In maths classes across the world, one of the most common things you will hear students mumble under their breaths (while they copy down yet another algebra problem) is: “When are we ever going to need this in real life?”
But there’s a special branch of mathematics that deals with problems ‘in real life’. This branch is called applied mathematics, and if you happen to become an engineer one day, you will find yourself using this kind of mathematics on a daily basis.
Applied mathematics is often used to solve complex practical problems. And it is when used by engineers that this kind of mathematics brings about the most invaluable real world solutions to our problems: How do we make a 300-ton aircraft fly through the sky? How do we build a bridge that can cross a 1km river? How do we stop skyscrapers from collapsing during an earthquake? As writer James A. Michener said:
“Scientists dream about doing great things. Engineers do them.”
In truth, all the greatest engineering accomplishments and inventions of the 20th century were feats of mathematics. But even with this knowledge, you might still be asking:
How exactly does maths translate into practical solutions to problems?
Let’s take one of the most important mechanical features in the automotive industry as an example: the braking system.
To ensure motorist safety, automotive engineers have to build brake systems that respond in a desired and predictable way, and they have to be able to build cars that ensure certain safety features and standards. To do this, engineers have to fine-tune the brake force of a car – the brake force being the amount of force or pressure that is needed to bring something to a complete stop.
To work out the brake force of a car, you have to consider all the different mechanical and physical components that come into play.
The brake force behind each wheel of a car can be determined using:
- The wheel torque
- The tyre rolling radius
The calculation to work out brake force would thus look something like this:
Brake force (kg) = Wheel torque (m-kgs)/(Tyre rolling radius(m)/12)
To work out the wheel torque, however, you would need to work out:
- The brake pad friction force
- The rotor effective radius
This would then be calculated as:
Wheel torque (m-kgs) = (Brake pad friction force(kg))x(Rotor effective radius(m)/12)
But then to get the brake pad friction, though, you need to work out:
- The calliper clamp force
- The measurement of the brake pad
Brake pad friction force(kg) = (Calliper clamp force(kg))x(µ of the brake pad)
While the rotor effective radius is calculated using:
- The rotor diameter
- The calliper piston diameter
Rotor effective radius(m) = [(0.5)(Rotor diameter (m))]-[(0.5)(Calliper piston diameter(m))]
And so it goes on (if you are interested in all of the calculations, you can read more here).
All of these equations are calculated by measuring or weighing different parts of the brake system. Using their numerical values, then, an engineer can make a precise calculation concerning the force needed to stop the car. He or she can consequently resolve problems such as:
“How do we reduce the time needed for a driver to respond in an emergency and bring the car to a complete halt?”
Why are such calculations essential?
While many car mechanics could make adjustments to a car’s braking system by fidgeting with car parts, the work of an engineer is different. Calculations like the one above help engineers build those mechanical parts and systems that the mechanics actually tinker with. Mathematics helps engineers achieve pure precision when building or adjusting something. As the saying goes:
Maths really is the cornerstone of all engineering. Without it, bridges would collapse under tension, lightbulbs might blow up each time you flip a switch in your house, and your car brakes would only work some of the time.
It is thus not surprising that mathematics is one of the main modules in all of the Nated Engineering Courses we offer at Oxbridge Academy. If you would like more information on these courses, and how you can study engineering from home via distance learning, simply: