Mythbusters Math to Compute G Forces from Falling in Bubble Wrap

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Bubble wrap just isn’t enough to save you if you fall from a tall building – but why not? Math has the answer. Image by genox

The Mythbusters busted the myth that a person could survive a 35 foot drop if protected only by bubble wrap. The “g forces” are far too great – but what is g, and what are g forces? How can we compute g forces from falling from a given height but cushioned by thick padding?

Math leads to a surprisingly simple calculation that might have saved the Mythbusters some trouble with their bubble wrap.

What is G? Distinguishing ‘G‘ from “G Forces”

In physics, g is acceleration due to gravity. Near the surface of Earth, “g=9.8 metres per second squared = 9.8m/sec2“. In other words, by ignoring wind resistance, aerodynamic lift and the buoyancy of helium-filled balloons, objects will fall at a constant acceleration of 9.8 metres per second, per second.

If we measure acceleration due to gravity in 32 feet/sec2, we calculate the number of g‘s by dividing by 32. In metric,  gravity’s acceleration is 9.8 metres/sec2, so g = acceleration/9.8. The number of g’s of acceleration is simply a larger unit than feet/sec2 or m/sec2.

However, the term “g forces” refers to the pressure or stress that a person or object feels when being accelerated. Normally a person experiences “1 g” when stationary. When you jump, you feel some g forces as you push upwards; none while airborne; higher g forces when you land; and the usual 1 g after settling down.

What are Velocity and Distance in Free Fall?

The velocity, or speed, of that falling object increases at a uniform rate of acceleration.

The distance covered increases as the square of the time during the fall.

What the Mythbusters Learned about G Forces from Falling into Bubble Wrap

The Mythbusters dropped Buster the test dummy, from different heights, with different thicknesses of bubble wrap as protection. Buster had an accelerometer in his chest cavity, to record the impact as measured in g forces.

What were the results of falling and crashing? The higher drops caused greater g forces on impact; thicker bubble wrap padding decreased the g forces. These results were not at all surprising.

The Math of Falling

These formulas will help you calculate the velocity of an object during a fall. Image by Mike DeHaan

The mathematics of falling is fairly simple. We will use ‘a’ for acceleration in metres per second squared. We use ‘f‘ as a subscript to indicate that we’re dealing with falling, rather than crashing. The falling object reaches its maximum velocity just before the crash.

  • The acceleration due to gravity while falling is af = 9.8m/sec2.
  • The distance of the fall is df. The Mythbusters deliberately dropped Buster from a known height, so df is given.
  • The formula for maximum velocity while falling, ‘vf‘, is “vf2 = 2*af*df“.

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