In the same way that geometry is the study of shapes, and algebra is the study of operations and their application for solving equations, calculus is the study of change. We can see an everyday example of Calculus in action by looking at Newton’s Second Law of Motion. We ordinarily write it down as:
Force = Mass x Acceleration (or F = ma),
which is highly useful in the Physics lab, but it was originally written by Newton himself as
“The rate of change of momentum of a body is equal to the resultant force acting on the body and is in the same direction”
which is a calculus operation. That sounds a lot more complicated than it is. The following video will make it clearer:
I’ve spoken to many pilots, and flying an airplane is as difficult as driving a car most of the time. You go faster or slower, left or right, and add one more dimension, up and down. The hardest part of flying is taking off and landing your airplane. Most of the rest of the time it’s surprisingly easy.
Before you leave…
The hard part comes before you even leave the ground. With modern jetliners it is becoming almost as easy as a point-and-shoot camera for taking pictures. You get in the cockpit with at least one other pilot and navigator/engineer, punch in your destination(s), and by taking turns you can fly virtually forever. It will be much the same for pilots in the future taking passengers to the Moon cities, lunar bases, or resorts; and possibly for much longer flights to Mars or mining colonies out in the Asteroid Belt.
However there is always the possibility that something will go wrong with the auto-navigation system, whether you’re flying from Buffalo to New York City or from the local spaceport to the city in Tycho Brae crater on the Moon. That’s when it’s going to be really handy to be familiar with your mathematics.
You still have to file a flight plan, whether you’re in a small private plane or a jetliner. Manually checking it takes a bit of geometry skill. Knowing your fuel consumption, weight of your plane and cargo, and passengers, and the limits all have to be checked. In addition, the plane needs to be balanced. Slight variations can be trimmed out with the controls, but major variations must be fixed or you risk poor flight characteristics and excessive fuel consumption wasted on compensation.
The plane rolls onto scales and the weight at each wheel is noted. Sometimes they’ll ask passengers (commercial jet) to move to any of five sectors in an unfilled plane for the take off, and then they can go back to their regular seats. In a full plane they may require ground services to add 25 kilogram (50 pound) sandbags as ballast if there is no additional cargo that can be added to balance the weight. In a small planes cargo may need to be shifted, including fuel (by internal pump) if wing-tanks are being used.
And of course it needs to be balanced both fore and aft as well as left to right. Every bit of deviation from level flight increases costs in terms of fuel. Worse yet, if the Centre of Gravity calculations are not done properly, something that is balanced at take-off may change during flight as fuel is consumed making the craft much more difficult or impossible to handle. Manufacturers supply specifications that take these things into account and it is up to the pilot to make sure they are within the specifications in order to have a safely flyable vehicle.
During the flight
During flight you must calculate fuel use and know when to switch from one tank to another so the weight remains stable in your ship. You must know how to measure visual ground, time and, compass to know when you have to change course. You have to calculate times to ascend and descend during your flight. For example, generally you exit a flight control space at 4,000 feet and enter one at 5,000 feet to keep a buffer zone between aircraft. You must know where you are and what altitude is expected. All this is basic mathematics.
Problems solved with Mathematics
You’ve probably heard the expression Dead Stick Landing (which most people think means the joystick-like control in old fashioned open cockpit aeroplanes, but really refers to the old wooden propellors which, if the engine failed, would just be a “dead stick”). Such a landing is actually not much different than a regular landing provided you have a proper landing surface. The Space Shuttle did it every single time it returned to Earth – no power, no engines and no chance to go around and do a second approach.
For example a Boeing 747 can glide for 150 kilometers (93 miles) starting at a normal cruising height of 10,000 metres (33,000 ft). It has a glide ratio of 15:1 or 15 horizontal units for each single vertical unit it gives up, in any measuring system you use. You simply look at your map, find an airport within your range, radio them to let them know you’re coming, and land there.
Requirements and conclusion
There are many routes you can take in order to become a pilot. As a Virgin Australia pilot says on their blog, “For younger aspiring pilots, completing Year 12 with a focus on Maths, Science and Physics can definitely be helpful. After school, there are various paths to take. You could look at joining the RAAF, a cadet program such as Virgin Australia’s own program, studying a degree in aviation, or building your experience via self-funding”. The UNSW offers an undergraduate bachelor degree in aviation with a flying stream that will allow you to gain your commercial pilot’s licence. For this course they recommend that students have undertaken 2-Unit Mathemathics at HSC (though it’s not a requirement you may struggle if you haven’t).
So if you think you would like to become a commercial pilot, make sure to ace your HSC maths exams and you could be on your way to getting your dream job. Check out the links below for further information on the different paths you can take to becoming a pilot and let us know in the comments section below if this is something you are considering and how you intend to achieve it.