US3650185A

US3650185A - Foot for compacting roller

Info

Publication number: US3650185A
Application number: US63075A
Authority: US
Inventors: Harry H Takata
Original assignee: Raygo Inc
Current assignee: Caterpillar Paving Products Inc
Priority date: 1970-08-12
Filing date: 1970-08-12
Publication date: 1972-03-21
Anticipated expiration: 1989-03-21
Also published as: BE770190A; CA932190A; DE2133539A1; FR2101480A5; BR7105194D0

Abstract

An earth compacting roller having toothlike feet projecting from its cylindrical surface, the feet being arranged in circumferentially and axially spaced staggered relationship and the feet having an elliptical cross section with the major axis of the ellipse normal to the roller axis and the surfaces of the feet so shaped that the leading and trailing edge surfaces of at least the base portions of the feet are defined by curved lines that are substantially involutes generated from a base circle the radius of which is no larger than that of the cylindrical surface of the roller.

Description

United States Patent Takata 1451 Mar. 21, 1972 54] FOOT FOR COMPACTING ROLLER 1,145,302 6/1957 France ..94/50 PR [72] Inventor: Harry H. Takata, Golden Valley, Mmn. Primary Examiner jacob L. Nackenofi. [73] Assignee: Raygo, Inc., Minneapolis, Minn. Attorney-Ira Milton Jones [22] Filed: Aug. 12, 1970 [57] ABSTRACT [21] Appl. No.: 63,075

An earth compacting roller having toothlike feet projecting from its cylindrical surface, the feet being arranged in circumferentially and axially spaced staggered relationship and the '1 feet having an elliptical cross section with the major axis of the [58] Field of Search ..94/48, 50, 50 PR, 301/43, 44 ellipse normal to the roller axis and the surfaces of the feet so I 56] References Cited shaped that the leading and trailing edge surfaces of at least the base portions of the feet are defined by curved lines that UNITED STATES PATENTS are substantially involutes generated from a base circle the 3 252 391 5/1966 D115 ..94 50 PR adhls which is larger than that cyhhdhca surface 3,483,806 l2/l969 Williamson ..94/50 R 3,276,337 10/1966 Gardner ..94/50 R FOREIGN PATENTS OR APPLICATIONS 996,262 6/1965 GreatBritain ..T..II.I94/"50 PR 12 Claims, 10 Drawing Figures PATENTEDHARZI I972 650, 1 85 SHEET 1 [IF 5 Harryflff'akaia PATENTED ZI i973 3,650,185

' sum 5 0F 5 DRUM C. D.

Her ETakaza FOOT FOR COMPACTING ROLLER This invention is concerned with the problem of compacting loose material such as earth, sand and dumped refuse and trash, by means of heavy roller equipped machines.

It has long been known that a plain surfaced cylindrical roller is by no means an effective tool for compacting loose material. This is because the area of the roller in contact with the terrain over which it rolls is so large that it imposes relatively low force per unit area upon the material to be compacted, with the result that the desired densification or compaction can be obtained only by numerous traverses of the roller, if in fact it can be obtained at all.

To increase the compacting force per unit area of such rollers, it has become conventional to equip them with feet that protrude radially from the cylindrical surface of the roller at axially and circumferentially spaced intervals. The well known sheeps-foot roller exemplifies apparatus of this type.

As the earth compacting art has advanced, it has been learned that the shape of the feet on a compacting roller is critically importantto the efficient operation of the machine. It has also been observed that a compactor foot, to be efficient and satisfactory in operation, must meet a number of different requirements; and accordingly a variety of differently shaped compactor feed have been proposed, each intended to fulfill one or more of these requirements. However, no compactor foot heretofore available has satisfactorily met all of these requirements.

One of the attributes of a good compactor foot is a selfcleaning shape so that despite the relatively close spacing of the feet on the roller required to assure that the weight of the compacting machine will be borne by the feet and not the surface of the roller from which they protrude, the material being compacted does not become lodged between the feet and any such material which does tend to adhere to the roller is easily cleared therefrom by stationary cleaning fingers that project between axially adjacent feet.

A good compactor foot also should have a tapered shape with a decreasing cross section towards the tip so that it sinks relatively deeply into the material when the density thereof is low, enabling the roller to effect rather rapid preliminary densification, and then as the density of the material increases, it sinks in less and less deeply. Accordingly at each successive pass the foot presents a smaller surface area to the material to insure that in the final few passes the material will be subjected to the highest possible compacting force per unit area obtainable with a given machine with the result that the maximum possible compaction is achieved in a relatively short time.

Another very important requirement of a good compactor foot is that it leave the material being compacted without disturbing the already compacted material. Not only does this capability assure against objectionable shearing of the compacted material, but it also gives 'the foot the desired selfcleaning characteristics, with the result that less power is needed to propel the machine across the ground.

The present invention provides a compactor foot that satisfies all of the aforesaid requirements.

In general, the invention is premised upon the recognition that the tendency for material to lodge between the feet of a footed roller can be substantially overcome by so shaping the feet that the included angle between all surfaces of adjacent feet is greater than the angle of friction of the material when it is in motion and the combination of this principle with a recognition of the advantages of involute curves as applied to the shape of a roller foot.

With these observations and objectives in mind, the manner in which the invention achieves its purpose will be appreciated from the following description and the accompanying drawings, which examplify the invention, it being understood that such changes in the specific apparatus disclosed herein may be made as come within the scope of the appended claims.

The accompanying drawings illustrate three complete examples of the embodiment of the invention constructed according to the best modes so 'far devised for the practical-application-of the principles thereof, and in which: FIG. 1 is a perspective view of a portion of a compactor roller that is provided with feet embodying the principles of this invention;

FIG. 2 is an end view of a portion of the roller illustrating several of the feet thereon in side elevation and depicting the manner in which the feet enter and leave the ground or other material being compacted;

FIG. 3 is a sectional view through FIG. 2 on theplane of the line 3-3 to illustrate the profile of the feet as viewed from either edge thereof;

FIGS. 4 and 5 are, respectively, a side view and a plan view, both on an enlarged scale illustrating how curved lines that are substantially involutes generated from a base circle having a radius substantially no larger than that of the roller surface are employed to govern or produce the fore and aft shaft of the feet in that embodiment of the invention shown in FIGS. 1-4;

FIG. 6 is a side view, on a smaller scale, of a foot like that shown in FlG. 4 but having an end surface of slightly modified shape;

FIGS. 7, 8, and 9 are respectively a side view, an edge view and a plan view of a foot which embodies the advantageous features of this invention but is especially well adapted for sanitary land fill usage wherein trash and rubbish and all forms of loose material must be broken up; and

FIG. 10 is a diagrammatic view illustrating the manner in which the fore and aft shape of the foot is derived.

Referring now more particularly to the accompanying drawings, the numeral 5 designates generally a compactor roller that is provided with a plurality of feet 6, each embodying the principles of this invention. Compacting machines which are not self-propelled usually have two such rollers, but in self-propelled machines there are four, each in the position of a wheel of a more or less conventional four-wheeled vehicle. In the embodiment of the invention illustrated, each roller comprises a cylinder or drum mounted on one of the rubber tired wheels 7 of the compacting machine, all four of which are usually power driven to afford traction for the vehicle.

The feet 6 are arranged in several ranks that extend circum-.

ferentially around the roller and in several rows that extend parallel to the roller axis. The feet in each row are in axially offset relation to the feet in the adjacent rows, and the spacing between circumferentially adjacent feet is less than the circumferential width of a foot. Thus, considering the roller generally, through its feet are in staggered relation to one another all around and along it, they are relatively close to one another, and definitely close enough to assure that the weight of the machine will be borne by the feet and not the roller from which they protrude.

Each foot has a longitudinal axis 9 which coincides with a radial to the roller axis as indicated in FIG. 4. The axis 9 also coincides with and defines the intersection of two planes of symmetry of the foot. One of these planes, designated by the line 10 in FIG. 5, is normal to the roller axis and the other, designated by the line 11 in FIG. 5 contains the roller axis.

Of particular importance is the shape of the base portion of the foot, that is, the portion of the foot which is nearest to the cylindrical surface of the roller proper, for any material that sticks to this portion of the foot tends to pick up additional material by adhesion and thus start a build-up.

The base portion of the foot of this invention is substantially elliptical in cross section, on any plane normal to the longitudinal axis 9, as best seen in FIG. 5. The major axis of the ellipse coincides with the plane 10 that is normal to the roller axis and lies on the longitudinal axis of the foot; the minor axis of the ellipse coincides with the plate 11 that lies on or contains both the longitudinal axis of the foot and the roller axis. In the embodiment of the invention disclosed, the dimensions of the foot on the plane of the major axis of the ellipse are between two and three times the dimensions thereof on the plane of the minor axis of the ellipse. The height of the foot should be at least one-half the maximum width of the foot at the base thereof where it is affixed to the roller.

Each foot tapers radially outwardly of the roller towards its longitudinal axis 9, with all opposite surfaces thereof converging towards one another. Even at the junction of the foot with theroller, the surfaces of the foot are tapered. Furthermore, along the height of the foot, the taper is increasingly greater.

The shape of the foot is such that every plane through the foot that is normal to the roller axis defines at its intersection with the foot surface a pair of opposite curved lines that are substantially involutes generated from a circle lying on the plate and concentric with the roller, which circle has a radius less than or at least not greater than that of the roller. A number of these curved lines or involutes" are depicted in FIG. 4 where they are designated a, b, c, d and e, and their corresponding planes depicted in FIG. 5 are identified pa, pb, pc, pd and pe. For the ideal shape, the curved surface-defining lines a, b, c, etc., should be true involutes generated from the base circle but, in practice, they maybe uniform radius curves which closely approximate true involutes. This is done to facilitate the making of the pattern for the feet.

The radius of the base circle determines the angle between the leading and trailing surfaces of the foot, on all planes intersecting the foot and normal to the roller axis, and the respective radials from the roller axis that lie on said planes and pass through the junctions of the foot surface with the surface of the roller. Hence, the determination of that radius begins with identification of the minimum acceptable angle between those foot surfaces and said radials. That angle is governed by the coefficient of friction between the foot surface and the material to be compacted.

The coefficient of friction between an average foot surface and earth, sand, gravel and the like, ranges between 0.25 and 0.36; and, for extreme conditions, it can be taken conservatively as 0.40. The angle whose tangent is 0.40 (and which angle will be identified hereinafter as the friction angle") is 21 48. Accordingly, the aforesaid angle between the surfaces of the feet and the radials passing through the intersections of those surfaces with the roller surface'should not be less than I05 54', which is one-half the friction angle.

With that angle identified and the diameter of the roller known, the base circle can be derived in the manner illustrated in FIG. 10. In this Figure, 0-F is a radial from the center of the roller which, at point P, passes through the intersection of the cylindrical surface of the roller with the surface of the foot, which may be its extreme leading or trailing edge surface or the intersection with the surface of the foot of any plane normal to the roller axis and passing through the foot. At the point P, a tangent to the foot surface must be at an angle E to 1 the radial 0-F of at least 10 54, which as already noted is one-half the aforesaid friction angle. That tangent is designated by A-B. (In FIG. 10 the angle E between 0-F and A-B is exaggerated for clarity of illustration). A perpendicular P-M erected upon A-B from the point P at which 0-F and AB intersect, will be tangent to the desired base circle, the radius of which is 0M.

Since the angle M0-P is equal to the angle E, the required radius of the base circle can also be obtained by trigonometry from the relationship:

' 0M OP cos E where OP is of course the radius of the roller and OM is the radius of the base circle.

Because all surfaces of the base portion of the foot are defined by curves lying in planes parallel to the direction of motion of the roller, which curves are defined by lines that are substantially involutes generated from a circle the radius of which is no greater than that of the roller surface, there are no re-entrant pockets between circumferentially adjacent feet, and, as illustrated in FIG. 2 the feet leave the material being compacted without laterally displacing or shifting the material. Such lateral displacing ment, generally referred to as shearing interferes with the attainment of the desired compaction since it disturbs the already compacted material. Accordingly the capability of the teeth to leave the depressions formed by the feet without disturbing the sides of the depressions, is a significant advantage of this invention. Not only diameter of the roller.

does it improve compaction of the material as the machine travels across the ground, but it also gives the feet the desired self-cleaning quality.

The spacing of the feet on the roller also has a bearing upon the shape of the feet. In order to assure effective compaction for a wide range of materials, the spacing of the feet must be proportioned to the size of the feet and the diameter of the drum. Under no circumstances, however, should the spacing between the feet be such-that the included angle between their nearest surfaces is less than the aforesaid friction angle. As long as this requirement is met, the material will not tend to stick to the feet.

The need to meet the foregoing requirement and the aforesaid determination of the involutes which define the shape of the sides of the feet, influences the cross sectional shape of the feet. To gain maximum compaction and traction, the leading and trailing surfaces of the feet that is, those surfaces thereof which are at the ends of the ellipse, should be relatively blunt. But such blunt leading and trailing surfaces have been found to require the outer portions 12 of the sides of the feet to be slabbed off, as shown in FIG. 4 especially where the feet are arranged side-by-side.

Preferably the feet are hollow, especially if they are relatively large, as for instance twelve inches wide and eight inches high. The outer ends of the feet are then formed by V-shaped pads 13 which are welded as at 14 to the feet. To facilitate welding the pads to the feet both have adjacent edge portions thereof chamfered to define weld pockets or channels which are filled by the welds 14. For the same purpose, the bottom edge of the base of the foot which fits against the cylindrical surface of the roller, has its outer margin chamfered at intervals to receive the welds 15 by which the foot is secured to the roller.

Attention is directed to the obtuse angle defined by the outer faces of the pads 13. As will appear from FIG. 2, this angle should be such that as a foot first steps onto the surface of the ground or other terrain being compacted, its pad comes down flat onto that surface. Accordingly the angle defined by the outer faces of the pad is a function of the An advantage of having the outer ends of the feet formed by welded-on pads is that it facilitates adapting the compacting feet to different soils. Thus by simply providing pads of different heights and different shapes, all interchangeable with one another, any type of soil can be compacted with the same basic foot. For instances where interlocking of sequentially placed layers of material is necessary, a pad thicker than that illustrated in FIG. 4 can be employed to increase the height of the foot and achieve deeper penetration, and where the soil is difficult to compact as in the case of wet adobe clay the pad 13 may have a shape such as shown in FIG. 6 wherein the outer surface thereof has substantial area and is curved and concentric to the roller axis to provide greater support and less surface disturbance with minimum penetration.

The modified embodiment of the invention illustrated in FIGS. 7, 8, and 9 is especially well adapted for sanitary land fill compaction in which it is necessary to cut and break up trash and rubbish'which may be strewn over the area to be compacted. With that in mind, the feet 20 (FIGS. 7, 8 and 9) have relatively sharp leading and trailing edges 21 which result from having both curved side faces 22 of the feet continue uninterruptedly to the leading and trailing edges 21 of the feet. The curvature of the side faces, as before, is such that all planes through the foot and normal to the roller axis are defined in part by opposite curved lines (a, b, 0, etc. in FIG. I which are essentially involutes generated from a base circle the radius of which in this case is quite a bit smaller than that of the roller surface. The involute lines of the leading half of the foot meet those of the trailing half on the transverse plane of symmetry designated by the line 11 in FIGS. 7 and 8 and as a result the opposite side faces of the foot have fairly well defined ridges 23 dividing the leading half of the side faces from the trailing half thereof.

Though the foot 20, as before, is hollow, its top or outer end is an integral part of the foot rather than a separate welded-on pad; but again the outer surface is formed by two flat faces 24 I disposed at an obtuse angle to one another.

From the foregoing description taken with the accompanying drawings it will be apparent that this invention provides a foot for a compacting roller that is highly efficient in compact ing loose material, has good cutting and crushing action on bulky material which might tend to form voids, and is substantially self-cleaning.

Those skilled in the art will appreciate that the invention can be embodied in forms other than as herein disclosed for purposes of illustration.

The invention is defined by the following claims:

1. A compacting roller of the type comprising a cylindrical drum having radially projecting feet at axially and circumferentially spaced intervals characterized by:

A. each foot having a longitudinal axis which is substantially radial to the drum axis, the foot being symmetrical to a pair of planes which lie on and intersect at said longitudinal axis, one of which planes lies on the axis of the drum and the other of which is normal to said drum axis;

B. the outer surfaces of each of the feet being tapered radi ally outwardly of the drum towards the longitudinal axis thereof so that all portions of the surface of any one foot are divergent to the surfaces of its adjacent feet, the angle between opposing surfaces of adjacent feet being at least as large as the angle of friction of material to be compacted by the roller;

C. the surface of the base portion of each foot being so shaped as to be substantially elliptical on planes normal to the longitudinal axis of the foot, the major axis of the ellipse lying on said plane which is normal to the drum axis; and

D. the surface of the base portion of each foot being further so shaped that every plane through the foot and normal to the drum axis intersectsthe surface of the base portion of the foot on lines that are substantially uniform curves which closely approximate true'involutes generated from a base circle concentric with the roller and having a radius 2. A compacting foot for a cylindrical soil compacting roller that has a predetermined radius, said foot having a longitudinal axis and being symmetrical to each of a first and a second plane that are perpendicular to one another and lie on said longitudinal axis, said foot being adapted for installation on the roller with a curved base surface on the foot matingly engaging the cylindrical surface of the roller and with said first plane normal to the roller axis and said second plane lying on the roller axis, said foot having a shape which is further' characterized by:

A. the base portion of the foot being of substantially elliptical cross section on planes that are perpendicular to both said first and said second plane, with the major axis of the ellipse coinciding with the first plane;

B. all surfaces of the foot other than said base surface being tapered outwardly from said base surface and toward said longitudinal axis; and

C. the surface of the base portion of the foot being so shaped that every plane through the foot parallel to said first plane intersects the surface of the base portion on lines that are substantially uniform curves which closely approximate true involutes generated from a base circle that is concentric to and smaller than the circumference of the roller, the radii of said substantially uniform curves being substantially equal for all of said planes.

3. The compacting foot of claim 2, further characterized in that the elliptical cross section of the foot is such that the ends of the ellipse are blunt.

4. The compacting foot of claim 3, further characterized in that all surfaces of the base portion of the foot are curved while, outwardly of the base portion, the sides of the foot are slabbed off and substantially flat.

5. The compacting foot of claim 2, further characterized in that the outer end portion of the foot is formed by a pad which is initially separate from the foot but is welded thereto.

6. The compacting foot of claim 2, further characterized in that the outer end of the foot is defined by a pair of obtusely divergent flat surfaces which meet along a ridge that is parallel to the minor axis of the ellipse and that lies on said second plane of so that said ridge forms the outermost boundary of the foot.

7. The compacting foot of claim 5, wherein the outer surface of the pad is defined by a pair of obtusely divergent flat faces which meet along a ridge that is parallel to the minor axis of the ellipse and that lies on said plane of symmetry which is parallel to the roller axis.

8. The compacting foot of claim 5, wherein the outer sur face of the pad is curved and concentric to the base surface.

9. The compacting foot of claim 6, further characterized in that the elliptical cross sectional shape of the foot is such that the ends of the ellipse are of small radius, so that the leading and trailing edges of the foot are relatively sharp.

10. The compacting foot of claim 2, further characterized in that on each of said planes through the foot, the angle between a radius of the roller that intersects its surface at the junction point of the surfaces of the foot and roller, and a line that passes through said junction point and is perpendicular to the radius of the curved line formed by the intersection of said plane through the foot with the foot surface, is .not less than one-half the friction angle of the material to be compacted.

11. The compacting foot of claim 10, wherein said angle is 1054.

12. A compacting foot for a cylindrical soil compacting roller that has a predetermined radius, said foot having a longitudinal axis and being symmetrical to each of a first and a second plane that are perpendicular to one another and lie on said longitudinal axis, said foot being adapted for installation on the roller with a curved base surface on the foot matingly engaging the cylindrical surface of the roller and with said first plane normal to the roller axis and said second plane lying on the roller axis, said foot having a shape which is further characterized by:

A. the base portion of the foot having an elliptical cross section on planes through the foot normal to its longitudinal axis, with the major axis of the ellipse lying on said first plane;

B. all surfaces of the foot other than said base surface tapering inwardly toward its longitudinal axis from the base of the foot to its outer end;

C. the base portion of the foot being so shaped that every plane passing through the foot and parallel to said first plane intersects the surface of the base portion on a pair of opposite convergent lines that are substantially uniform curves which closely approximate true involutes generated from a base circle that is concentric to the axis of the roller on which the foot is mounted, the radius of said base circle being substantially equal to the radius of the roller times the cosine of one-half the angle of friction of material to be compacted; and i D. the taper of the surface of the foot outwardly of its base portion being more abrupt than that of its base portion.

. UNITED STATES PATENT OFFICE (CERTIFICATE OF CORRECTION Patent No. 3 50 1 5 Dated March 2l, 1972- Inve fl Harry H. Takat a It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below: I

line .24; "feed" should read --feet-- Column 1 I Column 2 line 17; "shaft" should readshape- Column 2 line 46; "through" should read --though-- Column 2 line 68; "plate" should read --plane-- Column 3 line 10; "plate" should read --plane-- Column v3 line 17; "maybe" should read --may be-- Column 3 line 70; "displacing'ment" should re'ad--displacement-- Column 4 line 48; "instances" should read --instance--- Column 5 line 41 Claim 1 D; insert ---substantially equal to the "radius of the roller times the cosine of one- -half the angle of friction of material 'to be compactedafter radius-- Column 6 line 2G Claim 7',- delete "of symmetry which is parallel to'the rolleraxis" after "plane gn and sealed this hth day of July 19 (SEAL) Attcst:

,ED/IA'IUJ PLl-JMJIETClIL HQ, JR. ROBERT GOTTSCHALK Attes-ting Officer Commissioner of Patents FORM Po1O50(1o69) uscoMM-Desoam-Pesz U.5, GOVERNMENT PRYINTING OFFICE 1 I969 o366-334 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTIGN Patent No. 3,650,185 Dated March 21, 1972 Inventor(s) Harry H. Takata It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Column 3, line 38, "10 105 5 should read 10 54' Signed and sealed this 19th day of December 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissioner of Patents F ORM P04 050 (10-69) USCOMM-DC 60376-P69 U.S. GOVERNMENT PRINTING OFFICE I969 0-366-334,

Claims

1. A compacting roller of the type comprising a cylindrical drum having radially projecting feet at axially and circumferentially spaced intervals characterized by: A. each foot having a longitudinal axis which is substantially radial to the drum axis, the foot being symmetrical to a pair of planes which lie on and intersect at said longitudinal axis, one of which planes lies on the axis of the drum and the other of which is normal to said drum axis; B. the outer surfaces of each of the feet being tapered radially outwardly of the drum towards the longitudinal axis thereof so that all portions of the surface of any one foot are divergent to the surfaceS of its adjacent feet, the angle between opposing surfaces of adjacent feet being at least as large as the angle of friction of material to be compacted by the roller; C. the surface of the base portion of each foot being so shaped as to be substantially elliptical on planes normal to the longitudinal axis of the foot, the major axis of the ellipse lying on said plane which is normal to the drum axis; and D. the surface of the base portion of each foot being further so shaped that every plane through the foot and normal to the drum axis intersects the surface of the base portion of the foot on lines that are substantially uniform curves which closely approximate true involutes generated from a base circle concentric with the roller and having a radius

2. A compacting foot for a cylindrical soil compacting roller that has a predetermined radius, said foot having a longitudinal axis and being symmetrical to each of a first and a second plane that are perpendicular to one another and lie on said longitudinal axis, said foot being adapted for installation on the roller with a curved base surface on the foot matingly engaging the cylindrical surface of the roller and with said first plane normal to the roller axis and said second plane lying on the roller axis, said foot having a shape which is further characterized by: A. the base portion of the foot being of substantially elliptical cross section on planes that are perpendicular to both said first and said second plane, with the major axis of the ellipse coinciding with the first plane; B. all surfaces of the foot other than said base surface being tapered outwardly from said base surface and toward said longitudinal axis; and C. the surface of the base portion of the foot being so shaped that every plane through the foot parallel to said first plane intersects the surface of the base portion on lines that are substantially uniform curves which closely approximate true involutes generated from a base circle that is concentric to and smaller than the circumference of the roller, the radii of said substantially uniform curves being substantially equal for all of said planes.

8. The compacting foot of claim 5, wherein the outer surface of the pad is curved and concentric to the base surface.

10. The compacting foot of claim 2, further characterized in that on each of said planes through the foot, the angle between a radius of the roller that intersects its surface at the junction point of the surfaces of the foot and roller, and a line that passes through said junction point and is perpendicular to the radius of the curved line formed by the intersection of said plane through the foot with the foot surface, is not less than one-half the friction angle of the material to be compacted.

11. The compacting foot of claim 10, wherein said angle is 10*54''.

12. A compacting foot for a cylindrical soil compacting roller that has a predetermined radius, said foot having a longitudinal axis and being symmetrical to each of a first and a second plane that are perpendicular to one another and lie on said longitudinal axis, said foot being adapted for installation on the roller with a curved base surface on the foot matingly engaging the cylindrical surface of the roller and with said first plane normal to the roller axis and said second plane lying on the roller axis, said foot having a shape which is further characterized by: A. the base portion of the foot having an elliptical cross section on planes through the foot normal to its longitudinal axis, with the major axis of the ellipse lying on said first plane; B. all surfaces of the foot other than said base surface tapering inwardly toward its longitudinal axis from the base of the foot to its outer end; C. the base portion of the foot being so shaped that every plane passing through the foot and parallel to said first plane intersects the surface of the base portion on a pair of opposite convergent lines that are substantially uniform curves which closely approximate true involutes generated from a base circle that is concentric to the axis of the roller on which the foot is mounted, the radius of said base circle being substantially equal to the radius of the roller times the cosine of one-half the angle of friction of material to be compacted; and D. the taper of the surface of the foot outwardly of its base portion being more abrupt than that of its base portion.