08-08-2018, 03:32 AM | #1 |
Join Date: Nov 2013
Location: near Seattle WA USA
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using the "Interior and Terminal Ballistics" article with arrows
I've read the article "Interior and Terminal Ballistics for GURPS" article, and I found this example:
Example: Let's bend the system. We take a 23 gram wooden arrow, and apply a "pressure" of 1000psi. We use an 8mm diameter, an aspect ratio of 95:1, and a "barrel length" and "burn length" of 480mm (for a 760mm arrow); the case length we set at 1mm (it's irrelevant). This converts to about a 78lb draw weight, and propels the arrow at 121 m/sec, inflicting 1d+1 damage. Not bad! A 120 lb bow (1560psi) with the same properties would inflict 1d+2, firing the arrow at 151m/sec. Medieval bows were quite strong; it's not unrealistic to assume a 120lb bow, and the damage matches up very well for a longbow that requires ST15 to pull (a Thrust of 1d+1). The predicted velocities are a bit high compared to reality, but the predicted damages work well with GURPS canon material. How does the pressure relate to the draw weight here? Here's my look at the math: The arrow's diameter is 8 mm, so its cross section area is πr^2 = π×(4 mm)^2 ≈ 50.265 mm^2 ≈ 0.0779 inch^2. Dividing, (1000 pounds/inch^2)/(0.0779 inch^2) ≈ 12835 pounds. It seems obvious that I'm messing it up somewhere. Do I need to bring in the entire kinetic energy formula to include the burn distance (m), bore [arrow] area (m^2), fall-off volume (m^3), acceleration distance (m)? Or am I messing up somewhere else? |
08-08-2018, 05:49 AM | #2 |
Join Date: Jan 2010
Location: Brighton
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Re: using the "Interior and Terminal Ballistics" article with arrows
Without commenting on your maths in relation to that article can I suggest you look at "The Deadly Spring" by Douglas Cole (the same author) in Pyramid 3-33?
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08-08-2018, 09:23 AM | #3 | |
Join Date: Sep 2011
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Re: using the "Interior and Terminal Ballistics" article with arrows
Quote:
What you need to do is multiply pressure by cross-sectional area which yields 77.9 lbs. force, rounding to 78 lbs. draw weight. More generally, pressure as given in the formula in linearly proportional to the draw weight in lbs. and the conversion rate is 12.8 psi/lb. draw weight (accurate to 1 decimal place). |
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08-08-2018, 10:56 AM | #4 | |
Join Date: Nov 2013
Location: near Seattle WA USA
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Re: using the "Interior and Terminal Ballistics" article with arrows
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Thanks for the sanity check. |
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08-08-2018, 11:05 AM | #5 |
Doctor of GURPS Ballistics
Join Date: Sep 2004
Location: Lakeville, MN
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Re: using the "Interior and Terminal Ballistics" article with arrows
Wow. That's an old reference.
A few things I note: 1) A medieval war arrow was much heavier than I listed here. At least double, likely. For a powerful bow, they could be 11-13mm thick and 1500 grains (nearly 100g). So one of the reasons my velocity is high is that my arrow weight is very light. 2) Not sure what I was smoking on "burn length," but having full force for 480mm (19") is a bit nutso. On a 28-30" draw, using a simple spring model with a 78-lb draw weight (a hunting bow), one should probably set the draw weight to HALF the max draw and use the "burn distance" as the draw length of the bow, with the barrel set equal to the burn length. That won't give you good answers for "what happens at half-draw" or whatever, but it will at least account for the fact that the force on the arrow is zero at zero draw and only hits maximum value at full draw for a self-bow But ultimately, the kind of "we're burning powder to throw bullets!" calculations in this article are much less suitable than those in The Deadly Spring, which of course are themselves approximations to allow the results to get in the ballpark, which by and large they do.
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08-09-2018, 11:57 AM | #6 |
Join Date: Nov 2013
Location: near Seattle WA USA
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Re: using the "Interior and Terminal Ballistics" article with arrows
"The Deadly Spring"? What a great title! I will have to buy that Pyramid. (By the way, is there a bundle of Pyramid 3 issues? Or an easy to use index? I have not been a subscriber in a while.)
Also, does the article cover only ordinary cantilever spring bows and crossbows, or can it also handle things like ancient and medieval torsion bow siege engines, modern compound bows, and single arm weapons? I'm guessing that it does not cover counterweight or traction trebuchets, since those are not based on springs, and operate under rules that don't involve Hooke's Law. |
08-09-2018, 12:21 PM | #7 |
Doctor of GURPS Ballistics
Join Date: Sep 2004
Location: Lakeville, MN
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Re: using the "Interior and Terminal Ballistics" article with arrows
Pyr 3/33, and it covers bows and crossbows of all makes and models that, as you note, involve Hooke's Law. There's an attached spreadsheet to handle the gory calculations.
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08-17-2018, 09:35 AM | #8 |
Join Date: Nov 2013
Location: near Seattle WA USA
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Re: using the "Interior and Terminal Ballistics" article with arrows
The Deadly Spring brings to mind another idea for a subject of possible interest to gamers: melee weapon wounds. A spear thrust is similar to an arrow in terms of wounding characteristics. However, the kinetic energy comes from the muscles of the attacker, and continues after the initial impact, rather than coming solely from the inertia of an arrow. Or in the case of a set-against-charge spear strike, it comes from the inertia of the person charging. A blade slash has different wounding characteristics, because the point of impact are along an edge rather than a point.
Have you or others written about that sort of thing? |
08-17-2018, 09:40 AM | #9 | |
Doctor of GURPS Ballistics
Join Date: Sep 2004
Location: Lakeville, MN
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Re: using the "Interior and Terminal Ballistics" article with arrows
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So ultimately, this is just "how much damage and what type" and you don't need to convert from real-world units here: you start from the character's ST and figure out what the damage should be.
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08-17-2018, 07:12 PM | #10 |
Join Date: Nov 2013
Location: near Seattle WA USA
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Re: using the "Interior and Terminal Ballistics" article with arrows
Aha, so the point of "Interior and Terminal Ballistics" and "The Deadly Spring" wasn't so much to calculate real world units, with hit points as a by-product, but rather to hit points in a more physically justified way, with real world units as a means to that end?
In that case, because ST is pretty much defined in terms of how much hit point damage one can do in melee, deriving real world units in melee from ST (or from hit points) doesn't make a lot of sense, because hit points damage are the intended endpoint anyway. |
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