1. Measuring and related math for future Truckers - I
Unit 4: Measuring and securing loads, estimating weights, volumes, and handling loads and materials
Created by Leecy Wise for Utah State University-Eastern Campus, Blanding, UT, 2014
© Utah State University-Eastern Campus: Blanding, 2014

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3. Road humor
When you are laughing, you are learning, so laugh, laugh, laugh!
Transport Topics: The Newspaper of Trucking and Freight Transportation

4. Why do truckers need math?
If you drive your own car or pick-up, you might want to use math in different ways. You might want to know what kind of mileage you are getting, or the number of miles you need to travel, or the amount of time it will take to get from one place to another, or how safe you are on the road. You might even want to keep track of your expenses and create a budget for maintaining your vehicle.

5. A commercial trucker does not have those options
A commercial trucker does not have those options. A commercial trucker must use math for those reasons and many others. Truckers must be able to handle financial transactions, complete log reports, measure loads, determine road characteristics, convert measurements, apply formulas, and much, much more. They must also be able to solve problems both on the job and on exams. To commercial truckers, math is a critical skill. It can be just as important sometimes as being able to drive in challenging weather.

6. Heavy equipment operators also need to know the math that relates to their environments. Other units in this series, Angles and Gradients, work with measuring angles related to pitch or inclination. Knowing how to measure the degree of pitch on the road or on heavy equipment can avoid tragic accidents from happening on work sites. Be sure to cover that unit so that you can be sure that you and others are safe in a dangerous environment.

7. This unit will work with you to develop the following skills:
Determining or estimating the legal amount of weight and volume to be transported ( materials, tons, yards, and related metric conversions).
Determining axle weight limit.
Securing and inspecting cargo.
Estimating material quantities to be transported.
Determining total vehicle weight and cargo.
Transporting Hazardous Materials (HAZMAT)

8. A. MEASURING WEIGHT

9. If you want to know how much you weigh, you simply step on a scale and get your answer in pounds (lbs) and ounces (oz). You do the same to find out how tall you are. Your results will be shown in feet (ft) and inches (in). When you work with cargo, or very large amounts of weight or volumes of materials, you will get weight results in tons and volume results in yards.

10. The weight of different materials varies considerably, so you will need to know how much the specific material weighs. It is also important to know how much material you are carrying. That is why you need to know both how to measure the space occupied by materials (volume) and also know the weight of the material being transported. A box of nails weighs far more than the same box filled with matches or feathers. Weight and volume go hand in hand when you determine how much your truck can safely transport.

11. Commercial drivers must become very familiar with how to measure large amounts of weight. They must know the laws that govern the amount of weight transported by a rig, and they must know the terms that are used to express those laws.

12. In the United States, weights in heavy equipment and transportation industries are measured in tons. When you weigh yourself in the US, you will get results in pounds (lbs) and ounces (oz). In other countries, weight is measured in kilograms. In this unit, we will measure weights in the American English System.

13. There are two measurements used for tons: short ton and long ton.
In the US, when we refer to a ton, we automatically use the short ton measure. That is what we will use in this unit.
1 TON = 2,000 POUNDS
2,000 lbs =

14. 1 pound (lb)
16 ounces (oz)
1 ton (T)
2,000 pounds (lb)
2,000

15. In order to travel within safe weight limits, legal guidelines are expressed using certain terms and their abbreviations. Unless you know what those terms mean, they can be confusing. For example, A ton is 2000 pounds so does it follow that a half-ton truck weighs 1000 pounds. No. The name doesn't refer to the weight of the truck. In fact, half-ton pickups weigh much more than that.

16. The "half-ton" description loosely refers to the truck's payload capacity. This means that the truck can carry up to 1,000 pounds, or half a ton, of cargo and passengers in the cab and bed. Still, modern half-ton pickups, have payload capacities that exceed 1,000 pounds! Although early half-ton pickups could carry maximum loads of 1,000 pounds, new and improved half-ton pickups have been able to safely carry more. It really pays to understand how terms are used!

17. To common US measurements on the sites below.
ed.org/GeneralResources/Units/USCustomarySystem.htm
Continue to solve problems related to English length measurement units in the worksheets below. First, solve the problem, and then check your answers on the worksheet.
Units of English Measurements: Length

18. ESSENTIAL WEIGHT-RELATED TERMINOLOGY
To drive safely and within legal limits, you will need to define and memorize a number of terms.
For examples of the terminology you need to know, go to
1. Gross Vehicle Weight (GVW): The total weight of a single vehicle plus its load.
Read more about GVW at vehicle-weight +

19. 2. Gross Combination Weight (GCW): The total weight of a powered unit, plus trailer(s), plus the cargo. 3. Gross Vehicle Weight Rating (GVWR): The maximum GVW specified by the manufacturer for a single vehicle plus its load. + + +
Mercedes-Benz

20. 4. Gross weight or gross mass – The weight of the packaging plus the weight of its contents.
5. Gross Combination Weight Rating (GCWR): The maximum GCW specified by the manufacturer for a specific combination of vehicles plus its load.
To compare GCER and GVWR, go to training/lessons/FMCSA/GVWR_files/GVWR05.htm and click on the links in the left column

21. 6. Axle Weight: The weight transmitted to the ground by one axle or one set of axles.
To understand Axle Weight better, scroll down the page at GVWR.htm
7. Tire Load: The maximum safe weight a tire can carry at a specified pressure. This rating is stated on the side of each tire.
To understand Tire Load Ratings better go to tire-load-ratings.aspx
Also, CLICK HERE to find out more about how to distribute weight for transportation.

22. 7. Suspension Systems: Suspension systems have a manufacturer's weight capacity rating. 8. Coupling Device Capacity: Coupling devices are rated for the maximum weight they can pull and/or carry.
Your state’s Commercial Driver’s License (CDL) Manual will help you stay within safe and legal weight limits when you transport cargo. Get acquainted with your Manual right away!
Go to to practice more and test yourself on terms.

23. LEGAL WEIGHT LIMITS
States have maximums for GVWs, GCWs, and axle weights. Often, maximum axle weights are set by a bridge formula. A bridge formula permits less maximum axle weight for axles that are closer together. This is to prevent overloading bridges and roadways.
Notice how weight distribution in a long and a short wheel base affect the stability of the bridge in the images.

24. N = the number of axles in the group under consideration.
How do you apply the bridge formula to your load? Memorize the formula!
W = the overall gross weight on any group of two or more consecutive axles to the nearest 500 pounds.
L = the distance in feet between the outer axles of any group of two or more consecutive axles.
N = the number of axles in the group under consideration.
To understand better how the Bridge Formula works spend some time at the site below and practice, practice, practice.
Go to the next link to play with a Bridge Formula Calculator>

25. B. LOADING AND INSPECTING YOUR CARGO!
Before you transport cargo, it is critical that you inspect it before you leave, and 50 miles after you leave. Make adjustments as needed.
Later re-check your cargo during the trip. Check it after you have driven 3 hours or 150 miles following each inspection and readjustment. Also check it at every break you take.
Also, keep in mind that federal, state, and local regulations for commercial vehicle weight, securing cargo, covering loads, and where you can drive large vehicles vary from place to place. Know the rules where you will be driving.

26. It is also critical that you inspect your vehicle before you leave on any trip! Click on the links below to watch videos on completing a pre-trip inspection.
Inspection

27. LOADING GUIDELINES
Overloading can have bad effects on steering, braking, and speed control. Overloaded trucks have to go very slowly on upgrades. Worse, they may gain too much speed on downgrades. Stopping distance increases. Brakes can fail when forced to work too hard.
During bad weather or in mountains, it may not be safe to operate at legal maximum weights. Take this into account before driving.
1. Don't Be Top-heavy - A high center of gravity (cargo piled up high or heavy cargo on top) means you are more likely to tip over. It is most dangerous in curves, or if you have to swerve to avoid a hazard. It is very important to distribute the cargo so it is as low as possible. Put the heaviest parts of the cargo under the lightest parts.

28. 2. Balance your cargo weight - Too much weight on the steering axle can cause hard steering. It can damage the steering axle and tires. Under-loaded front axles (caused by shifting weight too far to the rear) can make the steering axle weight too light to steer safely. Too little weight on the driving axles can cause poor traction.
During bad weather, the truck may not be able to keep going. Weight that is loaded so there is a high center of gravity causes greater chance of rollover. On flat bed vehicles, there is also a greater chance that the load will shift to the side or fall off.
Go to the next slide and see images of proper weight distribution in transporting cargo.

30. More than half of truck driver deaths in crashes are the result of truck rollovers. When more cargo is piled up in a truck, the "center of gravity" moves higher up from the road. The truck becomes easier to turn over. Fully loaded rigs are ten times more likely to roll over in a crash than empty rigs. The center of gravity is the point where the whole weight of the load is concentrated.

31. Federal regulations require that the total working load limit of any system used to secure an article or group of articles against movement must be at least one-half times the weight of the article or group of articles. Proper tie-down equipment must be used, including ropes, straps, chains, and tensioning devices (winches, ratchets, clinching components). Tie-downs must be attached to the vehicle correctly (hooks, bolts, rails, rings).

32. Block and Brace Cargo - Blocking is used in the front, back, and/or sides of a piece of cargo to keep it from sliding. Blocking is shaped to fit snugly against cargo. It is secured to the cargo deck to prevent cargo movement. Bracing is also used to prevent movement of cargo. Bracing goes from the upper part of the cargo to the floor and/or walls of the cargo compartment.

33. 4. Securing cargo with Tiedowns – Tiedowns are critical safety elements to keep cargo from dangerously shifting or falling off. Federal regulations define the total working load limit of any system used to secure an article or group of articles against movement. That limit must be at least one-half times the weight of the article or group of articles.
Proper tiedown equipment must be used, including ropes, straps, chains, and tensioning devices (winches, ratchets, clinching components. They must be attached to the vehicle correctly (hooks, bolts, rails, rings).

34. Cargo should have at least two tiedowns
Cargo should have at least two tiedowns. Cargo should have at least one tiedown for each 10 ft of cargo. Make sure you have enough tiedowns to meet this need. No matter how small the cargo, it should have at least two tiedowns.

35. Department of Public Safety Driver License Division P.O. Box 30560
There are other regulations and suggestions on how to safely transport different types of cargo. Those are covered in your CDL Manual. Make it your friend and constant companion.
STATE OF UTAH
Department of Public Safety
Driver License Division
P.O. Box 30560
Salt Lake City, UT

36. C. MEASURING VOLUME

37. Unlike weight, we don’t really measure a person’s volume, but we might measure blood volume if needed. The total blood volume for an average 150-pound human is approximately 5 1/2 quarts, or a little more than 160 ounces! That is how much blood is held in the average human. Later, we are going to work with measuring air and gas pressure much like you measure blood pressure in humans. However, we do measure liquid volumes every day when we buy quarts of milk or gallons of gas.

38. What is volume and how do commercial drivers measure it when they work with load amounts?
Volume is the measurement of how much space is held in a three dimensional object, like a box, a freezer, or a canister. In trucking, that space might be the total space contained in a cargo unit.
You will certainly need to know how much your rig can hold both in space (volume) and weight in pounds or tons.

39. Volume is measured using three dimensions, not two
Volume is measured using three dimensions, not two. Let’s start discussing two dimensions.
A two-dimensional (2D) object only has two dimensions.
For example, if you want to find out what area is covered by a 2D object, like a rug, or a window frame, or a garden, you simply multiply the two dimensions: length and width. The formula looks like this:
When you multiply two dimensions, the answer is always reported in SQUARE terms. To show that a number is squared, you add a little superscripted “2” after the number.
5 ft x 2.5 ft = 11 ft2
L X W = A
Length X Width = Area Or
A = L X W
Area = Length X Width
width
length

40. For example, if Darrin wants to carpet a room that is 10 feet by 12 feet, he would multiply those two amounts, and the answer would be shown as squared.
10 ft X 12 ft = 120 ft2 ( The little number 2 above the answer means that the amount multiplies two dimensions: length and width.)
So Darrin would go to the store and ask for 120 square feet (120 ft2) of carpet. Notice the objects on the following page.
Width = 10 ft
Length = 12 ft
L X W = A
Length X Width = Area

41. 1 ft 1 ft 1 ft 1 ft 4 ft: = 4 ft 2 ft 2 ft 4 ft2: = 4 ft2 width = 2 ft+
1 ft + +
4 ft:
= 4 ft
2 ft X
2 ft
4 ft2:
= 4 ft2
width = 2 ft X
length= 2 ft
Go to the next slide to watch a video on this process.
Wait a few seconds for the video to load!

42. From https://www.youtube.com/watch?v=bCDdQC-zrPs
Allow a few seconds for the video to load.

43. 6 ft X 5 ft = 30 ft2 Don’t forget to square the answer
An object that is 4 ft2 covers this space. That means that the area covers four squares: 4 squares with 2 squares going up and 2 squares going across. Each square is 1 ft wide and 1 ft long. Paulo’s truck bed measures 6 ft long and 5 ft wide. He wants to lay down a rubber mat for when his dogs are with him. How much material does he need to purchase to cover the bed? (He’ll later cut out the areas for the wheel wells.) When you have the answer, click to check it.
2 Ft
2 Ft
6 ft X 5 ft = 30 ft2 Don’t forget to square the answer

44. The garden area is 6 square feet.
What is the area (square footage) of this garden? When you get the answer, click to check it.
3 ft long
2 ft wide
W X L = A
2 ft X 3 ft -= 6 ft2
The garden area is 6 square feet.

45. Let’s say you have a handheld computer, like an iPad
Let’s say you have a handheld computer, like an iPad. You want to buy a screen protector for it. Measure the two dimensions and find out how much plastic protection you will need to buy. Provide your answer in square feet.

46. CLICK HERE to watch Introduction to area
CLICK HERE to watch Introduction to area. CLICK HERE to read about how to grow a whole lot of food on one or more square- foot gardens! Practice measuring area in different environments.

47. But wait a minute. Those are three dimensions, not two! 12 ft long
Now, suppose that Susan has a flatbed with the following dimensions.
But wait a minute. Those are three dimensions, not two!
That’s absolutely right. Now we are going stop talking about area. When you measure three dimensions you are talking about volume. Susan needs to measure volume to know how much gravel, hay, or other materials she can carry.
12 ft long
6 ft wide
4 ft high

48. The object below has three dimensions (3D). What are those dimensions
The object below has three dimensions (3D). What are those dimensions? Click three times to check. To find out how much space is held inside this 3D object, you need to measure all three dimensions (3D)– not only width and length, but HIGHT! The holding capacity of a three dimensional object is called
length
VOLUME!
width
height

49. Truck drives need to know how to measure all three dimensions if they carry cargo. Otherwise, they might overload or leave cargo behind. Know the limits and capacity of your vehicle! For example, as you transport cargo, you will become familiar with freight container measurements. A freight container is a reusable container having a volume of 64 cubic feet or more. It is built to permit so that it can be moved and transported with its contents intact. How do you measure volume? You’ve probably figured that out by now.

50. To find the area of a two-dimensional object, you multiplied two dimensions and squared your results. To find the volume of a three-dimensional object… (Guess the answer and click to check.)
If you said, multiply the three dimensions, you were right! But instead of squaring your results as you did before your results will be in cubic inches, feet, or yards.
If you think of a cube, it has three dimensions. That will make it easier for you to remember to add “cubic” to your answer.
The formula for finding the volume of an object is… W L H
L x W x H = V

51. To represent a cubic quantity, add a “superscripted” number (little number above the quantity), but Instead of a “ 2” insert a “3”. When you add the cubic symbol, you are saying that three dimensions were multiplied. Find the volume for the figure below. Click to check your answer.
height: 5 ft
Length: : 12 ft
Width: 3 ft
12 ft x 3 ft x 5 ft= 180 ft3

52. Click on the links below to practice finding the volume of different rectangular prisms. Don’t be thrown by the term “prism.” A rectangular prism is a solid object that has six flat sides and all of its faces are rectangles (right angles). Check your answers only after you have completed the worksheet. Volume Worksheet I Answer Sheet Volume Worksheet II Answer Sheet

53. Go to the next slide to watch a video on this process
Go to the next slide to watch a video on this process. Allow time for the video to load!

54. From https://www.youtube.com/watch?v=lL9NyJKLjc8

55. D. estimating material quantities to be transported

56. Who is responsible for making sure that a load is secure and loaded at the proper weight? You are!
Commercial truckers transport cargo over long distances and in different circumstances. Therefore, it is imperative that they follow basic rules for travelling safely. If you load cargo wrong or do not secure it, it can be a danger to others and yourself. Loose cargo that falls off a vehicle can cause traffic problems and others could be hurt or killed. Loose cargo could hurt or kill you during a quick stop or crash. Your vehicle could be damaged by an overload. Steering could be affected by how a vehicle is loaded, making it more difficult to control the vehicle.

57. As you learned, when you deal with freight, you will need to how to measure weights and volumes. You will also need to estimate how those two go together to determine both the space occupied by the material (volume) and the weight of the material that occupies that amount of volume. The formula you will use will vary, of course, depending on the material in question. The density of the material you are using makes a difference! Density measures how compact your material is. Gravel is much more dense than sawdust, for example.

58. Length x Width = Square feet (ft2) (L X W = Area)
Below is the process for matching volume and weight measurements with sand, gravel, and similar materials with similar density.
A. CONVERT CUBIC YARDS (VOLUME) TO TONS (WEIGHT)
1. Find the square feet covered by the container. Remember?
Length x Width = Square feet (ft2) (L X W = Area)
2. Then apply the 1st formula: FT2 ÷ “X” = Cubic Yards for that material
X = a number that matches the depth (3rd dimension) in relation to the type of material. Let’s see how this formula works.

59. Let’s say that a bunker (container) has an area of 18 ft long x 9 ft wide. It is 4 ft high.
Now we can apply the formula ..
FT2 ÷ “X” = Cubic Yards for that material, so…
162 ft 2 ÷ “X” = Cubic yards of sand and gravel
But how much is “X”???
18 ft
9 ft
4 ft
18 ft x 9 ft = 162 ft 2

60. 162 ft 2 ÷ “X” is 162 ft 2 ÷ 81 ft = 2 Y3 (2 cubic yards)
You need to refer to an industry table, below, to find out.
With sand and gravel, with a container 1 ft high, “X” would be 324. (Click to see the match.)
If the container were 6 ft high, “X” would be 54, as you can see in the table below. (Click to see the match.)
The container is 4 ft high. So …
162 ft 2 ÷ “X” is 162 ft 2 ÷ 81 ft = 2 Y3 (2 cubic yards)
Inches deep
"X"
1"
324
2"
162
3"
108
4" 81
5" 65
6" 54
7" 47
8" 40

61. Cubic Yards X 1.4 = Tons (sand or gravel)
162 ft 2 ÷ 81 ft = 2 Y3
So now we have 2 Y3
B. NOW, convert Cubic yards (Y3) to Tons (T). Let’s apply a second formula:
Cubic Yards X 1.4 = Tons (sand or gravel)
2 Y3 X 1.4 = 2.8 T
That means that our original container that is 18 ft long, 9 ft wide, and 4 ft high, can carry 2.8 tons of sand or gravel.
18 ft
9 ft
4 ft

62. If we wanted to know how many Cubic Yards would be required to transport 2.8 Tons of sand and gravel, we would simply to division.
To convert Tons (T) to Cubic Yards (Y3)…
T ÷ 1.4 = Y3
2.8 T ÷ 1.4 = 2 Y3 of
To practice these conversions more, go to a discussion at htm
There are also many other sites that provide added practice in estimating material quantities. As your instructor if you want more practice!

63. E. Transporting Hazardous Materials (HAZMAT)
In trucking, the term HAZMAT refers to Hazardous Materials

64. All drivers should know something about hazardous materials
All drivers should know something about hazardous materials. You must be able to recognize hazardous cargo, and you must know whether or not you can haul it without having a hazardous materials endorsement on your CDL license.
Hazardous materials are products that pose a risk to health, safety, and property during transportation. Examine the table on the next slide, showing definitions for different types of hazardous materials.

66. Why have rules to govern the transportation of hazardous materials?
To contain the product.
Many hazardous products can injure or kill on contact. To protect drivers and others from contact, the rules tell shippers how to package safely. Similar rules tell drivers how to load, transport, and unload bulk tanks. These are containment rules.

67. To communicate the risk and to ensure safe drivers and equipment.
1. Shipping Papers - The shipper uses a shipping paper and diamond shaped hazard labels to warn dockworkers and drivers of the risk.
You must tab shipping papers related to hazardous materials or keep them on top of other shipping papers. You must also keep shipping papers:
In a pouch on the driver's door, or
In clear view within reach while driving, or
On the driver's seat when out of the vehicle.

68. 2. Placards.
In addition to posting shipping papers and labels, some drivers must post placards to warn others of hazardous materials.
Not all vehicles carrying hazardous materials need to have placards. You can drive a vehicle that carries hazardous materials if it does not require placards. If it requires placards, you cannot drive it unless your driver license has the hazardous materials endorsement.
Placards are signs put on the outside of a vehicle that identify the hazard class of the cargo. A placarded vehicle must have at least four identical placards. They are put on the front, rear, and both sides. Placards must be readable from all four directions. They are at least 10 3/4 inches square, turned upright on a point, in a diamond shape.
Go to the next slide to see examples of hazardous-materials placards.

70. Before leaving this unit, click on the link below to take a short quiz covering some of the topics your practiced in the unit. A page will open in your browser showing links to two different part of the quiz. Measurements I Quiz

71. You have completed another important module to prepare you to succeed in training to become a commercial truck driver or heavy equipment operator. It is important that you continue to practice math skills using the resources in this series and those that your instructor will give you. Remember that practice makes perfect! Ask your instructor for the next module.

72. CONGRATULATIONS! Your are ready for the next unit!

73. Math and TERMINOLOGY for future Truckers
This series was produced by Utah State University-Eastern Campus, CDL Program.
All content, with exception of links and references to online resources, is original and tailored to the needs of students hoping to succeed in earning their Commercial Drivers License.
All images are either original or taken from the following resources:
Utah CDL Handbook
Transport Topics: The Newspaper of Trucking and Freight Transportation-
Utah State University-Eastern Campus, Blanding, UT: All Rights Reserved, 2014
© Utah State University-Eastern Campus: Blanding, 2014