If you haven’t seen OK Go’s new video: Upside Down and Inside Out, you should do so now. If you thought their previous videos were awesome, this one is 10 times more epic. Basically it’s a video recorded inside an accelerating aircraft to produce a zero-g environment. Let’s get to the physics.

How do you become weightless in an aircraft?

We don’t feel gravity like most people think we do. Consider a person standing still on a floor on the surface of the Earth. Since the person is at rest, there are two balancing forces—the gravitational force pulling down and the force of the floor pushing up. It’s really the upward force of the floor that we feel as “weight” and not gravity. This is because the gravitational force pulls equally on all parts of our bodies unlike the floor which just pushes on our feet. I know that sounds crazy, but I can convince you with an example.

Go get in an elevator. Don’t use a crappy slow accelerating elevator like in my building. You want a really nice one. Start at the eighth floor and press the button to go the first floor. Since the elevator is at rest and then moving downward, it has to accelerate downward. Here are two force diagrams showing before and during the acceleration.

Spring 2016 Sketches key

The gravitational force depends on the mass of the Earth—and this doesn’t change. However, the force of the floor decreases when you accelerate down such that there is a net downward force. You feel lighter when this floor force gets smaller. If the elevator accelerates down with a value equal to the gravitational field, there will be NO force from the floor and you would feel weightless. This is the whole idea behind some of these dropping amusement park rides like the Tower of Terror.

This is also exactly why astronauts in orbit are weightless. Even though the gravitational force is slightly smaller (only slightly) in orbit, the International Space Station moves in a circular path such that the acceleration is the same as the gravitational field. It’s exactly like a falling elevator except that the space station never crashes into the ground.

The same thing can happen inside an accelerating aircraft. This is how OK Go created their awesome video. The aircraft flew in a way such that it was accelerating down to produce a weightless environment. It should be noted that the aircraft accelerates downward. This doesn’t mean it has to have a downward velocity. In fact, if the aircraft is moving upwards but slowing down it can still have an acceleration equal to the gravitational field. So, a parabolic flight path is what you want to give the passengers the longest possible zero-g experience.

Could you record this in one take?

If you look at the whole video, the weightlessness part lasts about 166 seconds. Could you fly an aircraft to produce weightlessness for this long? Let’s start with some assumptions.

  • The aircraft starts at an altitude of 10,000 feet (3,048 meters).
  • Cruise speed of 500 mph (not sure if this really matters).
  • Maximum altitude of 40,000 feet (12,192 meters).
  • The magnitude of the gravitational field is a constant value of 9.8 N/kg (mostly true at this altitude).

Since the goal is to maintain a constant acceleration, you don’t have to worry about air resistance. Fighting against lift and the air drag is why the aircraft will still need to use its engines during the maneuver.

Since this is a constant acceleration problem, it’s just like projectile motion. Let me start with the case of an aircraft starting at 10,000 feet with a speed of 500 mph and angled up at 45°. Here is a plot of the plane’s vertical position as a function of time.

This gives a weightless time of just 32.2 seconds. That’s not good enough. However, it also has the aircraft only going up to about 14.5 thousand feet. What about a different flight path? This one will start with a higher speed—let’s try 600 mph and starting at 30,000 feet. I will let the aircraft fly down to 15,000 feet before ending the weightless run (even though that’s probably too low).

This still only gives a zero-g time of 55.5 seconds. So, no. You couldn’t record this video in one take. Your best bet is to record in 30 second segments. That makes this a pretty tough job. However, if you watch closely you will see that the passengers don’t always float around. At about 20 seconds into the zero-g part, they all sit down and even the floating laptops sit on the ground.

Okgo 1

It’s probably at this point they make some type of magical video editing cut while the aircraft regains altitude to make another zero-g run. Looking at the video close, this seems to happen every 20 seconds. It’s very impressive when you think about it. Also, considering that these guys probably don’t have a lot of experience in zero-g environments these moves probably took some practice. On top of that, it could be quite dangerous. If you are at the ceiling of the aircraft in a zero-g maneuver and there is an unexpected acceleration, you could go crashing into the floor (or into another person).

Still there is one other great physics demonstration. I love when the two flight attendants rotate and change their leg position to increase their angular velocity. This is a great demonstration of the conservation of angular momentum—much in the way a figure skater does while spinning on ice but just much cooler.

Okgo 2

That’s just awesome. Still, I wonder how many times these guys barfed in the making of this video.

Excerpt from: 

The Physics of OK Go’s Epic New Zero-G Video