Math at 30,000 Feet: Math and Airplanes

Math at 30,000 Feet: Math and Airplanes

Have you ever flown on a plane and wondered how the pilot was able to fly the plane and bring you safely to and from your destination? Pilots receive specialized training before stepping foot behind the cockpit, but they also must bring a strong set of math skills. From calculating the correct angles to ensure a smooth takeoff and landing to performing basic math to ensure the plane can get off the ground into the clouds, math is integrated into the art of flying an aircraft.

At first glance it may be intimidating to think about the math knowledge required to be a pilot. You may have visions of pages and pages of complicated math equations and diagrams. Thankfully, you can breathe a sigh of relief. You will need to demonstrate some advanced math skills of course, but you can mostly rely on some tried and true formulas and basic arithmetic to make it a little easier. Let’s highlight a few ways airplane pilots would actively use math when operating a plane.

Calculating a Plane’s Weight and Balance

When traveling by air, one of the most important decisions a pilot must consider is the weight capacity on their plane. The “weight” of an object conveys how heavy it is. When passengers are required to weigh their carry-on luggage, it may seem like just another way for an airline to charge additional fees. However, there is a legitimate reason for the weight requirements.  As a matter of safety, if the plane has too much weight, it impacts the plane's ability to take off and land.

Planes have what is referred to as an "empty weight", or the amount of heaviness without anything loaded on the plane and a "maximum weight", the heaviest amount of cargo the plane can carry and still fly. The weight thresholds are based on each plane’s manufacturer and the maximum weight includes any luggage, passengers, extra cargo, and fuel that may be on the plane. To calculate how much free weight a plane can safely carry, referred to as the “useful load,” the pilot will use the following formula:

Maximum takeoff weight - empty weight = useful load

See? Not so bad, the formula just involves simple addition and subtraction.

Calculating the correct weight allowed on a plane is the first step. You then need to make sure the weight is distributed evenly throughout the plane. If you have ever been on a flight and were asked to move to a certain part of the plane, it's to make sure the weight on the plane is balanced. If the weight on the plane is not balanced properly it can affect the pilot's ability to control the plane during the flight by affecting its ability to gain speed and impact how the fuel is used. Most commercial airplanes now use software or the airplane’s flight manual to help the pilot determine the plane’s center of gravity, or the location point where the plane is balanced, but the pilot will still need to know the plane’s weight calculations to ensure correct use of the software.

Calculating Fuel Amounts

The last factor we will highlight is the calculation of fuel. Pilots must use math to make sure the plane has enough fuel for the trip. To determine this, the pilot must know how much fuel their plane burns hourly and the total trip time to plug into the following formula:

Fuel Amount per Hour X Hourly Trip Time = Amount of Fuel Needed

Using this formula as an example, if a plane uses 16 gallons of fuel per hour and your total trip is 4 hours, 64 gallons of fuel would be needed for the trip. Unlike the gas you use to fill up a car that is measured by the gallon, plane fuel is measured by the pound. The pilot would need to calculate how many gallons of fuel would equal to 1 pound and convert it. A gallon of aviation gas would equal to 6 pounds, so you could use the following equation:

Required amount of fuel X weight of each gallon.

 64 x 6 = At least 384 gallons would be needed for the trip.

Now the next time you board a plane or spot one moving through the sky, you will have an idea of the “pilot math” that was involved with getting the plane up and off the ground and safely to its destination. If sitting behind the pilot cockpit is in your child’s future plans, our Mathnasium center can help ensure your child has the math foundation to be successful. Offering specialized in-person and online instruction to students in grades 2 through 12, we can provide a strong math foundation for your child to pursue dreams in aviation or another field. Give us a call today or reach out to us online to schedule your child’s free assessment.