Triangle volume calculation formula12/5/2023 Dividing cubic feet by 27 converts to cubic yards. Where L represents the distance between the cross-sectional end areas being used in the formula, and 27 represents the number of cubic feet in 1 cubic yard. In formula form the process is as follows: This average is then multiplied by the distance between the two end areas to obtain the volume between them. The average end area method uses the end areas of adjacent stations along a route and averages them. Areas of the cross sections are most easily determined by using the elevations of the points and their locations from the centerline (coordinates). Comparisons between final cross sections and original cross sections are used to determine the volume moved. Each wants an accurate volume so payment for the work is correct.įor road projects, cross sections of the ground elevations are measured at the beginning of the project, during the project, and at the end of the project. It can be seen that accurate determination of the volume moved is critical to the owner and to the contractor. That is, the contractor will be paid per cubic yard of soil and will receive a separate price per cubic yard of rock. Payment for the removal and placement of dirt is typically on a unit cost basis. Often mountains of dirt must be moved to create a gentle grade for the roadway. In road construction the shape of the ground must be changed to remove the ups and downs of the hills and valleys for the planned roadway. These points can be used as coordinates to determine area. Cross-section data collected on a project represent elevation and location information for points on the ground. Once understood, this process is fast and the most accurate way of determining area. If cross-sectional field data are available, use of this data is the recommended method of calculating volume. This method may be cumbersome because of all the shapes that may need to be calculated. Geometric FormulaĪlthough a shape at first may seem irregular, it is often possible to break it into smaller regular shapes such as squares, rectangles, triangles, trapezoids, etc., that will allow the use of standard geometric formulas to determine the area. Inputting a scale factor into the planimeter results in a digital readout of the area. The irregular shape is drawn to scale and the planimeter is used to trace the outline of the shape. The electromechanical digital planimeter is a quick method of determining the area of irregularly shaped figures. Incomplete squares along the edges of the cross section are visually combined and averaged. Each square represents x number of square feet. Counting SquaresĪpproximation is possible by plotting the figure to scale on cross-sectional paper and counting the squares. If an area can be determined, it is generally easy to determine the volume. The volume of a cylinder is the area of the circle times the height of the cylinder. For instance, the area of a circle is pi times the radius squared. Most volume calculation formulas contain within them the formula for an area, which is simply multiplied by the height to determine the volume. The key to volume calculation is the determination of area. The field engineer will analyze the data and make decisions that result in the best estimate of the volume. Typically, approximations must be made and averages determined. Therefore, it must be understood that volume calculations do not give exact answers. It usually is not practical to take the time to collect data everywhere there is a slight change in elevation. Measurements for volume are nothing more than applying basic distance and elevation measurements to determine the locations and elevations of points where the volume is to be determined. Field Measurements for Volume Computations
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