Thursday, 3 September 2015

The Effect of Low Ceilings on Missile Fire

I've been busy creating a new adventure locale for my group (and the adventure went in an unexpected direction, which is good) so for the blog I've chosen an easier topic to resolve: Does the height of the ceiling significantly affect the range of missile weapons indoors?

Now in D&D Gary Gygax had this odd “distances are in yards outdoors, feet indoors” rule (AD&D DMG p39), which reduces all ranges and areas of effect by a factor of three in dungeons. To me this seemed firmly based upon reconciling the awesome power of Fireball in Chainmail with the desire to reign in the power of Magic Users for dungeon crawls, but it also applies to missile fire with the justification of low ceilings. Is this drastic universal range reduction justified? In particular it has a big effect on short range missile weapons like axes. The reduction on range for bows seems plausible (apart from his odd statement that Crossbow bolts don't follow a parabolic flight), but the 3" for throwing axes and spears from Chainmail (p10) means 30 yards outside, but only 30 feet indoors. The ranges are carried forward with minor changes through to AD&D where it's become 30ft for Axes, 60ft for Javelins (PHb p38).

I’ve run some simulations for missiles of different maximum ranges over various maximum ceiling heights, and calculated what the maximum range is reduced to. For my purposes I’ve made several simplifications: I’ve lumped all missiles with the same range together (ignoring different trajectories for different types of projectile due to wind resistance – it has little effect). I’ve ignored the height the missile was thrown at (which should be about 5 foot – it has little effect, and I ignored it when calculating ranges in the first place). I’ve omitted ceiling heights under 10’ high as that’s unlikely to be relevant, though note that it follows the same pattern.

The results are as follows: (all heights and ranges as per my standard "double every other category")

I’ve shaded the ranges which are reduced. I then simplify this table (below) by altering the reduced range to be the nearest category, allowing myself latitude in a couple of cases (marked red) where I round up for some results just less than halfway between to make the results fit a regular pattern.

Now the pattern in that table is easy to see but difficult to extrapolate from, but it's probably an acceptable simplification to drop every other column (who ever heard of a 15' ceiling anyway) and the resultant cut down table is much simpler, especially if we reverse the order of the columns:

So we note that unless you’re aiming at something more than 80’ away, the low ceiling has zero effect on range. Furthermore, if you’re shooting at more than 80’ you get a -12 range penalty on to hit. So range restrictions would only ever come into play if the target you’re aiming at is so far away that you’re unlikely to hit it in the first place!

So in summary, the range reduction can be quite easily reduced to a simple pattern which can be summarised in one short table. However, I think that it is extremely unlikely that this range reduction will ever actually have an impact on play (since it only ever takes effect over longer distances than are usual). Note that this result is absolutely nothing like “reduce the range threefold” except for long ranges with a 10' ceiling, and in fact ignoring ceiling height altogether would be a more accurate simplification for most situations!

Comparison with Delta's Results 
Delta did some similar analysis using D&D’s fixed ranges,  but in Explore the range varies according to the archer so these results are not much use to us except for comparison purposes to check the results.
Delta shows thrown weapons (range 90') having a reduced range only with a 10’ ceiling – when it is reduced to 63'. The nearest equivalent 80’ in Explore would only be reduced to 69’, which in this case I rounded up not down, hence in our case there’s no range reduction at all.
Similarly the three bows have fixed ranges 150/180/210/240 yards or 450/540/630/720 ft. In Explore we don’t have this level of granularity in ranges, but we get similar results: approx. one third range with a 10' ceiling, one half with a 20' ceiling, two-thirds with a 40' ceiling.


  1. I'm surprised at your results. How did you calculate the range truncation?

  2. I wrote a program in Java for calculating trajectories. You set the velocity so that it would achieve the max range at a 45 degree launch angle, then you put in a limit of the ceiling and increase the launch angle until it hits the ceiling.

    Delta in the link I gave had a link to an online trajectory calculator which you could use to check the figures.

    I've since wondered what effect it would have if you threw from 6' and had to hit at least 3' off the floor, and the only effect would be to lower the 80' at 10' ceiling to 60', which I don't think is worth sweating over.

  3. I have a 9' ceiling in my basement, we hit the ceiling all the time throwing the ball around, at a distance or 20' or 25 '.

    1. Yes, you will.

      If you throw near to the maximum range that you can throw then you have to throw near 45 degrees, and so it goes high in the air.

      If you throw just as hard, but flatter, you can throw it almost as far.

      I'm not saying that you won't hit the ceiling, I'm saying you can throw it a long way without hitting the ceiling, if you throw it fast.