[40k] Siege of Vraks, Earthshaker stats

[Raxmei]

This is from Imperial Armour 5, Siege of Vraks

The Earthshaker is the Imperial Guard's standard artillery piece. It is a 132mm calibre weapon, capable of firing a 38kg shell over 15kms at a velocity of 814 mps. So a shell fired to maximum range would take 19 seconds from firing to impacting.

I'm not the best artillerist in the world, but to me it looks like those numbers were generated for an elevation of about 15 degrees. A more sensible trajectory could get you 15km with a much lower muzzle velocity, or using the given velocity double the given maximum range.

The cannon itself is the model of reliability and consistency. It uses its standard five powder charges, but this can be increased with the addition of charges six and seven. This will increase the range at the risk of extra wear and stress on the gun itself. Firing higher charge shots induces considerable strain and erosion on the barrel and the firing chamber, so that the breach seal fails, drastically reducing the gun's velocity and increasing the risk of misfire. Because of this, the use of higher charges must be authorised by higher command, and the firing is recorded on each gun. No gun may fire more than twenty overcharged rounds.

Correct in principle, but the effect of overcharged rounds seems exaggerated. Might be AdMech conservatism, or maybe those last two increments are just really big.

[andrewgpaul]

Can you explain how you calculated the angle? To me, the flight time is simply 15,000/814; the "velocity of 814mps" is simply the range divided by flight time. The "true" velocity appears to be unknown, as is the angle; it could be firing at a shallow angle, with a true shell velocity slightly higher than 814m/s or with a higher, more curved trajectory with a significantly higher shell velocity.

[Raxmei]

I took 814 as the muzzle velocity, since 15000m/814m/s does not equal 19s. There's another approach that you can take if you think 814 is just the horizontal component, but it requires you to assume a value for g. You have a flight time of 19s, which with a given value for g gives you an initial vertical velocity. A shot at 45 degrees with a horizontal velocity of 814 m/s that takes 19s to hit the ground would only work out if g= 86m/s/s. That fails the sanity test, IMO. My initial calculation of 15 degrees at muzzle velocity 814m/s works out to a nonlethal g.

[Raxmei]

Found out this computer has a scientific calculator. 814 m/s horizontal component, 19s flight time, and earthlike gravity gives you a vertical component 93 m/s and an elevation of 6.5 degrees. Again, a bizarrely flat trajectory.

[Steel]

For a ballistic particle fired on a flat plane at angle u with speed v, in the absence of air resistance and with (uniform) local gravity, g, we obtain

range = (v^2/g)*Sin(2u)

and hence

time of flight = range/(v*Cos(u)) = v*sin(2u)/(g*Cos(u))

= 2(v/g)*Sin(u)

so if we're on an earth like planet and g = 10m/s^2, then with v = 814m/s and range = 15km

sin(2u)=0.226

so u = 6.5 degrees...

This then gives a time of flight of... 19 (~18.5) seconds!

For a range of 15km the lowest muzzle velocity needed is about 390m/s, obviously increases if there is air resistance.

Using an elevation of 15 degrees gives a time of flight of ~42 seconds, neglecting air resistance, so it is impossible that it is elevated that high, unless the muzzle velocity is significantly higher, as introducing air resistance will increase the time of flight quite a bit.

This all seems odd that an artillery piece has to fire practically flat, and I'll bet nobody did any numbers here, as they cant actually fit reality...

[Raxmei]

Yeah, 15 degrees gives you a rather uncomfortable 21 m/s/s for g. Really wish I wrote more things down when I was doing that. Considering that the Basilisk is invariably shown elevated higher than 6.5 degrees and is operated by seemingly normal humans at least some of the numbers given must be wrong.

[Ford Prefect]

I'm fairly certain that Earthshakers have been fired at targets with much greater range than fifteen kilometres in novels.

[Simon_Jester]

Correct in principle, but the effect of overcharged rounds seems exaggerated. Might be AdMech conservatism, or maybe those last two increments are just really big.

It's broadly consistent with supercharged rounds fired from real life artillery, I think. The limit of how much powder you put in a supercharged shot is defined by how much the barrel can take while reliably not exploding, after all; you can't expect it to be repeatable several dozen times.

There might be intermediate levels (10% more powder, half the barrel lifetime), but for game mechanic purposes those settings are irrelevant or likely to be unbalancing, so they wouldn't come up.

Found out this computer has a scientific calculator. 814 m/s horizontal component, 19s flight time, and earthlike gravity gives you a vertical component 93 m/s and an elevation of 6.5 degrees. Again, a bizarrely flat trajectory.

In the 4th Edition Guard codex, the default version of the Basilisk had a low-angle carriage and could only do direct fire. To get indirect fire you had to pay extra. So those flat trajectories may just be because they're using field artillery carriages, without the high elevation you can get from a howitzer.

You can mount an Earthshaker on a howitzer carriage, and for a lot of situations it's eminently reasonable to do so, but that doesn't mean they always will be.

[Raxmei]

Correct in principle, but the effect of overcharged rounds seems exaggerated. Might be AdMech conservatism, or maybe those last two increments are just really big.

It's broadly consistent with supercharged rounds fired from real life artillery, I think. The limit of how much powder you put in a supercharged shot is defined by how much the barrel can take while reliably not exploding, after all; you can't expect it to be repeatable several dozen times.

There might be intermediate levels (10% more powder, half the barrel lifetime), but for game mechanic purposes those settings are irrelevant or likely to be unbalancing, so they wouldn't come up.

In real life with the cannon I've shot charge 8 wears the barrel down ten times faster than charge 6. You can still shoot hundreds of charge 8 safely. It just seemed odd that they'd go straight from seriously reliable sustained fire to being limited to no more than 20 shots within two increments. None of this has any effect in the game.

Found out this computer has a scientific calculator. 814 m/s horizontal component, 19s flight time, and earthlike gravity gives you a vertical component 93 m/s and an elevation of 6.5 degrees. Again, a bizarrely flat trajectory.

In the 4th Edition Guard codex, the default version of the Basilisk had a low-angle carriage and could only do direct fire. To get indirect fire you had to pay extra. So those flat trajectories may just be because they're using field artillery carriages, without the high elevation you can get from a howitzer.

You can mount an Earthshaker on a howitzer carriage, and for a lot of situations it's eminently reasonable to do so, but that doesn't mean they always will be.

In the older codex it was a matter of training, not carriage. The indirect fire upgrade doesn't change any of the hardware.

[Brother-Captain Gaius]

As has been alluded to, the Basilisk/Earthshaker is not a rear line heavy artillery piece, but a "light"(er) mobile (in the case of the Basilisk) gun designed for direct fire support. It's analogous to a StuG or similar self-propelled gun. It's simply capable of indirect fire as well.

[andrewgpaul]

I took 814 as the muzzle velocity, since 15000m/814m/s does not equal 19s.

Well, 18.4s. Close enough.

[Simon_Jester]

In real life with the cannon I've shot charge 8 wears the barrel down ten times faster than charge 6. You can still shoot hundreds of charge 8 safely. It just seemed odd that they'd go straight from seriously reliable sustained fire to being limited to no more than 20 shots within two increments. None of this has any effect in the game.

Hmm. Probably just AdMech conservatism then. I see what you mean.

Some guns have been supercharged to the point where barrel life truly goes into the toilet in emergencies in the past, but my intuition is that you're right that increasing the powder charge by 40% probably shouldn't reduce barrel life by two orders of magnitude.

In the older codex it was a matter of training, not carriage. The indirect fire upgrade doesn't change any of the hardware.

Oh. My mistake, then.

[SAMAS]

I'm fairly certain that Earthshakers have been fired at targets with much greater range than fifteen kilometres in novels.

Well, he did say it seemed to invoke an uncommonly flat trajectory as it was...