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Answered 2013-01-14 00:51:31

how many case loads of bottled water can this semi truck practically haul?

A typical semi-trailer should not be expressed by 12.5x8x40 because a typical semi-trailer is bound by dept. of Transportation regulations that say max height is 13ft 6in and max width is 8ft 6 in. If there were 12.5 feet of usable height, the trailer deck would have to be 12 inches high which would leave no room for the tires. The deck on a typical semi-trailer is actually about 4.5 feet high which only leaves 9 feet of usable height. The average width on the highway today is 8 feet 6 inches and the two most common lengths used today is a 45 foot long trailer and a 53 foot long trailer.

Since we know that formula for the volume of a box is volume= length x width x height, we can now build our equation.

The volume of a 45 foot semi-trailer would be the product of V=(45)(8.5)(9) and expressed in cubic feet, so (45)(8.5)(9)=3,442.5 cubic feet of usable area.

The volume of a 53 foot semi-trailer would be the product of V=(53)(8.5)(9) and expressed in cubic feet, so (53)(8.5)(9)=4,054.5 cubic feet of usable area.

Now, the actual question was not the volume of a trailer but the number of cases of bottled water the truck can haul. The problem is that we can't accurately figure this without the dimensions of the cases of bottled water that are being loaded; however, I can use the measurements from a typical bottle of water to build an equation.

Using a 20 ounce bottle of Sam's Choice bottled water I found that the bottle is 7.687 inches tall and the circumference at the widest section is 8.625 inches. Since the bottle does not have smooth and flat surfaces, we will have to use the principles for stacking spheres and other irregular shaped geometric figures to determine the number of bottles that we can stack in a single case, as well as the number of cases we can stack in the usable area of our semi-trailer.

The principles for stacking spheres and other irregular shaped geometric figures, in layman's terms, states that in order to determine the volume needed to stack irregular shaped geometric figures, we must first determine the volume of the smallest possible regular shaped geometric figure in which the irregular shaped geometric figure could be completely contained. In this case, the closest geometric figure to our bottle would be a cylinder, so we must determine the smallest possible cylinder needed to completely encapsulate the irregular shaped bottle of water. We do this simply by measuring at the points of the bottle with the greatest dimensions. When stacking irregular shaped geometric figures, there will be a spaces between parts the objects that is not used.

We can determine that the area needed to stack our bottles will be a length of 2.75 inches, a width of 2.75 inches and a height of 7.687 inches. The Sam's Choice bottled water comes in a case with 6 rows of bottles, each row containing 5 bottles of water for a total of 30 bottles per case. To figure the length (l) of the case, we simply multiple the length of the bottle by the number of rows (2.75inches x 6 rows), so (l)= 16.5 inches. To figure the width (w) of the case we multiply the width of a bottle by the number of bottles per row, (2.75 inches x 5 bottles per row), so (w)= 13.75 inches. The height of the case is simply the height of the bottles, so (h)= 7.687 inches. We are now ready to build our equation for the volume of a case of Sam's Choice bottled water.

The formula for the volume (V) of a rectangle is: Volume= length x width x height and expressed in cubic inches, so V= (16.5)(13.75)(7.687) so the volume of a case of Sam's Choice bottled water is 1743.988 cubic inches or 1.0093 cubic feet

We can now take the volume of the trailer and divide it by the volume of a case of bottled water to determine a maximum number of cases that we can load onto our trailer.

The volume of a 45ft trailer is 3442.5 cubic feet and the volume of the case of water is 1.0093 cubic feet, so: 3442.5 cubic feet/ 1.0093 cubic feet= 3,410.779 so we can fit a total of 3,410 cases of water onto a 45 ft trailer.

The volume of a 53ft trailer is 4054.5 cubic feet and the volume of the case of water is 1.0093 cubic feet, so: 4054.5 cubic feet/ 1.0093 cubic feet= 4,017.14 so we can fit a total of 4,017 cases of water onto a 53ft trailer.

The problem with this is that along with the Dept. of Transportation regulations on height and width, we are also restricted to a maximum Gross Vehicle Weight of 80,000 pounds. The 30 count cases of bottled water each weigh 37.5 pounds. This means if we load the maximum number of cases onto a 45 foot trailer, the cargo weight alone would be 127,875 pounds and if we were loading a 53 foot trailer, our cargo weight would be 150,637 pounds. So we are not limited by volume, we are limited by weight.

Since this is the case, we need to determine the maximum number of cases we can load, without exceeding the weight restrictions.

The average semi-tractor with a typical dry van trailer weighs about 30,000 pounds empty. The weight difference between a 53 foot and a 45 foot is not significant enough to consider. With a 30,000 empty weight we would only be able to load another 50,000 pounds of cargo. at 37.5 pounds per case of bottled water, the maximum number of cases of Sam's Choice bottled water is:

(80,000 lbs - 30,000 lbs)/(37.5 lbs)= 1,333.333. The maximum number of cases we can load is 1,333 cases.

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