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Old 01-12-2009, 08:32 PM   #1
Nymdok
 
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Default Bows:From the Ground Up

This will be the first post. I will declare the reults of my research into bows and provide the generating equations. I will follow it up with Logic and Resources (How I came to this conclusion), Assumptions (all the chicken as a sphere foolishness), Modifications for Crossbows(Tension)and Examples. Note that these are consistent with Basic Set except for the weight of the shortbow.

Draw Strength of a Bow is BL x 4

Draw Strength/(Specifc Gravity of Material /.67) = Volume of the wood to be used.

VolumeOfWood/Length = Cross sectional area of the bow.

For composite bows, use the weighted average of the specific gravities.

Using these equations you can make a str 18 balsa wood short bow for your halfling, a ST 25 Iron bow for a giant and anything in between.

Nymdok

EDIT:
And so its done. Thanks to all who responded. The Final Product can be found here

http://sites.google.com/site/nymdoksgurpsaddons/

Last edited by Nymdok; 01-18-2009 at 03:09 AM. Reason: For the end
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Old 01-12-2009, 08:42 PM   #2
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Default Re: Bows:From the Ground Up

Assumptions:

All bows taper as they come to their ends.

Energy absrption is goverened dominately by the density of the material.

Energy is Distributed evenly throughout the bow.Thinner parts flex more, thicker parts have more material.(remeber its force * distance for energy)

Range and Damage are goverened by the strength of the bow, which is essentially the energy stored in the bow before loosed, no further fiddling is needed.

The Mary Rose relics and Otzi's bow are reliable representations of longbows.

The Draw length is assumed to be about 30" from braced.

Draw Strength is a 2 handed effort for 2 seconds. Eyeballing B353 we have BLx4.

Recurving bow does not have an appreciable (less than 10%) energy storage increase from a straight bow. The force required for a full draw remains unchanged.

Draw Length of a bow is equal to about half its height.

Draw SPan for a Humanoid creature is 1/2 their height.(Length of arm to center of chest)

Last edited by Nymdok; 01-21-2009 at 03:47 PM.
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Old 01-12-2009, 08:53 PM   #3
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Default Re: Bows:From the Ground Up

Logic and resources:


The resources I used were:

The Mary Rose Relics Data.

Otzi's Bow

http://www.archive.org/details/chapt...eevol017966mbp

http://www.bio.vu.nl/thb/users/kooi/kobe97.pdf

http://en.wikipedia.org/wiki/Longbow lists the world record draw for a bow at 200lbs/900N. This is ST 16 for 4xBL.

Nymdok

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Old 01-12-2009, 09:08 PM   #4
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Default Re: Bows:From the Ground Up

Modifications for Crossbows and other Draw Lengths:

The following covers only tension powered crossbows, not torsion.


To modify these for Crossbows, we need to pay attention to the energy invested. The Bows as listed above assume 30" draws which means that the energy under that curve is approximately:

30 x (BL x 4)

Now we need to get that same energy in a draw of about 15" for a crossbow bolt, but as we have our FULL basic lift at our disposal (8XBL) its not that tough. As you can see, we get the same energy

15 x (BL x 8) = 30 x (BL x 4)

So the trick here is to get the Crossbow prod length, which is somewhere between 24-36" depending on how you choose it. Then use the above equations.

EASY!

Nymdok

Last edited by Nymdok; 01-12-2009 at 09:24 PM.
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Old 01-12-2009, 09:20 PM   #5
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Default Re: Bows:From the Ground Up

Optional Additional Rules:

Crosssection: The D shaped cross section is the WORST possible shape and, sadly, is how english Longbows were made.

If you have a bow with a rectanuglar cross section, increase the length in Range and Damage calculations by 1/5 of its braced height.

Composites:
Historically, these were made with glue from animals. This makes them VERY susceptible to humidity. The ancient Chinese dried their bows for 6 months, the Turks for a Year! Roll against the HT of the bow for every Day in a high humididty environment (Jungle, Beach etc). On a failure it delaminates on the next pull rendering it useless!

To keep these numbers consistent with basic set, assume the Composite bows in the basic set have a recurve and a rectangualr cross section. For the players that do not want their bows recurved and rectangular, refer to them as Laminate bows as a more general term.

The Archers Paradox and Arrow Spine:
For ST higher than 14 all arrows must be custom made to fly straight. Multiply arrow cost by 10. For using regular arrows in High strength Bows, it is minus one for every 2 ST. A ST 14 bow using normal arrows results in a skill penalty of -2. Crossbows are NOT subject to this as they are centerfire weapons.

The One Second Pull: If your BL x 4 is double the draw strength of the bow, you may treat that bow as Shots 1(1) Meaning that with Fast draw arrow, you may fire an Arrow every turn!
Example: A ST 10 bow requires a 80# pull. A ST 15 charachter pulls at 180# and may (if he either has an arrow ready or fast draws one) Fire this turn.

Recurve makes it shorter: A recurved bow, due to its curvature, packs more wood into a shorter braced length. Treat as 1/5 longer than its braced length when calculating weight, range, accuracy, and Damage.

Essential Wood: For a bow with essential Wood cast upon it (For self bows) use TRIPLE the Specific Gravity in the calculations for Draw strength, but NOT bow weight.

Length and Accruacy:

This is just a basic Curve fit to match the Numbers in the basic set, but it leads to some interesting results.

Accuracy = 2.7-12*(Bowlength/ArcherLength -1)^2 (round)

THESE DO NOT APPLY TO CROSSBOWS.

Length and Damage:
GURPS allows longer bows to do more damge with the same arrows, Independent of ST. For every 1' increase in length, increase Damage +1. For every 1' decrease below 4' decrease Damage -1.

Length and Range:
This one is also tough, but Gurps Does allow Longer Bows more Range so we continue with their convention. 1/2 d range Multiplier is 2.5 times the length (Rounded to nearest 5) and Full range Multiplier is Length * 3.5 (again rounded to the nearest 5)


Length and Bulk:
Bulk is also dependent on the Weilder and Must be mated to the his size. Length of bow = to height of weilder is bulk -8. For every 1/3 of your height this increases, increase this penalty by 2. Decrease it likewise for for shorter bows. A 15 Foot tall Ogre would only have a Bulk modifier of -4 to conceal a 5' regular bow. A 6' Human trying to conceal a 15' tall bow would be at -13!


Nymdok
And Im spent.......

Last edited by Nymdok; 01-22-2009 at 08:41 AM. Reason: Added Essential Wood Rule
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Old 01-13-2009, 06:13 AM   #6
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Default Re: Bows:From the Ground Up

Quote:
Originally Posted by Nymdok
The ideal shape is rectangular as used by the Native North Americans.
I'm not familiar with this style bow, could you profide an informational link? Perhaps one with pictures also...
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Old 01-13-2009, 06:26 AM   #7
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Default Re: Bows:From the Ground Up

http://en.wikipedia.org/wiki/Flatbow

Remember that Flatbow/Rectangular refers to the cross sectional shape.

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Old 01-13-2009, 09:16 AM   #8
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Default Re: Bows:From the Ground Up

Finally, we have an Example.

First an Easy one, Red Maple with a specific gravity of .54.

We want a bow of light strength and short stature for a theif so we'll make it a ST 8 bow.

ST 8 =>Bow pull 51 Pounds.

We want a short bow.....really short....40 inches short.

So its 48/(.54/.67) = or 60 cubic inches of this material.

Divide the Cubic inches by the height to get the cross sectional area 60/40 = 1.5 square inches in the cross section. For smallish man sized hands 2 inches wide is plenty, so it has a thickness of .75 inches. Note that these dimensions are the average of the bow, its a little bulkier at the grip and thinner at the tips.

Since we used specific gravity up top, all we have to do to Find the carrying weight of the bow is multiply its volume, times the Density of water (.036 lbs/cubic inch) or in this case 60 * .036 which gives us a 2 pound bow.


There you have it! Steps to a bow accurately desribed in detail for your players, of the ST YOU chose and the material YOU choose and the length YOU choose!

So to sum up
ST: 8
Material:Red Maple
Length: 40"
Width: 2"
Thickness:.75"
ST Required for ROF 1(1) = 12 (pull = 115)

Ill do one of a more complex example later right now my boss is looking at me funny :)

Nymdok
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Old 01-13-2009, 10:04 AM   #9
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Default Re: Bows:From the Ground Up

The only issue I have here is that having a 50lb bow be ST8 is a bit harsh. In a different thread, we'd come to the conclusion that a person could draw a bow of BLx2 lbs, with StrongBow adding +0.5BL at DX and another at DX+2; Special Exercises (Arm ST) could be applied in two levels for the same bonus. So a specialized archer with good skill and special exercises could draw the bow with 4xBL of pull.

Otherwise, I worry that the damage of these bows will be extremely unrealistic. Using the firearms scaling style, I figured a 180lb warbow would likely only do 1d+2 damage...
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Old 01-13-2009, 10:16 AM   #10
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Default Re: Bows:From the Ground Up

I like it. You might want to consider editing your initial post to include units, however. Also, I'm curious as to why you used 48 instead of 51 in your calculation. Finally, what is your justification for using the .67 conversion factor? I seem to recall you justifying it, but can't find that anymore.

50# does seem rather high for ST 8. I personally struggle with a 50# compound bow, and my ST is probably around that level. I can do it, but (in GURPS terms) it costs FP for each shot. Were it not for the let-off of compounds, however, I probably wouldn't be able to manage at all.
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