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As my recent inquiries have shown, when a kinetic projectile has sufficient speed, it does more than 'penetrate and perforate'. It will have somewhat of an explosive effect, right?

Difference to the last question: This is not about what the maximum speed could be, but what speed would be needed to create the desired impact effect.

The formula for kinetic energy goes like $E_k = \frac12 m v^2$, where $E_k$ is the kinetic energy, $m$ is the mass of the projectile and $v$ its velocity.

I know volume (1l = 100 cm³) and density (~20g / cm³)
That means I know the mass of the projectile : 2000g or 2kg.

What I try to find out is how fast would the projectile need to be to have more than a 'kinetic effect' (I know that explosion are basically a kinetic particle effect)

I am aiming for a very intense local effect, something like a modern medium sized bomb would have, not for cataclysmic destruction.

So how much energy is needed to create that 'space rod' effect where it is akin to a warhead, although somewhat smaller, if possible? Is there something like a sliding scale of effects I could use?

Notes:

  • The target area is the ground of a sparse forest.
  • The firing range is about 100m.

I tried to google it and use a kinetic impact simulator (NASA i think) but they are used for much bigger projectiles (asteroids).

It would be extremly helpful to have some kind of resource to lookup impact effects for later parts of my story, when the damage needs to be even more intense.

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  • $\begingroup$ Thanks for adding the formula font! $\endgroup$ – user6415 Sep 23 '19 at 18:47
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    $\begingroup$ That depends on how well the projectile's kinetic energy couples with the target, doesn't it? If you fire a high velocity round at a paper target the round will just make a hole and pass through without doing any more damage than that. Designing projectiles to tranfer their energy to the target is not a trivial exercise, and the result depends on the characteristic of the target and the intended effect. $\endgroup$ – AlexP Sep 23 '19 at 18:53
  • $\begingroup$ The projectile is fired into the hillside in a forest. $\endgroup$ – user6415 Sep 23 '19 at 18:55
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    $\begingroup$ Relevant xkcd: "Imagine throwing a ripe tomato - as hard as you can - at a cake." $\endgroup$ – Dubukay Sep 23 '19 at 18:56
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    $\begingroup$ Small objects cannot travel at hypersonic velocities in the dense layers of the atmosphere, at least not for any non-trivial distance or length of time. They will very very quickly become very very hot and dissipate in a ball of gas. $\endgroup$ – AlexP Sep 23 '19 at 19:07
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That's pretty straightforward.

You know the mass of the bullet, you know the energy you want to deliver, and you know the relationship between the two through the velocity.

Therefore you just need to put in the formula the energy and the mass and extract the velocity:

$v=\sqrt{2E/m}$

A Mark 82 bomb delivers 227 kg of explosive. That corresponds to roughly $10^9 \ J$, assuming it is TNT, which would give, for a 2 kg bullet, to a velocity of about 32 km/s.

Since this is way lower than c, we are not in relativistic regime and the formula for the kinetic energy we have used is valid. Else we would have needed the relativistic formula for kinetic energy.

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  • $\begingroup$ What happens to a projectile travelling at Mach 100 in Earth's atmosphere is left as an exercise. $\endgroup$ – AlexP Sep 23 '19 at 19:01
  • $\begingroup$ Oh wow, I did not think about just plugging in the values of the bomb. Do you know if this is transferable between kinetic projectiles and explosives? That would make my task so much easier, I just had to look up a bomb that does the job and calculate my speed :) $\endgroup$ – user6415 Sep 23 '19 at 19:01
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    $\begingroup$ @openend: The point of the answer is 32 km/s. That's not much less than Mach 100 -- one hundred times faster than sound. I cannot think of any reasonable way to make that happen to such a small object -- any known material will be instantly converted into superheated vapor. $\endgroup$ – AlexP Sep 23 '19 at 19:03
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    $\begingroup$ Mach 10 is about as fast as things can practically travel at sea level, and even then you'll get some exciting burning on the outside even if your "bullet" is made of tungsten. $\endgroup$ – Starfish Prime Sep 23 '19 at 19:25
  • $\begingroup$ My understanding of the question was "How fast is the projectile to create an explosive effect instead of a projectile-like one?". IE if the projectile passes straight through the target (entry and exit woulds) but doesn't blow them up the OP is unsatisfied. This would depend on the target, for example tissue paper would require a faster projectile to "explode" than concrete because it less of the projectiles energy is deposited in the tissue on the way through. $\endgroup$ – Dast Sep 24 '19 at 15:55
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It's very easy: projectile needs to trevel faster than speed of sound in media. That creates shockwave, wich is sort of explosion.

For example, speed of sound in water is about 1,5 km/s. That means that even 10g bullet at that or higher speed could rip human limbs apart and kills even with seemly nonfatal body wounds.

For soil and wood this speed is about 3-5 km/s.

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