There's hardly any object in your home or school that hasn't been created thanks in part to a mechanical drafter-designer.

A mechanical drafter-designer is the person who takes an idea and turns it into a drawing. It's this drawing that allows the object to be made.

In recent years, computer-aided design (CAD) has changed the face of the occupation. CAD allows drafters to create a drawing on a video screen at computer workstations. This means those in the occupation don't have to draw as well as they once did. Plus, the computer also handles much of the mathematical requirements.

Even so, good drawing and math skills are still required of top-notch workers.

A big part of working in the mechanical drafting field is being comfortable with numbers, says mechanical drafter designer Tom Gilbert. That's because numbers are the language used by drafter designers and everyone they work with, from engineers and machinists to suppliers.

Numbers allow everyone involved in designing and building something to "speak the same language." For instance, every part in a motor has to be designed and built. And every part in that motor has to fit with and work with all the other parts. You can't just say, "This part should be as big as an apple." Everyone has a different idea about how big an apple is. So, that's why numbers are used. Numbers are precise and mean the same thing to everyone.

Once a mechanical drafter designer has calculated the numbers, the numbers must be interpreted. That is, the mechanical drafter designer has to decide, "Is this number the right number?" Once that judgment is made, the design and drafting process can continue.

Mechanical drafter designers use computers to help them do many of their calculations. For instance, Gilbert uses the CAD system to check stress and strain, calculate distances, and conduct other types of analyses. Still, it's very important for Gilbert to understand how the calculations were done and to work them out himself. That's because it's sometimes much easier to calculate a distance or angle by hand than it is to draw it in CAD.

"By the time I draw it on the machine, I could have easily done the calculation either by hand or calculator," he says. Many of the technicians that graduate from schools today don't have the ability to do this. Instead, they rely heavily on the computer, adds Gilbert.

"It limits them! Yes, you have to be able to use the computer, but as a tool," states Gilbert emphatically. For his business, he needs drafters who are flexible and can work in a variety of situations. For example, much of his company's work involves "fabrication drawings." These are the drawings used in fabrication or, in other words, manufacturing. When Gilbert is called out to the factory, he doesn't want to lug around his laptop computer -- especially into a dusty, dirty environment.

In these cases, Gilbert does many of the calculations right on the spot, either in his head or on a simple calculator.

With your classmates, name 10 things in your classroom that a mechanical drafter designer may have designed.

Discuss the following:

• What type of measurements and calculations would be involved during the design process?
• What design decisions would be made based on these mathematical calculations? (For example, too much material, not strong enough, item not balanced)

In small groups, perform the following series of measurements using a carpenter's square, a piece of string, and a protractor. Record these numbers on the Student Worksheet below. (If you don't have a carpenter's square, you can improvise one using two meter sticks placed at a 90 degree angle to each other.)

a) Hold a piece of string so it crosses both legs of the carpenter's square. Label the long leg of the square "a" and the short leg "b."

b) Measure the distance between the 0 point and where the string crosses the carpenter's square. Take the measurements from the carpenter's square.

c) Using a protractor, measure the angles formed by the string and the carpenter's square. Record these measurements as angle A and angle B.

d) Using the carpenter's square, measure the length of string between the two points on legs a and b. (You can do this by grasping the string where it crosses the square, then holding the string against one of the legs of the square to measure it.)

e) Move the string to create a new triangle. Take the measurements as set out above. Record these on the worksheet.

f) Create three more triangles, again taking the measurements and recording the results. Altogether, you will have created and measured five triangles.

You've just measured the length of the string and angles manually. Now, you'll calculate the lengths and angles mathematically. Two different mathematical formulas can be used to calculate the length of the string. These formulas allow you to quickly and accurately gather information about an object. They are:

Pythagorean Theorem

a^2 + b^2 = c^2

Trigonometric Ratios

• Sine Ratio: Sin = Opposite / Hypotenuse S = O / H
• Cosine Ratio: Cos = Adjacent / Hypotenuse C = A / H
• Tangent Ratio: Tan = Opposite / Adjacent T = O / A

Using the Pythagorean theorem and the data recorded on your Student Worksheet, calculate the length of the string in each of the five triangles.

Use trigonometric ratios and the data you recorded to calculate angle A and angle B in each of the five triangles.

Use the solutions to these calculations to complete the Student Worksheet.

Now, review the data. How do the calculated lengths and angles compare with the measured values?

You work for a company that is designing a ride for an amusement park. You are working on the plans for an elevator. A car measuring three meters by three meters will enter the elevator, which will spin it around 180 degrees while carrying it to the next floor. This means the car will enter the elevator on one floor in one direction, rotate, and then exit the elevator through the same door, but facing the opposite direction.

You must calculate the minimum dimension for the elevator that will allow the car to turn. Allow an extra 50 centimeters on each side for safety purposes.

How big must the elevator be to accommodate the car?

See solution below.

Extra Activities

1. Measure the rise and run of the stairs in your school and calculate the angle of inclination. Do all the stairways in the school have the same angle of inclination?
2. Measure the length and width of a rectangular table or desk. Calculate and then measure the diagonals of the table. Study the numbers and then come up with a rule regarding the length of the diagonals of a rectangular surface. Using diagrams, show how you could use this rule to ensure that a rectangular deck you are building will have square corners.
3. Using a protractor, tape measure, and a calculator, determine the height of a tall tree (without touching the tree).
4. Find an empty cardboard box. Calculate the longest piece of dowel that could fit inside. Draw a diagram for your solution.

Solution Sketch the car measuring 3 m x 3 m. Draw a diagonal line between two of the corners. Which is the longest dimension of the car? That's right -- it's the diagonal. To calculate the length of the diagonal, use the Pythagorean theorem. The theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. The diagonal of the car is 4.24 m. For safety, you must add 50 cm to each end, which will add a total of 1 m to the length. The elevator must be a 5.24 m square to accommodate the car.

Published in Partnership by the Center for Applied Academics, Bridges Transitions Inc., a Xap Corporation company and The B.C. Ministry of Education, Skills and Training. Copyright © 2002 Center for Applied Academics