Mushroom Ninja

2008-10-16, 05:03 PM

Disclaimer: Many catgirls have died to bring us this information...

For a while now, I have been troubled by an interesting question. This question is "If a character is moving very fast and runs into something, will any damage be dealt?" For a while I pondered this. Then I realized that if I were to calculate the character's velocity at impact time, and compare that to the instantaneous velocity at time of impact for something falling, by the rules section, "Damage from Falling Objects", I could determine how much damage would be dealt.

Here's the math:

Let's assume that my character, a wizard, weighed 200 pounds (with equipment).

He gets on his phantom steed (240 ft movement) and uses the run option (4x movement) to run into a dragon. His velocity on impact is 160 ft/sec.

240 ft movement x 4 (run modifier) = 960 ft

because this movement is moved over a course of a round, we divide this by 6 to get 160 ft/sec.

Now, to calculate the height that an item impacting ground at this velocity would have to be at, we're going to need to use some calculus. :smallbiggrin:

The position of falling objects formula is height = -16(time)^2 + (initial height). To find the velocity of a falling object at any given point, we're going to have to take the 1st derivative of that equation and get velocity = -32(time).

Now, we're trying to find the height of something that, when hitting the ground, has a velocity of 160 ft/sec. Because velocity is directional, I'm going to turn that into -160ft/sec so we don't come up with a negative time. This isn't necessary, but I'm going to do it anyway because I like positive numbers.

Okay, so we need to plug -160 ft/sec into the instantaneous velocity formula. This gives us (-160) = -32(time). With just a little simple algebra, we get (time) = 5.

From here, we just need to plug this value back into the position function, using 0 as the final height:

0= -16(5)^2 + (initial height)

By a little more algebra, we get the initial height to equal 400 feet!

This means that velocity of my wizard when he runs into the dragon is equal to the velocity of an object when it hits the ground after a 400 foot fall.

So, by the rules found here (http://www.d20srd.org/srd/environment.htm#tableDamagefromFallingObjects), we see that my 200 lb wizard is doing about 20d6 damage. Nifty! :smallbiggrin:

The one problem is, of course, due to those silly laws of physics, my wizard would also take 20d6 damage.:smallfrown:

Just thought others might want to know...

P.S.: If I've got my math wrong, please tell me so.

For a while now, I have been troubled by an interesting question. This question is "If a character is moving very fast and runs into something, will any damage be dealt?" For a while I pondered this. Then I realized that if I were to calculate the character's velocity at impact time, and compare that to the instantaneous velocity at time of impact for something falling, by the rules section, "Damage from Falling Objects", I could determine how much damage would be dealt.

Here's the math:

Let's assume that my character, a wizard, weighed 200 pounds (with equipment).

He gets on his phantom steed (240 ft movement) and uses the run option (4x movement) to run into a dragon. His velocity on impact is 160 ft/sec.

240 ft movement x 4 (run modifier) = 960 ft

because this movement is moved over a course of a round, we divide this by 6 to get 160 ft/sec.

Now, to calculate the height that an item impacting ground at this velocity would have to be at, we're going to need to use some calculus. :smallbiggrin:

The position of falling objects formula is height = -16(time)^2 + (initial height). To find the velocity of a falling object at any given point, we're going to have to take the 1st derivative of that equation and get velocity = -32(time).

Now, we're trying to find the height of something that, when hitting the ground, has a velocity of 160 ft/sec. Because velocity is directional, I'm going to turn that into -160ft/sec so we don't come up with a negative time. This isn't necessary, but I'm going to do it anyway because I like positive numbers.

Okay, so we need to plug -160 ft/sec into the instantaneous velocity formula. This gives us (-160) = -32(time). With just a little simple algebra, we get (time) = 5.

From here, we just need to plug this value back into the position function, using 0 as the final height:

0= -16(5)^2 + (initial height)

By a little more algebra, we get the initial height to equal 400 feet!

This means that velocity of my wizard when he runs into the dragon is equal to the velocity of an object when it hits the ground after a 400 foot fall.

So, by the rules found here (http://www.d20srd.org/srd/environment.htm#tableDamagefromFallingObjects), we see that my 200 lb wizard is doing about 20d6 damage. Nifty! :smallbiggrin:

The one problem is, of course, due to those silly laws of physics, my wizard would also take 20d6 damage.:smallfrown:

Just thought others might want to know...

P.S.: If I've got my math wrong, please tell me so.