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What is the smallest amount of conventional explosives possible to create a crater that is roughly 7 meters in diameter and four to five meters deep?

Bob needs to know this in order to successfully create compact hunter killer bomb drones that take over the world.

Edit: the explosions are blown in packed dirt mostly.

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    $\begingroup$ What is the worldbuilding problem here? It looks like a "I better not google it and let someone enter the fed blacklist for me" problem $\endgroup$
    – L.Dutch
    Sep 16 '20 at 10:29
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    $\begingroup$ Can’t be answered anyway. Not without specifying in what material the crater must be blown. $\endgroup$
    – Tonny
    Sep 16 '20 at 10:30
  • $\begingroup$ I need the specific crater dimensions in order for a specialised landscape in my world. The other things are not important, just how little conventional explosives I need for these specific crater sizes. $\endgroup$ Sep 16 '20 at 10:31
  • $\begingroup$ Bombs can be lethal (due to the shock wave) out to a far larger range than the crater size. The crater size is a bit of a distraction in terms of how effective the weapon is and the actual target type and how well the weapon does against those is what what matters. E.g. cluster or napalm bombs might be a much better choice for some targets but others might require something else. $\endgroup$
    – StephenG
    Sep 16 '20 at 11:15
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    $\begingroup$ There is a large difference between flour and TNT. Not to mention packaging, place of explosion, direction od impact, pressure etc. This look like lack of research. $\endgroup$ Sep 16 '20 at 11:48
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There have been military munitions (usually cluster bombs with submunitions) specifically designed for cratering, in order to rend (for instance) an airfield's runway useless for conventional aircraft. The submunitions for this purpose are larger than you need, however, for two reasons. First, they need to crater paved runway surfaces (concrete or asphalt) and second, they can't depend on penetrating below surface level to crater efficiently; instead, they need to use much higher pressure to shatter, lift, and move the pavement and substrate from above.

An efficient cratering charge would be buried -- drilled in and the hole stemmed, ideally, or at least dropped into a hole and covered with soil. For air delivered munitions style charges, they would need to be designed to penetrate the soil.

This requires a munition that looks rather like an arrow -- fin stabilized (for simplicity, since you're apparently going to use millions or billions of them), with a sharply pointed, hard nose cone and a high sectional density, in order to push soil out of its way to the necessary depth. Further, the explosive needs to be the right type -- shattering power (like from straight dynamite or C-4) is less effective here than lifting power (meaning you want an explosive with high gas volume, more than one with high detonation speed). This is very different from what's usually packed in military munitions.

Once your "powder" is packed in the arrow-like penetrators, however, it can do the most efficient job only on unpaved, packed soil; if the soil is soft it will overpenetrate and produce less cratering (because it can't lift the broken soil clear of the crater) and if it strikes pavement (or concrete buildings, or other hard material) it won't penetrate enough and will produce shallow surface damage without much if any crater.

Therefore, any mining engineer could tell Bob that this isn't a job for a single, cheap to ultra-mass-produce munition, but will require at least three types -- one with less penetration (blunt nose?) for soft soils, one with the classic arrow design for packed earth, and a third with much higher sectional density and harder point to penetrate stone, concrete, and so forth.

To directly answer the original question, however, back in WWII, a satchel charge was commonly used for cratering, among its many other applications, and still produces less of a crater than you want -- and a common satchel charge size was 2.5-4.5 kg of TNT (the "satchel" was because this came with wire, one or more blasting caps, and an electric dynamo style detonator). If delivered 3-4 meters below ground in packed earth, a charge from this size to about four times this size might produce the size crater you want fairly reliably.

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  • $\begingroup$ 2.5 kg vs 4.5 kg is a substantial difference in size. Like giving a range of a nuclear bomb as being berween 2.5 kton and 4.5 kton. Almost twice the size. So your 'four times this size' becomes moot. 'Twice the size of twice the size'? 4.5 is already twice the size. Four times the size of 4.5 is EIGHT times the size of 2.25. $\endgroup$ Sep 16 '20 at 12:42
  • $\begingroup$ I gave the approximate weight of explosive in a satchel charge, and estimated that anything from that size to four times that size would be the minimum to create the desired crater. Given the variations in the working condition, you're lucky to get a range of only 8:1. Even if you were breaking rock you'd need to know what kind and condition, and even then you'd have to drill and shoot a test hole to be sure of your loading density. And wasn't Little Boy estimated (after it was used) at between 15 and 30 kilotons? $\endgroup$
    – Zeiss Ikon
    Sep 16 '20 at 12:49
  • $\begingroup$ No arguement with your qualifier 'might produce', I thought it a weird flex to use a multiplier 'four times larger' on a multiplier that was already 'two times larger'. The end result can become as much as 'eight times larger'. I have a vision of a demolition rookie using a charge 'eight times larger' instead of just 'four times larger'. Big badda boom. $\endgroup$ Sep 16 '20 at 13:04
  • $\begingroup$ This is for Bob, who's presumably having millions to hundreds of millions of these things built. Presumably, he (or his mining engineer) has sense enough to test first. Even Stalin's underlings managed that. $\endgroup$
    – Zeiss Ikon
    Sep 16 '20 at 13:39
  • $\begingroup$ Nah. Bob is a plumber. The Engineer is an Ossian. Bob is more likely to confuse 4.5 kg of explosives with 4.5 kTon of nukes. Probably blow the world up. $\endgroup$ Sep 16 '20 at 17:42

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