[High-Tech] Grapeshot rules

[Icelander]

While trying to use the Multiple-Projectile Loads for TL3+1 mechanical artillery, I came across a significant oddity. The rules for grapeshot specify range in relation to the shot diameter, not the original range of the cannon.

This means that if we take a historical cannon, such as the Napoleon 12-pounder and load it with a historical grapeshot load (9 cast iron balls of 1.12 lb and 2.06 inch diameter) we get a higher maximum range for the grapeshot than round shot from the same gun.

The listed maximum range for the Napoleon is 2000 yards. Theoretical maximum range is 3,100, but the lack of elevation makes that impractical.

Now, this does not appear to square with the fact that our historical grapeshot round comes out to around 250/2500 in range. A gun firing one big bullet ought to outrange the same gun firing nine smaller ones.

Seeing as this oddity holds true for pretty much all grapeshot loads at low TLs, I'm reluctant to use these rules as the basis for any system for mechanical artillery rounds.

[RyanW]

I would suggest that range would be no more than normal range * (D/B)^2, where D is the diameter of the shot and B is the bore of the weapon.

This would give your Napoleon a max range with canister of about 1300 yards.

[Icelander]

Originally Posted by RyanW

I would suggest that range would be no more than normal range * (D/B)^2, where D is the diameter of the shot and B is the bore of the weapon.

This would give your Napoleon a max range with canister of about 1300 yards.

What's that formula based on?

Does it have general applications or just work at or around the velocity and projectile design of cannon?

[Anthony]

The maximum range of grapeshot is normally a function of air resistance, because with very few exceptions air resistance matters before gravity matters. If for some reason you are using grapeshot in a very low velocity weapon, I'd probably just limit grapeshot to having no more range than the base weapon.

[Verjigorm]

Originally Posted by Anthony

The maximum range of grapeshot is normally a function of air resistance, because with very few exceptions air resistance matters before gravity matters. If for some reason you are using grapeshot in a very low velocity weapon, I'd probably just limit grapeshot to having no more range than the base weapon.

Wouldn't the lower mass of the lower projectiles mean they lose their momentum more quickly than the large ball? After all, the single large ball would be receiving the lions share of the initial impulse from firing, while the smaller multiple balls would recieve less energy. The greater diameter of the large ball would to some degree be offset by it's mass providing greater inertia, correct?

[Anthony]

Originally Posted by Verjigorm

Wouldn't the lower mass of the lower projectiles mean they lose their momentum more quickly than the large ball?

Smaller projectiles have more air resistance compared to their mass, and thus shorter range. The existing grapeshot rules account for this. The problem is only with super-low velocity weapons.

[RyanW]

Originally Posted by Verjigorm

After all, the single large ball would be receiving the lions share of the initial impulse from firing, while the smaller multiple balls would recieve less energy.

Well, if the solid shot has X joules, and the breech is sealed just as well with canister as with solid shot, that means the canister round will have X joules. If we assume that the canister weighs, in total, the same as the solid shot, it will leave the barrel at (roughly) the same velocity.

Once they are going down range, the smaller balls will experience acceleration due to drag proportional to m^(-1/3) or d, where m is the ratio of mass, and d is ratio of diameter, to that of a full bore projectile. My formula models that, probably poorly. Douglas Cole would be the guy to ask about stuff like this.

[RyanW]

Originally Posted by Icelander

Does it have general applications or just work at or around the velocity and projectile design of cannon?

Actually, I just realized I copied the formula I came up with wrong. Replace square with square root (i.e. normal range * (D/B)^0.5).

I assume that grapeshot will leave the barrel at about the same velocity as solid shot. Since each projectile has (D/B)^3 mass and (D/B)^2 drag, it will experience B/D acceleration, and so <mumble, mumble> (D/B)^0.5 times range.

Honestly, it gives range less than solid shot, a scale that resembles a physics equation, and results that don't look hideously off.