Friday, August 19, 2011

More on Catapults & Giants

In the past few weeks I was looking closely at the mechanics for OD&D catapults, giant stone-throwing, and fireball spells, which really all share the same single mechanic originating in Chainmail. If you recall how catapult-like-attacks function in Chainmail, they land at some declared range by the attacker, killing everything within an area-of-effect diameter of 2" or 3.5" (depending on light/heavy category; some survival allowed for heroic-type targets; but otherwise ignoring any armor considerations). Particularly with catapults, you then get into questions of what scale this is intended to be -- I argued that they're best understood at Siege/Man-to-Man scale, and somewhat accidentally shoved into the mass combat section.

As usual, Gygax's Swords & Spells book (which counts as being in the OD&D line) gives some nice additional perspective if you hunt around in it enough. In these 1:10 mass-combat rules, catapults are explicitly said to be 1:1 scale, which I think bolsters my previous argument:
Artillery: As the various artillery pieces represent but a single scale engine, only a single figure is needed to represent crew for each... [S&S, p. 10]
Catapults (both light & heavy) have decreased rate-of-fire from 1/2 or 1/3 [CM, p. 12] to 1/4 here [S&S, p. 9]. Meanwhile, bow archery has increased rate-of-fire from 2 per turn [CM, p. 11] to 3 per turn [S&S, p. 9]. And as far as giants go:
Giants act as 20" range -- light catapults with a fire arc of 45% [sic] left or right, but they must stand one-half move to fire. [S&S, p. 10]
That's an oddball rate-of-fire: sort of between the allowances for ROF 1 or 2 [S&S, p. 9], now much more potent than a mundane light catapult (by a factor of 4), similar to the description in Chainmail but without following the Swords & Spells reduction to catapult speed. This is backed up by the Example of Game Play at the back of the book which features giants throwing rocks on each of subsequent turns [S&S, p. 38].

Now, the thing I thought particularly interesting is that the result of catapult/giant fire is already no longer an area-of-effect. And I think this is particularly reasonable if we're interfacing between scale 1:1 throwers and 1:10 targets. The effect is now simply an application of a certain number of hit points damage to the target unit [S&S, p. 26]:

STONE CASTERS Target About Man-sized Larger
Small Catapult 30 15
Large Catapult 40 20
Trebuchet 50 25

Consider: The effect of the small catapult (i.e., giants) in these rules is to kill 30/4.5 = 6.7 normal men. That's actually very close to the number of men you'd kill if the Chainmail/OD&D area-of-effect was applied over man-to-man figure bases areas: Pi*r^2/Fig^2 = 3.14*1^2/(0.75)^2 = 3.14/0.5625 = 5.6 normal men. The large catapult kills 40/4.5 = 8.9 normal men, compared to Chainmail's heavy catapult which at man-to-man scale would kill at most Pi*r^2/Fig^2 = 3.14*1.75^2/(0.75)^2 = 9.62/0.5625 = 17.1 normal men (i.e., about twice as many).

2 comments:

  1. Interesting. The assumption of giants is that must "run and throw" in order to get range with a boulder, like an olympic javelin toss.

    I'm confused about your math on #of targets (im not a mathemetician) can you go into a little more detail?

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  2. UWS guy said: "can you go into a little more detail?"

    Sure, I'm just dividing the "area of spell effect" by "area of figure base" to see how many figures it would cover, in principle.

    For a small catapult, the area is a circle with diameter 2", i.e., radius 1". The area of a circle is A = Pi*r^2. So in this case A1 = Pi*r^2 = 3.14*(1)^2 = 3.14*1 = 3.14 square inches.

    Meanwhile, I'm assuming normal-man figures stand on a square base with side width 3/4", i.e., 0.75" (about 25mm). The area of a square is A = s^2. So here A2 = s^2 = (0.75)^2 = 0.5625 square inches.

    Dividing the first by the second should tell us how many figures can be covered by the spell effect. That is: A1/A2 = 3.14/0.5625 = 5.58, or about 6 figures, if the figures are packed together as tightly as possible. (Which as I pointed out is coincidentally [?] about the same as the total damage indicated in S&S).

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