Steve Jackson Games - Site Navigation
Home General Info Follow Us Search Illuminator Store Forums What's New Other Games Ogre GURPS Munchkin Our Games: Home

Go Back   Steve Jackson Games Forums > Roleplaying > GURPS

Reply
 
Thread Tools Display Modes
Old 08-08-2018, 03:32 AM   #1
SteveS
 
Join Date: Nov 2013
Location: near Seattle WA USA
Default 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?
SteveS is offline   Reply With Quote
Old 08-08-2018, 05:49 AM   #2
Tomsdad
 
Join Date: Jan 2010
Location: Brighton
Default 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?
__________________
Grand High* Poobah of the Cult of Stat Normalisation.
*not too high of course
Tomsdad is online now   Reply With Quote
Old 08-08-2018, 09:23 AM   #3
Curmudgeon
 
Join Date: Sep 2011
Default Re: using the "Interior and Terminal Ballistics" article with arrows

Quote:
Originally Posted by SteveS View Post
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?
The problem with your math is that you've divided the pressure by the cross-sectional area in an attempt to get force in lbs. Doing so, your answer is not 12,835 lbs. but 12,835 lbs/(sq.in.) squared.

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).
Curmudgeon is offline   Reply With Quote
Old 08-08-2018, 10:56 AM   #4
SteveS
 
Join Date: Nov 2013
Location: near Seattle WA USA
Default Re: using the "Interior and Terminal Ballistics" article with arrows

Quote:
Originally Posted by Curmudgeon View Post
The problem with your math is that you've divided the pressure by the cross-sectional area in an attempt to get force in lbs. Doing so, your answer is not 12,835 lbs. but 12,835 lbs/(sq.in.) squared.
Wow, I feel silly. That's what I get for trying to do calculations on a calculator at 2:30 am, instead of on paper when I'm fully awake.

Thanks for the sanity check.
SteveS is offline   Reply With Quote
Old 08-08-2018, 11:05 AM   #5
DouglasCole
Doctor of GURPS Ballistics
 
DouglasCole's Avatar
 
Join Date: Sep 2004
Location: Lakeville, MN
Default 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.
__________________
My blog:Gaming Ballistic, LLC
My Store: Gaming Ballistic on Shopify
My Patreon: Gaming Ballistic on Patreon
DouglasCole is offline   Reply With Quote
Old 08-09-2018, 11:57 AM   #6
SteveS
 
Join Date: Nov 2013
Location: near Seattle WA USA
Default 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.
SteveS is offline   Reply With Quote
Old 08-09-2018, 12:21 PM   #7
DouglasCole
Doctor of GURPS Ballistics
 
DouglasCole's Avatar
 
Join Date: Sep 2004
Location: Lakeville, MN
Default Re: using the "Interior and Terminal Ballistics" article with arrows

Quote:
Originally Posted by SteveS View Post
"The Deadly Spring"? What a great title! I will have to buy that Pyramid.
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.
__________________
My blog:Gaming Ballistic, LLC
My Store: Gaming Ballistic on Shopify
My Patreon: Gaming Ballistic on Patreon
DouglasCole is offline   Reply With Quote
Old 08-17-2018, 09:35 AM   #8
SteveS
 
Join Date: Nov 2013
Location: near Seattle WA USA
Default 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?
SteveS is offline   Reply With Quote
Old 08-17-2018, 09:40 AM   #9
DouglasCole
Doctor of GURPS Ballistics
 
DouglasCole's Avatar
 
Join Date: Sep 2004
Location: Lakeville, MN
Default Re: using the "Interior and Terminal Ballistics" article with arrows

Quote:
Originally Posted by SteveS View Post
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?
I have not. Well, not exactly. A lot of the "rescaling melee weapon damage" stuff comes from the fact that you're basically talking about the ST damage progression for melee weapons, and the very basic thing your describing is "how much ST is effectively applied?" and "what is the appropriate damage type and wounding modifier."

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.
__________________
My blog:Gaming Ballistic, LLC
My Store: Gaming Ballistic on Shopify
My Patreon: Gaming Ballistic on Patreon
DouglasCole is offline   Reply With Quote
Old 08-17-2018, 07:12 PM   #10
SteveS
 
Join Date: Nov 2013
Location: near Seattle WA USA
Default 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.
SteveS is offline   Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Fnords are Off
[IMG] code is Off
HTML code is Off

Forum Jump


All times are GMT -6. The time now is 07:35 AM.


Powered by vBulletin® Version 3.8.9
Copyright ©2000 - 2024, vBulletin Solutions, Inc.