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Old 05-03-2017, 08:37 PM
swaghauler swaghauler is offline
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Join Date: Jan 2015
Location: PA
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Default The Physics of Projectile Weapon Damage

Obviously, Twilight2000 uses Kinetic Energy to determine damage and this has led to the "undervaluing" of projectile weapons. The principle reason for this that the devs (along with significant numbers of the shooting community) only did PART of the equation for determining damage. If one reviews the Ethical Hunting Chart I posted above (used to determine the minimum KE needed to hunt various sizes of game animal), you will see that rifle (and pistol) bullets on average, require 60 TIMES the KE to ethically harvest game that a bow or crossbow would require. Why?

Kinetic Energy's "dirty little secret":
If you increase the Velocity of an object, any other object that object contacts must DOUBLE its own resistance to the contacting object. This is part of the Law of Conservation of Momentum. So what does this mean? It means that if two objects possess the SAME KE, the HEAVIER OBJECT will take longer to decelerate. This is because the faster object is meeting more resistance and shedding speed faster than the slower but heavier object. The lighter but faster object exerts more "force" per inch traveled, but because resistance is squared, it is decelerating faster than the heavier object and therefore penetrates less.
This is why a .30-06 will stop in a dirt-filled box that an arrow will cleanly penetrate. This is the difference between Kinetic Energy (the total energy an object has) and Momentum (the energy an object "exerts" over a given time and distance).

How Cross-Sectional Density Affects Penetration:
What's the difference between a 100mph arrow and a 100mph baseball? In a word, cross-sectional density. Milano discusses this in his own firearms upload (which I HIGHLY recommend). The 5oz baseball has a CSD of 0.0014 PSI (CSD is a measure of surface pressure) while a modern 540-grain arrow (even ignoring the mechanical advantage of its cutting head) has a CSD of 0.653 PSI. An 180-grain .30-06 bullet has a CSD of 0.285 PSI. The arrow exerts 2.25 times the surface pressure that the bullet does and a whopping 466 times the pressure that the baseball does. This is why the arrow penetrates the object while the bullet stops and the baseball bounces off.

Adjusting Twilight2000 V2.2's Damage:

I would multiply a projectile weapon's KE by a modifier BEFORE doing the calculation for basic damage dice. This modifier needs to take into account the SCD of the weapon. With that in mind, here's a test sample of modifiers.

Sling Stone (with a low SCD): 10 X KE, then use the Twilight2000 Formula.
Sling Bullet (higher SCD): 20 X KE, then use the formula.
Bows, Crossbows, and Atlatls (much higher SCD): 30 X KE, then run the formula.

This should get projectile weapons closer to real-world effectiveness.

Determining Range in Twilight2000:

I would use the Bow's Design, Draw Length and SKILL Level (yes skill) to determine the base range of projectile weapons.

Bow Design: Compound, Composite, and Recurve Bows. These bows tend to have better Efficiency than Long or Self Bows. The Compound Bow does this through its Cam and Pulley System. The Composite Bow's multilayer construction increases Efficiency and the Recurve Bow's forward facing limbs use a longer "stroke" (impulse of fire) to impart more energy to an arrow. These all will help increase the Range of the arrows fired from these bows. Compound and "Reverse Arm" Crossbows would have a similar "efficiency advantage" over basic Recurved and all of these would have an advantage over basic "self-bow" crossbows.

The Base Range could be: Compound Bow - 20m, Reverse Compound Crossbow - 30m, Compound Crossbow - 25m, Composite Bow/Recurve Bow (20m for a Composite Recurve like the Mongol Bow) - 15m, Recurve Crossbow - 20m, Long Bow/Self Bow - 10m, Self Crossbow - 15m.

Draw Length: Bows (and crossbows) could be classified as Short, Medium or Long by their Draw Length. Longer Draw Lengths add velocity (at about 10fps per inch of length) which adds Range.

The Draw Length adds could be: Short Draw Length is 24" or less (bows) OR 7" or less (crossbows) - SUBTRACT 5m from Range (minimum 5m rng). Medium Draw Length will be from 25" to 29" (bows) OR 7" to 12" (crossbows) - NO ADD to Range. Long Draw Lengths will be 30" or more (bows) OR 13"+ (crossbows) - ADD 5m to Range. You MUST use the ARROW length to determine the Range Add. Shooting a 24" arrow from a 30" Recurve bow gives a 5-meter range penalty.

Skill Level: I would add the archer's Skill Level to the Base Range of the weapon. Also, remember that Commercial Compound/Recurve and Long Bows will generally have Pin Sights that make aiming easier. These bows would have an Average Skill for a Snap Shot, while more traditional (or home-made) Bows would have a Difficult Snap Shot. Slings would be a Formidable Snap Shot.

This is just my take on Bows. As always, use what you will and discard the rest.

Swag.

Last edited by swaghauler; 05-04-2017 at 09:18 PM.
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