## DEEP HOLES, FRAIL BONES – FALL DAMAGE IN THE CELESTAR RULESET

This is a bit mathematics-heavy for most, so only read if you’re interested in how I derived my “simpler falls” rules for Celestar!

One very common mishap in both RPGs and action movies are falls, whether as part of a move mid-fight, as part of exploration, or as a way of sentencing an enemy to death. Ideally, the rules for fall damage should be simple enough for the GM to remember off by heart, so there’s no need to pause play to consult equations and tables when this happens. Dungeons and Dragons handles the “ease of damage calculation” well enough, with a creature taking 1d6 damage per 10 feet fallen, to a maximum of 20d6. However, it notoriously scales terribly with HP – a 10th level fighter can, on average, survive a fall from any height, and continue fighting at full capacity seconds after landing. This is an example where the rules are too simple – many other vital aspects are missing as well, like proper rules for dropping objects on creatures.

Closer to the opposite end of the “overly simple” to “overly complex” spectrum are the GURPS rules for fall damage. The rules in Basic Set span three pages, and finding the damage for any given fall involves cross checking various rules, equations, modifiers, and of course, a big table – not ideal for fast-paced play! GURPS Lite gives a simpler section, but still falls into the trap of needing to using both tables and equations. Action 2: Exploits only requires a table, but even then, it’s difficult to remember the table, and it only applies to situations where the “average human” falls. Ideally, we want to simplify the GURPS falling rules without making them lose the important detail that makes them good. This is what I’m doing in this post today.

It’s worth noting that although this post is fairly long and maths intensive, the vast majority of this post is dedicated to discussion and the derivation of simplier rules!

#### REVERSE ENGINEERING – DAMAGE FOR A GIVEN FALL

In order to create a simplified ruleset, I decided to work out how the existing tables were derived, by reverse engineering them. To start with, I looked at the table in Action 2: Exploits, and compared the average damage for a fall with the distance fallen.

The relationship between the two variables is given by the equation shown on the graph above. This isn’t an equation that can be done in your head, so we’ll definitely have to simplify it! After tinkering and experimenting around with the table, I found that the true equation was y = 3.25 ⨯ √x. As the average of 1d of damage is 3.5, by changing the 3.25 to 3.5, we can have dice of damage = √(yards fallen) – something that is far easier to work out in the heat of play. I think I’m fine with GMs making rough guesses for the most appropriate “closest square number” to use when approximating damage dice – for example, if a character falls 70 feet, the closest square number is 64, for 8d dice of damage.

This formula tells us the damage for a fall, but doesn’t tell us about damage from collisions, or what happens when the colliding object isn’t an “average human”. To start adding to this basic formula, I’ll look at the rules in Basic Set, as this is the section which all others are based on.

#### SCALING DAMAGE WITH HP, AND A NOTE ON (TERMINAL) VELOCITY

In Basic Set, the damage an object takes from a fall is proportionate to its HP value – an object with more HP takes (and deals) more damage in a fall. As the “average person” has 10HP, we can assume the table in Action 2: Exploits is an object with 10HP.

The formula itself in Basic Set for dice of damage is damage dice = (HP velocity)/100. For a 10HP object, this can be simplified to damage dice = (velocity)/10. This gives us a handy rule we can use for collisions where the speed is known, but not the distance fallen: 1 dice of damage per 20mph (10 yd/s) of speed (as GURPS velocity is in yards per second, and 1 yards per second = ~2 miles per hour). This rule can also be applied to work out the maximum damage from a fall. An object won’t move faster than its terminal velocity, which, for a human (according to Basic Set) is 120-200 miles per hour, depending on body position – this means that damage dice for a human would cap out at 6d-10d!

When using this equation to estimate velocities using the table in Action 2: Exploits, we find that the velocities in Basic Set are half those of the ones in Action 2: Exploits. This is explained by the Hard Objects rule, which doubles the HP for hard, immovable objects like the ground, which has the same effect on damage dice as doubling velocity. So the reason for the difference in Action 2: Exploits is that the damage has already been doubled for us.

Of course, the above rules assume that the colliding object has 10HP. This is definitely not the case a lot of the time! We need a hard-and-fast rule for GMs to quickly apply when colliding objects have different HPs. Using the aforementioned equation, and the fact that the rules above assume a 10HP baseline, we’ll change the damage relative to the 10HP level; for example, a 12HP creature takes 20% more damage (as 12 is 20% more than 10).

Essentially, this means “for every full (10/3.5) above 10HP, take an additional 1 point of damage per die”. We can approximate (10/3.5) to 3 for simplicity, so it’s “for every full 3 above 10HP . . .” instead. Going below 10 works the same, just in reverse – for every full 3HP below 10HP, take 1 fewer point of damage per die.

With these rules, for example, a human with 22HP falling 9 yards takes 3d+12 damage (average 22.5, just enough to give them a chance of being knocked out), and a 10HP human falling 9 yards takes 3d damage (average 10.5, just enough to give them a chance of being knocked out too!).

#### EXPANDING TO ACCOUNT FOR COLLISIONS

These rules are currently limited to falling, but they can easily be expanded to collisions by changing “distance fallen” to “distance travelled relative to the obstacle in the last second”. We can also account for a variety of obstacle types by saying that damage is halved if not colliding with a hard, immovable object.

#### JUMPING AND FALLING INTO LIQUIDS

The only other “formulaic” part of the rules here relates to jumping into water. A successful Swimming check completely negates all fall damage, but recieves a penalty dependent on the distance fallen. The relationship between the penalty and distance fallen is shown in the graph below:

As we can see, there’s definitely a very consistent equation, being y = {10(1/6) ⨯ ln(x)} + 2. This is absolutely not something a GM will be able to do in their heads! This calls for a rougher, simpler equation. Unfortunately, there are no “near-perfect” solutions like the one for the general equation we discussed earlier.

The closest is to just say “you take a penalty equal to the number of dice of damage you would take if you failed the roll and it were solid ground – for example, a 64 yard dive (8d damage if it were against hard ground) would apply a -8 penalty to pull off successfully. The difference between the penalty given in Basic Set and the “per die” penalty is shown in the graph below:

As we can see, there are a few minor problems. The “per dice” penalty is a bit lower at smaller distances, and gets larger at distances above ~60 yards. Given that the differences are fairly small, and only apply in a limited set of situations, I’m inclined to stick with the simpler “per die” penalty anyway.

#### CRIPPLED LIMBS

There’s a small box on B431 detailing how a fall might cripple limbs, but it relies on random hit locations (which we’re not using). However, it seems reasonable to assume limbs could be broken from falls, so incorporating this box somehow seems reasonable. In essence, this box indicates if a limb is hit and enough damage is dealt to it to cripple it, it’s the limb is crippled, and there’s a 2-in-6 chance that all limbs of that type are crippled. With random hit locations, there’s a 49.52% chance of hitting a limb. If you include extremities, this rises to 56.93%. To simulate this crippling effect, you can say “if the damage from a fall would cripple a limb, roll 1d. On a 2-3, a limb is crippled. On a 1, all limbs of one type are crippled!”

#### OTHER RULES

Other rules, such as all armour counting as flexible for the purposes of blunt trauma, a successful Acrobatics check reducing a fall by 10 yards, impalaing/piercing dealing different damage multipliers, dropping objects on targets, maximum damage, whiplash, and overrun can be kept. – they don’t involve any complex formulae, and can be summarised in a sentence or two anyway. There are also rules for changing velocities on different planets, but we can cover this later when we talk about the effects of different gravities in general (and that too can be explained in a couple of sentences).

#### SUMMARY

To summarise:

• dice of damage = √(distance travelled relative to the obstacle in the last second)
• For every full 3HP above (below) 10HP, take an additional 1 (-1) point of damage per die.
• Damage is halved if not colliding with a hard, immovable object.
• For collisions where velocity is known, but not the distance fallen: “Inflict 1 dice of damage per 20mph moved relative to the obstacle in the last second”.
• Terminal velocity for a human is 200 mph (so they cannot take more than 10 dice of damage (plus adds) from a fall).
• If you’re falling into water, a successful Swimming check (with a penalty equal to the number of dice of damage you would take if you failed) negates all damage.
• If the damage from a fall would cripple a limb, roll 1d. On a 2-3, a limb is crippled. On a 1, all limbs of one type are crippled!