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United States Patent 3745658
Measuring and calculating apparatus with which engineering functions necessary to the designing layout and construction of structures such as roads, canals, etc., can be performed easily and accurately directly from a contour map of the area in which the structure is to be constructed, thereby eliminating the need for extensive on-site observations or time consuming template utilization.

Application Number:
Publication Date:
Filing Date:
Primary Class:
Other Classes:
33/1V, 235/88R
International Classes:
C08F10/00; (IPC1-7): G06C3/00; G01B5/26
Field of Search:
33/1V,1SB,1R,121,122 235
View Patent Images:
US Patent References:
2975521Area measuring deviceMarch 1961Holmes
2972810Device for computing areas and volumesFebruary 1961Davis
Primary Examiner:
Tomsky, Stephen J.
I claim

1. A slope intercept point indicator comprising

2. A slope intercept point indicator as in claim 1, wherein

3. A slope intercept point indicator as in claim 1, wherein the radiating scale has a groove running the length thereof; and the bar scale is arranged to slide freely in said groove.

4. A slope intercept point indicator as in claim 3, wherein

5. A slope intercept point indicator as in claim 1, wherein


1. Field of the Invention

This invention relates to measuring and calculating apparatus for performing engineering functions in connection with the layout and design necessary to construction of roads, canals, etc. While the engineering structure described herein in connection with the apparatus of the invention is a road it will be obvious that the same apparatus can be used in the design and construction of other similar constructions.

2. Prior Art

Modern road construction has developed in many areas in recent years. Formerly, roads were constructed to closely conform to the existing terrain and cut and fill operations were held to a minimum, This was satisfactory, so long as vehicles did not travel too fast and so long as the number of vehicles using them was not too great. Roads so constructed often produced a roller coaster effect on vehicles traveling over them and with the development of faster vehicles, and the great increase in the number of automobiles such roads were no longer satisfactory. It is now well recognized that modern highway construction requires a road with smooth surfaces and gentle horizontal and vertical curves. This means that extensive excavation and filling is often necessary to provide a smooth roadbed. Inasmuch as the expenses of construction are to a large extent directly related to the costs of excavating and the hauling and compacting of fill materials, it is highly desirable to construct a road such that a minimum amount of material must be moved and to make the haul lengths for that movement as short as possible.

The present invention provides an apparatus with which cut and fill volumes can be easily computed to offset each other, to the extent possible, by enabling an operator of the apparatus to calculate slope stake locations and to compute the effect of such locations as to fill and cut requirements from a contour map.

While some calculating devices have been available in the past for use in plotting a highway location, none have enabled an operator, using merely such apparatus and a contour map, to easily locate the intersection of the ground with that of a proposed side slope of the road and, based on that intercept point, to compute the volume of earth to be removed or needed to fill to achieve the desired construction. Instead, in the past, it has been necessary to plot cross-sectional areas at selected intervals along the road centerline prior to the computation of earthwork volumes. Such plottings frequently require actual on the job surveys and if a centerline is subsequently relocated, because of a terrain obstacle, for example, the plottings must be repeated. Since the cross-section plottings are taken at set stations along the road centerline radical terrain changes between the stations may not be considered in making the volume calculations.


Principal objects of the present invention are to provide apparatus for utilization with a contour map in determining intercept points between the ground and a road, or other such structure, side slope and in determining the volumes of material to be cut and to be filled incident to construction of the structure.

Another object is to provide such an apparatus that can also be used to quickly and easily properly position culverts, ditches and other such drainage structures necessary to proper construction of the structure to be built.

Principal features of the present invention include an indicator and a calculator, each of which is separately useful for various functions but that are used together to perform the total engineering functions set forth in the foregoing objects.

The indicator is used to locate intercept points of the ground and the side slope, thereby enabling computation, utilizing the calculator and without plotting, of either the amount of material needed to fill a section between stations to the desired roadbed level or the amount of material needed to be cut to produce a roadbed at the desired elevation and with the required side slopes.

The slope intercept point indicator consists of a series of radiating scales, each having a slot therein to receive a sliding bar. The bar has a pair of pointers mounted to slide therealong. A number of radiating scales are used to make up a complete set, with each having an indice on it expressing the relationship between gradations on the radiating scales and gradations on the associated sliding bar. Thus, the relationship may be any ratio between 1/2:1 and 10:1, to encompass the most common side slope ratios used. Obviously, however, other scales could as well be used in conjunction with other side slope ratios, should these be desired. The slope to be utilized, i.e. 2:1, 4:1, etc., is determined by the height differential between the road and the slope intercept point and the proper ratio is therefore determined by the point of intercept. Accordingly, several radiating scales may have to be tried before the proper one is determined. The indices on the radiating scales and sliding bar are scribed thereon in accordance with the scale of the contour map which is to be used. Generally, in highway construction operations, a map scale of 50 feet or 100 feet on the ground to a 1 inch map distance is used. Therefore, the indices on the radiating scales and sliding bar are preferably scribed in sets so as to provide for a utilization of the same radiating scale with either a 50 foot to 1 inch or 100 foot to 1 inch contour map. Either map can then be used, with different indices of the radiating scales and sliding bar being utilized as necessary.

As previously noted, the sliding bar has a pair of pointers mounted to travel on it. One such pointer may be utilized to transfer a proposed highway width from the sliding bar to a map starting reference point and the other pointer may be used to locate the point of intersection between an indice on the radiating scale with an actual map contour, which intersection establishes the slope intercept point.

Additional features include scales on the individual radiating scales which are used to compute either cut or fill. Folding scales are provided and have a zero beginning point located so as to facilitate computations. Means are provided to lock the sliding bar to the individual radiating scale when their proper relative positions are achieved.

The slope point indicator is used to locate an intercept point on a contour map, i.e. a point where the highway side slope intersects the normal terrain. The contour map used reflects elevations, so the difference in elevation between the intercept point and the highway shoulder at any station along the road is readily ascertainable, with the slope point indicator positioned so as to locate the intercept point. The indice markings between the side slope intersection and the roadbed correspond to elevations along the proposed slope line. The difference in elevation between the side slope elevation, as read directly from the slope point indicator, and the actual ground as indicated by the contours of the contour map, are readily determined.

The calculator is utilized to compute a running total of the various height differentials for a given section. Preferably, the calculator has two wheels axially connected to rotate independently of one another and a pointer, also connected so as to rotate about the axle. Scales are scribed on the wheels such that they can be used to input the elevation differentials, which are added or subtracted in the computer to give a total plus (fill) or minus (cut) of the height differentials incrementally determined along the base. The pointer may be arranged to turn an indicator located in the face of the top wheel so that each time the zero indice is passed on the scale, each zero passed representing 100 feet of height differential, one digit, in either a positive or a negative direction, depending upon whether the 100 foot of height differential represents cut or fill is changed with respect to the indicator. Utilizing two other scales scribed on each wheel, which scales correspond to the C and D scales of a standard slide-rule, the total net height differential can be multiplied by the increment of distance selected i.e. 5 or 10 feet, for example, to thereby determine the accumulated cross sectional area above or below the base line. To determine earthwork volume the distance between bases at adjacent stations along the road is multiplied by the cross sectional area computed, again using the C and D scales of the calculator, to thereby obtain the volume in cubic feet of material to be filled or cut. The volume thus obtained comprise the volume of cut or fill material necessary to construction of the highway side slope between stations along the road. The volume of cut or fill material necessary to construction of the highway roadbed itself is calculated by determining the differential elevation between the desired highway elevation and the ground elevation, multiplied by the width of the bed and the distance between stations along the road. The calculator is used to determine the summation of height differentials and the C and D scales are used to multiply the calculated total height differentials by the length between stations, to determine the earthwork volume necessary to adjacent stations.

The combined use of the indicator and calculator apparatus enables user to determine side slope locations and earthwork volumes without the use of extensive profile drawings or the need for on-site observations. As will be apparent the apparatus can be used with contour maps having any scale if the scale distances on the radiating scales and sliding bar are arranged to reflect the map scale.

Further objects and features of the invention will become apparent from the following detailed description, taken together with the accompanying drawings.


FIG. 1 is a top plan view of the cross sectional area calculator;

FIG. 2, a side view of the cross sectional area calculator taken on line 2--2;

FIG. 3, a side view of a segment of the cross sectional area calculator taken on line 3--3;

FIG. 4, a top plan view of the slope intercept calculator;

FIG. 5, a schematic view showing the drive assembly for the indicator of the calculator; and

FIG. 6, composite contour map section with proposed highway centerline thereon and a typical cross sectional profile.


Referring now to the drawings:

The cross sectional area calculator 10 consists of two wheels 11 and 12. Wheel 11 has the largest diameter and is fastened beneath wheel 12. The two wheels surround a common central post 13 and are held in place by a screw 14 threaded into one end of post 13. An indicator arm 15 is also held in place on the center post 13 by screw 14. A calculator base 16 is also provided and is secured to center post 13 by a screw 17 threaded into the other end of the post. While not always necessary an indicator 18, FIGS. 1 and 2, is preferably incorporated in the calculator and is connected to the indicator arm 15 such that as the arm is turned past a zero marking on a scale B of wheel 12, to thereby reflect 100 feet in differential elevation, the indicator 18 registers a 1, and so forth. The gearing for this relationship of the indicator arm 15 to indicator 18 is shown schematically in FIG. 2 and consists of a gear train having two gears 18a and 18b. Gear 18a is turned by the indicator arm 15 and as it rotates it turns the gear 18b which is formed around the indicator 18.

Wheel 11 has inner and outer scales C and A, respectively, scribed thereon and wheel 12 has inner and outer scales D and B scribed thereon. Scales A and B are reflections of one another and are arranged to be adjacent. Scales C and D, while separated by scales A and B are also reflections of one another.

In operation of the calculator to determine transverse cross sectional areas at stations along a roadway, for example, the A and B scales are utilized to determine a cumulative vertical height between the actual ground elevation and the proposed slope line at predetermined horizontal increment points spaced, for example, 5 feet apart. This cumulative height is calculated by setting the hairline indicator 15a on indicator arm 15 over the zero on scale A and rotating both scale A and indicator arm 15 together until the hairline indicator is aligned with a number on scale B representative of the ground elevation. Scales A and B are immobilized and indicator 15 is rotated to align the hairline indicator with the height of the proposed slope elevation on scale B. Scale A is released from scale B and, with indicator 15 held to scale A, is rotated until the hairline indicator 15a is aligned with the next ground elevation, as read on scale B. Scales A and B are again held together and the hairline indicator 15a is rotated until it is aligned with the height of the proposed slope line at the next increment point, as read on scale B. The procedure of unlocking scales A and B and rotation of hairline indicator 15a is then repeated at each predetermined selected increment point with the final reading on scale A reflecting the cumulative positive or negative height differential of the proposed slope to the ground at the selected increments. The cross sectional area is then determined by a multiplication of the cumulative height by the predetermined increment of distance, which in the example given is five feet. These multiplication functions are easily accomplished as conventional slide-rule operations merely by utilizing the C and D scales of the present invention. To multiply with the scales, indicator hairline 15a is rotated until it is in alignment with the number 1 on scale D. The indicator hairline 15a and the number 1 on scale D are then rotated until they are in alignment with the number on scale C which is to be multiplied. Scales C and D are then immobilized and the indicator hairline is rotated until it is aligned with the multiplier on scale D. The answer is then read under the hairline from scale C. Successive multiplications can be accomplished by relocating the indicator 15 and the number 1 on scale D to be in alignment with said resultant on scale C and thereafter rotating the indicator to a new multiplier on scale D before reading the new answer on scale C.

Example 1 -- Utilizing the contour map and highway side slope profile shown in FIG. 6, the cross sectional area of fill in this embodiment is calculated from a determination of the slope intercept point X. This point is determined utilizing the slope intercept point indicator as will be hereinafter described in detail. The proposed highway side slope is then drawn from the point Y, which is located at the edge of the proposed highway and therefore has a predetermined proposed elevation, to point X. The difference in elevation between the slope intercept point X and the highway edge Y is then readily determined from the contours and the corresponding indice on the slope point indicator to be 18 feet and the horizontal distance between these two points is scaled off and is found to be 25 feet. The indices of the slope point indicator when it is positioned so as to locate the slope intercept between the highway shoulder and the intercept point reflect the elevations of the proposed slope. Therefore by determining what increment of distance is to be used, by a direct reading of the contour map and the positioned scale at that point, the proposed slope elevation and the actual ground elevation can be determined without additional calculations or readings. The slope line elevation minus the ground elevation beneath each increment point gives the depth of the fill required at that increment point.

The desired cross sectional area is determined by setting indicator hairline 15a over the zero reading on scale A, holding the aligned indicator 15 and scale A together while turning them until the hairline is aligned with the ground elevation, i.e. 20, on scale B. Scales A and B are then held together and the indicator hairline 15a is rotated until it is aligned with the highway elevation, i.e. 30, on scale B. Scale A is released from scale B and the indicator 15 is held with respect to scale A and is rotated until the hairline 15a is over the ground elevation, i.e. 18, at the first five foot increment on scale B. Scales A and B are again held together and indicator 15 is rotated to place the hairline 15a over the elevation of the side slope, i.e. 261/2, at the first five foot increment on scale B. This procedure is cumulatively followed at each 5 foot increment point until point X is reached at which point the side slope intersects the ground. Scale A reflects the total cumulative combined height differential between the ground and the proposed side slope as obtained at the increment points, i.e. 33.0 feet, in this example. Using the C and D scales, this differential 33.0 feet is multiplied by the increments of distance (5 feet) to derive the total cross sectional area (165 ft.2) between the slope line and ground.

By adding together adjacent areas calculated as above described and dividing this sum by two to obtain an average and thereafter multiplying the result by the distance between the areas, the volume of earth to be removed or filled along the segment of road calculated can be readily determined.

The slope intercept point indicator 20 includes a radiating scale 21 which has indices commencing at zero points 21a, 21b, 21c, and 21d that continue in increments of ten and which indices are scribed thereon corresponding to scale distances on contour maps used therewith in highway planning. The distances between the indices, shown scribed along the sides of the scale 21 in FIG. 4, reflect the map scale of a highway planning type contour map such as the map shown in FIG. 6. Such contour maps usually incorporate scale relationships of 50 or 100 feet on the ground as equal to an inch on the contour map. Therefore, an inch on the radiating scale 21 or on a sliding scale 25 of the invention will normally reflect a ground distance of either 50 or 100 feet, depending upon the contour map intended for use. FIG. 4 shows an enlarged top plan view of the radiating and sliding scales 21 and 25 making up the slope intercept point indicator 20 of the present invention. As shown therein, the radiating scale 21 indices are identified at increments of 10 by a plurality of reference numerals. The different numbers aligned with particular scale indices markings represent scales commencing at different starting, or zero points 21a, 21b, and 21c respectively, that continue through 100 along the radiating scale 21, forming what are commonly known as folded scales. An operator can select a most convenient folded scale for use, as will be discussed later herein, in locating a slope intercept point on the particular contour map. Commonly the indices will correspond to the distances of maps having a map distance of one inch equal to either 50 or 100 feet on the ground, these being the ground-map distance ratios most commonly used for highway design work. As shown in FIG. 4, from the indices markings zero points 21d and 21c. Each of the indices extends in increments of ten to points 21e and 21f, respectively, that have assigned values of 90. The indices on the radiating scale 21 are laid out on opposite edges of the scale to represent cut or fill requirements. Thus, the indices shown generally at 22 are applicable for cut determinations and the indices shown generally at 23 are applicable for fill determinations. Each radiating scale 21 represents a ratio of horizontal versus height (i.e. 10:1 to 1/2:1) as marked adjacent to the indices. The ratio requirement used in any instance is determined by the amount of cut or fill required to construct the highway in accordance with government established highway design criteria. A complete set of radiating scales 21 will provide a scale for any possible established ratio.

Each radiating scale 21 has a sliding bar 25 in the center thereof arranged to reciprocate longitudinally. The sliding bar 25 has indices 25a numbered from zero to 600 scribed thereon representing to a ground distance corresponding to the scale of the particular contour map being used. Thus, the map ratios, i.e. 50 foot to 1 inch of ground distance to map distance, are represented by the indices on the sliding bar 25.

Sliding scale 25 reciprocates freely within a central channel 26 of the radiating scale 21, and can be locked to the radiating scale by turning a set screw 27, which acts to bind the sliding scale 25 within channel 26.

Moving across sliding scale 25 and traveling within grooves 28a and 28b formed in the sides of said scale, are two slide pointers 29 and 30. The pointers 29 and 30 each incorporate pointed ends 29a and 30 a respectively that extend therefrom to travel over the indices on each side of the radiating scale 21 as the pointers travel in grooves 28a and 28b. The pointers are used to locate points on a contour map with respect to relative settings of the radiating and slide scales.

To operate the slope intercept point indicator for the purpose of determining intercept points between the actual ground and proposed highway slope, pointer 29 is first set at the zero indice mark on the sliding scale 25. Pointer 30 is then set at a point on the sliding scale 25 corresponding to the width of the proposed highway, from its control line to its shoulder. Sliding scale 25, having the pointers 29 and 30 so positioned is then moved within groove 26 until pointer 30 is opposite a point on radiating scale 21 corresponding to the last two digits of the elevation of the highway shoulder at a station where the side slope is to be determined. Scales 21 and 25 are then clamped in their relative positions. The clamped scales 21 and 25 are then positioned on the contour map being used such that the pointer 29, which is positioned at zero on sliding scale 25, is on the highway control line with the pointer 30 indicating the shoulder or station from where the side slope is being determined. The clamped scales are then unclamped and the slding scale 25 is made to slide in groove 26 in scale 21 and within pointer 30 until the edge of pointer 29 butts thereagainst, whereat the scales are again clamped together and are made to extend normal to the highway. Pointer 29 is thereby positioned on the located shoulder and indicates on scale 21 the height of said shoulder. From an examination of the roadway elevation and the proximate contours, it is possible to determine whether the cut 22, or fill 23, indices arranged along the opposite edges of the radiating scale 21 should be used, which cut and fill indices 22 and 23 have the same equivalent relationship to the scale of a contour map, such as the contour map of FIG. 6, but which indices are numbered oppositely to one another. An inspection is then undertaken of radiating scale 21 to find the location at which an indice marker intersects one of the map contours. Some interpolation may be required as the contours and indices of the radiating scale 21 are normally marked in two foot increments, but accuracy should be possible to within one foot. After the intersection is located pointer 30 is moved thereto to identify the intersection until the map can be appropriately marked.

Example 2- Utilizing the contour map of FIG. 6, the slope intercept point indicator is used to locate slope intercept point X. Highway construction standards dictate the ratio of horizontal distance to height for various slopes. Therefor, based on experience and the nature of the terrain, the operator will first select the radiating scale having the ratio (2.1, 4.1, etc.) that he believes will fit the existing conditions. If his selection is in error he will have to select another indicator and recompute the slope intercept point. To locate point X using the radiating scale selected, pointer 29 is positioned over the zero reading on sliding scale 25 and pointer 30 is moved to a point on sliding scale 25 reflecting the highway width from a control line, i.e. 30 feet. So aligned, the sliding scale with pointers positioned thereon is moved within groove 26 in radiating scale 21 until pointer 30 is opposite to the last two digits of the elevation of the highway shoulder from where the proposed highway slope is to be constructed (coincidently 30 in this example). Scales 21 and 25 are then clamped together in their relative positions by set screw 27. The terrain over which the proposed roadbed is travelled is evaluated, by inspecting the contour map, to determine whether the proposed roadbed, having a known predetermined elevation at any point will be above the ground, thereby requiring fill for the side slope or below the ground so that cutting of the side slope will be required. In the example given, the proposed roadbed is above the ground and fill is therefor required. Accordingly, an appropriate fill indice on the radiating scale 21 is used.

Scales 21 and 25, that locked together, are placed on the contour map of FIG. 6 and are positioned such that pointer 30, arranged on scale 21 to indicate numeral 30 to be the last two digits of the proposed shoulder elevator of 6030 feet, is positioned on the control line, extending normal thereto, with pointer 30, resting at a point representing 30 feet on scale 25, indicates on the map the location of the highway shoulder shown herein as point Y and pointer 29, is spaced apart from pointer 30, and rests on a zero indices marking on scale 25. After the map is appropriately marked the scales 21 and 25 are released and scale 25 is made to slide within pointer 30 that is held stationary to scale 21 and in groove 26 in radiating scale 21 until pointer 29 butts against pointer 30, whereat the scales are again clamped together. Pointer 29, aligned with zero on scale 25, is thereby positioned above point Y, allowing pointer 30 to be moved therefrom to be used in locating the scale 21 and the contour map intercept point. Point Y is representative of any point on the edge of the road from which a slope line is to extend. The scales 21 and 25 are positioned to extend transverse to the proposed highway centerline. A point of intersection of the radiating scale 21 with a contour on the contour map is sought i.e. where there is a junction of a point on the radiating scale 21 reflecting a height crosses a corresponding contour also reflecting height (in this example point X is at 12 or 6012). Pointer 30 is moved to this intersection or junction to reflects the slope intercept point of the proposed slope with the ground. Once located, the height differential between the intersection and the proposed highway is determined. This differential is checked to see if the proper ratio, 2:1, 4:1, etc., was used as per highway construction standards. If an incorrect scale was used, another scale must be selected and the process repeated. If the selection was correct, the actual slope intercept point has been obtained and the indices on the slope point indicator between the setting for point Y and the junction with the ground X indicate the elevations of the proposed side slope above the ground. Volumes of material can therefore be calculated using the process of Example 1.

Once the intercept point has been determined, it can be used to calculate areas and volumes as heretofore described using the cross sectional area calculator.

The entire process of point interception and volume calculation can be accomplished using the outlined apparatus and a contour map. Obstructions can be recognized and planned for by relocation or adjustment of the height of the roadbed. Using the apparatus herein described, a large amount of highway planning can be accurately and quickly accomplished in an office and many of the time consuming and expensive on-site observations heretofore required can be eliminated.

Although a preferred form of the apparatus of my invention and a preferred method of its use has been herein disclosed, it is to be understood that the present disclosure is by way of example and that variations of both the apparatus and method are possible without departing from the subject matter coming within the scope of the following claims which subject matter I regard as my invention.