Damage of a high mass object falling at terminal velocity

[Kfireblade]

How would I calculate the damage and effects of a massive rod of metal dropped from orbit or near orbit? (say a 640 ton rod.)

[Anthony]

Depends on its terminal velocity, which will require ballistic computations that are beyond the scope of GURPS. However, assuming you made an effort to streamline it, probable effect is it hits the ground at near orbital velocity and creates a modest size crater (yield is a couple kilotons).

[Agemegos]

Originally Posted by Kfireblade

How would I calculate the damage and effects of a massive rod of metal dropped from orbit or near orbit? (say a 640 ton rod.)

Imperial College London and Purdue University have an online impact calculator that you might find useful. The only problem with it is that it implicitly assumes a near-spherical impactor rather than your rod. I think that means that it over-estimates the ram pressure and effects of air resistance, which means that it has objects going slower at impact and more likely to shatter than you really want.

Note that the density of iron is 7700 kg/m³, so your 640-ton (short ton) metal rod could be entered into the calculator as a 5.2-metre diameter object. If you want to assume some other metal such as tungsten you might get a smaller object of greater density or vice versa.

Earth's circular orbit velocity at low altitude is 7.9 km/s: this is the speed at which an object "dropped from orbit" will enter the air.

A lot depends on the angle of impact with the atmosphere. If this is very shallow the impactor will be slowed gradually and land intact. If it is steep the ram forces will shatter the impactor and it will land as a scattering of fragments.


Note concerning the thread title: an object re-entering from orbit does not necessarily slow down all the way to terminal velocity, and probably doesn't unless it is small. At a very shallow angle of impact it might. Or at a steep angle of impact it might shatter into a swarm of fragments, and those might land at terminal velocity.

[Anthony]

Originally Posted by Agemegos

Imperial College London and Purdue University have an online impact calculator that you might find useful. The only problem with it is that it implicitly assumes a near-spherical impactor rather than your rod. I think that means that it over-estimates the ram pressure and effects of air resistance, which means that it has objects going slower at impact and more likely to shatter than you really want.

Yeah, I tried an impact simulator on a 5 meter object and it told me the object exploded in the upper atmosphere.

[Agemegos]

Originally Posted by Anthony

Yeah, I tried an impact simulator on a 5 meter object and it told me the object exploded in the upper atmosphere.

And still made a crater 130 metres wide?

Try a shallower angle of impact.

[Anthony]

Originally Posted by Agemegos

And still made a crater 130 metres wide?

Generated no crater at all. How did you get a 130 meter crater?

[Agemegos]

Material strength of the impactor seems to be irrelevant. You could try modelling a rod by using an impactor with diameter equal to the rod diameter and density equal to the rod density times the length-to-diameter ratio times 1.5

That seems to work as you'd expect. At an impact angle of 45 degrees the impactor lands intact producing a bang equivalent to about 800 tons of TNT, a crater 230 metres wide and 49 metres deep, and ground shaking felt at a couple of kilometres, but no fireball.

[Agemegos]

Originally Posted by Anthony

Generated no crater at all. How did you get a 130 meter crater?

INPUT

Distance from Impact: 1.60 km ( = 0.99 miles )
Projectile diameter: 5.20 meters ( = 17.10 feet )
Projectile Density: 7700 kg/m3
Impact Velocity: 7.90 km per second ( = 4.91 miles per second )
Impact Angle: 45 degrees
Target Density: 2500 kg/m3
Target Type: Sedimentary Rock

RESULTS

…

Crater dimensions

Crater shape is normal in spite of atmospheric crushing; fragments are not significantly dispersed.

Transient Crater Diameter: 129 meters ( = 425 feet )
Transient Crater Depth: 45.8 meters ( = 150 feet )

Final Crater Diameter: 162 meters ( = 531 feet )
Final Crater Depth: 34.4 meters ( = 113 feet )
The crater formed is a simple crater

The floor of the crater is underlain by a lens of broken rock debris (breccia) with a maximum thickness of 16 meters ( = 52.4 feet ).
At this impact velocity ( < 12 km/s), little shock melting of the target occurs.

[Anthony]

Your Inputs:
Distance from Impact: 1.60 km ( = 0.99 miles )
Projectile diameter: 5.20 meters ( = 17.10 feet )
Projectile Density: 7.7 kg/m3
Impact Velocity: 7.90 km per second ( = 4.91 miles per second )
Impact Angle: 45 degrees
Target Density: 2500 kg/m3
Target Type: Sedimentary Rock

Atmospheric Entry:
The projectile begins to breakup at an altitude of 102000 meters = 333000 ft
The projectile bursts into a cloud of fragments at an altitude of 85200 meters = 279000 ft
The residual velocity of the projectile fragments after the burst is 6.57 km/s = 4.08 miles/s
The energy of the airburst is 5.44 x 109 Joules = 0.13 x 10-5 MegaTons.
No crater is formed, although large fragments may strike the surface.

It looks like I'm hitting a different version of the program, but it's the same URL.

[Agemegos]

Check your impactor density. It's off three orders of magnitude. I think you used specific gravity (kilograms per litre) where the form specifies kilograms per cubic metre.