US 3746425 A
The specification describes a reflective road marking means or traffic aid consisting of an aggregate comprising a multiplicity of reflective glass spheres incorporated into a matrix, the ability to reflect the impinging light being provided by the sphere portions protruding from and exposed at the surface of the traffic aid. Such multiplicity comprises a first plurality of spheres of given essentially uniform diameter and at least a second plurality of much smaller spheres arranged in the interspaces between the first spheres, to improve the population and the exposure of reflective spheres in and at the exposed surface of the traffic aid.
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Eigenmann [451 July 17, 1973 REFLECTIVE ROAD MARKING MEANS AND AGGREGATE (76} Inventor: Ludwig Eigenmann, Vacallo, Canton Ticino, Switzerland  Filed: Mar. 31, 197] [2|] Appl.No.: 129,921
 Foreign Application Priority Data Apr 7, 1970 Italy 23O0l A/7O (52] US. Cl 350/109, 350/105, 94/1.5 [5 l] Int. Cl. G02b 5/12  Field of Search 94/l.5;
 References Cited UNITED STATES PATENTS 2,330,843 l0/l943 Rodli et al. 350/105 2,294.930 9/1942 Palmquist 350/l05 3,030,870 4/1962 Gill, Jr. 350/105 Primary Examiner-David Schonberg Assistant ExaminerMichael J t Tokar AttorneyMichael S. Striker  ABSTRACT The specification describes a reflective road marking means or traffic aid consisting of an aggregate comprising a multiplicity of reflective glass spheres incorpo rated into a matrix, the ability to reflect the impinging light being provided by the sphere portions protruding from and exposed at the surface of the traffic aid. Such multiplicity comprises a first plurality of spheres of given essentially uniform diameter and at least a second plurality of much smaller spheres arranged in the interspaces between the first spheres, to improve the population and the exposure of reflective spheres in and at the exposed surface of the traffic: aid.
10 Claims, 6 Drawing Figures REFLECTIVE ROAD MARKING MEANS A'ND AGGREGATE BACKGROUND OFTHE INVENTION This invention relates to the art of road marking and more particularly of providing on a road surface and more specifically on the surface of a strip material laid upon and firmly secured toa roadsurface aplurality of properly arranged and spaced elements eachtcapable of brilliantly reflecting light striking the same elements, regardless of the angle of incidence of that light, the said elements consisting individually of a heterogeneous composition, or aggregate, comprising a multiplicity of light reflecting spheres, such as the glass spheres known asiBallottinhand a suitable binder,-gen
erally a solidified plastic material, adapted for making the said element capable of resisting weather and withstanding heavy traffic without fracture. Usually, such elements consist of moulded pads ,permeated by said spheres, which constitute the major partof the weight of each pad.
This art is a well worked one and a wide technical and patent literature has heretofore been published thereabout. Whenrelating specifically toaroad marking strip material consistingofa base strip for superimposing onand securing to a road surface, and having a plurality of reflective elementsor .padssecured in the upper face of said base strip, reference ishereinmade to my prior US. Pat. application Ser. No. 757,409, filed on Sept. 4, l968.(NowU.S. Pat. No. 3,587,415). In such my prior patent specificatiomhow acomposite traffic aid of the character referred to .abovecan be provided, has been described indetail, materials and composition inclusive and, therefore, no further expla nations as to said materials and compositions are believed to be necessary for-complete understanding of the invention as defined and described below, and how the same can be carried out by combining the features and the improvements of the invention with :the said prior art. I
' Briefly focusing now the aspects of interest forthe invention, it is evident that the reflective ability of each element or pad is a function of the *ratiobetween the exposed area of the pad and that provided by the sum of the actually exposed areasof the glassspheresrSuch aggregate elements consist of a multiplicity of spheres incorporated in a matrix of plastic material, and the glass spheres adjacent to the upper orexposed surface of the element or partprotrude more orless-and canbe impinged by light. Therefore, it is desirable to incorporate as many glass spheres in the plastic matrix as is consistent with obtaining a satisfyingly strong and not easily crumbled device. The prior art (see forexample the British Pat. No. 688,3l0,to R. S. Clare & Company Limited) has taught that up to 60 percent of glass spheres canbe used and has been foundtoproducesatisfactory results. ltis howeverto be taken into account that such ratio, by weight, is far fromproviding a corresponding ratio betweenthe actual exposed areaofthe notreflective matrix and that-of the sum of the exposed areas of the spheres. It is also to be taken into account that the average projection of the spheres from the actual surface of the adjacent matrix is far less than the radius of samespheres. When a sphereisnearly half exposed, it will readily be stripped off bythe traffic. The total reflectivity of elements of the type referred to above is therefore, more precisely, a function of the actual ratio of the volume totalled by the spheres to the volume of the heterogeneous mass consisting of the spherestand of the matrix. On the other part, a mass prejudice of the resistance to crumbling and weather.
Consequently, itis an object iof this invention to provide a new and improved reflective element or pad adapted to improve the nighttime visibility of road, markers, having an exposed surface on which a multiplicity of reflective and generally small spheres are partially exposed, and wherein said multiplicity comprises anumberof bright spots forming spherical portions, remarkably greater than heretofore possible, thus im- .provingthe brilliancy of the reflective elementor pa'd,
when impinged by light.
BRIEF SUMMARY OF THE INVENTION Essentially, the invention comprises providing a first plurality of first reflective spheres of substantially uniform given diameter and adapted? to be essentially orderly arranged .in a given volume, forming voids or spaces therebetween, providing at least a secondplurality of second reflective spheres of diameter less one 'fifthof-said given diameter, the amount ofsaid second spheres being such that substantially all said second spheres can be located in the said voids or spacesbetween said first spheres, and 'a matrix-forming material in such amount to fill .all voids or spaces resulting be tween said first and second spheres thus arranged in said givenvolume, forming a heterogeneous aggregate consisting of said first spheres, said second spheres and said matrix-forming material in the said volumetrically determined amounts, and producing highly reflective elements onpads from said aggregate, said elements or pads being heterogeneous but coherent and essentially freeof voids and thus capable to withstand weatherand heavy traffic when used to form an efficient aid tberedrawing,-forming an essential component of i this disclosure.
THE SEVERAL VIEWS OF THE DRAWING FIG. 1 illustrates, diagrammatically, partly in elevation and partly in sectional view, the theoretical rarrangement in the space of the lesser number of spheres of two different diameters, necessary for forming a three-dimensional arrangement;
FIG. 2 fragmentarily illustrates, in enlarged scale, an aggregate produced according to the invention, in a cross-sectional view taken in the plane indicated at Illl in FIG. 4, the spheres being shown in side view;
FIG. 3 illustrates diagrammatically and fragmentarily, the exposed surface of a heterogeneous mass consisting of the aggregate of FIG. 2, as viewed in the direction indicated by arrow III in FIG. 4 wherein a layer adjacent to said surface is shown, in still more enlarged cross-sectional view, taken in the plane indicated at IV-IV in FIG. 2;
FIG. 5 is a graph which visualized the relationships between the volumes of heterogeneous mass and of spheres of given different diameters which can be present in said mass; and
FIG. 6 is another graph which approximately visualized the improvement of the invention, in term of the area of reflective components exposed to light.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT The principles found and applied according to the invention will be apparent upon a consideration of FIGS. 1 to 4 inclusive. There it is assumed that given threedimensional confined space, having a very great volume (so that marginal effects can be disregarded), is filled with a multiplicity of first spheres 10 of uniform given diameter D, which are arranged so that the greatest possible number of them will be located in said space, any group of four adjacent spheres being arranged as shown in FIG. 1. More particularly, assuming that such space if formed by the inside of a box having a planar bottom surface, such surface will firstly be covered by a layer of spheres 10 arranged as shown in FIGS. 2 and 4, this arrangement providing the maximum surface coverage. The centers of spheres 10 in each group of three adjacent spheres define the vertices of an equilateral triangle. The said surface will be completely covered by a multiplicity of such triangles. At the center of each group of three co-planar adjacent spheres a cavity will be formed within the spherical surface of said spheres. By then arranging a second layer of similar spheres 10 on the thus arranged bottom layer, each sphere of the second layer wil seat into one of such cavities and the spheres will be similarly arranged to define, with their centers, similar equilateral triangles, the vertices of which will be located over the centers of the triangles formed by the centers of the spheres of the underlying layer, and so on until complete filling of the three-dimensional space available. As above stated, this arrangement is the one which ensures that the maximum possible number of spherical bodies can be contained in a space very great relative to the individual volumes of the spheres.
In such arrangement the centers of any group of adjacent spheres 10 of uniform diameter D define the vertices of a tetrahedron.
Upon an easy mathematical analysis, it can be found that the sum of the individual volumes V,) of all spheres represents about 74 percent of the volume of the confined space V,), according to the expression which justifies the teaching of prior art.
It is evident that the mathematically calculated 74 percent is a purely theoretical value. It could be attained only by making use of perfectly spherical bodies of exactly uniform diameter (which inter alia involves a very costly selection) and a perfect and even arrangement of spheres in the available space. In the actual manufacture of an aggregate for use in the field of the invention, a volumetric occupation of 60 percent of the available space is however quite feasible. It has been experimentally found that a value such as V, 60% V, can be generally attained by carefully mixing, with 40 percent by volume of conventional matrixforming compound, 60 percent, by volume, of spheres the percent at least of given diameter D plus-minus 10 percent and where the amount of spheres of diameter greater or smaller than plus or minus 20% D is nearly insignificant. This value 10/6 of the ratio V /V, can be therefore assumed as actually valid, even being not limitative for the invention, as being influenced by several factors, such as the uniformity of the available glass spheres, the mixing procedure and so on.
Now, it is evident that in a confined space, filled by spheres 10 of given diameter D, at least 74 26 percent, theoretical, and actually at least 100 60 40 percent about of the available volume will remain unoccupied by reflective material. According to the invention, a substantial part of such remaining volume (V,) is at its turn occupied by spheres of smaller diameter d, provided that such smaller diameter d is not greater than one-fifth of diameter D (the maximum theoretical ratio d/D is l/4.45 about), for seating at least one smaller sphere l2 inside any group of four tetrahedrally arranged spheres 10, as shown in FIG. 1.
This remaining volume (V,) is however formed by the sum of the complex shaped spaces defined by the convex tangentially abutting surfaces of the adjacent spheres 10 of greater diameter D. Theoretically only by making use of spheres 12 of infinitesimal diameter d there would be possible to occupy the 74 percent of the theoretical 26 percent of the original volume (V,), which is unoccupied by the bigger spheres 10, to obtain that all spheres 10 and 12 will occupy the (0.74 (26/100) 0.74 93.24 percent of the original volume. Actually, the degree of volumetric occupation of the spaces confined between the bigger spheres 10 of diameter D is a function of the mean diameter d of the smaller spheres 12. The mathematical analysis of such degree is not only extremely complicated but also improper in view of the unavoidable variations of the actual diameters D and d and of the actual arrangement of the bigger and smaller spheres, these parameters causing that only statistical considerations are valid.
The graph of FIG. 5 indicates, in percent, the volumetric occupation of a given volume in actually practicing the invention. The value of percentage is indicated by whole numbers along the ordinate at left, the level 100 corresponding to the entire volume V, of the aggregate. On the ordinate at right there is indicated the remaining volume V to be occupied by the matrix. The percentages are indicated as a function of the value of ratio d/D, indicated on the abscissa. The nearly horizontal curve V,, at 60 percent about indicates that the bigger spheres of diameter D take up the 60 percent about, thus leaving a remaining volume V,- of 40 percent about, available for the smaller spheres and for the matrix.
The curve V, indicates how the smaller spheres 12 can take up as much volume as the diameter d thereof decreases, the curve V tending to flatten at 24 percent about, this latter percentage being the 60 percent of the remaining 40 percent of volume V unoccupied by bigger spheres. The curve V indicates the total volume jointly taken up by the agglomerated bigger and smaller spheres and 12, respectively. From the graph of FIG. 5 there is readily evident that by properly mixing suitably selected volumetric amounts of spheres of substantially uniform diameter D and of smaller spheres of diameter d not greater than 1/7 D, a substantial increase of the volume actually occupied by the spheres can be obtained. By selecting a quite feasible ratio d/D of 0.1, the volume occupied by the spheres is well over the 80 percent of the total volume V, of the agglomerate.
Considering now the actual structure of an aggregate produced according to the invention: the prior art has suggested the use of glass spheres of diameter up to 3 millimeters about and, preferably, of l millimeter about. It has been surprisingly found that an agglomerate comprising suitably proportioned bigger and smaller spheres, as above, has a markedly improved property of weather and traffic resistance, and that reflective elements and pads, very difficult to be crumbled, can incorporate glass spheres of diameter up to 6 mm. about. Taking further into account the availability of satisfyingly spherical glass spheres, it has been found that an agglomerate according to the invention can be provided by mixing 100 parts, by weight, of reflective spheres consisting of 95 parts, by weight, of glass spheres of from 6 to0.08 mm. and preferably from 1.2 to 0.2 mm. diameter, and 5 parts, by weight, of glass spheres of from 0.8 to and 0.01 mm. and preferably from 0.2 and 0.03 mm. diameter, provided that (a) the ratio d/D between the diameters of smaller and respectively of bigger spheres is comprised between 0.2 and 0.05 and preferably between 0.17 and 0.08, and that (b) at least 80 percent and preferably 90 percent of the bigger spheres have diameters differing not more than plus 10 percent or minus 10 percent from the selected avarage diameter D thereof.
When the batch is to be mixed (a conventional mixer, such as a Bambury mixer, might as well be continuously fed with metered amounts), care is to be taken about the fact that the ingredients (bigger and smaller spheres and the matrix forming compounds) must be volumetrically measured, or their weights must be calculated from a volumetric basis. The suitably selected matrixforming components (according to the best current art) must be made use of in amounts calculated in terms of the actual volume which will be occupied by the matrix, when set, on the basis of the remaining volume V unoccupied by the spheres. A suitable excess, such as of 2 to 3 percent by volume, of said matrixfoming components, is preferably added to prevent any even minor void in the agglomerate'.
It has been surprisingly found that by agglomerating thus proportioned bigger and smaller spheres a sharp improvement of the brightness of the thus formed traffic aids, when impinged by light, has been obtained, said improvement being well greater that it might result from the increased volume occupation (from 60 percent about to 80 85 percent about) discussed above. The graph of FIG. 6 and the showing of FIG. 3 will now be referred to in the following proposed explanation of such unexpected phenomena.
It has been found that properly produced conventional agglomerates, that is comprising reflective spheres of one and essentially uniform given diameter,
when made use of in form of traffic aids on a road surface, have exposed surfaces wherein the spheres project from their matrixes for from one-half to one-fifth their radii. If, hypothetically, all spheres were half exposed, the trafi'lc aid surface will appear as shown in FIG. 2 (the part comprising the small spheres l2 representing the matrix, in such occurrence). The surface area actually covered by the uncoated half-spheres might comprise up to over percent of the said exposed surface (to 91 percent about, according to the expression 1r V576). On the contrary, the wearing of the matrix averages (according to extensive experimentation) down to a level such as indicated at L in FIG. 4, that is the glass spheres project above said level for a height S which is one fourth about of the radius r of the spheres.
In such most usual occurrence, the exposed surface of a traffic aid, comprising even theoretically perfectly matched and arranged spheres, will appear as shown in FIG. 3, where the exposed spherical bowls 10a of spheres l0 jointly cover not more than 40 percent or less of the said exposed surface. The curve A, of FIG. 6 indicates the sum of the exposed. areas of the spheres in terms of percent of the total area of the exposed surface of the traffic aid (percent A,), as a function of the ratio S/r between the actual projection of the spheresv from the matrix and the radius of each sphere, such curve tending to level at 91 percent about, for S/r 1.
Now, by providing a second plurality of smaller spheres evenly arranged in the matrix and therefore partially exposed in the hatched area of FIG. 3, the actual areal exposure of reflective components steps up to about twice the above indicated values. The curve A, of FIG. 6 illustrates how suchexposure increases as a function of the projection of the spherical bowls of both smaller and bigger spheres. Such increment, which is particularly important when S/r is relatively small, is explained by the fact that when the bigger spheres are deeply embedded in the matrix, some of the smaller spheres are located and exposed above the concealed portions of the bigger spheres, that is in the annular areas about the exposed spherical bowls 10a of FIG. 3 and within the circles, shown in phantom lines which indicate the contours of the corresponding concealed part of the spheres. Actually, the brightness of the improved reflective pads produced according to the invention is well over twice that of conventional ones, of like exposed surface and shape, because the smaller spheres average a projection proportionately greater than that of the bigger spheres.
In practicing the invention, it has been found that, while a substantial uniformity of diameter D of the bigger spheres is advantageous, that of the smaller ones is not critical, provided that the above discussed ratio d/D is maintained with relation to the diameter d of the greater ones of smaller spheres. A certain amount of still smaller spheres has been found useful as such smallest spheres can reach the locations where the spacing between the convex surfaces of the bigger spheres is very little.
Further, the invention has been described with reference to the use of only two pluralities of bigger and smaller spheres, in certain critical relationship. A third plurality of still smaller spheres can be made use of for occupying a part of the volume remaining between the smaller spheres. Such provision is quite feasible, in particular if bigger spheres of substantial diameter are made use of. For example, agglomerates from which pads and similar traffic aids having a surprisingly high reflective property and brightness can be produced, can comprise, for example, 60 percent about, by volume, of glass spheres of essentially uniform diameter of 3 mm. about, 22 percent about, by volume, of glass spheres of essentially uniform diameter of 0.3 mm. about, and 10 percent about, by volume, of glass spheroids of diameter not greater than 0.04 mm and including smallest spheres of diameters down to 0.01 mm. about, the volume occupied by reflective bodies totalling up to 92 percent about of that of the agglomerate, the matrix representing only 8 percent about of the latter. Spheres of 3 mm. and of 0.3 mm. of diameter and mixtures of spheroids of from 0.04 to 0.01 mm. diameter are easily available on trade, and, upon careful mixing, an agglomerate exceptionally resistant to weather (as being nearly totally inorganic) and to heavy traffic can be made.
It is evident that such further improved aggregate and the resulting marking means are well within the spirit and meaning of the invention and encompassed by the scope of the appended claims, together with any other equivalent structure, aggregate and traffic aid which can be construed from the approach and the teaching of same invention.
I claim: I
1. A marker, particularly for use on roadways to provide reflectivity when impinged by light, comprising a plurality of first spheres having substantially equal first diameters, said first spheres being arranged adjacent to each other and together occupying not less than approximately 60 percent of the total volume of the marker; a plurality of second spheres having substantially equal second diameters, said second diameters being at most equal to one-fifth of said first diameters, said second spheres being arranged in the spaces between said first spheres and substantially filling these spaces, and said second spheres together occupying not less than approximately 20 percent of said total volume; and binder material connecting said first and second spheres to each other and at least in part filling any remaining spaces between said spheres.
2. A marker as definedin claim 1, wherein the largest of said second diameters at most approaches oneseventh of the smallest of said first diameters.
3. A marker as defined in claim 1, all of said first diameters being between 6 mm and 0.08 mm whereby the average of said first diameters is between 6 mm and 0.08 mm, at least percent of said first diameters differing from the average thereof by at most 10 percent, all of said second diameters being between 0.8 mm and 0.01 mm whereby the average of said second diameters is between 0.8 mm and 0.01 mm, the largest of said second diameters differing from the average thereof by at most 10 percent, and the ratio of said largest second diameter to any of said first diameters being between 0.2 and 0.05.
4. A marker as defined in claim 3, all of said first diameters being between 1.2 mm and 0.2 mm whereby the average of said first diameters is between 1.2 mm and 0.2 mm, at least percent of said first diameters differing from the average thereof by at mpst 10 percent, all of said second diameters being between 0.2 mm and 0.03 mm whereby the average of said second diameters is between 0.2 mm and 0.03 mm, and said ratio being between 0.17 and 0.08.
5. A marker as defined in claim 1, wherein said second diameters are approximately equal to one-tenth of said first diameters; and further comprising a plurality of third of spheres having third diameters at most equal to one-eighth of said second diameters, said third spheres substantially filling the spaces formed by said first and second spheres.
6. A marker as defined in claim 5, said first spheres together occupying approximately 60 percent of said total volume, said second spheres together occupying approximately 22 percent of said total volume, said third spheres together occupying approximately 10 percent of said total volume, and said binder material occupying the remainder of said total volume.
7. A marker as defined in claim 1, wherein said first spheres together occupy approximately 60 percent of said total volume, and said second spheres together occupy approximately 20-24 percent of said total volume.
8. A marker as defined in claim 1, wherein said binder material completely fills all of the remaining spaces between said spheres.
9. A marker material as defined in claim 6, wherein said binder material occupies at most 8 percent of said total volume.
10. A marker material as defined in claim 1, wherein said first and second spheres comprise reflective glass spheres.
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