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Estimating Bucket Capacity

Volume = Cross Sectional Area x Length

We all know that the volume is calculated by multiplying Width x Height x Length or Area of the end x Length. But what if the area is not a simple geometric shape, or in the case of Heavy Equipment Buckets, how do you define the shape for the volume to be calculated?

The total amount of material carried by a bucket is the amount inside the bucket plus the amount piled on top of it. This is called the Heaped or Rated Capacity. The amount of material piled on top of the bucket, (heap), is determined by the angle of repose of the material being handled. The Society for Automotive Engineers, SAE, for purposes of creating a standard for comparatively rating buckets, has defined two different angles of repose:
  • Wheel Loader Buckets; 2:1
  • Hydraulic Excavator Buckets; 1:1
Of course, if Actual Capacity is being calculated for a specific bucket to handle a specific material for which an actual angle of repose is known, then the actual angle of repose is substituted.

Calculating the capacity of odd shaped objects was not an easy task before the use of computers and CAD drafting came into common use. The formal method involved breaking the shape down into geometric shapes, calculating the area of each them and adding all the areas together for the total cross sectional area. Alternately, a planimeter was used to directly measure it.

Today, if sufficient information is available to duplicate the shape with a computer CAD program, the area of any shape can be accurately calculated in a few seconds. Our Field Worksheet, "Measuring Wheel Loader Buckets" is an example of the detail needed to define a shape so that an accurate capacity can be calculated. Buckets for Hydraulic Excavators require similar information but we have not yet published a field worksheet.

Below is a 6 step graphical method for estimating the Heaped or Rated capacity of buckets. It approximates the results that would be obtained by using the more formal methods CWS uses as outlined in:
  • RATING BUCKETS - Wheel Loaders
  • RATING BUCKETS - Hydraulic Excavators
Six Steps to Estimating Bucket Capacity

1 Trace the outline of the bucket to be measured on a large piece of cardboard or paper. While interior shape should be accurate, the exterior shape can be included as reference.
1 - Trace Bucket Shape
2 Define the Cross Section of the load by constructing the heap area on top of the area contained within the bucket.
  • Start by drawing a base line between the cutting edge and the top of the spillboard
  • At the center of that line, draw a new line perpendicular to the first. For Wheel Loader Buckets using the 2:1 heap, the perpendicular line should be 1/4 the length of the base line. For Excavator buckets using the 1:1 heap, it should be 1/2 the length
  • Connect the ends of the base line to the end of the perpendicular line to enclose the heap.

2 - Define Cross Section of Load - Construct "Heap" and add to Inside Load
3 Draw a grid of horizontal and vertical lines over the whole bucket load. For larger buckets the lines can be on 12" centers yielding squares of 1 square foot each. For smaller buckets, use a smaller grid, perhaps 6" centers to yield 1/4 square foot per square, for more accuracy.
3 - Draw a grid over the load area
4 Sequentially number all the whole squares that cover the load in the bucket ignoring for the moment, any parts of the load that are not covered by whole squares.
4 - Count up all the whole squares covering the load
5 Group bits and pieces of partial squares to add up to whole squares.Count up all the additional squares that are made up of all the small pieces. (Try to be accurate but don't go overboard with this exercise. Where some squares might be a little under filled, others will be over, canceling out error.) In this illustration we have 52 squares so the cross sectional area of this load is 52 square feet.
5 - Group partial squares into whole squares
6 Calculate the volume by multiplying the cross sectional area in square feet by the length in feet. Using the 148" width as an example: 148 inches in feet is:
148 / 12 = 12.33 feet In North America, most bucket capacities are expressed in cubic yards so it is important to know that one cubic yard contains: 1 yard = 3 feet
so
3 ft. x 3 ft. x 3 ft. = 27 cubic feet
Volume is: 52 sq. ft. x 12.33 feet = 641.33 cu. ft. Or expressed as Cubic Yards is 641 / 27 = 23.7 Yards3 Where this method has only applied the angle of repose in two dimensions, the SAE Standard Formula applies it in three. Therefore experience tells us that the actual rated capacity of this bucket will be closer to: 23 or 23.25 Yd3 6 Calculate Volume