Explosive math (second opinion welcome)

[Grumpy RPG Reviews]

Edit: I am open to comments, corrections and second opinions.

So I’m working on an adventure involving flying a caravel through the astral plane at a high rate of speed, relative to the fixed geography of Earth. It then occurred to me, what happens if the crew runs the ship into a fixed object at such speed?

Below is the math I am working on, but assistance is welcome. Please note, all the numbers are rounded from the decimal.

The caravel weighs 300 tons, or 600,000 pounds, or 272,155 kg

Is it traveling at 1,124 mph, or about 1,809 kph
or 30 kp minute
or .5 kp second
or 500 meters per second

To calculate the impact in joules I have;

272,155 kg x (500 m x 500 m) = 68,038,750,000 / 2 = 34,019,375,000 J or 34⁹ J (a bit more than the explosive power of about 8 tons of TNT)

A hand grenade (like the Russian F1) releases 251,000 joules. For the sake of argument, let’s say that equals 1d6 of damage.

Then the impact does 135,535d6 damage to the vehicle, everyone one and everything aboard, and whatever it impacts.

This is why you should not travel at ludicrous speed.

 

[Bawylie]

Edit: I am open to comments, corrections and second opinions.

So I’m working on an adventure involving flying a caravel through the astral plane at a high rate of speed, relative to the fixed geography of Earth. It then occurred to me, what happens if the crew runs the ship into a fixed object at such speed?

Below is the math I am working on, but assistance is welcome. Please note, all the numbers are rounded from the decimal.

The caravel weighs 300 tons, or 600,000 pounds, or 272,155 kg

Is it traveling at 1,124 mph, or about 1,809 kph
or 30 kp minute
or .5 kp second
or 500 meters per second

To calculate the impact in joules I have;

272,155 kg x (500 m x 500 m) = 68,038,750,000 / 2 = 34,019,375,000 J or 34⁹ J (a bit more than the explosive power of about 8 tons of TNT)

A hand grenade (like the Russian F1) releases 251,000 joules. For the sake of argument, let’s say that equals 1d6 of damage.

Then the impact does 135,535d6 damage to the vehicle, everyone one and everything aboard, and whatever it impacts.

This is why you should not travel at ludicrous speed.

Neat. But I think you want to look at delta-V instead of joules.

 

[tomBitonti]

8 metric tons of TNT looks right.

Neat. But I think you want to look at delta-V instead of joules.

I’m thinking, “fixed” means the target is either much larger than the projectile, or is somehow magically fixed in place. Then, the joules will be correct.

What else matters is how the impact energy is distributed. The energy will be distributed across both parts of the impact. Also, comparing straight with the grenade energy is probably not very accurate, as the grenade delivers its energy in a very specific way, and that has a lot of loss.

But, another way to look at the collision is to consider the parts of the projectile separately. A person in the collision will need to dissipate their own energy safely, regardless of what else happens.

Thx!
TomB

 

[Grumpy RPG Reviews]

Neat. But I think you want to look at delta-V instead of joules.

At first I thought you meant like the Delta rocket, rather than the formula. And it occurred to me that there have not been enough empirical studies of what happens when you ram 300-pounds of wooden Middle Ages ship into a stationary target. Really, it's just a gap in the literature.

Anyway, my post is a thought experiment. The game I am working on posits people using astral color pools like jump gates; they can move people and vessels into the astral plane, which itself functions like hyperspace. But what if the PCs ram the ship, full speed, into the Gith city? What happens if they fly through the color pool jump gate at full speed, and hit the docks of Waterdeep at 1,100 mph.

Nothing good is what happens.

 

[Grumpy RPG Reviews]

I’m thinking, “fixed” means the target is either much larger than the projectile, or is somehow magically fixed in place. Then, the joules will be correct.

Yes, that is the intent here. Running into an asteroid, a planet or a ship of the same (or larger) size.

What else matters is how the impact energy is distributed.

This is true, but the math gets complicated pretty quickly.

Also, comparing straight with the grenade energy is probably not very accurate, as the grenade delivers its energy in a very specific way, and that has a lot of loss.

I was trying to find an analog for a fireball. The damage of a fireball is quantified, meaning it is possible to theorize how the damage could scale up. An analog for a fireball is a grenade - it is not perfect, but it is a place to start.

 

[GMMichael]

...which itself functions like hyperspace. But what if the PCs ram the ship, full speed, into the Gith city? What happens if they fly through the color pool jump gate at full speed, and hit the docks of Waterdeep at 1,100 mph.

Been watching the Last Jedi, have you?

 

[Grumpy RPG Reviews]

Been watching the Last Jedi, have you?

Yes.

But you know as well as I do that if there is a possible way for a PC party to blow the entire game right the hell up, they will find it. And do it. Twice, if they can.

 

[Ovinomancer]

Yes.

But you know as well as I do that if there is a possible way for a PC party to blow the entire game right the hell up, they will find it. And do it. Twice, if they can.

Color pools don't allow you to carry over momentum. Problem solved.