I've seen a few threads on here about people saying "If I run at a speed of X into something, how much damage do I inflict on them as per fall damage rules?"

This thread should answer that for you. It makes a few important assumptions to streamline the process:

1: The target is not moving. This might not be true, but we will have to assume that they made their move and then paused long enough to be run into by the attacker.

2: Falling doesn't hurt you - it's the sudden stop. In this case, I've assumed that the impact time of landing on a hard surface is the same as the impact time of hitting the target. This is not true, but again, smooths out the calculations.

The maths:

This is all in feet per second because that marries up with D&D.

The final speed of falling in increments of 10ft, assuming no wind resistance, is given by . V is final velocity, U is starting velocity (0), A is acceleration due to gravity (32ft per second per second) and S is the distance fallen. This tells you their speed in ft. per second after falling this distance. So then you multiply this by 6 to give you their speed per turn.

The effect - damage dice used vs speed in ft. per turn:

This corresponds with 10ft of movement for each row, IE 10ft., 20ft., 30ft. etc.

This is the total damage dice used, but now you have to establish how much damage each creature gets - it makes no sense if a giant sprints into a fairy that they both take half the damage! So now, we have the following table 2 (The left one is for information only):

So if a huge giant hits a tiny fairy, the fairy takes 100% of the damage and the giant takes 0%. If a medium monk hurtles into a gargantuan tarrasque fast enough to do damage, the tarrasque takes 15% of the damage and the monk takes 85% of the damage. All makes sense - but how many dice is that?

Cue table 3!

So, to use these tables - work out how fast you're moving per turn, put that into table 1 to get the number of dice you're using. Then compare sizes with what you're hitting on table 2, and get the % each creature takes. Then put that % and number of dice into table 3 and that gives you how many dice each of the creatures get assigned from the impact.

So, if a tabaxi monk (medium) goes running into an ogre (large) at 650ft. per turn, the impact would deal 18d6 damage in total; 11d6 to the tabaxi and 7d6 to the ogre.

One important note - this all relies on the fact that the two creatures hit each other and then keep moving - this doesn't cover landing on top of someone!

I also appreciate that this is way, way too much to actually use, but it's realistic, at least!

I ran the numbers up to 200ft drops. The highest I've seen someone claiming to move per turn was 3300ft., which I can say would cause 472d6 damage! At this point you're better off using a calculator, but it deals 307d6 damage to the tabaxi and then (due to quirks in the rounding) 189d6 damage to the ogre. They probably both die!

-Scratch that, I've just found someone who worked out how to do 7,980ft per turn!

That works out as a fall of 27,220ft., for 2722d6 damage total. Whilst this is probably worth handwaving as "and they both turn to red mist", the results for this tabaxi running at this speed into a tarrasque:

tabaxi takes 85%, tarrasque takes 15%, so tabaxi takes 2314d6 damage and the tarrasque takes 408d6 damage. So yeah, red mist.

I really love this, but are we sure that falling damage is the model we want to use? The thing about the ground is that it doesn't move, so no energy gets transferred and lost by say, getting knocked out of the way.

Really impressive amount of work here, though.

That seems to be taken care of by the rules of how damage is divided between the creatures / objects. If a pixie flies into a giant, it might as well be a brick wall. But if two equal-sized creatures collide, they share the damage.

I really love this, but are we sure that falling damage is the model we want to use? The thing about the ground is that it doesn't move, so no energy gets transferred and lost by say, getting knocked out of the way.

Really impressive amount of work here, though.

This has been taken into account.

The physics I've chosen to model this on considers that the damage is inflicted by the amount of acceleration you experience hitting the floor. By assuming the impact time is the same when you hit a creature as it is when you hit the floor, you can say that the damage inflicted is proportional to the change of speed, as the time taken is the same.

My calculations incorporate momentum to determine the speed the creature hits and the speed the creatures end up moving together, as momentum is conserved. From this I calculated the change in speed when two objects of these relative masses collide, and this determines the damage dealt. Because both creatures receive damage, it works out the same as fall damage (fall damage being where the floor takes 0 damage). The energy "lost" in this case is transferred into the creature you hit - so instead of you going from 600ft. per turn to 0, hitting a creature the same size as you slows you to 300ft. per turn, and accelerates them to 300ft. per turn, in the same amount of time as hitting the floor takes - so it amounts to both creatures taking half of the damage.

I would at least allow a dex save if something comes charging towarsds you really fast you should have a chance to dive out the way.

I am also not sure if it can make speed builds masively overpowered. The fact that the creature with speed also takes damage should mitigate this but slowfall should not apply to this. I am not sure how fast you can make a mount, if a supercharged warhorse runs into a creature does the rider take damage? If not you could end up with balancing problems, For the same reason I would not allow mounts to do this while not being ridden (e.g. a Paladin's ind steed)

That equation translated poorly; it lost a + sign. It should be V^2 = U^2 + 2AS. In any case, applying physics to D&D is pretty much going to be a failure.

I would at least allow a dex save if something comes charging towarsds you really fast you should have a chance to dive out the way.

I am also not sure if it can make speed builds masively overpowered. The fact that the creature with speed also takes damage should mitigate this but slowfall should not apply to this. I am not sure how fast you can make a mount, if a supercharged warhorse runs into a creature does the rider take damage? If not you could end up with balancing problems, For the same reason I would not allow mounts to do this while not being ridden (e.g. a Paladin's ind steed)

That equation translated poorly; it lost a + sign. It should be V^2 = U^2 + 2AS. In any case, applying physics to D&D is pretty much going to be a failure.

Honestly, I wasn't expecting this to be used in any real games. I just thought it an interesting experiment, as I had seen at least 2 threads recently regarding "if I run his fast into that, how much damage would I do?"

Regarding V^2 = U^2 + 2AS, that is the equation used. I assume that the falling creature starts at 0 speed (the top of the fall) and accelerates at 32ft per second per second (or 9.81m/s^-2, in English money). U = 0, so V^2 = 2AS, so V = square root(2AS). that's your final speed when you hit the floor, in feet per second.

Assuming the same contact speed in all collisions, the impact time becomes arbitrary and you can simple focus on the change in velocity (acceleration is change in velocity over time, which can be rewritten as A = dV x 1/T. T being assumed to be constant, we can say A is directly proportional to dV (change in velocity).

To work out the change in velocity you need to conserve momentum (momentum = mass x velocity), so you need to estimate the weight of creatures, work out their new speed when the weight combines (M1V1 + M2V2 = M3V3, where M is mass, V is velocity, 1 is the runner, 2 is the victim, and 3 is them combined. If the victim is stationary, V2 = 0 so it becomes M1V1 = M3V3. We know M1, V1 and M3, so V3 = M1V1/M3.

When you have V3, you have to compare V1 and V2 to it to determine Acceleration. If V1 was 500ft per second, V2 was 0 and V3 was 10ft per second, then the runner's dV is 490fts-1 and the victims dV is 10fts-1, meaning the runner took a much harder impact than the victim - they slowed down a lot to speed up the target a little. So they take more damage.

This is where tables 2 & 3 come in to distribute that energy between the two parties involved.

As I said, it's not intended for actual use in games - more for people who want to say "if I run this fast, how much damage do I do?".

That equation translated poorly; it lost a + sign. It should be V^2 = U^2 + 2AS. In any case, applying physics to D&D is pretty much going to be a failure.

Honestly, I wasn't expecting this to be used in any real games. I just thought it an interesting experiment, as I had seen at least 2 threads recently regarding "if I run his fast into that, how much damage would I do?"

Regarding V^2 = U^2 + 2AS, that is the equation used. I assume that the falling creature starts at 0 speed (the top of the fall) and accelerates at 32ft per second per second (or 9.81m/s^-2, in English money). U = 0, so V^2 = 2AS, so V = square root(2AS). that's your final speed when you hit the floor, in feet per second.

I assumed that, it just took me a moment to figure out because whatever you were using to render the equation failed to render the + sign.

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I've seen a few threads on here about people saying "If I run at a speed of X into something, how much damage do I inflict on them as per fall damage rules?"

This thread should answer that for you. It makes a few important assumptions to streamline the process:

1: The target is not moving. This might not be true, but we will have to assume that they made their move and then paused long enough to be run into by the attacker.

2: Falling doesn't hurt you - it's the sudden stop. In this case, I've assumed that the impact time of landing on a hard surface is the same as the impact time of hitting the target. This is not true, but again, smooths out the calculations.

The maths:

This is all in feet per second because that marries up with D&D.

The final speed of falling in increments of 10ft, assuming no wind resistance, is given by . V is final velocity, U is starting velocity (0), A is acceleration due to gravity (32ft per second per second) and S is the distance fallen. This tells you their speed in ft. per second after falling this distance. So then you multiply this by 6 to give you their speed per turn.

The effect - damage dice used vs speed in ft. per turn:

This corresponds with 10ft of movement for each row, IE 10ft., 20ft., 30ft. etc.

This is the total damage dice used, but now you have to establish how much damage each creature gets - it makes no sense if a giant sprints into a fairy that they both take half the damage! So now, we have the following table 2 (The left one is for information only):

So if a huge giant hits a tiny fairy, the fairy takes 100% of the damage and the giant takes 0%. If a medium monk hurtles into a gargantuan tarrasque fast enough to do damage, the tarrasque takes 15% of the damage and the monk takes 85% of the damage. All makes sense - but how many dice is that?

Cue table 3!

So, to use these tables - work out how fast you're moving per turn, put that into table 1 to get the number of dice you're using. Then compare sizes with what you're hitting on table 2, and get the % each creature takes. Then put that % and number of dice into table 3 and that gives you how many dice each of the creatures get assigned from the impact.

So, if a tabaxi monk (medium) goes running into an ogre (large) at 650ft. per turn, the impact would deal 18d6 damage in total; 11d6 to the tabaxi and 7d6 to the ogre.

One important note - this all relies on the fact that the two creatures hit each other and then keep moving - this doesn't cover landing on top of someone!

I also appreciate that this is way, way too much to actually use, but it's realistic, at least!

I ran the numbers up to 200ft drops. The highest I've seen someone claiming to move per turn was 3300ft., which I can say would cause 472d6 damage! At this point you're better off using a calculator, but it deals 307d6 damage to the tabaxi and then (due to quirks in the rounding) 189d6 damage to the ogre. They probably both die!

-Scratch that, I've just found someone who worked out how to do 7,980ft per turn!

That works out as a fall of 27,220ft., for 2722d6 damage total. Whilst this is probably worth handwaving as "and they both turn to red mist", the results for this tabaxi running at this speed into a tarrasque:

tabaxi takes 85%, tarrasque takes 15%, so tabaxi takes 2314d6 damage and the tarrasque takes 408d6 damage. So yeah, red mist.

Make your Artificer work with any other class with

174 Multiclassing Feats for your Artificer Multiclass Character!DM's Guild Releases on This Thread - latest release; the Harvest Sprite, a playable Jack-o-Lantern Race!Or check them all out on DMs Guild!

DrivethruRPG Releases on This Thread - latest release: The Promethean Scientist (Dr Frankenstein) Artificer Subclass!!I also dabble in art on here

(my art thread)That seems to be taken care of by the rules of how damage is divided between the creatures / objects. If a pixie flies into a giant, it might as well be a brick wall. But if two equal-sized creatures collide, they share the damage.

This has been taken into account.

The physics I've chosen to model this on considers that the damage is inflicted by the amount of acceleration you experience hitting the floor. By assuming the impact time is the same when you hit a creature as it is when you hit the floor, you can say that the damage inflicted is proportional to the change of speed, as the time taken is the same.

My calculations incorporate momentum to determine the speed the creature hits and the speed the creatures end up moving together, as momentum is conserved. From this I calculated the change in speed when two objects of these relative masses collide, and this determines the damage dealt. Because both creatures receive damage, it works out the same as fall damage (fall damage being where the floor takes 0 damage). The energy "lost" in this case is transferred into the creature you hit - so instead of you going from 600ft. per turn to 0, hitting a creature the same size as you slows you to 300ft. per turn, and accelerates them to 300ft. per turn, in the same amount of time as hitting the floor takes - so it amounts to both creatures taking half of the damage.

Make your Artificer work with any other class with

174 Multiclassing Feats for your Artificer Multiclass Character!DM's Guild Releases on This Thread - latest release; the Harvest Sprite, a playable Jack-o-Lantern Race!Or check them all out on DMs Guild!

DrivethruRPG Releases on This Thread - latest release: The Promethean Scientist (Dr Frankenstein) Artificer Subclass!!I also dabble in art on here

(my art thread)I would at least allow a dex save if something comes charging towarsds you really fast you should have a chance to dive out the way.

I am also not sure if it can make speed builds masively overpowered. The fact that the creature with speed also takes damage should mitigate this but slowfall should not apply to this. I am not sure how fast you can make a mount, if a supercharged warhorse runs into a creature does the rider take damage? If not you could end up with balancing problems, For the same reason I would not allow mounts to do this while not being ridden (e.g. a Paladin's ind steed)

That equation translated poorly; it lost a + sign. It should be V^2 = U^2 + 2AS. In any case, applying physics to D&D is pretty much going to be a failure.

Honestly, I wasn't expecting this to be used in any real games. I just thought it an interesting experiment, as I had seen at least 2 threads recently regarding "if I run his fast into that, how much damage would I do?"

Regarding V^2 = U^2 + 2AS, that is the equation used. I assume that the falling creature starts at 0 speed (the top of the fall) and accelerates at 32ft per second per second (or 9.81m/s^-2, in English money). U = 0, so V^2 = 2AS, so V = square root(2AS). that's your final speed when you hit the floor, in feet per second.

Assuming the same contact speed in all collisions, the impact time becomes arbitrary and you can simple focus on the change in velocity (acceleration is change in velocity over time, which can be rewritten as A = dV x 1/T. T being assumed to be constant, we can say A is directly proportional to dV (change in velocity).

To work out the change in velocity you need to conserve momentum (momentum = mass x velocity), so you need to estimate the weight of creatures, work out their new speed when the weight combines (M1V1 + M2V2 = M3V3, where M is mass, V is velocity, 1 is the runner, 2 is the victim, and 3 is them combined. If the victim is stationary, V2 = 0 so it becomes M1V1 = M3V3. We know M1, V1 and M3, so V3 = M1V1/M3.

When you have V3, you have to compare V1 and V2 to it to determine Acceleration. If V1 was 500ft per second, V2 was 0 and V3 was 10ft per second, then the runner's dV is 490fts-1 and the victims dV is 10fts-1, meaning the runner took a much harder impact than the victim - they slowed down a lot to speed up the target a little. So they take more damage.

This is where tables 2 & 3 come in to distribute that energy between the two parties involved.

As I said, it's not intended for actual use in games - more for people who want to say "if I run this fast, how much damage do I do?".

Make your Artificer work with any other class with

174 Multiclassing Feats for your Artificer Multiclass Character!DM's Guild Releases on This Thread - latest release; the Harvest Sprite, a playable Jack-o-Lantern Race!Or check them all out on DMs Guild!

DrivethruRPG Releases on This Thread - latest release: The Promethean Scientist (Dr Frankenstein) Artificer Subclass!!I also dabble in art on here

(my art thread)I assumed that, it just took me a moment to figure out because whatever you were using to render the equation failed to render the + sign.