I was reading about flash bang grenades, and I was really surprised to learn that in an M84 grenade there is only 4.5 grams of actual explosive (flash powder made from magnesium and ammonium nitrate). The specs claim that the explosion creates between 170 and 180 decibels of noise within 5 feet. That seems like a lot from such a small payload, so I was wondering if there was math to verify it. I found the Sadovsky equation which calculates the increase in air pressure at a given distance for a known type and mass of explosive. Intuitively that seems like it would relate to the noise produced, but I don't have the physics chops to translate into decibels. Any brilliant insights would be appreciated. Thanks!
OK, I did some more research on this and I think I have an answer, but I would still appreciate someone who actually knows what they're doing checking my math.
First, I used the Sadovsky equation to calculate the increase in pressure in atmospheres. The equation is here:
The explosive mass has to be multiplied by a relative effectiveness factor (REF) to account for the type of explosive. For example, the REF of ammonium nitrate is .42, because it has 42% of the explosive power of TNT.
Second, I found that pressure can be converted to decibels with the equation:
Db = 20*log(P/Pref) where:
P=The pressure caused by the explosion
Pref-The reference pressure for 0 decibels, which is the threshold for human hearing. It's 20 microspascals, or about 1.97 EXP-10 atmospheres.
So using a distance of 1.5M, a REF of .42, and a mass of 4.5 grams, the Sadovsky equation tells me the air pressure will be increased by about .091 atmospheres. Plugging that into the equation above yields a decibel level if 173.3, which is right in line with the specification.
So I guess the takeaway is that it takes very little explosive to make a major noise if you're close enough to it. Thanks everyone for your help.