Light Fall 1.2.0
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This calculator calculates how fast you're moving afterfalling a certain distance — your free fall speed. It ignoresfriction (air, rock, rope, or otherwise) and relativistic effects: Wehope that you won't fall far enough to have either of these make muchof a difference! If you fall out of an airplane, however, you'llwant to scroll down to terminal velocity.We don't advocate trying to empirically validate these results usingyour body.Climbing is dangerous.Insert standard disclaimer here.
If you fill in the height, you'll get the time and speed at the end of your fall. If you're kind enough to supply your mass, you'll also get the energy in joules (newton-meters) when you hit the deck. :-) See the plot at the end of the page to see how impact velocity varies with height.
As is probably obvious, the higher you are, the harder you land. The relationship looks like this, in km/h:
In other words, falling from 50m high is the equivalent of getting hit by a car going 112 km/h, or 70 miles per hour — what would happen if you ran out into a busy freeway. If that's not a decent argument against free soloing, I'm not sure what is.
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Free fall / falling speed equations
The calculator uses the standard formula from Newtonian physics to figure out how long before the falling object goes splat:
- The force of gravity, g = 9.8 m/s2
Gravity accelerates you at 9.8 meters per second per second. After one second, you're falling 9.8 m/s. After two seconds, you're falling 19.6 m/s, and so on. - Time to splat: sqrt ( 2 * height / 9.8 )
It's the square root because you fall faster the longer you fall.
The more interesting question is why it's times two: If you accelerate for 1 second, your average speed over that time is increased by only 9.8 / 2 m/s. - Velocity at splat time: sqrt( 2 * g * height )
This is why falling from a higher height hurts more. - Energy at splat time: 1/2 * mass * velocity2 = mass * g * height
Ignoring air friction: Terminal velocity
This calculator doesn't take into account air friction. But think aboutwhat happens if you stick your hand out of the window while driving downthe freeway: The wind pushes pretty hard against you. That's air friction.The faster you're going, the harder it pushes back. In fact, it pushes backwith theLight Fall 1.2.0 Update
square of your speed, whereas the acceleration of gravityis constant. This means that at some point, the force of air againstyou equals the force of gravity, and you stop accelerating.That point is called terminal velocity (see this wikipedia article for more information). It dependsa lot on your position — something shaped like a bullet will have a higherterminal velocity than something shaped like a flat pancake parallel to the earth, because the latter has more surface area exposed to air friction.
The calculator doesn't take any of this into account.In practice,terminal velocity on earth will prevent you from going more than about320 km/h, or about 200 miles per hour. If you're lying belly-to-the-earth,you'll only travel about 195 km/h (122 miles per hour). As you can see fromthe graph above, you'd have to fall from higher than 50 meters abovethe ground for this to really matter much, and at that point, you'd bein enough trouble to not care much. Skydivers, however, should goread the Wikipedia article.
About the calculator
This is a javascript-based calculator. For you history buffs, thefirst version used a 10-iterationimplementation of Newton's methodto compute the square root needed for some of the equations, becausein the days of yore, many browsers didn't support sqrt()natively. You can see the original code here:newton_sqrt.js - Square root using Newton'sMethod in Javascript.
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Light Fall 1.2.0 Ideas
The equations are standard and I verified them, but they're alsopartly taken from posters onon the old rec.climbing newsgroup — the people who wanted the splatcalculator in the first place. Boggles the mind.It's allClyde Solesfault for suggesting it.
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Light Fall 1.2.0 Download
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Light Fall 1.2.0 Wallpaper
(Disclaimer on the picture: Please, I'm not advocating soloing. I'mactually only about 10' off the deck).