Indoor Missile Ballistics

I wrote a bit about missile ballistics previously. Part of that discussion is predicated on the observations that (a) the move and range statistics given in Chainmail show signs of excellent research, and are very historically accurate, but (b) the transition in OD&D from outdoors-to-indoor via a simple yards-to-feet conversion (and no time scale conversion at all) was pretty much not thought out at all. Here's a bit more on that.

If we take the original Chainmail maximum ranges for missiles as a starting point (assuming base level of historical accuracy), in each case we can use some ballistics calculations to back-calculate the launch speed of the missile in question. Then we can use that value to calculate the indoor range of the missile, under different ceiling heights. Consider the following results:


Tools and Assumptions

• I used the "Ballistic Trajectory Calculator" by Stephen R. Schmitt to compute outdoor launch speeds, the greatest possible angle for a given ceiling height, and the resulting maximum ranges.
  
• Maximum outdoor range is automatically given by a 45-degree shot, but with a limited ceiling overhead the maximum possible launch angle (to avoid hitting the ceiling) is usually between 5 and 20 degrees or so.
• Distances have been crudely converted using a simple 1 meter = 1 yard = 3 feet assumption. Resulting ranges in inches have been rounded to the nearest multiple of 3, the same as in classic D&D.
• We presume Earth-like gravity (9.8 m/sec^2) and an initial launch height of about a normal man's shoulder (1.5m).
• The "Thrown" category includes spears, hand axes, daggers, etc. The "Crossbow" has the same range parameters as a Composite Bow.
  

Results and Analysis

Obviously, the range of the maximum possible shot indoors is dependent on the ceiling height; a higher ceiling allows for a longer potential shot. Also, the effect on different missiles is not linear; that is, the more powerful weapons suffer more than the lighter weapons. The overall effect is to "bunch up" the ranges of the weapons closer together, minimizing differences.

An interesting data point to look at is under the 10' ceiling, played with the "old school" game scale of 1"=10'. It turns out that the Shortbow has exactly the same game range as we started with; it's 15" in both Chainmail and our ballistics-accurate indoor conversion. However, Thrown weapons are not as hamstrung by the low ceiling, and in fact their in-game range has doubled to 6". Meanwhile, a weapon like the Heavy Crossbow is relatively more disadvantaged, with a resulting game range of 18" (a quarter less than its Chainmail range of 24").

Note that Thrown weapons outdoors actually have a maximum-shot height of only 8.8 meters (27 feet) -- so as soon as the indoor ceiling height reaches something above 20 feet, they can effectively achieve the maximum-possible shot range of 90 feet (30 yards/meters), the same as outdoors.

Suggestions and Options

What to do with this? Here are several different options for using this in your D&D game:

1. One option is to use the tables above directly in your game for indoor missile fire. That may be overly complicated, however, and unnecessary: ranged combat will usually be much more limited by room size or extent of lighting.
2. If you actually game at an "old school" scale of 1"=10 feet, then you can use the standard Chainmail ranges in inches and you'll be pretty close to the physically realistic results above (however, see below).
   
3. Assuming a "new school" game scale of 1"= 5 feet, you might take the classic game ranges for bows and just double them (giving max ranges like 30/36/42/48 inches); thrown weapons quadruple (to 12"). This is pretty close to the ranges shown above for a 10' ceiling, but it's still pretty complicated, and is overly generous to the more powerful weapon types.
4. We might approximate the different bows as being practically of equal range in a typical 10' high corridor or room. For example, stipulate that every type of bow has a 30" range indoors (150 ft); again, thrown weapons travel 12" (60 feet). That's probably close enough to our improved-accuracy model.
   
5. Or, you might choose to basically dodge the whole issue, saying that additional obstruction issues reduce ranges back to the Chainmail givens of 15/18/21/24 inches (again, thinking 1"=5 feet here); lighting will probably always be less than that anyway, and we thereby keep the same balance with other movement/spell/special abilities in the game. Nevertheless, I'd strongly recommend increasing the thrown weapons range to either 6" or 12", depending on your taste in the matter.
6. Whichever option you pick above, it's pretty easy to account for different ceiling heights (if you want to). Take a 10' ceiling as your base. For a 20' ceiling add +50% to the chosen ranges. For a 40' ceiling, double the listed ranges. Regardless, thrown weapons can't ever travel more than 90 feet (the maximum outdoor range, effectively achieved with a 20 foot ceiling).
   

At the moment, for simplicity I'm going with suggestion #5 above (range in inches as in classic Chainmail, except for thrown weapons which can be hurled 12" indoors, i.e., 60 feet). If anyone uses a more sophisticated option, I'd be delighted to hear how it works out.