Fantastic Frontiers: Encumbrance Weight Calculations

No one likes encumbrance systems, but games need weight limits to force meaningful choices. This is a fact of life, and it only becomes harder to manage when everything is operating at the level of large scale battles. When you fire a single arrow at a time, you just take the weight of an arrow and multiply it by the number of shots to figure out how much your load has lightened. But what about in a 20 minute skirmish (roughly 1 "round" in a larger battle), where longbowmen can toss off arrows at a rate of 10 per minute?

A few quick estimates:

• Food will need to amount to about 4000 calories a day for an adult male in a physically demanding environment. You can get this many calories from about 2 lbs of hardtack. If a ration is about 1 lb (for convenience) this amounts to saying that two rations a day puts your team on "full rations", and one a day is on "half rations". This is about a factor of two below the modern military standard of a 20 oz MRE providing around 1200 calories, but American soldiers eat pretty well by the standards of medieval armies!
• A longbowman will probably go through somewhere between 20 and 60 arrows per battle round, depending on initial engagement range. If these are war arrows, they weigh around 1200 grains, or about 3 oz. That's roughly 2/10ths of a lb. So each battle will expend somewhere between 4 lbs of ammunition and 12 lbs. That's a lot of arrows! For a slow-firing weapon like a crossbow, you can cut that in half.
• Gunpowder and shot would be spent much more slowly. It would take a talented soldier to reload a matchlock inside of a minute. An arquebus ball would maybe be an ounce, with a roughly equal amount of powder. Even with a very stead rotation of volleys, that's unlikely to use up more than 2 lbs of ammunition over a round. However, unlike arrows and bolts, you can't gather any of your spent powder off the battlefield even if you win!

If we break this down to units, then it makes sense to define a "ration" of food as weighing 1 lb (with 2 rations a day standard), a "battle's-worth" of medieval ammunition as 5 lbs (double that for longbows), and a "battle's-worth" of firearm ammunition as 2 lbs. It's pretty clear that the common denominator of all these values is about 1 lb, which is pretty convenient (if not particularly metric!) So it's worthwhile to measure everything in pounds, instead of something larger like stones, but it's definitely not worth the trouble to break down below 1/10th of a pound.