the calculationsare made.

Snells law is applied in the calculation of the orientation of each tangent plane. However, Snells law consists in effecting the calculation on one plane of reference, and not in an X Y Z axis-system. The method of calculation which is disclosed herein is, as far as is known, novel. This is an application of descriptive geometry which has not been made before.

Any point R can be associated, a priori, with a given point P. However, once the image of the source which is obtained on a plane mirror located at P and oriented in such a way that the light is focused around a given point R has been determined in size and intensity, and once such determination has been made for a plurality of couples of given points P and R, it will but remain to properly modify the positions of the points R until corresponding images (which will not, in practice, vary in intensity and size) form a continuous pattern on the area to be illuminated. For each modification of the position of a point R, the corresponding modification which should be effected on the orientation of the plane mirror at P will be easily calculated. The initial choice of points P and R is not arbitrary, but a mere matter of optimization. The following modification of the position of points R are but minorcorrections. The

whole process is fully mastered through calculation and practically no trial-and-error job is involved therein.

All of the reflectors obtained through application of the method will comprise an assembly of elementary mirrors each having a skew surface, (in French: surface gauche, which does not only mean curved: a sphere or a cylinder have no skew surfaces) delimited by four arcs of a circle, said mirrors having their vertical sides connected together through redans.

Apart from these skew mirrors, all the reflectors obtained through the method will comprise at least one light relay portion (as the front 42 portion of the reflector in FIG. 8) adapted for reflecting the light from the source on to the skew mirrors.

Cooperation of skew mirrors portions which directly reflect the light on the area to be illuminated with relay portions are another feature of the invention.

A purely trial-and-error designing would consist in modifying the shape of the reflector until a certain distribution of light is obtained: this means measuring the geometrical shapes would be used in a trial-and-error method.

Portion 44 of the top surface does not play any part in the light distribution and is but an unavoidable linking surface. Portion 44 has been shaped so as substantially to avoid any reflection from light thereon, and thus, does not disturb the light distribution as determined by the other portions of the reflector.

The orientations of the tangent planes in a vertical section vary very little from the top to the bottom of the reflector. However, the orientations of the tangent planes in an horizontal section are subjected to a comparatively large variation for instance from mirror 20 (in FIG. 7a) to the mirror adjoining mirror 24. This results from the determination of the general envelope of the reflector, in accordance with step A of the method. This determination also provides that the mirrors of the side portions of the reflector should have a given orientation.

It is clear from FIG. 7a, that this implies the presence of a large redan 24, if one desires to avoid getting out of the generally circular horizontal section. Finally, the redans are a practical way of linking together a plurality of mirrors having predeterminal orientations and generally located within a predetermined roughly cylindrical envelope. They do not perform a positive function in the light distribution.

The socket may be mounted inside the top of the reflector. This will avoid projecting any shade on the ceiling. However, this should not at all be considered as a necessary feature of the invention and the bulb could be positioned in other ways, forinstance, as depicted.

The flaring at 28-35, FIG. 7b results from the specific method of manufacture which has been used and is not part of the invention.

Various shapes and types of incandescent light bulbs are manufactured throughout the world. This will not require the use of different types of reflectors. In fact, what essentially matters for determining the shape of the reflector is the filament position (not the filament or bulb shape).

This position may be adjusted through the use of different types of sockets.

THE REMAINING ILLUSTRATED EMBODIMENTS FIG. 10 shows another example of the construction of a reflector according to the invention using preferably an opalescent or frosted bulb. Inside contour 58 which bounds the external surface of the reflector, may be seen reflecting

surfaces

59, 60, 61, 62, 63, 64, 65 and 66 separated by

bends

67, 68, 69, 70, 71 and 72 distributed over the lateral surface of the reflector. Furthermore, in order to recover the light energy emitted by the bulb in the direction of the upper wall of the projector, additional reflecting surfaces were formed on this wall; those numbered 73, 74, 75, 76 and 77 separated by

bends

78, 79 and 80 send back the light energy which they receive, towards the work plane, and those numbered 81 and 82 send back the energy which they receive, upwards, through openings made in the upper back of the projector, thus creating an environment.

It is also possible to place mirrors such as 83 below the'bulb which prevent the light emitted downwards by the bulb from creating an area of intense illumination at the stand of the reflector which is generally undesirable. The said mirrors send back said light towards the work plane through opening 84. Finally, it is also possible to place, below the bulb, mirrors such as 85 which send back the light directly towards mirrors such as 62 or 75 from which it is directed towards the work plane.

FIGS. 11a and 11b show a reflector 86 constructed according to another embodimentof the invention and partially enveloping a bright incandescent bulb 87', the entire assembly being placed inside a lampshade 88 which may or may not be translucent, giving mainly a decorative effect obtained by masking the bulb-reflector assembly. Said reflector, for example, may be constructed by pressing a polished and anodized aluminum plate. A very strong useful illumination is thus obtained in a lateral direction with respect to that which might be obtained using a lamp not provided with a reflector.

FIGS. 12a and 12b show another design of a projector 89 partially surrounding a light source which can be advantageously used for lighting shop windows.

FIG. 13 shows a cut-away section of a decorative glassware arrangement obtained by molding, in which the lower part 90 has been molded on a core calculated so as to have the same characteristics as the internal surface of the projector shown in FIGS. 7a-7b, said lower part 90 being coated internally with a deposit of glossy material applied under vacuum, thus giving to this part the character of a reflector while the upper part 91, not coated with glossy material, remains translucent, and contributes to an environmental illumination. These glassware arrangements will be used in a valuable manner as a bedside or work lamp or still as wall fittings.

FIGS. 14a and 14b are similar to FIG. 3, but relate to a fluorescent tube. These figures show a solid angle of apex P containing all the rays originating from fluorescent tube 92, ending up at P and making an angle withthe perpendicular to said fluorescent tube, which is smaller than, or at most equal to 60. As shown, these rays are those which send the strongest contribution in radiating energy to point P. The total sum of rays reflected by point P in the direction of the work plane to be illuminated and corresponding to rays providing a strong contribution in energy as determined above, is contained in a cone of apex P which has a right section in the form of a very elongated oval, whose central strongly illuminated zone may be perfectly defined as far as value, form and direction are concerned. The various reflecting surfaces comprising the reflector may therefore, in accordance with the method disclosed hereinabove, be determined so as to solve a particular illumination problem such as the illu mination of a desk, shop, classroom, etc.

FIGS. a and 15b show a reflector 93, constructed according to the method disclosed hereinabove and providing for the distribution of light energy produced by a fluorescent tube 94 on a defined work surface. FIGS. 16a, 16b and 160 show another embodiment of a reflector associated with a fluorescent tube. The internal surface 95 of this reflector comprises sets of elementary reflecting surfaces forming a checker-work.

orientation of these elementary reflecting surfaces makes it possible to give a very inclined orientation to'the image of the source on the work plane with respect to the axis of the fluorescent tube, which can even extend to a position perpendicular to said axis. This arrangement is particularly valuable, for it makes it possible to illuminate a room with devices located on the sides and therefore outside the visual field of the users located in the central part of said room.

The devices according to FIGS. 15a-15b and 16a-16b-l6c may be provided, at the stand of the tube, with opaque plates whose dimensions are suitable for masking the tube from direct view. These devices may, in addition, if necessary, be closed by Plates made of spa e tmateria s Such projectors may be constructed by those skilled in the art by any appropriate means, in particular, by pressing or cambering of metal plates ultimately polished by any appropriate means or still further by molding of metals, glass or plastic materials which can eventually be polished by any appropriate means, or still further by forging, spinning, milling of a metal block or other.

What is claimed is:

1. A reflector for an illuminating device which has a light source for reflecting light, emanating from the light source, upon a work surface to illuminate the work surface according to a pattern, said reflector comprising:

a plurality of elementary reflecting surfaces each having an upper edge, a lower edge and two opposite side edges, said reflecting surfaces being disposed adjacent one another in at least one group having substantially continuous transitions between edges of vertically adjacent reflecting surfaces and having discontinuous, stepped transitions between edges of laterally adjacent reflecting surfaces;

each of said elementary reflecting surfaces comprising a skew concave mirror, each of the four said edges thereof being an arc of a circle, each of the four arcs being of different curvature;

the skew concave mirrors in said one group being individually oriented to collectively reflect light from said light source to an area of the work surface which is offset from being aligned with he portion, two laterally opposite side portions and a front portion and having a top wall surmounting said sidewall;

means defining an upper circular opening through said top wall and means defining a lower circular opening of said structure at and bounded by the lower periphery of said sidewall, said upper circular opening having a center which is substantially offset from the center of said lower circular opening toward said rear portion of said sidewall;

said structure being symmetrical about an axially extending diametral plane extending through said centers and bisecting said front portion and said rear portion;

said at least one group of elementary reflecting surfaces comprising said skew, concave mirrors being disposed upon one of said sidewall side portions;

said at least one group of elementary reflecting surfaces further comprising a second group of elementary reflecting surfaces comprising skew, concave mirrors each having an upper edge, a lower edge and two opposite side edges, said reflecting surfaces being disposed adjacent one another in at least one group having substantially continuous transitions between edges of vertically adjacent reflecting surfaces and having discontinuous, stepped transitions between edges of laterally adjacent reflecting surfaces; each of the four edges of each skew, concave mirror of said second group being an arc of a circle, each arc of the four arcs being of different curvature;

said second group of elementary reflecting surfaces comprising skew, concave mirrors being disposed on the other of said sidewall side portions;

the front portion of said sidewall having substantially circular-arc cross-sections in planes perpendicular to the longitudinal axis of said upper circular openmg;

the rear portion of said sidewall having means defining a plurality of stepped reflecting surface portions thereon;

the rear portion being disposed to reflect light incident thereon from said light source to an area of said work surface below said reflector offset in the direction of the front portion of said structure sidewall; and

the front portion being arranged for reflecting most of the light incident thereupon toward the rear portion of said sidewall.

3. The reflector of claim 2 wherein said top surface, adjacent said upper circular opening and adjacent said front portion of said sidewall is generally conically curved in a sector arranged to avoid incidence of light thereon from said light source.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION' Patent No. 3, TOO, 882 Dated October 2 4, 1972 Inventor(s) Jean PlanChOn It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Add to the heading:

Foreign Application Priority Data January 12, 1967 France 90,783

Signed and sealed this 13th day of March 1973.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT 3OTTS CHALK. Attesting Officer Commlssloner of Patents F ORM PO-OSO (IO-69) USCOMM-DC 6Q37b-P69 n us. GOVERNMENT FRINHNG O'IICI nu o-asa-ua

Claims

1. A reflector for an illuminating device which has a light source for reflecting light, emanating from the light source, upon a work surface to illuminate the work surface according to a pattern, said reflector comprising: a plurality of elementary reflecting surfaces each having an upper edge, a lower edge and two opposite side edges, said reflecting surfaces being disposed adjacent one another in at least one group having substantially continuous transitions between edges of vertically adjacent reflecting surfaces and having discontinuous, stepped transitions between edges of laterally adjacent reflecting surfaces; each of said elementary reflecting surfaces comprising a skew concave mirror, each of the four said edges thereof being an arc of a circle, each of the four arcs being of different curvature; the skew concave mirrors in said one group being individually oriented to collectively reflect light from said light source to an area of the work surface which is offset from being aligned with he light source; the plurality of elementary reflecting surfaces further including at least one additional group thereof having substantially continuous transitions between edges of vertically and laterally adjacent reflecting surfaces; and the concave mirrors in said one additional group being individually oriented to collectively reflect light from said light source onto said at least one group comprising said skew, concave mirrors.

2. The reflector of claim 1 comprising: a generally inverted bowl-shaped structure having a generally cylindrical sidewall divided into a rear portion, two laterally opposite side portions and a front portion and having a top wall surmounting said sidewall; means defining an upper circular opening through said top wall and means defining a lower circular opening of said structure at and bounded by the lower periphery of said sidewall, said upper circular opening having a center which is substantially offset from the center of said lower circular opening toward said rear portion of said sidewall; said structure being symmetrical about an axially extending diametral plane extending through said centers and bisecting said front portion and said rear portion; said at least one group of elementary reflecting surfaces comprising said skew, concave mirrors being disposed upon one of said sidewall side portions; said at least one group of elementary reflecting surfaces further comprising a second group of elementary reflecting surfaces comprising skew, concave mirrors each having an upper edge, a lower edge and two opposite side edges, said reflecting surfaces being disposed adjacent one another in at least one group having substantially continuous transitions between edges of vertically adjacent reflecting surfaces and having discontinuous, stepped transitions between edges of laterally adjacent reflecting surfaces; each of the four edges of each skew, concave mirror of said second group being an arc of a circle, each arc of the four arcs being of different curvature; said second group of elementary reflecting surfaces comprising skew, concave mirrors being disposed on the other of said sidewall side portions; the front portion of said sidewall having substantially circular-arc cross-sections in planes perpendicular to the longitudinal axis of said upper circular opening; the rear portion of said sidewall having means defining a plurality of stepped reflecting surface portions thereon; the rear portion being disposed to reflect light incident thereon from said light source to an area of said work surface below said reflector offset in the direction of the front portion of said structure sidewall; and the front portion being arranged for reflecting most of the light incident thereupon toward the rear portion of said sidewall.