Six-Degrees of Freedom

Photo credit Paul Burger, Houston

I’ve had an epiphany of sorts.

I was flying with friends as night was falling. We were over a mile up, the air was clear and still, not a bump to be found. City lights and major roads could be seen from over 45 miles away. We seemed to be suspended in space, with only the movement of lights sliding below our wings betraying the fact that we were traveling at 145 knots over the ground.

The fellow sitting in the seat to my right seemed interested in taking the controls, something he had never done before. I first let him handle the yoke. With the autopilot holding track so we wouldn’t get too far off course I let him see how the elevator worked to raise and lower the nose, controlling pitch. Then as I turned the autopilot off completely, I had him experiment with the rudder pedals to see how that affected the aircraft. They made the plane yaw to the left and right. Next I showed him how the ailerons on the wings work with the rudder on the tail to smooth out turns by applying roll simultaneously with yaw. That created a coordinated turn which is the most efficient and comfortable way to change direction in the air.

He was getting a mini-lesson in flying, and doing quite well for a novice.

Then I told him to point the nose of our bird towards a light on the horizon that would keep us headed in the right direction, towards our home base some 90 nm away.

He had the plane swaying slightly from side to side, but I did not interfere or correct him. Now that I think about it, he may have been doing it deliberately as he learned how the ailerons and rudders work in unison. And then he said something interesting: “It’s six-degrees of freedom.”

Granted, my friend is a mechanical engineer, and in his student days he had done a project with wind tunnels and model airplanes. That was where he gained both academic and practical experience about the six-degrees of freedom in aviation.

Image credit: Horia Ionescu, Wikipedia Commons

The six degrees involve three degrees of translation, and three of rotation. In the following illustrations, aside from the three rotational axes commonly applied to aircraft, roll, pitch and yaw, the other three axes are also shown. In a ship, motion in those translational axes are called heave, sway, and surge. In an aircraft they have less colorful terms; motion fore and aft, left and right (port and starboard), and up and down. The figure to the right shows all six degrees of freedom irrespective of the craft or method of motion.

Illustration by S. W. Halpern


For me, the  epiphany was the realization that my favorite things on earth (or slightly above it) involve six-degrees of freedom. Physically, there can be no greater freedom, and that freedom is found in flying and diving. No wonder I love them.

Birds live in that six-degree of freedom world, and perhaps that’s why we envy them. While we may not envy fish, per se, perhaps it is the six-degrees of freedom that lures so many of us to diving underwater. I well remember the first time I glided over a vertical precipice in crystal-clear water and realized with supreme pleasure that the laws of physics no longer compelled me to tumble over that precipice. Even now, quite a few years later, I still enjoy diving in the Florida Panhandle Springs, and finning directly over a rock face that drops vertically towards a sand bottom some 25 or so feet below. I’ll float over it, looking down, then bend at the waist and glide effortlessly to the bottom.

This is the stuff of flying dreams, of which I am also enamored.

A soul floating in space prior to incarnation, an embryo floating in utero prior to implantation; these are ways we might have once had the same freedom of motion. But soon after becoming a fetus we lose that freedom. There is no where else that freedom of motion can be experienced in a sustained manner than by  flying and diving.

Photo credit: Mass Communication Specialist 1st Class Jayme Pastoric


The following video is the best example I’ve found to demonstrate the true meaning of six degrees of freedom. Go to full screen, high def, volume up, and enjoy! (Disclaimer: I have no connection to the featured company or equipment used in the making of this video.)

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