One thing that I have occasionally found myself wanting/needing to know is how to stat real-world situations or things based on the force that they exert. I rankled at trying to determine how many newtons of force are equivalent to a damage die for a long time. Then, whether by suggestion (and I just forgot), or whatever means it occured to me that it may be possible to determine the ratio of Newtons to Damage die by investigating what the draw force and/or impact force of a longbow was. Since the longbow is a weapon in D&D with a specific statistic referring to damage (1d8), I figured that if I could find a range of numbers then I could find either a median or a mean average that would tell me how many newtons of force equaled one d8.
There are many variables that go into determining how effective the impact of an arrow is in terms of damage. Indeed assigning a die roll to such a widely variable thing is a dramatic simplification. Since the damage can vary based on angle of impact and firing angle, wind, accuracy, the target's material properties, precisely how far the bow was drawn, gravity and probably many other variables, I decided to ignore this side of the equation and instead look at a number that has much more precision (relatively speaking) and fewer variables: the draw weight of a longbow. Admittedly this isn't likely to be as accurate as measuring the impact forces from a wide berth of tests from many angles with one set of tests done in a vacuum chamber (removing air resistance), some outdoors, and some indoors, using a mechanical drawing mechanism to ensure consistent bowstring draw position and so on. But I think that given the limitations it may be the best I can do under the circumstances to base my ratio on draw weight.
People debate the draw-stengths of longbows heavily and the results are only slightly consistent. The most persuasive case to be made for an average draw-force of a longbow for the purposes of a medieval fantasy rpg like D&D is one that refers to the many longbows recovered from the sunken ship named the Mary Rose. This rating, from the English Warbow Society (http://www.theenglishwarbowsociety.com/warbow_EN.html) puts the ratio at a 140 lb (622.75 N) per 1d8. But since the idea of the most common draw-weight of a longbow is one so heavily debated, I figured that I would make a list of every rating I found and would present each of them here for other DMs to consider when deciding what ratio of force to damage die they want to use.
Force to Damage Die Ratios:
Honestly, it seems that the longbow was inconsistently made in terms of their draw-weights and that as such this causes for so much debate. But I honestly like the Mary Rose concept of taking a very common (relative to other finds) draw weight and basing the statistic on the mode average from those findings. In the end I feel it's best to present what I found and to let people decide for themselves with this as a suggested guideline.
My Suggestion: 140 lbf. - 622.751024 N - 1d8
Full Table of Ratios: