Math problem! Gamer/Mathletes needed!

[Tom Cashel]

My players, please don't read this.









Okay, here's the deal:

My players' TARDIS has broken down, leaving them in a hostile situation, surrounded by enemy troops. The troops are aware of the (camouflaged) TARDIS, and are planting explosives (six lbs. of C-4) to try to blow open the door.

I'm using an online TARDIS Manual for my info. It states that "Although external momentum [e.g. shock waves] is transferred to the interior, is it dampened by a factor of mI/mE, where mI is the mass of the interior, and mE is the mass of the exterior."

Given that six pounds of C-4 will generate 14d6 damage/shock (with the possibility of 28d6, or even 42d6, with a superlative Demolitions check), how do I use the above formula to determine how much of that damage is transferred to the interior?

Am I better off just making up an arbitrary amount? Say, only one-quarter or one-third of the damage gets through?

Thanks in advance for your help!

 

[Thanee]

Well, since the damage of the explosives is already highly arbitrary, I'd just use a number that sounds right rather than worry about real world physics.

Also, this "thing" (never seen the show ) seems to be rather durable...

The TARDIS can safely withstand the blast from 400 megatonnes of trinitrotoluene (TNT) detonated point black. Increasing the amount of explosives above 500 megatonnes of TNT and malfunctions and structural damage start to occur, and the field of dimensions inside is disturbed (See: ). After 550 megatonnes of TNT the outer-hull breaks up completely, letting energy through, and the complete outer plasmic shell structure starts to breaks up. The result, as discussed later, is that the whole TARDIS is reduced in size and completely destroyed. To avoid this disaster, the HADS circuit should be used.

And once the hull breaks, the complete "thing" gets destroyed!?

Anyways, I'm not sure, if 6 pounds of C-4 will even scratch that hull, if you need over 500 Mt of TNT.

Bye
Thanee

 

[DMScott]

Well, in another section they give this example:

A fission grenade is placed next to the TARDIS and detonated. Although the exterior is not harmed, the shock waves caused by the bomb have damaged the central control console, knocked the occupants senseless and taken down some interior wall. The outer plasmic shell was not harmed by this explosion, but the resulting shock waves were passed through to the interior causing a considerable amount of damage.

Assuming that a "fission grenade" means some kind of tactical nuclear explosive and that only results in a little damage and the occupants being knocked senseless, I'd imagine that all a few pounds of C4 are going to do is shake things around a bit. That seems in line with the show, too.

 

[Tom Cashel]

Also, this "thing" (never seen the show ) seems to be rather durable...

Anyways, I'm not sure, if 6 pounds of C-4 will even scratch that hull, if you need over 500 Mt of TNT.

True...nothing those Demolitions guys do will damage the hull.

But since energy and shock waves are transferred to the internal dimension (where the people are), it's possible that an explosion could fail to even scratch the outer hull while liquefying the people inside.

Edit: Yeah, DMScott, I was considering that passage as well. Wasn't quite sure that a "fission grenade" would be comparable to a small nuke, but suffice to say that the enemy troops have no access to superscience like this.

"In line with the show" is also a great angle for me to remember here.

 

[tjoneslo]

I can't see in the document where it explains what the mass of the interior or exterior of the TARDIS.

In any case, the phrase you are concerned about says that however much energy is transferred to the exterior, it is evenly spread through the interior. If the exterior is a large box (say 500 lbs), and the interior is a large building (say 500,000 lbs), the energy of the explosion is dispersed by a factor of 1000. So everything in the TARDIS takes the full damage of the explosion, divided by 1000. The characters might feel the explosion, but won't take any damage from it.

Once the bad guys get out the heavy artillery and begin doing 285+d6 damage to the Tardis, the characters will really feel it (and take damage).

 

[Tom Cashel]

Thanks tjoneslo...that explains a lot!

Good to know they won't actually get liquefied...but better to know that they're still truly terrified of what might happen when the C-4 explodes.

 

[Achan hiArusa]

Damage

I base explosive damage on Masque of the Red Death (the original):

Sticks
of Blast
Dynamite Damage Radius
1 1d6 5'
2-3 2d6 10'
4-7 4d6 15'
8-15 5d6 20'
16-31 6d6 25'
32-63 7d6 30'
64-127 8d6 35'
128-256 9d6 40'

Each doubling adds +1d6 damage and +5 feet to blast radius. Each stick of dynamite 1 lb. and is equivelent to an ounce of nitroglycerine or a keg of black powder.