More Lego

Watch this.  Do it at double speed, takes only 10 minutes.

Step one.  Establish a scale.  Don't base the scale on the size of lego figures; that would make the whole castle at the base no more than 25 ft. square.   Lego is designed to build vertically; we could argue that the horizontal scale is 3:1 the vertical; this would make the make the castle, oh, approximately 75 ft. wide and 42 ft. high.  Doesn't matter exactly what the scale is, however; each person's free to decide for themselves what the best scale would be.

Step two.  Weigh every piece.  Every kind of piece, I mean.  They don't weigh much, but a precise scale can be obtained ... or a large number of the same piece can be weighed together and divided by the number.  Lego names every piece, so a nomenclature exists — for all I know, it might be possible to get the amount of plastic necessary to make each piece.

One could possibly identify every piece's volume by sinking the pieces in water, but with surface tension you're bound to produce bubbles if you don't add soap or detergent to the water.  And again, you've got to work to get exact volume displacements for each piece.

Our best approach would be to clay up the hollow interior of each piece to determine it's water displacement as solid objects.  That is a step better.

Step three.   Okay, we have a scale and a weight for every piece.  By calculating the piece's displacement in water we know the specific gravity for each measure is 1.  This means we can calculate the weight of the piece, in our scale, if it were made of marble, granite, iron, lead, wood ... whatever.  That means we can get an near-enough exact weight of each piece whatever the material it's made from.

Step four.  Have the player build his or her castle in whatever way they want.  Record the pieces being used, so that an accurate accounting of total materials needed to build whatever the final product happens to be is enabled.  We know the volume of materials, so we can easily calculate cost of materials.

By establishing an amount of time needed to place each piece, we can calculate a building time also.  One fun way might be to time the player as he or she goes through the process, complete with puzzling out the design and reversing decisions made.  If the individual takes, say, two hours to assemble a unique castle of their own design, we can argue six, many nine months per hour ... 18 months to build, including making up the plans (the puzzling time for the player).   That's 4.5 days per minute.

And once paid for an built, if the character wants to make a change that involves dismantling any part of the castle, they can take their structure apart and put it back together ... at a cost of 13.5 days per minute.  Changes that merely add on can be calculated at 4.5 days per minute.

Of course, those are my numbers.  Someone else can charge 3 or 5 or 6 days per minute.  Or only a double time cost for dismantling, not triple.  Times can also be adjusted based on the amount of metal, wood, stone and what else is being used.

Step five.  Siege.  The enemy targets specific pieces in the lego structure, which are removed when hit.  Each siege engine is empowered to destroy a certain size and quantity of lego structure on each hit, depending on the material the lego piece represents.  Destroyed pieces are permanent; for replacement, see time and material cost above.

Conclusion.

Solves the siege problem.  Seems like a fun process for the player.  Can be used to build ANY structure out of ANY material.  The only serious issue I see is that once the structure is built, its plan has to be carefully recorded, with duplicates filed with the DM, before the pieces can be used to build something else.

I'd do a test run except, at the moment, I don't own any lego.

Not the Mangonel

Upon further consideration, I don't think I'm going to incorporate the mangonel into ship's weaponry at all.  My reconsideration follows further research into the subject ... which determined uncovering a lot of bad research accompanied by diagrams.  For example, this is not a mangonel (though the website says it is):

And this is not a mangonel (though the website says it is), though I thought it was when I wrote the post a few days ago:

Nor is this a mangonel (though the website says it is):

Nor is this, plainly a trebuchet, but included on the Dutch wikipedia site as a mangonel:

Nor this, though I'm sure the artist thought this was a very clever title:

This is not a mangonel, though someone has gone to great lengths to draw the picture and include it on this educational site:

As you might guess, this is very, very frustrating.  This is the best picture the English wikipedia page could come up with:

Which, as it turns out, is accurate, but in fact totally useless because it does not explain how the instrument works.  It took me a while to find a somewhat realistic depiction:

Actually a mangonel.

I have now found enough examples to feel confident that I've nailed down the engine accurately.  And what's depicted above, first, doesn't weigh 3 tons (though I did find a website that gave that weight for a "mangonel" that was probably for a trebuchet) and second, is way, way to tall for a ship.

So, apologies to Homer, who may have known what an actual mangonel looked like, and was therefore scratching his head at my comments - sorry, Homer, I was misinformed.  I'm quite prepared to keep the correct mangonel in my world and as an existing siege engine ~ but not aboard ships (which is a pity, as this reduces the options to fill hardpoints).  So those changes will be incorporated into the wiki, though I'll leave the blog post as it is.

Targets

Yesterday, Rod in a comment did indeed get a monkey off my back with this quote (reproduced in part):

”... mechanical artillery, however well developed, never quite acquired the power to bring down entire walls in the manner subsequently made possible by gunpowder and cannon ...”

That is a sentiment I intend to embrace with all my heart and mind. My world has long operated on the principle that the existence of magic has belayed or caused disinterest in the development of gunpowder as a terror weapon – in fact, the employment of a single cantrip (dampen, change, ravel) could be used with alacrity by an ordinary mage’s apprentice spy to cause a cannon to blow itself up. This logic allows me to keep beautiful castles for my Renaissance Era campaign without seriously disturbing the milieu’s credibility ... and here Rod nicely adds an additional argument.

So apart from shooting at people on walls and dropping dung, plague victims and human heads over a castle’s wall, the chief problem becomes what can be done by siege weapons against wooden targets – like other siege weapons and ships.

Well, to begin with, yesterday I pointed out that the density of wood was about half that of a human being. We can add to that the inflexibility of wooden structures compared to human beings, and we thus establish reasonably that the amount of damage which a siege weapon might do against a wooden structure would be equal to 2d6, or 1d12, per newton. (I hope you’re following here, because I’m not going over it all again – note the last four posts).

That’s twice as much as against a human target, which makes it easy and convenient for comparison and for evaluating damage. One of the annoyances in the DMG is that, on p. 110, there is no effort whatsoever to equivocate the ‘defensive point values’ listed to hit points. Of course, it probably never occurred to anyone that it would need to be ... except that I’ve found that constructions often don’t happen to exactly duplicate things that appear in the DMG, and that calculating new fortifications is a huge headache. Wouldn’t it be convenient if there was one single list that incorporated the amount of damage done by a charging knight on horseback to a human being and the amount of damage done by same said knight against a palisade fence? Believe me, in many years of playing, these things have come up.

How many defensive point value points of damage are done by a herd of animal controlled charging rhinos? Oh wait, the inventors of the game never thought to include that on the list of ‘Siege Attack Values’ on p. 109.

All right. Now people can argue as long as they like about the accuracy of this number, but I have listed on my equipment list that a ‘large ballista’ weighs 4,793 lbs. And I have argued previously on this blog that the body mass of an adult male human being (175 lbs.) would be worth 1d8 hit points (in addition to those hit points gained from skill & luck).

From these two numbers we can postulate that the number of hit points possessed by a large ballista is equal to 4,793/175 x 4.5 (average of a d8), which equals 123 hp. Taking the previously establish damage measurement from recent blog posts, I can suggest that the amount of damage done against the ballista by a 1-second shot (within the range of the missile travelling less than one second) would be equal to 20 newtons, or 20d12 (remember, twice the damage as against a living creature) ... the average of which would be 130. Now, isn’t that just bloody sweet?

I didn’t plan it out that way. I’ve been pretty much working out this system as I’ve gone along these last few days, and this is the first time I’ve calculated these figures. Just lucky, I guess.

There will be those out there who will argue that half damage or three quarter damage against the ballista would be enough to render it useless. But I would remind those voices that half damage or three quarter damage against your character does not reduce their chance to hit or do damage in any way. The 123 hp of the ballista is the amount of damage necessary to stop it from being a ballista.

Of course, it could be healed. And by my stunning rules, the ballista, if it suffered up to one quarter of it’s hp per round, it couldn’t fire (it would have to be re-adjusted and even partly reloaded).

Off hand, I’d estimate that any force applied against the ballista that would be less than 1 newton could be disregarded as non-effective, according to the arguments I made on my last post. That would exempt a swing with a dagger, but not necessarily an arrow ... which seems problematic to me. However, the arrow would have to be fired within 23.5 m of the ballista, a circumstance which wouldn’t likely come up that often. But some rule would have to be made regarding the original mass of the instrument being used to do damage.

This brings us to the question of actually hitting the target. I think I would use the DMG here, and say that the stationary target would allow a +3 to hit, and then additional plusses for subsequent shots. Unlike the DMG, however, I think that each individual subsequent shot should add an additional, cumulative bonus – not +4 as suggested, but +3. Therefore, the first shot would be against AC -10 at +3, the second at +6, the third at +9 and so on ... provided the target is not moved between shots. Eventually, you will hit a motionless target. That is because an artillerist knows that machinery ballistics, unlike the process of re-aiming with your arm every time, is a methodical series of adjustments. A skilled artillerist would know his instrument, and would know how to adjust it following each recoil and eventually hit his mark. It’s not chance. That is why artillery units quickly stop firing their weapons once they’ve come under fire, and move them forward, back, or elsewhere.

Okay. The next logical step from here would be to talk about actual buildings – specifically, ships, which is what I was working on offline that got me started on this subject. But I want to tell you, I am dead tired on this subject and I want to stop now. I will pick it up in the future, just as I intend to pick up my Civilization posts where those stopped – metal casting, which I haven’t written yet. The problem with a series of articles is that they tend to dry a writer out. For the present, then, I’ll put this down, do a little side work on ships and come back to it when I have something more to say.

In the meantime, you should be able to do the math yourself. Calculate the weight of the building and that equals its number of hit points. If you want to know a stone structure’s hit points, remember the density of stone (you can find densities for a lot of things on the SI Metric link on this blog), compare it to human flesh (900 kg/cub m, to put it in the idiom of the SI Metric site) and calculate the weight for the volume of stone represented by the fortification.

Have fun.

Resistance

Human beings cannot quite accurately be described as bags of water ... although that is often used as a joking comment in describing the percentage of water which makes up our composition. The actual percentage varies ... from 55% to 78%, depending on how hydrated you are at any given moment, as well as how old you are, whether you’re male or female, the climate you live in and so on. My point is that there is a difference between hitting you in the chest with a club, as opposed to hitting a free standing column of water appearing to be the same size and shape as you ... but it isn’t what you think.

Let us imagine such a column of water, and let us further imagine that the water is somehow able to keep its shape – magically, if you like. In any event, there is no hard membrane within the water, nor outside it. And finally, let us suppose this water column is YOU.

Swinging the club through water, I will encounter some resistance – depending on the relative thickness of the water. As the thickness is the same as you are, I will probably be able to complete a swing completely through the pure water version of you. The resistance will probably make me grunt, and depending on the thickness of the club I might have to bend my elbows some at the end of my swing.

If, on the other hand, I try to drive the club straight down through your pure water head, chances are the club won’t get as far as your torso. Something as narrow as a baseball bat might.

But let’s say I don’t use a club, I use a sword. Now obviously, the sword is going to cut through you, and quite easily, no matter which direction I swing. There’s a terrific benefit to the sword having a sharp edge.

Obviously, I don’t think any of this is news to the gentle reader – but I want to put you in the right frame of mind.

Let’s go back to you being you again, composed of blood, bone, sinew, gray matter, what have you. Your body is better designed to withstand the beating of clubs and the cutting of swords – whatever pain they might cause – as you are, to some degree, armor plated. If I were to swing a sword against your naked body, I would do damage – I might even kill you. But the sword would not pass willy nilly right through your body, as though you were made of water. Of course, you don’t re-assemble as easily as water, but your complex body provides you with other gifts. Being able to hold a sword, for example.

But there is another aspect to being hit with clubs and swords which I haven’t mentioned. Your body moves.

Let’s say I hit you in the chest with a club, just as I did when you were composed of water. This time, as the club hits you, your ribs flex inward, retaining your integrity, and your whole upper body ripples, redistributing the blow. Every joint down to your fingertips will loosen and separate, as in effect your body momentarily ‘liquefies.’ You also fall down, or at least you fall back ... further distributing the momentum of the blow to your environment.

I’d like to bring up an interesting point – your mass as a flesh and blood creature is actually less that it would be if you were composed of pure water. This is not merely because you have air in your body; the various composite parts that your body is fashioned of – blood, bone, sinew and so on – are as a whole less dense than water. Bone, for example, is only 81% as dense as water. Your overall specific density is about 0.9 grams per cubic centimetre, compared water, which has a density of 1.0.

The human body – any animal’s body, really – would make poor building material. The old saw about a body dropped into a cornerstone of a stone building under construction would soon liquefy and weaken the whole structure. Cracks would form and the building would collapse.

Except for your ability to redistribute force when struck by it, you’re not a very resilient material for making fortifications.

Obviously, stone works much better. If I make an equivalent of you made with stone, suddenly even the sword doesn’t work very well. The club is a dead loss. Both weapons lack mass, and the club lacks density as well ... spruce has a specific density of only 0.45 – half as much as you. Even the hardest woods are only as dense as 0.93.

Granite, on the other hand, has a density of 2.7. That means that a granite statue the size and shape as you weighs three times as much. In terms of resistance against force, that’s considerable.

This has been a long way around the barn, but I want to make a point, and I want us to be on the same page. When we compute the amount of damage done by a sword or an arrow against flesh, there is a point where the amount of force is so negligible that no damage is done. If I gently slap a sword against my palm, the sword does not penetrate my skin and I experience no noticeable injury. If I were to do it a thousand times, I would still fail to cause a single hit point of damage – though my hand might be a little stiff, with an ordinary rush of adrenaline it would probably continue to function normally. The same is true for a club swung against the chest of a stone statue. Though you stand there all day, hammering away with the club, at some point you might succeed in overcoming the club’s resistance (breaking it), but the stone is going to be just fine.

Where computing the damage done against a fortification, it helps to keep this sort of thing in mind. A ballista bolt will have more than a superficial effect on you ... but even at point blank range, it isn’t likely to do much damage to a stone wall. To determine such damage, a threshold of force must be taken into account. If your weapon only applies force that's less than that threshold, no effect.

I feel this is worth noting on a post all of its own because it applies to other aspects of D&D as well – often overlooked. How much damage, really, can a quarterstaff do against a dragon covered with scales? Or a club against an oliphant? Accepted, the weapon might hit, but does it break the skin? Does it imaginably bruise the skin? Would it make a difference if an 18/00 strength was behind it ... given that the club’s mass is still the club’s mass, no matter how hard it is swung. Isn’t it more likely that the 18/00 strength would break the club against the dragon’s hide, before it would break the dragon’s hide?

I’m nowhere close to proposing rules to cover these things. I’m struggling just now with applying some sort of threshold in the amount of damage done to castles and ships ... and I am at a loss. I can’t find much data – that I can comprehend – on the effects of resistance against force, along the lines I’ve just described.

Sometimes, I’m just not smart enough.

Splinters

I’m learning as I go.

Let’s throw out some of what’s been said up to now and let’s simplify some of the numbers where we can. Still using newtons for force, let’s designate a long bow as equal to 1 newton, a ballista as equal to 20 newtons and a catapult equal to 100 newtons – but don’t worry, I’m about to add a few wrinkles to those numbers.

Before we begin, however, I want to make this perfectly clear: I really do not care if this post meets the requirements of physics – my goal is not to pass a university examination, it is to produce a fairly believable, accessible set of rules for game play. In order to do so, I will have to bend the laws of momentum, with the caveat that in some instances the missile would actually have more momentum than what is assessed and in other cases less. We’ll just say that in the long run, it evens out.

For the calculations that follow, I’m going to simply ignore penetration. I can’t be bothered to take the math course necessary to do the calculations ... but you are welcome to take the general concept described below and complicate it however you desire. The principles should work for whatever cranks your brain fluid.

All right, the ballista. Let’s say that any target that can be hit within the period of 1 second will be hit with the full power of the weapon, that being 20 newtons as I said. And let’s incorporate Chris’ point from two posts ago and note that within 2 seconds, the momentum will be less – one half. If the initial velocity is 65.48 m/s, then at the end of 2 seconds we can describe that velocity as equal to 32.74 m/s. But what about the time between 1 and 2 seconds?

We can’t be accurate in any case unless we calculate for every possible distance, so let’s say for simplicity’s sake that for any period greater than 1 but less than 2, the velocity will be divided by 1.5 seconds. This changes our missile’s velocity at 1.2 seconds and at 1.8 seconds to 43.65 m/s. Accurate? No. But as I say, that’s not my concern.

Reducing the momentum also reduces the force of the ballista’s bolt, to the same degree: 20/1.5 = 14 newtons (it’s 13.33 actually, and a repeating fraction, but let’s not quibble; we want an even number).

Following this forward, and rounding it to the nearest whole number, the bolt’s force between 2 and 3 seconds would be 20/2.5 = 8 newtons, and between 3 and 4 seconds would be 20/3.5 = 6 newtons. These are fairly easy numbers to work with.

Given that 1 newton = 1 long bow, then we can define 1 newton as 1d6 damage (average 3.5). To get a wider average, we can define 2 newtons as 1d12 damage (average 6.5). Therefore, 20 newtons would be 10d12 damage. 14 newtons could be 7d12 damage, 8 newtons 4d12 damage and 6 newtons 3d12 damage. Simple? You bet.

So let’s fire a ballista at an opponent 60 hexes away. I define hexes as 5’ in diameter, so that’s 300 feet.

In the first second, the ballista bolt travels 215 feet. Within 2 seconds, the total is 358 feet (remember, the projectile is slowing). Thus, our target, if hit, suffers 7-84 damage. Isn’t that easy?

It is, so let’s throw in a wrench or two.

(By the way, before I forget, you can’t use the slowing momentum described above to determine the maximum range of the weapon. There are variables, like wind resistance, I’m not taking into account. I told you, I’m not a physicist. Sometimes my creativity fails to recognize my limitations. Aristotle would understand)

I said yesterday that it would be wildly difficult to hit a moving individual with a siege weapon – I would think something equivalent to hitting AC -10. But I think we can do something about that (it is at this point, definitely, that I throw penetration considerations out the window - shoot me).

The bolt fired by a ballista weighs, as I said, 0.325 kg, or slightly less than a pound. This would be a springy shaft about 1.5 times as long and four times as thick as an ordinary arrow. I would like to treat it as something that could potentially bounce, and even splinter. This would enable us to treat the bolt within the rules of a ‘grenade-type’ missile - meaning that it would be okay to miss, as long as you got close.

The rules under grenade-like missiles reads (bottom right hand corner of p. 64, DMG), “If the ‘to hit’ die roll indicates a miss, roll 1d6 and 1d8. The d6 indicates the distance in feet the missile was off target ... the d8 indicates the direction in which the distance in feet of the miss is measured ...”

Given that we’re talking a greater range of fire than a hand-held missile, I think we can stipulate that the d6 is the distance in hexes, not feet. But okay, we have something we can work with here.

Let us presuppose that our artillerist, Jeremy, needs a 23 on a d20 to hit Grunk in the front row of his armed force, and that he fully expects to miss. However, Jeremy isn’t concerned with that. Once he’s missed, he has a 1 in 8 chance of dropping his shot right in front of Grunk ... and that given the momentum of the missile, it’s going to bounce or splinter with a low trajectory, still causing damage.

How much damage? Let’s take make an ad hoc assumption on that, and say that the momentum of the missile is reduced by 75% ... dividing the number of newtons by 4. If Jeremy fires at Grunk at a distance of 60 hexes, the number of newtons would then be reduced from 14 to 4 (remember, we’re rounding to whole numbers). Grunk would still suffer 2d12 damage.

But we can do better than that.

When the missile splinters, it need not continue in a straight path. The largest and most deadly piece might spin off in a modified direction ... in D&D this is usually expressed as within a 60-degree angle. Consider the following picture.



Grunk is depicted here as within the 60 degree shadow of the missile, but not on the central trajectory. Suppose that, for every hex removed from that trajectory, we divide the force again – in this case, Grunk is two places removed, and the number of newtons is again divided by 4. Now Grunk need suffer only 1d6 damage ... but at least the ballista is not wasted. Note that under grenade missiles, if you are within a certain range of the missile, damage is automatic - you do not need ‘to roll’ to hit again

If Grunk had a couple of pals who were also within the shrapnel arc, the DM might randomly determine who gets hit by the missile ... or potentially, if more than one individual is hit. It might be suggested that a ballistae missile can only reasonably hit one person ... but a catapult stone will create additional fragments from the ground where it hits – splitting trees and throwing up gravel, depending on the location. More than one person might be hit therefore.

It occurs to me that Jeremy, our artillerist, would be wise to aim his shot in front of Grunk, rather than at Grunk, and thereby reducing the chance of the missile going long. But not too far in front ... there is a sweet spot, where the likelihood is best for some damage, if not maximum. Plus, there’s always a chance that the missed missile will land right in Grunk’s hex. Smoosh!

Get enough siege weapons firing into a massed crowd using these rules, you could do some serious damage. It would be particularly effect on board ship. It was working out shipboard combats that started me thinking along the lines of siege weapons in the first place. That, and mass combat rules – another bugbear of the game, eternally unsolved, eternally needed.

Well, please feel free to cut my math to pieces. It could do with a good chopping. I’m always learning, after all. I’m sure I made lots of mistakes ... I’ve only read it over once.

In the meantime, I shall turn my mind to the question of damaging fortifications – along with destroying ships, other siege weapons and so on. Until then.

Accuracies

For my last post, I got a terrific response from Chris, who made several salient points regarding penetration, energy transfer and psychological effects. Zzarchov, too, made a good point, which Chris embellished. Before reading any of this, you should read the full comment. I’d like to say that I agree with every point made.

Chris is absolutely right when he says, more than once, that hard numbers on the net are hard to find. What is available comes from data which has been gathered from modern recreations of old siege weapons, as obviously there are no functioning originals anywhere. From an historian’s perspective, this is very much like going to a Renaissance fair – if you think your experience is anything like that of an individual from the 14th century, you have a high self-delusion potential.

In any case, regarding my failure to take into account such things as penetration and how much force from a ballista’s shot is transferred to the body of the victim, I am happily disinterested in producing anything like an ‘accurate’ account of siege weaponry damage. If we were to begin talking about accuracy where it comes to D&D weapons, I think someone could write a long and uninteresting thesis on the irrationality of short swords and clubs causing the same amount of damage to an unarmored opponent.

Once upon a time, my friends and I played with the Armor Class Adjustment table on page 38 of the Player’s Handbook (I don’t now, it’s just annoying). Later we tried we tried using the numbers and applying them to the amount of damage done rather than as a ‘to hit’ adjustment. Flails, halberds and bardiches got very popular. My point is that however you play the system, whatever system you play, inaccuracy is the inevitable ghost in the machine.

Granted, where it comes to my post on physics and siege weapons, the ghost here is a free-floating phantasm thirty feet wide and glowing in a scintillating array of three or four dozen colors. Yet I think we can all agree that the DMG is two pages of shit on this subject. I’m only searching for some measure that works ... and later on, as Chris suggested, if I feel the need to publish, I’ll seek out a professor. For now, we’ll accept our failings and try to move on.

Oh, I must address Zzarchov’s point. He’s also right, by the way. “You can have a weapon put a clean hole straight through someone’s arm and do little tissue damage.”

As I understand the combat system, the roll ‘to hit’ does not strictly specify contact between one’s weapon and the enemy. It is presumed that you are striking your sword against the enemy’s armor, against the enemy’s weapon, or harmlessly against the enemy’s horns, scales, bone plates or what have you, or harmlessly through the slushy or ethereal equivalent of the enemy’s ‘outer barrier’, where it applies to a number of jellied substances and magical beings.

At some point you reach a threshold in your die rolling that indicates that damage is to be done. But whether you hit the opponent by rolling exactly what you need to hit, or seven points over what you need to hit, the damage you do is precisely the same – that indicated by the weapon you are using. At that point, the accuracy of the weapon is no longer relevant. It is the damage die that determines if the weapon glances off the opponent’s helmet, dazing him slightly (minimum damage) or stabs him through the body cavity (maximum damage)

There are certain individuals and creatures in the game who never cause the sort of damage that can be described as ‘glancing off the opponent’s helmet’ where it comes to damage. A player with an 18/00 strength never does less than 7 points of damage against an ordinary opponent – so we must assume the player is habitually hitting the opponent’s torso, and not his baby finger. Obviously an iron golem doing 4-40 damage won’t be nicking your cheek with his weapon. It is inherent in the game that certain instances suppose that the weapon and the wielder are so massive that the damage done must be extravagant. There are no saving throws, no special skills or dexterity bonuses which will reduce this damage, once it has been indicated to have occurred.

I am presupposing that damage from a ballista, a catapult or a trebuchet would be subject to similar rules. My personal belief is that such weapons, due to the difficulty with which they are aimed, would be wildly, ridiculously inaccurate against one foe marching towards them. However, I believe that if it should happen that you are hit with a catapult, according to the premises of the game, then chances are your character is going to be, as Chris says, unrecognizable pulp. A monk may dodge the stone; a sufficiently high-level fighter might get lucky and stand the hit; but virtually everyone else will be quite simply dead. So sorry, thank you for playing.

This would at least justify the enormous cost of siege weapons, the difficulty in setting them up and hauling them to their targets, or building tailored castle hard points on which to mount them. Since they were mounted in reality, largely for the purpose of striking other, immobile siege engines (which would be easier to hit than a moving man), we should presume they presented some value in combat. As it stands now, in D&D, they aren’t worth the effort.

I would like to imagine that if a dozen ballistae were trained on a mass of men (easier to hit than one man), that the effect would be more than three hits and 21 total damage. I’m working towards changing that. Frankly, I don’t know precisely how.

But we will take some of what Chris says under advisement, and we will get to the points I promised to address: hitting fortifications and multiple soft targets. But this is a post already, so I will post it.

Newtons

No matter how many times I sit down to redesign siege weaponry, I am always unsatisfied. I was trying to run a mock combat based on rules I designed before the creation of this blog, and as always, they are cumbersome and unwieldy. So I’ve been thinking about it the past few days.

To begin with, damage.

Let’s begin with an arrow, which we’ll suppose weighs .04536 kg and leaves a bow at a speed of 23.5 m/s. To calculate the force the arrow represents, we multiply kg times m/s over seconds squared, giving us a force of slightly under 1.07 newtons.

This is a force somewhat equivalent to swinging a 1.26 kg dagger (the blade point can be estimated to travel at 0.844 m/s, at least from what I can find online). Yes, an arrow does more damage than a dagger, but one can argue that the force from the arrow is concentrated on its tip, whereas the dagger’s force is spread over a wider surface.

Here’s where my weak knowledge of physics fails me. Alas, I have no calculation to determine the effects of surface area on the force inflicted by an object when it hits. If anyone out there wants to check and challenge my math, I’ll say up front that I am probably wrong somewhere. But I won’t let that worry me and I’ll just keep going.

From what I can find, a large ballista fires a 0.325 kg bolt at a velocity of 65.48 m/s, giving us a force of 21.28 newtons.

Considerably more force than the arrow. If a successful hit from an arrow results in a ‘glancing blow’ off an opponent, we judge that the arrow has caused 1 hp. The above figures would tend to suggest that a ballista bolt which glances off an opponent ought to cause somewhere in the neighborhood of 20 times as much (21.28/1.07).

Yes, I know that the ballista arrow loses momentum faster than the flight arrow, but again, weak physics. I can't find those calculations. If anyone wants to offer, I'm open to looking over your math.

It suggests that damage from siege weapons is severely under-rated, and I think they are. The damage quoted in the DMG for a ballista is a mere 2-12 (3-18 vs. large creatures, a rule I don’t use). Sounds plenty pathetic to me. Minimum damage ought to be 8-32 ... which averages 20.


Suppose instead that for a ballista missile’s damage, first a ‘siege’ damage (SD) is rolled: 1-6, just like an arrow. From this total, subtract 1. The remainder is multiplied by 20 and then 8d4 are added. Thus, if the ballista hits for ‘4’ points of siege damage, the total caused to a living being would be 60 + 8d4, or 68-92 damage. The benefits of calculating it this way will become evident later one.

All right, let’s take a catapult. The best stats I can find (that I can remotely understand from the gobbledy gook that make up these sites) are for a 10.86 kg object fired at 9.79 m/s, indicating that a catapult (onager, mangonel, what you will) has a considerably lower initial velocity in exchange for a much larger missile. The total equals 106.32 newtons of force, almost one hundred times an arrow.

Following the logic thus far, the minimum damage from a catapult ought to be something like 18d6. As before, we could roll an initial SD of 1-6, adjusting the total damage accordingly. Probably, any hit against an actual human person will result in automatic death. The same can be said for hits by trebuchet.

The real effectiveness of the siege weapons is not how large a rock do they throw, but how fast do they throw them. I for one will have to reduce the size of catapult/trebuchet shots as they appear on my equipment table, downwards.

I’ll leave off this for the present, to see if I get a storm from people smarter than me. Tomorrow, I’ll take up one of two problems I see: 1) how often does a siege missile hit more than one person; and 2) what does it do against fortifications.

Incidentally, I know I’m often full of myself, and I know that many who read this blog show great self-restraint in not pointing it out daily. I’m kind of glad for that, but there is not need, really. I don’t bite.