0006262: Rounding Error in Calculation of Projectile Velocities

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Date Submitted

Last Update

0006262

Dwarf Fortress

Throwing/Shooting

public

2012-12-12 05:18

2014-08-03 13:29

Reporter

Pirate Bob

Assigned To

Toady One

Priority

normal

Severity

trivial

Reproducibility

always

Status

resolved

Resolution

fixed

Platform

Computer

Windows/Linux

OS Version

all

Product Version

0.34.11

Target Version

Fixed in Version

0.40.05

Summary

0006262: Rounding Error in Calculation of Projectile Velocities

Description

Projectile (bolts, arrows, blowdarts) velocities appear to be calculated using the formula:
velocity=[SHOOT_FORCE]/(([SOLID_DENSITY]*[SIZE])/1,000,000),
and then capped to [SHOOT_MAXVEL]. All numbers are treated as integers throughout, and therefore floored to the nearest integer after each multiplication/division. [SHOOT_FORCE], [SIZE] and [SHOOT_MAXVEL] are defined by the launcher (bow, crossbow, etc) and [SOLID_DENSITY] by the ammo material. See this thread for details and derivation: http://www.bay12forums.com/smf/index.php?topic=116151.msg3716892;topicseen#msg3716892 [^]

As a result:
1) Any bolts/arrows with [SOLID_DENSITY] between 6666 and 13333 (all metals except adamantine) will have velocity equal to [SHOOT_FORCE].
2) Bolts lighter than [SOLID_DENSITY:6666] (wood, bone, adamantine) will have velocity equal to [SHOOT_MAXVEL].
3) Since both [SHOOT_FORCE] and [SHOOT_MAXVEL] are 1000, all bolts will have velocity 1000.
4) Armor penetration (in most cases) and damage depend on bolt momentum, so bolts made of denser materials will be more effective.

Steps To Reproduce

Download the script chkproj.lua from http://www.bay12forums.com/smf/index.php?topic=116151.msg3716892;topicseen#msg371689 [^] and use it to check projectile velocities, which are given by the variable unk22. By changing [SHOOT_FORCE], [SHOOT_MAXVAL] and bolt [SOLID_DENSITY] one can quickly verify the rounding behavior.

This has also been verified by measuring deflection of bolts off armored targets. All metal bolts were found to have exactly the same rate of deflection as a function of momentum when momentum was calculated using the velocity formula described, and mass=([SOLID_DENSITY]*[SIZE])/1,000,000. See http://www.bay12forums.com/smf/index.php?topic=116151.msg3733282#msg3733282. [^]

Additional Information

This could easily be fixed by changing the velocity calculation to:
velocity=1,000,000*SHOOT_FORCE/[SOLID_DENSITY]/[SIZE]
If this is not possible, then the original calculation could be used with all numbers converted to floating point within the calculation, and then the final velocity rounded to an integer.

The effects of this bug cannot be detected without modding/hacking in the current version because all bolts have such high momenta that small differences have no noticeable impact. I have therefore marked it as trivial. However, if bolt momenta were reduced to give armor a chance of stopping projectiles (see [url=http://www.bay12games.com/dwarves/mantisbt/view.php?id=5516 [^]]5516[/url]), then this bug would become significant.

It is also possible, but I think very unlikely, that this is "intended behavior". This bug renders the [SHOOT_FORCE] parameter almost useless, as all projectiles are fired with the same velocity. If Toady wanted all projectiles fired with the same velocity, he could have just set a fixed projectile velocity rather than calculating it from [SHOOT_FORCE].

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Relationships

related to	0005516	resolved	Toady One	Absurdly Powerful Bolts/Arrows
related to	0006364	resolved	Toady One	Weight fraction not considered when calculating weapon velocities
related to	0006870	resolved	Toady One	Bolts, crossbows and other ranged weapons have excessive SHOOT_FORCE values, leading to ranged combat issues