Zero-gravity (0g) parabola

If you ever dreamed of being an astronaut and feeling absolutely weightless due to absence of gravity… But never became an astronaut, well, looks like you’re in luck. Did you know that you can create this situation using an aircraft? This is often called zero-gravity, 0g, zero g, free fall or weightlessness. It’s all the same!

I’ve been asked many times how it works, so I decided to write up a page to describe it. Note that I don’t recommend doing this by yourself!

Here is an example. The ESA (European Space Agency) uses an Airbus A300 to perform parabola that can last up to 30 seconds each. This relatively long time of 30 seconds is due to using a fast aircraft. Cost for the public is unfortunately very high, somewhere around 5000 euros per person for one flight.

<span style="line-height: normal; -webkit-text-size-adjust: auto; background-color: rgba(255, 255, 255, 0);">http://youtu.be/FX8yFEK9yJk

Maneuver

Many people ask me how this works, so here is the explanation, in 5 steps.

  1. 1g: normal level flight, with nose of the plane on horizon
  2. 2g: pull until reaching 45° nose up attitude
  3. 0g: push until reaching 0g (you know you’re at 0g because you’re no longer sitting on your seat, you’re floating and the seat belt keeps you in place). Keep forward pressure on the stick to stay at 0g, until reaching -45° nose down attitude
  4. 2g: pull until nose on horizon
  5. 1g: normal level flight

The blue line represents the flight path of the aircraft. In this case, it’s starting at about 230 km/h so the 0g section only lasts 7 seconds.
The orange line represents a free fall parabola. It’s like throwing an object in the air and watching it fall back on earth.

Basically, the aircraft follows the free fall parabola – and then resumes normal flight

Zero-gravity flight path

Zero-gravity flight path, with an aircraft flying at 126kt

This graph takes into account the following data:

  • 1g flight path at speed 126kt
  • Start of 0g parabola at 97kt and 40° pitch up
  • Gravity is 9,81 m/s²

With all other things being equal, the faster the initial speed, the longer the time in zero g. Also, the higher the pitch angle, the longer the time in zero g. The limit is at the apogee, where sufficient airspeed must be available to allow maneuverability of the plane.

 

Want more detail? Read below:

  1. Before starting, aircraft flies at 1g: The aircraft flies at a given altitude and airspeed. Before starting the procedure, the airplane is flying at 1g, meaning everything is weighting its normal weight, like on the ground. On the earth ground, we feel an acceleration of 1x the gravity. The ground helps us not fall further, but we still feel this gravity. In the air, the wings create sufficient lift to cancel weight (like ground does on earth), but we still feel the gravity just like on the ground. So, we’re at 1g.
  2. Pull back on the stick, aircraft flies at 2g: The pilot starts the procedure by increasing the aircraft’s attitude until reaching a certain angle to the horizon, for instance 45° up. This is achieved by pulling on the controls stick and monitoring the pitch angle on the artificial horizon. During this phase, the plane is accelerating upwards, and it is therefore experiencing a greater acceleration than normal. The increased acceleration can vary depending on how far the control stick is pulled back, and also on the aircraft speed. Usually, the perceived acceleration is around 2g during this phase. Of those 2g: 1g comes from the gravity, and 1g comes from the upward acceleration. Our body still feels 2g, and weighs twice its weight. Try to lift your arm or leg, and you’ll see how hard it is! This phase lasts 3 or 4 seconds in our case. OK, the pilot reached the target angle, time for the next phase.
  3. Push forward on the stick, aircraft flies at 0g: The airplane is now at a positive attitude (say 45° up), and climbing. The pilot then pushes forward on the controls to decrease the pitch angle until the opposite angle (say -45°). During this phase, the climb is leveled out and becomes a descent. If the pilot pushes with the right force, he can reach the perfect situation where the aircraft acceleration is downward with a value of 1g. This cancels out the gravity of 1g. The math gives: 1g – 1g = 0g. So we are now flying at 0g. Your seat is no longer carrying you. You are just floating above it. What happens is that the airplane is actually providing exactly 0 lift, so the plane is just falling, and following the gravity parabola. At some point, the pilot reaches the target pitch angle of -45°, which triggers the next stage.
  4. Pull back on the stick, aircraft flies at 2g: The airplane is now in a descent. The pilot pulls again on the controls to level off the aircraft. During this phase, the plane is at 2g for 3 to 4 seconds.
  5. Level flight recovered, aircraft flies at 1g: When the plane is leveled off, it is flying at 1g, as usual.

 

Comparison of high vs. low speed aircrafts

In this graph, a comparison is made between a single prop plane (Cessna 172) and a jet (A300). Because of the A300’s higher initial speed (4x larger), it can stay in 0g longer (4x longer).

0g parabola - C172 vs A300

0g parabola – C172 vs A300


Select initial speed to maintain control at apogee

The following table gives for each initial airspeed V0, the maximum angle possible to keep 65kt at the apogee (the speed chosen for minimum maneuverability), the 0g-time, and the height gained in feet.

0g parameters for Vmin = 65kt

0g parameters for Vmin = 65kt

Formulae

Here are the formulae that allow these calculations.

0g Formula

0g Formula

  • g0 is the gravity (9,81 m/s² on earth)
  • V0 is the initial speed in m/s (when starting the push at 0g)
  • α is the initial pitch angle (when starting the push at 0g) – excel calculates it in radians.

Restrictions

A few things to know about this maneuver:

  • If the airplane is not allowed to fly at 0g, then this maneuver should not be attempted, as damage to the structure may occur. This specification is listed in the operating manual. In the case of a Cessna 172 (see extract below) in the normal category, the acceptable load range is between +3.8g and -1.52g, so the plane can withstand 0g.
  • If the aircraft’s fuel supply system is solely based on gravity (high wings, gravity-fed fuel), then the engine will stop when the aircraft nears 0g or goes negative g. Once the number of g increases above 0g, fuel is fed to the engine again, and the latter restarts due to its existing rotation caused by the airflow.
  • Maneuverability: as pointed out in a paragraph above, a minimum airspeed must be available at the apogee to maintain control of the aircraft. A stall may also occur if loading the wing at low airspeed (i.e. pulling back when the plane has not recovered a higher airspeed).
  • Other issues are possible. Always check with your instructor before attempting anything new in aviation.
C172 g-load specifications

Cessna 172 g-load specifications

Gravity of other planets

Using the same maneuver, it is possible to achieve the gravity value at the surface of other planets. For instance, Mars (0,37g) or the Moon (0.17g).

Check out this video! Actually, the first parabolas of commercial/scientific zero-g flights start with Mars and the the Moon to accustom passengers to lower gravity, before repeating 0g parabolas.

In a small aircraft

Another example is a Cessna 172 performing zero g parabola that last 4 to 5 seconds each.

Disclaimer

The purpose of this page is solely to explain the physics behind a physical phenomena which can be achieved with an airplane. The purpose is not to recommend this maneuver.

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