Tuesday, June 6, 2017

The Hurt Locker: How Tough is Wood?


Guest Post by Euan Hastie

So how touch is wood anyways? In GURPS terms? First up a quick reference table for the GM in a hurry.


Species of Timber
DR per inch of thickness
Buloke, Quebracho, Quebracho Colorado, Lignum Vitae
7
Brazilian Tiger Mahogany, snakewood
6
Ebony, Ipê, Olivewood, Ironwood
5
Composite Bamboo, Bloodwood, Live Oak, Southern chestnut, Turpentine tree
4
Purple heart, Mesquite, Rosewood, Tigerwood, Hickory, Pecan
3
English Oak, Ash, Maple, Teak, Siberian Larch, American Beech
2
Walnut, Mahogany, Radiata Pine, Douglas Fir, Basswood, Chestnut
1
Balsa, Cuipo, Cottonwood, Northern White Cedar, Duru
0.5 or less


How these numbers were determined.
Basic set mentions that wood is either DR 2 (Damage to Objects, p. B483) or DR 1 per inch of thickness (Structural damage table, pg 558) Most or all of us will know that wood comes in a wide range of durabilities however. A question on the GURPS Discord server “How much protection does a luxurious table provide?” sparked my interest and I did some research. There is a commercial measure of wood hardness known as the “Janka hardness test” which records how much force is required to drive a .444 inch (11.28mm) BB .222 inches (5.64mm) into the wood. I looked up the force of a similar sized object that had a known GURPS damage, a .45 ACP, from this I was able to calculate how gurps damage related to force in this situation. Using this data the following DRs for various type of wood can be determined. This list is not definitive as there are about 60,000 species of tree in the world, It is however hopefully illustrative.

Timber
DR per inch
Type
Buloke
7.4
Australian hardwood
Quebracho
6.9
Tropical hardwood
Lignum Vitae
6.6
Tropical hardwood
Snakewood, Brazilian tiger mahogany
5.7
Tropical hardwood
Puriri
5.6 (estimated)
Subtropical hardwood
African pearwood, Ipê
5.4
Tropical hardwood
Grey Ironbark
5.3
Austrailian hardwood
Ironwood, Ebony
4.8
hardwoods
Live Oak
3.9
Subtropical hardwood
Mesquite
3.4
hardwood
Osage Orange
3.0
hardwood
Purple Heart, Jarrah
2.8
Tropical hardwood
Hickory,
2.7
Hardwood
Yew
2.3
Softwood
Hard maple, Sugar maple
2.1
Hardwood
Ash
1.9
Hardwood
Teak
1.7
Tropical Hardwood
English Oak
1.6
Hardwood
Mahogany
1.2
Hardwood
Pinus Radiata
1.1
Softwood
Douglas Fir
1.0
Softwood
Balsa
0.1
Hardwood (Yes)

Notes
Grey Ironbark is the hardest wood mentioned as suitable for bows. Osage Orange is also suitable for bows.

Quebracho translates as “Axe breaker”.
Ebony was used in ancient Egypt.
Hard Maple is favored for pool cues.
Many species are known as Mahogany.
Some of the timbers mentioned are plantation grown others are old growth.


Fictional Timbers
In sci-fi, the Deathstalker books have “ironwood” which is too strong to be cut with steel, The Night's Dawn trilogy has Mayope another incredibly hard timber that comes from huge trees. The DR per inch for these is about 80 and 30 respectively. The tree (Bob) that grows out of Harold’s head in Fallout would have a DR of 1.8 per inch.

Compared to sci-fi fantasy has a larger range of fictional timbers, however these seem to be far outnumbered by telepathic, animated and sentient varieties. Discworld has sapient Pearwood which is completely resistant to magic and quite hard, DR 16 per inch. The Earthsea books mention Arhada a species of long lived (possibly) Oak, DR 8 per inch. Middle earth has several trees mentioned, Mallorn loved by the Elves would have a DR of 8 per inch as well as many other beneficial properties.


Other variables
  • Green wood is between 69% (softwoods) and 80% (hardwoods) as hard as seasoned (dry) wood. 
  • Wood grown in managed plantations is generally softer than wood harvested from old-growth (wild) trees. This is down to primarily growing conditions and age. Exact numbers are hard to find though, at a guess plantation grown wood will be 80%-90% as hard as old-growth timber. It is of a more consistent quality and is easier to work with however.
  • Smaller objects can be made of more specific pieces of timber, as such harder compression or reaction wood which while harder has less tensile strength. As there are many variables involved assume an improvement of hardness of no more than 10%. 
  • Variability with a species, not all trees grow the same way, this results in some trees containing harder wood than others of the same species. Going off the density range of one species of New Zealand hardwood this has the effect of changing the hardness by 10% in either direction. In general timbers have a range of up to 20% though a smaller range is more likely in harder timbers. Statistically though there is probably a very small amount of even harder wood available. It is up to the GM’s discretion as to how much harder it is. An elven master forester or the like would the person to locate wood like that. 
  • Grain, some trees have a different internal structure than others, Puriri timber for example has interlaced fibres. Supposedly buckshot can ricochet off Puriri[2], as a result it saw use as palisades during the New Zealand wars. 
  • The Janka test covers woods that are used as timber or lumber commercially, some trees that are unsuitable for milling may contain harder wood. 
  • Magic, the spell Essential Wood (GURPS Magic, p. 164) triples the DR, HP and possibly the density of wood. The standard pattern for materials with magical properties in GURPS is the triple the beneficial numbers. 
  • The type of wood selected for weapon and tool handles will be chosen based on more criteria than just how tough it is. It should be noted that Brazilian Tiger Mahogany is reputed to be good for handles. 
  • When harvesting wood it is important to remember that only a percentage of a tree is heartwood, the rest is softer sapwood. The exact ratio varies too much to be generalised. But old growth trees will likely have more. 
  • Wood can soften with age and poor care, as a GM feel free to set any wood to a lower toughness as a result. In general stories about wood hardening with age are more a case of the hardest wood lasted the best.
  • Sometimes more than one species of timber can be sold as the same wood leading to confusion. 
  • Density, compared to DR 1 woods the densest woods are up to 2.5 times as heavy by volume.

Maths
A .45 ACP pistol delivers 400 ft-lbf (542 J) of energy[1]. Using the average damage (7) of a .45 ACP pistol this results in 1 GURPS damage being equal to 57.1 ft-lbf (77.4 J) when applied through a .45 sized object.
The energy required to penetrate the wood to a depth of an inch with a .444 sized object can be calculated from the force given in the Janka Hardness test.

lbf * 0.083 equals the energy required to penetrate an inch of wood with a .444 diameter object in Foot pound-force (Ft-lbf).

N * 0.0254 is the energy required to penetrate an inch of wood in Joules (J).

By referring to the Janka hardness test we can get the relative hardness of various timbers and work out the damage required to penetrate an inch of timber. It is 0.0003281654 times the newtons on the Janka test or 0.001453590 times the lbf.


Density and Hardness

There is a correlation between the density of timber and how hard it is. It is safe to assume all woods with a DR higher than 4 will sink when placed in water. The density of seasoned timber is measured as its specific gravity at 12% moisture content (G12). To approximate how hard a timber is based on its specific gravity at 12% moisture content use the following calculations.

        Softwoods, Hardness (lbf) = 2,560(G12/(1+0.162G12)). 
        Hardwoods, Hardness (lbf) = 4,090(G12/(1+0.162G12))


Metals
The Brinell Hardness number is a similar test used for metals for those who are interested.


Armor
Pyramid #3/52 uses wood as a material to construct armor, it lists oak or teak as the species used to achieve a DR of 2.


Deadly Spring Damage Calculations
“The Deadly Spring” (Pyramid #3/33: Low-Tech) has another formula for turning real world kinetic energy into damage, I’m not going to reproduce it here but I will use it to show a slightly different range of values. These calculations also move the typical hardness of wood up to DR 2 per inch but reduce the overall range compared to the earlier calculations.

Species of Timber
DR per inch of thickness
Buloke
5
Brazilian Tiger Mahogany, snakewood, Quebracho, Quebracho Colorado, Lignum Vitae, Ebony, Ironwood, Ipê, Olivewood
4
Composite Bamboo, Bloodwood, Live Oak, Southern chestnut, Turpentine tree, Purple heart, Mesquite, Rosewood, Tigerwood, Hickory, Pecan
3
English Oak, Ash, Maple, Teak, Siberian Larch, American Beech, Walnut, Mahogany, Radiata Pine, Douglas Fir
2
Basswood, Chestnut, Balsa, Cuipo, Cottonwood, Northern White Cedar, Duru
1



Footnotes
[1]Douglas Cole’s spreadsheet puts the number a little higher at closer to 450 f-lbf if so the calculations are out by 12.5%. 64.3 f-lbf (87.2 J) per point of damage. DR equals 0.000291284 times the Janka rating in Joules instead.

[2]I can’t find a source for this, but I have seen it mentioned several times, from personal experience I can attest that bird shot richocetes from a 90 year old Puriri fence post at close range (<1m).


References

Wikipedia Janka Hardness test: Estimating Janka Hardness from specific gravity for tropical and temperate species

Michael C Wieman and David W Green, USDA Research paper FPL-RP-643.

7 comments:

  1. Sweet article, but the tables aren't showing up (Firefox 52.1.2).

    ReplyDelete
  2. Black table and text on black background. Even less pleasant to try to read than the murky blue text.

    The ideas look good, though.

    ReplyDelete
  3. You had me at "Essential Wood"

    Sorry dick jokes are too easy to pass up

    ReplyDelete
  4. Hmmm. Don't know why it did that. I fixed it I think.

    ReplyDelete
  5. Can't believe I'm just now coming across this post. Now this is some crunch I can believe in!

    While I haven't studied to hard on the subject of wood armor from what I know of how armor is figured in GURPS in general these numbers look good. GURPS also makes the correlation between density and hardness (in fact most of the woods listed in GURPS books have a DR roughly equal to their density). So yeah man, good stuff.

    ReplyDelete
  6. I just checked my data with an incredibly unscientific "Wack it with an axe test" Puriri sap wood vs Pinus radiata. The average depth of the cuts was 4.5mm (puriri) vs 19.3mm (pine) so the ballpark is about right.

    ReplyDelete