[LT] Rated ST for bows and crossbows

[Anthony]

Originally Posted by SuedodeuS

No easy way, but Bill mentioned the energy would scale roughly with weight, and from collision rules it seems GURPS damage scales as approximately the square root of KE.

No, from collision rules damage is linear in velocity. However, bow efficiency varies with the weight of the arrow relative to the weight of the bow, which generally forces a heavier bow to use heavier arrows, and the scaling is only 1/3 in the weight of the projectile (due to how HP progression works).

[Ze'Manel Cunha]

Originally Posted by vierasmarius

Is there an easy patch to differentiate the weight and cost of these bows? Perhaps multiple the weight and cost by the BL of the rated ST, divided by some constant (20 to keep ST10 bows the same)?

If you're talking about bows made from a single piece of wood, or with the exact same design, the same exact string¥, and the same exact everything, then a good rule of thumb is to increase weight by 1/5 lbs per 5 FPS (+1 GURPS ST*) added to arrow speed.


So if a ST 7 Short Bow weighs 2 lbs, then a ST 12 Short Bow would weigh 3 lbs, and a ST 17 Short Bow would weigh 4 lbs.


*Gotta rate it somehow...

¥Of course sometimes just upgrading to a less stretchy string on a bow can increase its draw weight, or crack the bow, if it can't handle it the less stretchy string.

[SuedodeuS]

Originally Posted by Anthony

No, from collision rules damage is linear in velocity.

Kinetic energy is 0.5*m*v^2. GURPS damage is 3.5*C*v*m^(1/3)/100, with C being 2 for living, 4 for unliving, and 8 for homogenous; and m being mass in pounds per G. If we drop the constants (which are unimportant for scaling) and square damage, we have KE as m*v^2 and damage^2 as m^(2/3)v^2. This is rather close to equal, although when v is low the difference in m is more pronounced.

Originally Posted by Anthony

However, bow efficiency varies with the weight of the arrow relative to the weight of the bow, which generally forces a heavier bow to use heavier arrows, and the scaling is only 1/3 in the weight of the projectile (due to how HP progression works).

This is part of why I noted the scaling as being very rough. May we assume that a bow that is 2x heavier gets normal efficiencies out of an arrow that is 2x heavier?

Originally Posted by Ze'Manel Cunha

Gotta rate it somehow...

If we assume arrows to be homogenous objects (for HP calculations), this gives out typical 0.1 lb arrow between 3 and 4 HP (3.71 HP). Average collision damage is typically calculated as 3.5*3.71*v/100. This means each +1 corresponds to around 7.7 yards per second (16 mph) - or it would, were it not for the rule that impaling objects get half normal collision damage. This boosts our speed for each +1 to 15.4 yards per second (31 mph). It may be appropriate to disregard the half-damage rule here, in which case every +1 to ST corresponds to a +3.8 yards per second boost (every +2 is a +1 to damage).

Note this implies an ST 12 longbow flings arrows at around 70 mph, while maintaining the half damage rule (and thus having 7.7 yards/sec per +1 ST) means such arrows fly at a rate of 140 mph. I have no idea how fast an longbow flings arrows, so I can't rule which (if either; keep in mind GURPS arrow damage is probably on the high side) is more realistic.

[Anthony]

Originally Posted by SuedodeuS

Kinetic energy is 0.5*m*v^2. GURPS damage is 3.5*C*v*m^(1/3)/100, with C being 2 for living, 4 for unliving, and 8 for homogenous; and m being mass in pounds per G. If we drop the constants (which are unimportant for scaling) and square damage, we have KE as m*v^2 and damage^2 as m^(2/3)v^2. This is rather close to equal, although when v is low the difference in m is more pronounced.

The equivalent to this used for bullets is D = sqrt( KE/B ), where B is the caliber of the weapon and should vary as the 1/3 power of mass.

Originally Posted by SuedodeuS

This is part of why I noted the scaling as being very rough. May we assume that a bow that is 2x heavier gets normal efficiencies out of an arrow that is 2x heavier?

Sure. 2x mass, 2x energy, so no change in velocity, and it will do 1.26x as much damage.

Originally Posted by SuedodeuS

Note this implies an ST 12 longbow flings arrows at around 70 mph, while maintaining the half damage rule (and thus having 7.7 yards/sec per +1 ST) means such arrows fly at a rate of 140 mph. I have no idea how fast an longbow flings arrows, so I can't rule which (if either; keep in mind GURPS arrow damage is probably on the high side) is more realistic.

A modern bow probably manages around 300 fps (200 mph) but uses a fairly lightweight arrow and significantly different technology than the low tech bow; a longbow is probably under 200 fps.

[Ze'Manel Cunha]

Originally Posted by SuedodeuS

Note this implies an ST 12 longbow flings arrows at around 70 mph, while maintaining the half damage rule (and thus having 7.7 yards/sec per +1 ST) means such arrows fly at a rate of 140 mph. I have no idea how fast an longbow flings arrows, so I can't rule which (if either; keep in mind GURPS arrow damage is probably on the high side) is more realistic.

We had a couple of threads around here where we went into this, what I came away with was that basically:

Short Bows are generally 120-185 FPS, (ST 7-20). [80-125 mph]
Long Bows are generally 200-250 FPS, (ST 11-20). [135-170 mph]

You can always shoot a bow stronger than you, it just starts to wobble/tremble and reduces your accuracy as it goes past your comfort zone.

Oh, and if you're going to catch arrows you should really do it from a ST 7 Bow at 120 FPS...

[Bruno]

Originally Posted by Ze'Manel Cunha

We had a couple of threads around here where we went into this, what I came away with was that basically:

Short Bows are generally 120-185 FPS, (ST 7-20). [80-125 mph]
Long Bows are generally 200-250 FPS, (ST 11-20). [135-170 mph]

You can always shoot a bow stronger than you, it just starts to wobble/tremble and reduces your accuracy as it goes past your comfort zone.

That part, at least, works out fairly well with the GURPS standard rule of -1 skill per 1 ST below the required ST. However you determine required ST.

Originally Posted by Ze'Manel Cunha

Oh, and if you're going to catch arrows you should really do it from a ST 7 Bow at 120 FPS...

With a tennis ball or boffer thing on the end.

Alternately, you can be a chambara action hero and get to slow the scene down until the arrows tootling along at a leisurely 30 FPS, pluck it gently out of the air, and pose dramatically before everything speeds up again. :)

[Anders]

Well this is for DF, so realism is very optional. I'll eyeball some numbers and let you know what happens. The campaign won't start until autumn earliest, so...

[Icelander]

As for why weight doesn't vary with rated bow ST, I can tell you the reason for that. It was determined during playtest, with extensive research, that the individual variation between differerent bowyers or lots of wood was more significant than any variation for rated poundage at human-scale ST. In short, all longbows were between 1.75 lbs. to 3 lbs., but the correlation between the heaviest bows and the heaviest draws was weak enough so that it would not have been realistic to establish one in game rules. The weight given for bows in Low-Tech are close enough to functional averages of real examples to be fine.

Also, there are no engineering challenges involved with making bows of any draw that humans can draw. If you can draw a ST 25 bow, there's no reason why you can't make one, really. As for anything that is a special order, it is probably going to be more expensive, largely because the wood that is set aside for bow-making will usually be aimed at less heroic archers, but in a world of DF barbarians, I don't see any need to assume this. Just increase weight and cost as normal for different SMs and maybe require bows at the upper edge of the possible ST for that SM to be Fine (Materials) or add a similar CF surcharge. But that depends on the setting assumptions as much as on any rules.

Crossbows are fundamentally different in this respect. This is why I argued for statting them for their rated poundage and dissassociating them from ST entirely. Higher ST does increase crossbow weight and there are significant materials-based limits on how powerful they can get.

Ignoring this and allowing composite and self-crossbows to have any ST the character wants, for no extra cost, makes a mockery of steel crossbows and is patently unrealistic. But that's the way that Bill chose to go.

[SuedodeuS]

Originally Posted by Icelander

As for why weight doesn't vary with rated bow ST, I can tell you the reason for that. It was determined during playtest, with extensive research, that the individual variation between differerent bowyers or lots of wood was more significant than any variation for rated poundage at human-scale ST. In short, all longbows were between 1.75 lbs. to 3 lbs., but the correlation between the heaviest bows and the heaviest draws was weak enough so that it would not have been realistic to establish one in game rules. The weight given for bows in Low-Tech are close enough to functional averages of real examples to be fine.

Interesting. It might be interesting to slightly randomize bow weights, but from the sound of things just using the LT stats will probably be ideal.

Originally Posted by Icelander

Ignoring this and allowing composite and self-crossbows to have any ST the character wants, for no extra cost, makes a mockery of steel crossbows and is patently unrealistic. But that's the way that Bill chose to go.

Indeed. As it stands, the humble Crossbow is superior to any of the steel designs - equipping it with a x2.5 cranequin lets it use 2.5x the user's ST with a draw time of 50 seconds. Compare this to the best steel crossbow available, the Siege Crossbow, which only uses 1.5x the user's ST, has the same* reload time, costs 3x as much, and weighs 2x as much.

*Our modified crossbow takes as long to draw back as the siege crossbow does to reload, meaning a little time would be added to place the bolt.


EDIT: Incidentally, do you happen to still have any notes on what proper steel crossbow stats - or just the mechanical limits of wooden crossbows - would look like?

[Nikolai]

I just wanted to post a thread asking about the maximum rated ST of crossbows (and bows) and then found this one.

I find the current (obviously non-existent) rules on it very unsatisfactory. Without a limit on maximum rated ST, the four TL4 steel crossbows on p. 76 of Low Tech are unbelievably unattractive.

Originally Posted by Bruno

Leaving the only "Official" cap being the traditional 3xMinST cap.

Originally Posted by whswhs

I'm pretty sure we just assumed that the max ST for a bow of a given type was the same multiple of min ST as usual.

That is in no way official as far as I can tell. P. B270 specifically says "For a melee weapon, your effective ST for damage purposes cannot exceed triple the wapon's minimum ST. [emphasis by me]"
Almost the same in Low Tech: The description of the ST column for melee weapons on p. 64 mentions the limit of triple ST while the description of the ST column for muscle-powered ranged on p. 75 weapons does not.

So as per the rules as written, there does not seem to be any limit on maximum ST for ranged weapons.

But even if we assume that the melee weapon limit "triple ST" applies to crossbows as well: Steel crossbows would still totally suck due to their rated ST being halved for damage and range.
The TL3 Composite Crossbow could have ST 8*3=24, the Siege Crossbow could have ST 14*3=42 halved to only 21.
Which means the Composite Crossbow does an additional point of damage and has an additional reach of 90 yards.
But the Steel Crossbow is much heavier and bulkier. It costs about the same. A Windlass or Cranequin can be used both with the Composite Crossbow and with the Steel Crossbows.

So there is no way one would ever want one of the steel crossbows with the rules as written. They seem to represent technical "progress" at its worst! ;-)

Originally Posted by whswhs

The minST for a bow has nothing to do with how much damage it can inflict, and therefore cannot be based on its draw weight. I took it that minST was "can I pick up and handle a bow of this type without its being awkwardly heavy?" It's kind of an arcane question but I don't see that else it could be. Unless you want to suppose that a short bow inherently cannot have a draw weight less than X; I suppose that could be a sort of "minST," too.

According to the description for the ST column on p. 75 of Low Tech, it is explicitly the latter: "The ST score on the table for a given type of bow or crossbow is the minimum rated ST for that type."

Which I agree doesn't seem to make much sense, it would seem far more sensible to be the former ("can I pick up and handle a bow of this type without its being awkwardly heavy?").