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.