Crunching Noah’s Ark

PZ Myers started it by linking to the original collection. Then Greg Laden singled out the video of Noah’s Flood engulfing the world. Now it’s my turn:

[youtube=http://www.youtube.com/watch?v=fVF2bYeIl0Y&rel=1&border=0]

Just for fun, let’s crunch some numbers, shall we? The last few seconds of the video show the Flood about to strike the Ark. Let’s see if we can calculate the height the Ark would have to fall from in order to equal the impact it’s going to experience when that big wave hits.

The video shows an undersea eruption of some kind starting off the flood. It follows roughly the line of the Mid-Atlantic Ridge (with a corresponding eruption along the, um, Mid-Pacific Ridge), sending a mountainous wall of water hurtling eastwards and westwards. The time from initial eruption until the covering of the entire earth is about a minute and a half, or 90 seconds. Let’s round that off to 100 for easier calculations. So we have two eruptions, each generating two waves, that circle the earth until they meet, and each wave covers roughly one quarter of the earth.

The earth is about 24,900 miles in circumference, so each wave has to travel 6,225 miles in those 100 seconds, giving us an average speed of 62.25 miles per second at the equator. The distance around the earth at higher latitudes would be smaller, so the speed wouldn’t need to be quite so high. Let’s make a conservative estimate and say the wave would have been traveling at only 30 miles per second at the location of Noah’s Ark. 30 miles per second is roughly 160,000 feet per second, give or take a percent or two. Let’s call it 150,000 just to make it even more conservative.

The acceleration of gravity is 32 feet per second squared, and velocity equals acceleration times time, so we can calculate how long the Ark would need to fall to reach a spead of 150,000 feet per second: t = v/a = 150,000 / 32 = 4,687.5 seconds. The formula for how far the Ark would fall in 4,687.5 seconds is s = 1/2 at^2 = 16 * (4,687.5^2) = 351,562,500 feet.

So the force of impact when that wave hits the Ark is roughly equivalent to the impact the Ark would experience if dropped onto the ocean from a height of 350 million feet, or about 66,500 miles–about 1/4th of the way to the moon.

This, of course, neglects the effect of air resistance and friction compression. The famous SR-71 Blackbird, cruising in the lower air densities at 80,000 feet, was heated to a surface temperature of 300 degrees Celcius (three times the boiling point of water) due to air friction compression at speeds of just over 2,000 miles per hour. The wave, traveling at 30 miles per second, or about 158,000 miles per hour, would have generated much higher temperatures. Let’s be ridiculously conservative and say the heat generated was only ten times higher than that experienced by the SR-71, i.e. 3,000 degrees Celcius. Mere pyroclastic flows are granny’s old icebox by comparison!

So before the wall of water smashed into the Ark, it would have been engulfed by an incinerating cloud of superheated gases under extremely high pressure. And then whatever was left would be hit by the water itself, with an impact like falling from a height of 66,500 miles into the sea.

And darn, I haven’t looked at the question of how much force would be needed to accelerate that wave to a speed of 158,000 miles an hour in less than 30 seconds in the first place. Or how much mass would have been in those waves, or what effect would result from that much mass moving from inside “the depths of the earth” to the surface of the earth in a minute and a half. But hey, I have to leave something else for other people to blog, right?

 
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Posted in Amusements, Science. 2 Comments »

2 Responses to “Crunching Noah’s Ark”

  1. bacopa Says:

    The SR-71 and re-enterng spacecraft heat up much more from compression rather than friction. Think about how a bicycle pump heats up as you use it. The SR-71 compress the air MUCH more severly than the pistion in the air pump, and the Shuttle compresses air even more. But you are correct that the Ark would not survive the wave unless gopher wood was solit carbon nanotubes.

  2. The Professor Says:

    And even then, the Ark might survive, but the contents wouldn’t.

    Good point, thanks for the correction.