# Calculating the damages caused by an impact of a free falling rock from (relatively) low altitude

I understand that there is an on-line site, named Impact Earth!, that allows us to calculate the damage caused by an impact of an asteroid using some parameters.

In my novel, I have an impact from a solid rock with approximately 500 meters in diameter on the ocean bed, free falling at a 90º angle.

Trouble is, the calculator only allows for a minimum velocity at impact of 11 Km/sec since that is the lowest speed an asteroid may hit the Earth.

But my solid rock isn't an asteroid, but rather one of these airborne islands, floating 1.500-2.000 meters above ground. The initial velocity would be 0, so, according to my calculations, it would hit the surface of the sea at a velocity of 170-190 m/sec, much lower than the minimum velocity of 11 Km/sec allowed by Impact Eart!

Could anyone help me with these calculations?... I am interested mainly on the height of the tsunami waves and on any atmospheric changes that would be visible (if any).

Note: I have yet to decide on the ocean depth and the distance from the coast at the site of impact... I would like the impact to be relatively near the shore, maybe some 3 to 5 Km away from the beach.

• when you say 'on the ocean bed' are you referring to it falling into the sea? this would probably slow it down if so... – marcellothearcane Mar 25 '17 at 14:47
• The energy when it hits the water is $$mgh = 4.4608\times10^{10}\times9.8\times1500 = 6.557376\times10^{14}\; \mathrm{Joules},$$ assuming a cone of granite with radius and height of 250m. I can't find any info for calculating tsunami effects though. It sounds pretty complicated though! – marcellothearcane Mar 25 '17 at 15:14
• About 157 kilo tonnes: wolframalpha.com/input/?i=6.56*10%5E14+joules+to+kiloton which is a relatively low modern nuclear warhead yield. – Feyre Mar 25 '17 at 15:25
• I think that's right, yes. Apparently the Little Boy atomic bomb exploded with an energy of about 15 kilotons, so 10 of them. – marcellothearcane Mar 25 '17 at 15:25
• Same here.. hopefully somebody will be able to make something of it! The trouble with comparing this with tsunamis is that tsunamis happen at the sea bed, not just the surface, which makes them have more effect. (the effect of this doesn't seem to be negligible though) – marcellothearcane Mar 25 '17 at 15:35

Let's think about the volume of water displaced by the island: your 500-metre floating rock has a volume of $\pi r^2 h\approx 40\times10^6\ m^3$. (I'm guessing a thickness of 50m)

Now lets model a tsunami as a wall of water, in a ring, 500m wide with a height of h. At a radius of 5km, the volume of this ring would be $h\pi(5000^2 - 4500^2)=40\times10^6$. Giving a value for h of about 40cm. Now tsunami grow in size when they reach land, you can, therefore, expect a significant amount of wave action.

Taking the value $E\sim 10^{14} J$ from the comments, and using http://alabamaquake.com/energy.html#/ to convert this to an Earthquake, gives your island hitting with the equivalent energy of a 6.5 magnitude quake. That would be a potential minor tsunami, of about 10cm However all the energy of the impact is converted to wave energy. so we can expect a larger tsunami that would be predicted for a 6.5 magnitude quake: consistent with the 40cm tsunami calculated by considering displacement.

All this points to a potential significant tsunami of several metres when the wave has been compressed in shallow shore waters, but not a catastrophic wave of 10s of metres.

The "splash" would be impressive, but I don't think that there would be atmospheric effects. It would be loud, but not "Krakatoa" loud

• Could you please elaborate (or estimate) how much "several metres" would be? Because the range of your comment goes from 2 ("metres" - plural) to 9 ("not a catastrophic wave of 10s of metres"). – Pedro Gabriel Mar 25 '17 at 22:47
• I'd estimate the low end. My model is a 40cm wave, which is growing with a shortening wavelength as it interacts with shallow water, but I haven't done any detailed analysis. – James K Apr 30 '17 at 16:17

You can proceed along this path:

1. Estimate the kinetic energy of the "rock" when it impact the ground/sea with velocity v. This is $$E = 1/2 mv^2$$
2. Calculate the equivalent amount of TNT which, exploding, deliver the same amopunt of energy. Use as reference $$1kton = 4.18 TJ$$
3. Use some reference explosion to have an hint of the damages:

• Typical airborne bomb= 0,00025 kton

• Halifax Harbor explosion (6th Dec. 1917)= 3 kton

• Nagasaki atomic bomb = 10 - 30 kton