Use Your Head…for Math!
Posted by drdavescience on March 19, 2008
When I was young, I wanted to earn my pilot’s license. All my teachers knew this, and they always told me that pilots were good at doing math without calculators.
During my flight training, I encountered all sorts of math problems in the form of how to properly loading the plane with people and fuel (weight & balance) and navigation. I am very glad I followed my teachers’ advice.
Let’s take a closer look at the issues pilots have to face and examples of the problems they have to solve. Towards the end, I will share how I do math in my head.
Weight and Balance
Flying an airplane is a balancing act. Think of an airplane as a seesaw.
Pilots try to achieve the a condition similar to when a seesaw is in balance. This is possible by distributing the weight evenly. If an airplane is out of balance, it will fly poorly or not at all. Gasp!
Navigation
Pilots have to know how to get to their destination using tools like radios and GPS. Modern airplanes have a lot of fancy computers onboard that make navigation easier, but mistakes can occur. I was trained to always double check the computer because the best onboard computer is the pilot’s brain.
Always Ask, “Does the Answer Make Sense?”
When I was in elementary school, I had a friend who used calculators a lot. On the day of a big test, his calculator broke and so he borrowed a calculator that was different from the one he was used to; it had twice as many buttons. He did very poorly on this test, and he blamed the calculator for giving him the wrong answers. It turns out he was at fault. Why?
Calculators and computers are just machines that do exactly what you tell it to do. For example, if your problem is 44 x 5, but you accidentally type 44 + 5, the math will be correct, but the answer will be wrong.
Similarly, onboard flight computers are very useful tools for flying, but it is up to the pilot to make sure the computer is correct. How do we do it?
The Power of Estimation
When flying an airplane, I have to deal with numbers that are not as easy to use. Let’s say that my cruising speed is 167 miles-per-hour (mph), and my destination is 302 miles away.
The onboard flight computer says it will take 1 hour 49 minutes.
Is the flight computer right? Does this flight time make sense?
If I used the exact numbers in my head, I would probably be more focused on doing math than flying the plane. This is dangerous. Instead, I will round numbers up or down to make the math easier.
The Easy Way
In this example I would round the distance down to 300 miles (from 302 miles) and use 150 mph (instead of 167 mph).
300 miles divided by 150 mph is easy to solve.
The answer is 2 hours, which is close to what the onboard computer is saying.
Also, since I know I am going faster than 150 mph, I know I will reach my destination sooner than 2 hours. My logic agrees with the onboard computer and so the flight time “makes sense.”
It Works!
I have been in a situation where my flight examiner intentionally programmed an error into the onboard flight computer. I noticed that the error early on because I always asked myself “does the flight computer make sense?” I was able to catch the error before it became a problem later in the flight. The examiner was impressed.
Asking, “does the answer make sense” when solving any sort of problem helps to check your work. I can remember many times where I checked my work without a calculator, using estimation and simple math, and I uncovered a calculation error.
My teachers were right; doing math in your head is an important skill. Thanks to their advice, my dream came true and I earned my pilot’s license.
-Dr. Dave
P.S. There is another way that I use to solve the flight time problem shown above. It is more advanced so I saved it at the end for those who are interested.
A Little More Advanced
I know that 10% of 150 mph is 15 mph. If I add 150 mph with 15 mph, I get 165 mph, which is very close to 167 mph.
If I am going 10% faster than 150 mph, I know I will arrive 10% sooner than 2 hours (120 minutes). 10% of 120 minutes is 12 minutes.
Arriving 10% sooner means I will arrive in 2 hours – 12 minutes, or 1 hour and 48 minutes.
This agrees with the flight computer!
