Gear Rifles - design assistance requested

[Varyon]

Originally Posted by Anthony

The problem with the chain idea is that you have to move the entire chain to move the projectile, which means you have a large efficiency loss unless either the chain is very light, or you can keep the chain spinning between projectiles.

Hmmm... an excellent point. Two of the good reasons to use a chain (which I envision as a continuous loop on each side) are that the links themselves give something for the teeth of the gears to hook into, and that the cup can "slip" through some of them when it strikes the brake, so that the gears don't have to come to a sudden stop (which could damage them - and probably whatever chain/string is being used). For a string setup, which should markedly reduce the extra weight that needs to be accelerated, I feel we wouldn't want a continuous loop, but rather have one end of the string firmly attached to a spinning reel that would wind up the string. The "slip" would still be possible, by extending the string past the cup and tying knots in it (with a sufficiently large one at the end to make certain the cup doesn't slip off). However, once it's slipped past some of the knots, how would we get it back in front of them so it can slip next time?

Thinking on this, what if the tab (for pulling the cup back) isn't actually attached to cup, but rather to the ends of the strings? To pull it back into position, we have to pull the knotted portions of the string back through the cup. A large knot that it can't slip past, right in front of where the cup is meant to be, means when we pull the tab back, we pull the string back into proper position to allow slipping on impact, with the cup where it needs to be to be loaded. Does that sound feasible?

Originally Posted by thrash

Sounds as if you could be describing a scaled-up Red Ryder BB gun (HT, pp. 88-89). Skip the gears; use air as a working fluid. Put the piston under the barrel and back it with a strong coiled spring. Since you don't have to emulate a lever-action, you can increase the strength of the spring -- say, brace the butt on the ground and use two hands to cock it.

Not as delightfully clock-punk as a gear rifle, but certainly plausible. Real-world metallurgy and gun-smithing weren't up to the strengths and tolerances required, but you don't seem concerned about that.

Containing highly-compressed air - particularly containing it for a decent chunk of time (these weapons are meant to be able to be loaded, then go at least several hours without firing, if needed, like firearms) - seems unfeasible to me when limited to ~TL3-4 materials. While I'm certainly not wanting strict scientific rigor, it makes more sense to me that superscience (well, cinematic anyway) methods could yield clock-punky mechanical batteries than that it can contain air compressed to the many atmospheres of pressure needed to have a weapon that is competitive with muskets. Probably just my own idiosyncrasies. Also, with regards to clockpunk, [tantrum]IwantitIwantitIwantitIwantit!!![/tantrum]

Originally Posted by Fred Brackin

We already have an Orichalcum Spring Gun in DF6. It's basically a ST12 Crossbow with 8 shots but without those inconvenient arms.

Sadly, I don't have that DF book. But it does sound like the same general concept, yes (but I don't want to be reliant on fantastical materials... particularly given an ~indestructible material like orichalcum may well not even exist in Oubliette, not even within the dungeons).

[Donny Brook]

I wonder if a grosser movement than cranking could be a faster way to charge the weapon, like a long lever or a pull-cord.

[thrash]

Originally Posted by Varyon

Containing highly-compressed air - particularly containing it for a decent chunk of time (these weapons are meant to be able to be loaded, then go at least several hours without firing, if needed, like firearms) - seems unfeasible to me when limited to ~TL3-4 materials.

Not meaning to quibble, but the point of the "Red Ryder" piston mechanism (vs. historical air guns, which did use a reservoir) is that the energy is stored in the spring, not in compressed air. You increase the pressure delivered by making the piston much larger than the bore. Another benefit is that the pressure is consistent, rather than diminishing as the reservoir empties.

Again, a spring (particularly a coiled spring) this strong isn't historically accurate, but it is probably minimally invasive as unobtainium goes. Maybe they have to be harvested from Hell Gnome traps...

[Varyon]

Originally Posted by Donny Brook

I wonder if a grosser movement than cranking could be a faster way to charge the weapon, like a long lever or a pull-cord.

I suspect not. A goat's foot takes 20 seconds to use and increases effective ST by 30-40%. A windlass takes 9 seconds to wind up the crossbow, and increases effective ST by 50%. Overall, I think using the two ends up taking a comparable amount of time, but that's because a windlass takes longer to attach and detach than a goat's foot. So I think winding is probably the most efficient. Note also that most devices that use muscle power to charge a battery also use cranks (some instead have you shake them, but personally I feel the winding ones work better).

Originally Posted by thrash

Not meaning to quibble, but the point of the "Red Ryder" piston mechanism (vs. historical air guns, which did use a reservoir) is that the energy is stored in the spring, not in compressed air. You increase the pressure delivered by making the piston much larger than the bore. Another benefit is that the pressure is consistent, rather than diminishing as the reservoir empties.

Again, a spring (particularly a coiled spring) this strong isn't historically accurate, but it is probably minimally invasive as unobtainium goes. Maybe they have to be harvested from Hell Gnome traps...

Ah, I misunderstood you. Looking it up, it looks like you could base it on a fire piston, but with a narrow tube at the end the air can escape through... once it's accelerated the bullet wedged in there. It would still need to be something that you can charge over the course of several seconds (to generate enough force to propel the projectile at a higher effective ST), but seems workable, still with something soft to cushion the impact of the piston striking. It doesn't have all the clockpunk accoutrements, but has a certain simplicity that is enticing. And it makes rifling as simple as, well, just rifling the barrel. You do need the bullet to be largely flush with the walls of the barrel (to prevent air from escaping around it), but soft lead (or a softer wax jacket) should help with that. I'm not sure a flechette would be possible, although perhaps if it's contained within a sphere of wax? It seems like that would let it fit snugly in the barrel, then when it impacted its target the wax layer would be left behind, with the flechette simply cutting its way out and into the target. It also seems like a longer barrel wouldn't be as useful - for firearms a longer barrel means more of the powder burns before the bullet leaves, but this has all the pressure generated in an instant, going down as the bullet travels down the barrel. Perhaps this mechanism is (somehow) less efficient, but is used for pistols and short rifles, where its inability to benefit much from a longer barrel isn't an issue? I'll have to think on it.

[thrash]

Originally Posted by Varyon

I'm not sure a flechette would be possible, although perhaps if it's contained within a sphere of wax?

Or just a flat plate plug as a sabot. Wax would add weight and drag and thus slow down the round.

It also seems like a longer barrel wouldn't be as useful - for firearms a longer barrel means more of the powder burns before the bullet leaves, but this has all the pressure generated in an instant, going down as the bullet travels down the barrel.

Right -- but as long as the bullet is still plugging the barrel, it continues to get some residual acceleration from the pressure behind it even as that pressure drops. Ideally, I imagine you'd need the pressure to be above (1 atm + friction + drag at muzzle velocity) as the bullet exits the muzzle. That, in turn, should be a function of the ratio between volumes of air in the piston (before firing) and the barrel (after). Since both of these depend (in part) on the overall length, I suspect there's an optimal length for any given caliber.

[Varyon]

Now that I've slept on it and am beyond my initial knee-jerk "But mine's better!" reaction, I'm really warming to the idea of an air piston.

For design, I'm thinking the piston and its chamber (which it never fully exits while in use) should be made of metal, with a soft leather stopper at the end of the piston, serving both to form an air-tight seal (which introduces more friction, but I feel that's necessary) and soften the impact when the piston reaches the end of the chamber. The piston, like the cup before it, would have a tab that comes out of the stock, but on the side rather than the top, for pulling it back into position after shooting. There would still be a safety lever, but this time it would be for being able to pull the piston back with ease (you disengage whatever pushes the piston forward - I'm thinking a pair of gears, with the piston having slots matching up to their teeth - from the battery, so it slides back without resistance, then re-engage it so you can shoot again; incidentally, I think a character with ST matching that of the weapon would be able to pull the piston back while it's still engaged, recharging the battery for one shot at the same time). I'm seeing reloading as a four second process - Ready to flip the safety and pull the piston back into position; Ready to draw a bullet; Ready to flip open the cover, drop in the bullet, and replace the cover; and a final Ready to reshoulder the weapon and flip the safety to prepare it to shoot again. Fast Draw reduces this to 3 seconds; the Rapid Reload Perk further reduces it to 2 seconds. This assumes your battery still has shots left, of course - otherwise you've got to draw and attach the crank, wind it up, detach and stow the crank... and then see the rest of the party is already looting the corpses.

I'm a little concerned about the air reservoir, but I feel I probably shouldn't be. When the character pulls the piston back, the only air supply to the reservoir is from the barrel itself, which has to pull the air from outside. For a character with Rapid Reload, we're probably looking at less than a second between the character starting to pull back the piston and blocking off the air supply with a bullet. Is that likely to be enough time, or should the chamber have air holes just in front of the piston when it's in ready position? Might that be a good idea anyway, in case the character goes out-of-order and loads the bullet before pulling back the piston?

Originally Posted by thrash

Or just a flat plate plug as a sabot. Wax would add weight and drag and thus slow down the round.

I worry about the flechette maintaining its orientation in the barrel without something to stabilize it to the sabot, but feel when it exits and the sabot tears off (due to it having so much higher air resistance), whatever stabilized it is going to try to hold onto it, causing it to get deflected from what should be its path. Perhaps something like a flat plate, with thin rods going between the fins? That would hold up the flechette so it doesn't get out of proper orientation, but simply slide off when it hits the wall of air outside the barrel. If this would still be likely to distort flight (due to the plug not falling off evenly), you could have a detachable brake at the end of the barrel that catches the sabot, letting the flechette through; this would slow down the reloading time when using flechettes, as you'd need to pull off the brake and let the spent sabot fall out and put it back on, in addition to the other steps. This is probably doable with a two Readies (reduced to one with Fast-Draw) - tilt the weapon down, pull off the brake, let the sabot fall, then reattach the brake. How might this be sped up? Might it work to have a brake that can swing open, with springs to close it again and a lanyard going back to the base of the weapon? That seems like it would be one additional Ready (tilt the weapon down, pull back the lanyard while pulling back the piston, then release the lanyard for the brake to swing closed once the sabot falls out), or no extra time with Fast Draw. Is it feasible that something that could be swung open fairly readily would hold fast when the sabot struck it?

For the sabot itself, I think a soft wood would work alright. One possible concern would be heat, given we're basically looking at something akin to a weaponized fire piston, but I suspect (given the projectile is going to be accelerating even before the piston strikes the stop) the temperature won't get high enough to be an issue - at most, the back of the sabot might get a bit charred, but I'm thinking these things are single-use anyway.
EDIT: Gear rifles would have to be designed specifically to be able to shoot sabots, as you'd need a different shape of barrel cut-out to accommodate such, and probably something at the end for the brake to attach to. Such weapons would still be able to shoot normal bullets, of course, so long as the brake is removed before doing so (otherwise the bullet is likely to break the brake).

Originally Posted by thrash

Right -- but as long as the bullet is still plugging the barrel, it continues to get some residual acceleration from the pressure behind it even as that pressure drops. Ideally, I imagine you'd need the pressure to be above (1 atm + friction + drag at muzzle velocity) as the bullet exits the muzzle. That, in turn, should be a function of the ratio between volumes of air in the piston (before firing) and the barrel (after). Since both of these depend (in part) on the overall length, I suspect there's an optimal length for any given caliber.

Every doubling of barrel length would halve the average amount of pressure during the acceleration. That makes a longer barrel a zero-sum game - doubling barrel length doubles the distance over which the force operates, but halves the average force (with constant area, pressure simply becomes force), and given kinetic energy is equal to force times distance, that gives us constant KE. Considering friction and drag, that actually indicates a longer barrel results in less velocity. Am I missing something? Firearms get to avoid this issue because their propellant continues to burn (offsetting the pressure loss of expanding to fill the barrel), but a gas-piston rifle has no such luck. As I mentioned above, the projectile should start accelerating before the piston strikes home, due to the constantly-increasing pressure, but once the piston has struck and we reach peak nominal pressure, any further barrel length is a net loss. It seems to me the bullet wouldn't travel very far before this happened... but perhaps I'm mistaken?

Or should I just flip physics another middle finger and say "I want longer barrels to result in more velocity, so that's what's gonna happen, and no more lip from you, Newton!"

EDIT: Just to get a glimpse, I decided to plug the damage for a "typical" gear rifle - 2d-1 pi, with a 10mm bullet - into DouglasCole's damage equation, to see how fast that bullet would be going as it would hit this velocity immediately following the piston striking home. The equation, for those playing at home, is Damage = (KE/cal^0.4)^0.5 * 0.6, with Damage in points (and corresponding to the average - 6 in this case), KE in Joules, and cal being the caliber in mm. That's 251 J (for about 63% efficiency, given it takes 4 seconds for an ST 10 person to wind, and said person can generally output around 100 W*). A lead sphere that is 10mm in diameter would mass 47.6 g, or 0.0476 kg. KE = 1/2 m*v^2, for a muzzle velocity of 103 m/s. Given the bullet starts at rest (velocity 0), that means the average velocity while it traveled down the barrel was 51.5 m/s. I wanted this rifle to have a 1 yard barrel; let's just call it 1 meter for simplicity. This indicates the piston took roughly 0.02 seconds to ram home.

Honestly? I think that works. So, no middle finger for physics, and sorry for calling you out, Newton, but I think this all works. I'll need to think on how this would impact optimal barrel length for other BL's - and projectiles... and then decide if that has the game effects I like, or if I should abandon all that. One thing this indicates is that clay bullets are going to see a damage reduction because rifles meant for firing lead bullets are too short for them (a 10mm clay sphere would mass somewhere around 5 g, for a muzzle velocity of 317 m/s, and average velocity of 158.5 m/s; with a 0.02 second power stroke, that calls for a 3.17 m barrel).

*This is sustained output, resulting in the character losing FP at something like 1 FP per hour (comparable to hiking). Someone trying to wind a gear rifle during battle is probably more akin to jogging than hiking, for doubled output (going All Out is akin to sprinting, for a further doubling of output). So, if we assume it would take 4 seconds for an ST 10 person using Readies in combat to wind up an ST 20 gear rifle, that indicates it's actually storing 800 J, for only around 30% efficiency.

[Anthony]

Originally Posted by Varyon

Every doubling of barrel length would halve the average amount of pressure during the acceleration. That makes a longer barrel a zero-sum game - doubling barrel length doubles the distance over which the force operates, but halves the average force (with constant area, pressure simply becomes force), and given kinetic energy is equal to force times distance, that gives us constant KE. Considering friction and drag, that actually indicates a longer barrel results in less velocity. Am I missing something?

Yeah. Pressure isn't constant in the barrel, so you have the same pressure at 6" away from the bullet entry point regardless of final length. Length typically doesn't give you really large velocity increases, but it's non-zero. In principle there are methods of introducing gas from the sides of the barrel that result in substantially higher velocities, but hard to do without electronic switches.

[Varyon]

Originally Posted by Anthony

Yeah. Pressure isn't constant in the barrel, so you have the same pressure at 6" away from the bullet entry point regardless of final length. Length typically doesn't give you really large velocity increases, but it's non-zero. In principle there are methods of introducing gas from the sides of the barrel that result in substantially higher velocities, but hard to do without electronic switches.

Ah, I think I see what I'm missing. For simplicity, let's assume our projectile doesn't start moving until we reach peak pressure. It is some distance, D, from the base of the barrel, and in the space between we're at peak pressure, generating a peak force, F. Because the cross sectional area of the barrel is constant, the force scales linearly with pressure. This starts accelerating the bullet. At distance 2D (total distance traveled of D), force has dropped to F/2, but average force between D and 2D would be equal to the average of F and F/2, or 0.75F, for kinetic energy equal to 0.75DF. At distance 4D (total distance traveled of 3D), force has dropped to F4, but average force between D and 4D would be equal to the average of F and F/4, or 0.625F, for kinetic energy equal to 1.875DF. It looks like you rapidly reach a steady state where each additional D worth of length adds +0.5DF to kinetic energy (technically, +0.5DF per +D is the limit), so in terms of the % increase this keeps dropping, but it is indeed a net gain indefinitely (although eventually you're going to reach the point where losses from friction and drag cancel it out).

Looking at our example rifle - 2d-1 pi, 10 mm, 1 meter long barrel - and assuming the projectile is located 10 mm from the piston chamber (so D is equal to projectile diameter), we're at 100D, and our kinetic energy is at 49.995DF. Setting this as exactly 6 damage (2d-1), and rounding normally (so 6.5 is 7), we need to go to 1.18m for +1 damage, 1.57m for +2 damage, and 2.01m for +3 damage. Meanwhile, shortening our weapon to 0.85m has no effect on damage, going as short as 0.57m is -1, 0.35m is -2, and 0.18m is -3. If instead round down (so 6.999 is still 6), we need to go to 1.37m for +1, 1.78m for +2, and 2.25m for +3; meanwhile, -1 to damage can be as short as 0.7m, -2 can be 0.45m, and -3 can be 0.26m.

I'll play around with the values and see what falls out. Thanks!

EDIT:
Me: "I'm not aiming for scientific rigor."
Also me: "Let's integrate the pressure curve to see how KE and damage change with the length of the barrel!"

[Varyon]

Took a bit to get back into messing with this, with how much of a downer Real Life has been recently (if you don't live under a rock, you probably know what I'm referring to; if you're currently literally living under rock because some a**hole looked at your country and cried "IwantitIwantitIwantit," you definitely know what I'm referring to), but at least for now, back to messing around with it. Things are coming together, but I'm a bit stuck where I always was with the firearm design - MinST. This seems like it would be the greater of whatever ST is needed to hold the weapon in place (I'm currently thinking one-handed firearms can be up to BL/2, while two-handed ones can be up to BL), and whatever ST is needed to manage recoil. That latter is the sticking point. I've read that some old British guidelines suggested no more than 20 lb-force of recoil for a service rifle, and that most modern service rifles are around 15 lb-force of recoil, so I'm tentatively saying something like the above - BL/2 for one-handed firearms, BL for two-handed ones. The issue is... I don't know how to calculate this for my gear rifles. I can work out the recoil energy for them, provided I ignore the secondary recoil from accelerating the working fluid (I think this can be done safely in this case). After messing with the math a bit*, it looks like the recoil energy is equal to the muzzle energy multiplied by the mass of the bullet, divided by the mass of the rifle - Rk = Bk*Bm/Rm. But that gives me energy, and the values I have to work with to set "Is this wieldable?" are in terms of force. Now, given that kinetic energy is equal to force times distance, I can get force by dividing by distance... but what distance is at play here? The length of the barrel? How far the rifle moves back while dumping its energy into the shooter's hands/shoulder? I'm thinking it's the latter but... what would that actually be, assuming a competent shooter with minimal or no padding? How much would it change if the shooter is wearing a gambeson or similar padding?

*For those playing along at home (and because I'd like someone to check my math to make certain I didn't screw something up), the variables of note are Bm (mass of the bullet), Bv (velocity of the bullet), Bk (muzzle energy), Rm (mass of the rifle), Rv (velocity of the rifle), and Rk (recoil energy). We start with conservation of momentum, which gives us
Bm*Bv = Rm*Rv (there should be a negative sign here, given velocity is a vector, but I only care about absolute values, so we ignore that)
We need kinetic energy in the equation, so we use
Bk = 0.5*Bm*Bv^2
Rk = 0.5*Rm*Rv^2
I opted to solve this for Bm and Rm, so that I could avoid needing to bother with square roots
Bm = 2*Bk/(Bv^2)
Rm = 2*Rk/(Rv^2)
Substituting these into the momentum equation (Bm*Bv = Rm*Rv), we get
2*Bk*Bv/(Bv^2) = 2*Rk*Rv/(Rv^2)
Which simplifies down to
Bk/Bv = Rk/Rv
And solving for Rk gives us
Rk = Rv*Bk/Bv
Of course, we don't know what velocity our rifle is getting accelerated to, and frankly we don't care. Fortunately, we can solve our momentum equation for Rv, giving us
Rv = Bm*Bv/Rm
Substituting this in with our recoil energy equation, we get
Rk = (Bm*Bv/Rm)*Bk/Bv
Which simplifies down to
Rk = Bk*Bm/Rm

[Anthony]

Originally Posted by Varyon

The issue is... I don't know how to calculate this for my gear rifles. I can work out the recoil energy for them, provided I ignore the secondary recoil from accelerating the working fluid (I think this can be done safely in this case). After messing with the math a bit*, it looks like the recoil energy is equal to the muzzle energy multiplied by the mass of the bullet, divided by the mass of the rifle - Rk = Bk*Bm/Rm. But that gives me energy, and the values I have to work with to set "Is this wieldable?" are in terms of force.

If it's expressed in units of force it's almost certainly in error, the peak instantaneous force for a .223 rifle is in excess of 2,000 lb and that's a relatively low recoil rifle. I suspect the sources you were looking at were actually giving foot-pounds, which is a unit of energy.