I think this has come up in almost every group that has an Alchemist. The question of "How do I make the boom even bigger?"
The most common one I've seen was a delayed or remote explosive bomb in a pony keg of black powder or for incendiaries a few vials of Alchemist Fire glued to the final bomb vial. I think my favorite one was a door breaching charge consisting of an iron powder horn and ton alchemical glue soaked cloth strips (AKA duck tape).
Alternatively I personally have summoned a small fire elemental and had it sprint into a fireworks factory. No context needed.
I've been settling it with craft alchemy / bomb / or trap depending on context but I've always tried to figure out what kind of damage these things do. My general rule of thumb is 1d6 fire and an extra 1ft to the burst per charge of powder or alchemist fire (5 charges / flasks = 5ft).
I'd like to see some other ideas slash experiences.
If you're going to allow PCs to duct-tape together multiple alchemical devices, then Gods help you.
Next they'll want to duct-tape multiple wands with the same command word.
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In general it's really a bad idea to allow this to happen.
It sucks to say, but the game simply can't handle it. Otherwise you end up with someone putting 20 alchemist fire potions in a sack and dropping them from the air on an enemy. Expensive and nearly impossible at level 1. By level 10 you can kill a lot things with this sort of tactic if you let it work.
I know it breaks the simulation to say "No you can't do this thing that seems entirely reasonable" but the problem becomes apparent when you tell the players "Well if you do that, the next enemies will do it to your party". And then the players are usually far less keen on being killed with virtually no means of defending themselves.
This same sort of discussion was recently had with regard to grenades in Starfinder and using detonators to set off multiple grenades.
We spit balled some different ways you could handle it, but everyone (except one person) agreed that allowing for a linear damage increase per item was a bad idea and breaks the game to an unplayable point.
The answer is: How easy is what you want to do accomplished by existing magical effects?
For instance, a Wand of Fireballs (CL5) costs 11,250 gold. This means that setting off a single fireball is worth 1/50th that amount or 225 gold. Thus, I would be fine with the party expending 225 gold to create a single 5d6 Fireball (DC 14) like effect from another source. If the party is the one creating the effect through their own resources, rather than purchasing it from someone else, then it also follows the crafting rules of 1/3rd item cost for a mundane item and 1/2 the item cost for a magical item.
If the party is fine expending the gold per "Fireball" then we have no problems/
The trouble comes when they want to use 20 of those fireballs on a single attack. Or more. Why stop at 20?
One thing limiting these types of tactics is that even in the real world explosives are not always cumulative. Fire for example does damage by burning things. The amount of damage done by fire is based on the temperature of the flame. Adding more fuel to a fire may not increase the temperature of the fire. There is a point of diminishing return on fire and fuel. When large amount of fuel catches fire it usually increases the size and duration of the burn. Basically there is a diminishing return on the amount of damage more fuel when it comes to fire damage.
The trouble comes when they want to use 20 of those fireballs on a single attack. Or more. Why stop at 20?
The trick is to limit it the same way you limit fireball, 1 standard action per use. If they can find 20 people to help them set them off, sure that works.
Mixing magic and technology has a time-honored background in D&D, ever since Gary's very early article "Sturmgeschutz and Sorcery" in the Strategic Review in the mid-70s. But we're not talking about that. We're talking about using an arbitrarily large number of doses of alchemical weapons tied, taped or bagged together. There's no logical reason not to allow this, and no logical reason to require 20 people to set off your bag of 20 vials of alchemist's fire. Or twenty writings of Explosive Runes or whatever.
All we have is a gentleman's agreement not to push the system in ways it wasn't meant to go. And to keep damage potential roughly tied to level advancement and action economy.
5d6 fire damage spread over a 20ft radius spread IS an arbitrarily large quantity of Alchemist Fire's. Infact it is 5 alchemist fires per cube over 11 cubes totally, which is naturally 55 alchemist fires. 55*20gp per fire is 1100 gold worth of Alchemist Fire's. Yes, it is not 55d6 points of damage to a single cube, but thats because area effect attacks don't stack like that.
If folks want a non rules based reason, then we are down to "Because the GM says so" which is the gentleman's agreement the entire game runs on. Thus, its not really worth noting the existence of said agreement since the entire game ceases to work if the players and the GM are not in said agreement.
EDIT: Dealing tons of damage to a single target could be replicated from Clashing Rocks, 20d6 bludgeoning and a 1 time use could be made for 3825 gold (9*17*25), slap on a DC 23 (10+9+4) vs Prone and you've got a mighty bomb. Course the DC to craft this out of alchemical gear would be absurd, probably about 40, and they would not be easily purchased in most places do to how dangerous this type of explosive, so only available on the black market or to the military. If folks wanna expend 191.25 alchemist fire's worth of gold to deal 20d6 damage then more power to them.
Does black powder even exist in Pathfinder? In which book?
Ultimate Combat. The same book that introduces the gunslinger class.
For the original question:
When it comes to black powder, the best I can think of without handwaving is stacking as many powder kegs as possible, each doing 5d6 in a 20 foot radius and likely setting off the others. Mechanically, it's a bunch of separate explosions, meaning fire resistance will really pay off. The radius never gets any larger, though.
We already do this sort of thing with fire seeds (the holly berry bombs version). Check the forums for some egregious examples of maximizing single-target damage using that spell.
So I run a low magic campaign, and have since just after Pathfinder was launched...
I add special effects most elementals spells, such as fireball being 1/2 fire and 1/2 sound (concussion) with and Explosion added effect.
Similar I've ruled that black powder (used almost exclusively be gunslingers) becomes VERY unstable around Arcane magic (more like nitroglycerin than black powder).
As for should you allow multiple usages of these things to stack? Well there was a great episode in Game of Thrones when a certain temple was blown to smithereens by a couple of hundred barrels of what could only be called Alchemist Fire. Even in GoT however the simple fact that this much of the stuff existed in one place was enough to scare the hell out of those that found it. They feared if they so much as sneezed it would explode.
So what is to stop the PC's (or the bad guys) from stock piling the stuff? Nothing. Let them do it. Then write in as part of your adventure how some terrorist cell was going to use the stuff as a weapon of mass destruction (on people or structures) but something went wrong and it blew their building to kingdom come! This sets the tone and lets your players know that this could have been them.
They want to put the stuff in a catapult and fling it at their enemies? Sure, but does it blow up in the catapult first? Does it destroy the catapult in the process?
Also don't forget to track the cost of these potions. If this is a tactic used commonly it will stop the player from having other nice items they may have otherwise been able to afford
Very carefully I would imagine (rimshot).