By Greg Anderson
Comm-Inst. Boeing 707, KC-135
USAF Aircraft Commander (Ret)
By Greg AndersonDo you get out of the cockpit after a flight refreshed and invigorated? Or maybe wishing you could turn the clock back? Do you leave the airplane with a spring in your step, maybe feeling younger? Or do you amble away feeling a bit older?
Did you know being older or younger may depend on how high and fast you flew, and whether you flew east or west?
According to Albert Einstein, the principles of relativity are at work along with lift, weight, thrust, and drag when we fly.
Although its effects are infinitesimal, relativity affects pilots more than most because we tend to travel faster, farther, and higher than our earthbound peers.
We’ve all heard about astronauts getting younger as they circle the globe. And for GPS satellites, it’s a big deal. For me, flying KC-135s across the International Date Line was pretty cool. But it’s fun to think about time speeding up and slowing down in all the airplanes we fly.
Of course, all pilots use time when we calculate speed, flight duration, fuel burn, endurance, and many other measurements. We make day and night flights and change time zone without much thought, but they are symptoms of the forces of relativity that act on us all the time.
Einstein used a train in his famous explanation of how time stretches and slows, but we can use an example of flight to oversimplify the principles. Say we’re flying along in our piston-powered Cessna and we drop a wrench out the window.
To us, the wrench drops straight down, but to someone on the ground, the wrench follows an accelerating, curving arc. Relativity – in theories of “special” and “general” – relates to different frames of reference and the effect of gravity. According to Einstein, with the speed of light held constant, time alters or “warps.”
In pilot training, we all learned to make flight calculations with the old E6B flight computer. Let’s climb into the left seat of a Boeing 737 airliner for an imaginary flight from New York to Los Angeles. Our copilot is a guy who needs a haircut badly, and his name is Albert Einstein. The E6B would still work for him, but he applies an additional equation that calculates time dilation: ∆t ≈ t × v²/(2c²).
For our cross-country flight, we will throw out the E6B and turn to my artificial intelligence (AI) friend Claude for assistance with higher math. Einstein informs us the effects of special relativity from our speed for our 5 ½ hour flight work out to us being approximately 6 nanoseconds – billionths of a second – younger when we land.
However, our altitude of, say, 36,000 ft means that gravity is very slightly weaker, and the general relativity effect is that our clock runs a bit faster, not slower. With a typical commercial flight, the reduced gravitational effect overcomes the velocity effect. Einstein tells us that with the 2 effects combined, we will be infinitesimally older than if we had stayed home. Certainly not enough for crew rest.
Now for our direction east or west. Relatively speaking – pun intended – flying east or west matters quite a bit because of the Earth’s constant rotation of about 735 mph at mid-latitudes. Flying west, we are moving against rotation, so our total speed through space is lower than a ground observer’s, reducing the slowdown effect of the clock.
This isn’t speculation. According to an experiment in 1971, when commercial aircraft flew atomic clocks twice around the world, first eastward and then westward, comparing them to a reference clock at the US Naval Observatory revealed the eastbound clock lost 59 nanoseconds, while the westbound clock gained 273 nanoseconds.
Thus, westbound trips end up aging us more than going east, even though absolute numbers are still nanoseconds either way.
Varying our speed for the velocity effect of special relativity and our altitude for the gravity effect of general relativity will alter our time warps – small as they are. Astronauts on the International Space Station (ISS) fly much faster, and the velocity effect overcomes the gravity effect. After a month aboard the ISS, Claude tells me an astronaut comes home about 0.3 to 0.5 milliseconds (thousandths of a second) younger.
Before they are launched into space, the atomic clocks on GPS satellites are programmed to run more slowly than clocks on Earth in order to counter the effects of their speed and altitude. Without such correction, Claude estimates GPS positioning errors would accumulate to roughly 10 or 11 kilometers per day, rendering our navigation apps useless.
Now consider the effects of relativity on the Voyager 1 spacecraft launched in 1977. Traveling at 38,000 mph, Voyager 1 is outside our solar system, approximately 16 billion miles from Earth, and the reduced gravitational effect (from the Sun) is far larger than the velocity effect. According to Claude, the net result is that Voyager’s clock runs faster than Earth’s. Over 49 years of flight, the spacecraft is now 10 to 13 seconds older than if it had stayed on the ground.
As we can see, everything really is relative. I doubt flying with Einstein will make us better pilots, but it appears that flying low, east, and fast are the best way to make yourself relatively younger. Maybe the fountain of youth is out there somewhere. Now in retirement, I love flying my Air Cam across counties, not countries – low and wherever curiosity leads me, but verrry slowwwly.
Alas, I am still getting older. And so far, my wife’s not buying my argument that whenever I fly I earn myself a nap.
