# NASA, Flying and Slope Formula

Bart Epstein is the Senior VP, Corporate Development and General Counsel at Tutor.com. He has previously written about his love of flying and volunteer Angel Flights.

NASA recently released a new “Fly By Math” simulator as part of their Smart Skies program. They are calling it “a fresh look at traditional distance-rate-time problems.” This is a great way for students to see a practical application of linear equations.

The other day I was flying my favorite plane 8,000 feet above the ground, slicing across the sky at about 200 miles an hour, when I realized that I needed to whip out the old slope formula from algebra:  Y = MX + B.

Flying a plane isn’t like driving a car.   When you’re up high, going fast, your plane is loaded with “potential energy” that needs to be dissipated during the approach to landing.    Part of being a good pilot is about managing that energy wisely by descending at a rate that is efficient in terms of lift/drag ratio, fuel usage, passenger comfort, and of course safety.   (Flying along at 8,000 feet until you get to your airport and then spiraling down to a landing would be inefficient, wasteful, and weird for the passengers, who prefer smooth descents.)

As I did my math I realized that I wanted to stay up relatively high that day because the winds were in my favor and also because the temperature at 8,000 feet was about 20 degrees cooler than on the ground on a hot day. I settled on a 500 foot-per-minute descent rate (slope) and then got out my pencil to do the math to figure out how far away I should begin my decent.

I calculated that flying at a speed of three miles per minute, while descending 500 feet per minute would mean that I would get six miles closer to the airport for every 1,000 feet of altitude that I descended.    Being 8,000 feet above the ground therefore meant that I would need to start my descent forty two miles before my destination for a nice glide right to my home runway.

Lucky for me, the air traffic controller that day was able to give me the exact descent rate (slope) that I wanted.   But it doesn’t always work out that way, usually because there are lots of other planes up there, and the air traffic controllers must make sure we all land safely.   It’s times like these that I am glad I paid attention in algebra class.