[40k] Calcing the LeMan Russ

[Connor MacLeod]

[
The Wrath was hit by a projectile carrying some 6E5 newtons. I derived a mass and velocity from that (600 kg, which would be pretty silly, and a velocity of 1000m/s). I took those numbers and tossed them through the KE equation.

You mean newton-second, or kg*m/s (momentum) because as Winston just explained, force and momentum are different. (momentum is the mass x velocity that allows you to calculate KE - you'd need a timeframe with the force to derive momentum..)

And the Wrath scene has at most a ~250,000 kg*m/s momentum limit - probably closer to ~100,000 kg*m/s.

[Stark]

Wouldn't the armour material need to be way stronger, in order to deal with the uberpowerful 40k weapons?

[Connor MacLeod]

Wouldn't the armour material need to be way stronger, in order to deal with the uberpowerful 40k weapons?

Probably. But its no worse than the sort of recoil forces a TL turret or an SPHA-T is expected to withstand. (If anything, this is less goofy - some people argue the SPHA-T carries as much firepower as a heavy TL remember. recoil in that case is a royal bitch

Besides, 40K is rife with insanely strong materials, much like SW. And forcefield technologies (which can also help - see the aforementioned inertial dampers.)

Edit: and don't forget the ridiculously strong stormtrooper armor. Including the insane (implausible) spear throwing incident

[Ford Prefect]

It has clearly been a long time since I have done any physics.

[Stark]

Probably. But its no worse than the sort of recoil forces a TL turret or an SPHA-T is expected to withstand. (If anything, this is less goofy - some people argue the SPHA-T carries as much firepower as a heavy TL remember. recoil in that case is a royal bitch

Besides, 40K is rife with insanely strong materials, much like SW. And forcefield technologies (which can also help - see the aforementioned inertial dampers.)

I meant how Shep declared the armour to be 23% better than rha. Since 40k has SW-level weapons, that doesn't seem like it's going to cut it (even if it IS 200mm sides).

[Connor MacLeod]

I meant how Shep declared the armour to be 23% better than rha. Since 40k has SW-level weapons, that doesn't seem like it's going to cut it (even if it IS 200mm sides).

Ah, apologies then.

From what I gather Shep's just doing some modelling or predicting rather than going from observed performance in examples. Alot of people like trying to argue that 40K tank armor isn't better than "modern" stuff but that's pretty absurd, given that multi-GJ anti-tank weapons (krak grenades as per the Soul Drinkers omnibus, meltaguns from various sources like Caves of Ice, multimeltas from Storm of Iron, meltabombs, etc. all come out in the single or double digit GJ range, and those generlaly only do light to moderate damage, without slagging a substantial portion of a tank's structure.)

I'm inclined to say their armor is going to be at LEAST an order of magnitude better than modern stuff in terms of physical impactors, and probably with substnatially greater energy weapon resistance

(The fun part to consider - a Krak Grenade is basically a shaped charge, and it can incinerate a single corpse. That's around 1-3 GJ. Now imagine how that compares to modern shaped charges in terms of performance - parrticularily since there are "krak" rockets and missiles.)

[Stark]

Yeah, any 61t tank that can tank hits from the highend 40k infantry weapons is clearly not made from steel. It was just an odd number for Shep to throw in there - I guess he's trying to make a 'modern analogue' of the Lemas Russ to compare to other tanks, or something?

[Connor MacLeod]

Well even if it WERE somehow steel, 40K has forcefield technologies (even in the man-portable "personal deflector shield" sense and they're not exactly unique objects) and that has to be accounted for as well.

[Shroom Man 777]

And where does all that energy go? Handwavium land? Do the magic space fairy pixies take it away?

Magic. This is the grim darkness of the far future where there is only war, space demons, space elves, space monsters, and armies of darkness of soul-sucking undead zombie robot vampires from SPAAAAACE.

No, seriously. Chaos is known to have logic defying stuff. Why can't the IoM have its own subtle weird stuff that doesn't make sense?

[Winston Blake]

What on earth are you doing? You just found the energy required to lift the tank upwards 4m. At the very least we'd need to model the sideways reaction force as viscous damping, which would depend on the terrain.

IIRC from Honour Guard the terrain was basically "flat" (forest close to a town cleared of trees for about a kilometer's distance.) It was a close range shot (few tens of meters) on ground that inclined slightly downwards from where the Conqueror was (the enemy tank which caused the Conqueror to lurch would be firing upwards.)

That suggests flat, firm terrain where the tank probably just skidded across the ground without digging in at all. We could model it as a constant friction force applying a constant deceleration, which makes things easier. Let's assume that the projectile transfers its momentum instantly and that a 'lurch' is about half a second in duration.

[v = u + at] and [v^2 = u^2 + 2as].
Final velocity v is zero, so: [a = 2s / t^2].
For s = 4m, t = 0.5s: [a = 32 m/s^2].
So initial velocity [u = at = 16 m/s].

So for a tank mass of 62 tonnes, the impactor must have had a momentum greater than about 1e6 kg*m/s. If it was a 120mm M829A2, then (by Shep's data) it'd need a speed of over 200 km/s. If it was as heavy as a 155mm shell, then it would need over 22 km/s.

Does anyone know if Leman Russes have ever fired shots into space from the surface of an Earthlike planet?

[Ford Prefect]

I don't recall any instances, but I doubt it. It wouldn't be the first instance that the Imperium has fielded a weapon with a much great maximum range than 'effective'.

[Connor MacLeod]

That suggests flat, firm terrain where the tank probably just skidded across the ground without digging in at all. We could model it as a constant friction force applying a constant deceleration, which makes things easier. Let's assume that the projectile transfers its momentum instantly and that a 'lurch' is about half a second in duration.

[v = u + at] and [v^2 = u^2 + 2as].
Final velocity v is zero, so: [a = 2s / t^2].
For s = 4m, t = 0.5s: [a = 32 m/s^2].
So initial velocity [u = at = 16 m/s].

So for a tank mass of 62 tonnes, the impactor must have had a momentum greater than about 1e6 kg*m/s. If it was a 120mm M829A2, then (by Shep's data) it'd need a speed of over 200 km/s. If it was as heavy as a 155mm shell, then it would need over 22 km/s.

I think half a second is too short a period of time. The quote implies about a second, here:

Re-laying the gun took a vital second. In that time, the second tank fired again and hit the Wrath squarely. The impact was enough to lurch all sixty-two tonnes of armoured machine several metres sideways. But it didn't penetrate the twenty centimetre-thick armour skin. Inside, the crew were dazed and they'd lost most of the forward scopes."

Am I correct in figuring that "s" equals the distance covered (IE "several meters?" If so then its probably only more like 2-3 meters as well. Given those variables, I'm expecting a much lower momentum (though still considerably greater than that of a modern MBT)

Does anyone know if Leman Russes have ever fired shots into space from the surface of an Earthlike planet?

Considering that its a chem-propelled cannon for the most part, I doubt it. They might achieve some boosted velocity by using cannon propellant + internal rockets in the ammo (bolters can use both the propellant from the gun and the propellant of an internal rocket ot generate extreme speeds.) but I'd guess its not going to be more than 3-4 km/s tops.

Like I said, I suspect the actual momentum is alot less

[Ford Prefect]

Tanks in the Imperium appear to be hardier than their bunkers. We had a Leman Russ variant (Demolisher, I think) take fairly significant damage from a multimelta, the same weapon that turned a bunker into 'molten hell'.

[MKSheppard]

An impact from such a shell would not be able to lurch a 62 tonne mass as described. Energy is irrelevant here, momentum is the important quantity. An inelastic collision would give:

Thank you for the physics correction.

Much appreciated.

Using your formula, it turns out that the amount of force to accelerate a LeMan Russ to 4 m/sec on a perfectly flat slippery surface is:

330 kg @ 750 m/sec; which is equivalent to roughly a 12" naval gun round.

I meant how Shep declared the armour to be 23% better than rha.

I did say that I was open to increasing the protection factor to 150%. It's basically an arbitrary number I picked that doesn't rape reality horribly to the point that it's driven insane.

Yeah, any 61t tank that can tank hits from the highend 40k infantry weapons is clearly not made from steel.

The problem is that we have the thickness of the armor specifically stated by Games Workshop to be from 200-45mm, along with the weight of the vehicle being 62 metric tons, along with precise dimensions of how long it the LeMan Russ is, so we can actually work out the density of the armor material itself. It appears to be somewhere around 4~ g/cm3, which seems to me to be just too light for the amount of protection that's attributed to it, e.g. can stop the equivalent of a 12" round, despite being only 200mm thick.

I don't know about you, but that just seems a bit off, and strange to me; there's just something about it that I can't quite place my finger on...

But anyway, since the round shoving it is roughly equivalent to a 12", here we go: NavWeaps on 12"/50.

At point blank range, you need about 643mm of armor to stop the shell; so it seems that the KE effectiveness of the armor is is 3.5 or even 4. We'll average it to 3.75.

That gives us the following statz:

Front Hull Armor------1061--------Resistant to Modern 120mm
Side Hull Armor------169----Resistant to 40mm L70 APFSDS
Rear Hull Armor------169-----Resistant to 40mm L70 APFSDS
Top Hull Armor------169------Resistant to 40mm L70 APFSDS
Hull Floor Armor------169---Resistant to 40mm L70 APFSDS

Front Turret Armor------894.27-----Resistant to Modern 120mm
Side Turret Armor------201.21--------Resistant to 40mm L70 APFSDS
Rear Turret Armor------168.75------Resistant to 40mm L70 APFSDS
Top Turret Armor------168.75--------Resistant to 40mm L70 APFSDS

-----------------------------------------

In comparison, the M1A2 has:

Front Hull Armor------600
Side Hull Armor------120
Rear Hull Armor------190
Top Hull Armor------100

Front Turret Armor------970
Side Turret Armor------300
Rear Turret Armor------170
Top Turret Armor------100

(The fun part to consider - a Krak Grenade is basically a shaped charge, and it can incinerate a single corpse. That's around 1-3 GJ. Now imagine how that compares to modern shaped charges in terms of performance - parrticularily since there are "krak" rockets and missiles

Shaped charges' effectiveness are based on two things:

1.) Diameter of the charge itself. A bigger diameter obviously means a lot more penetration.
2.) The Material lining the charge itself makes a lot of difference; however, the best material may not be chosen due to cost.

Teh Krak Grenades seem to be about the same diameter of a standard hand grenade: 6 cm.

Teh rule of thumb formula for best HEAT penetration is the diameter of the shaped charge by 6, while present day Russian 125mm ammo is 4; averaging these is 5.

60mm x 5 = 300 mm base penetration

Which is more than enough to poop through top armor like it's not there.

As for incinerating the corpse; uhm, that would require an absurdly large shaped charge jet.

Pic of Krak Grenade

More likely, the "bumps" along the grenade are filled with prometheium, so that you can have a two-fer-one inciendary/Anti-armor grenade in one.

[Marko Dash]

is there anywhere to get a free download for editing xls spreadsheets, thats not over 15 mb. i only have excel veiwer so i can't play with the program.

[Stark]

I don't know about you, but that just seems a bit off, and strange to me; there's just something about it that I can't quite place my finger on...

You mean the part where it's an imaginary design from a high-end scifi universe full of absurdly powerful materials and weapons? If you're trying to define a 40k vehicle but not prepared to accept the retarded strengths of 40k materials, it strikes me that you might be going in circles.

[JGregory32]

is there anywhere to get a free download for editing xls spreadsheets, thats not over 15 mb. i only have excel veiwer so i can't play with the program.

Try OpenOffice at http://www.openoffice.org it's free, works on many platforms, and is cross compatable with most versions of MS Office.

[Shadowtraveler]

Tanks in the Imperium appear to be hardier than their bunkers. We had a Leman Russ variant (Demolisher, I think) take fairly significant damage from a multimelta, the same weapon that turned a bunker into 'molten hell'.

Most likely this is due to the Russ being an STC design. I mean, hell, isn't it really just a tractor with weaponry?

[JGregory32]

Ghetto Edit:
Opps, overlooked the size requirement. Openoffice is about 98 megs for the full suite.

I know of nothing thats under 15mb for editing excel files.

On a side note why does it have to be under 15mb?

[Marko Dash]

so it doesn't take all day to download, 2mb takes about 10min

[Winston Blake]

I think half a second is too short a period of time. The quote implies about a second, here:

Re-laying the gun took a vital second. In that time, the second tank fired again and hit the Wrath squarely. The impact was enough to lurch all sixty-two tonnes of armoured machine several metres sideways. But it didn't penetrate the twenty centimetre-thick armour skin. Inside, the crew were dazed and they'd lost most of the forward scopes."

Am I correct in figuring that "s" equals the distance covered (IE "several meters?" If so then its probably only more like 2-3 meters as well. Given those variables, I'm expecting a much lower momentum (though still considerably greater than that of a modern MBT)

Yep, s is the distance. I interpreted the excerpt to mean that the only the re-laying period was one second long. Anyway, with values of 1 second and 2 m, I get about 5.6 km/s for a 155mm-mass shell, which is much more reasonable. Feel free to play around with that - plug 330kg into it and you get Shep's velocity of 750 m/s, confirming that a shell of that mass would mean parity with a 12" naval gun.

[Connor MacLeod]

Yep, s is the distance. I interpreted the excerpt to mean that the only the re-laying period was one second long.

Well it could, although as I see it the enemy tank firing and hitting is going to take far LESS than a second at a distance of around ~40 meters or so, so the rest of that second has to be spent somehow (and the tank's pretty much going to have the momentum imparted on impact, even assuming a rocket-propelled round.)

Anyway, with values of 1 second and 2 m, I get about 5.6 km/s for a 155mm-mass shell, which is much more reasonable. Feel free to play around with that - plug 330kg into it and you get Shep's velocity of 750 m/s, confirming that a shell of that mass would mean parity with a 12" naval gun.

Better, though I doubt its that massive a round. I just recalled that the tank firing it is stated to have a 105mm round (tungsten ammo) not saboted AFAIK. Its probably closer in mass to the 155mm shell than the mass of the 12" gun, even allowing for the tungsten's greater density and the high velocity came from the round being rocket-propelled.

Incidentally, when this calc has come up in the past, some people (or idiots) inssited it wasn't a kinetic impactor, but rather an explosion shoving the tank. How would that affect the calcs? (I doubt it could be omnidirectional, so it would probably have to be a shaped-charge, like a krak shell.)

[Connor MacLeod]

The problem is that we have the thickness of the armor specifically stated by Games Workshop to be from 200-45mm, along with the weight of the vehicle being 62 metric tons, along with precise dimensions of how long it the LeMan Russ is, so we can actually work out the density of the armor material itself. It appears to be somewhere around 4~ g/cm3, which seems to me to be just too light for the amount of protection that's attributed to it, e.g. can stop the equivalent of a 12" round, despite being only 200mm thick.

I don't know about you, but that just seems a bit off, and strange to me; there's just something about it that I can't quite place my finger on...

You mean like stormtrooper armor taking a spear with at least 1000 kg*m/s worth of momentum? I doubt stormtrooper armor is all that dense/heavy...

Seriously, density isn't the only factor here. The thermal properties (specific heat and metling point) as well as its handling properties with regards to force/pressure and whatnot. Which, as i recall, are not intrinsically tied to "density", especially in sci fi materials (again see Stormtrooper armor.)

Besides, as I noted, the parameters on a Russ are highly VARIABLE, including armor and masses (and we're not even sure what the mass figures represent, as they vary as much as all the other parameters.) We don't even know the composition or nature of the armor itself, ,aside from the fact its got to be able to stand up to insane directed energy weapon attacks a swell as kinetic or shaped-charge attacks.

Shaped charges' effectiveness are based on two things:

1.) Diameter of the charge itself. A bigger diameter obviously means a lot more penetration.
2.) The Material lining the charge itself makes a lot of difference; however, the best material may not be chosen due to cost.

Teh Krak Grenades seem to be about the same diameter of a standard hand grenade: 6 cm.

Teh rule of thumb formula for best HEAT penetration is the diameter of the shaped charge by 6, while present day Russian 125mm ammo is 4; averaging these is 5.

60mm x 5 = 300 mm base penetration

Which is more than enough to poop through top armor like it's not there.

doesn't that "rule of thumb" make certain assumptions regarding the kind of shaped charge in general? We're bound to be talking about a "shaped charge" which is probably at least equivalent (if not greater) than anti-ship warheads or torpedoes, much less something on an anti-tank scale.

As for incinerating the corpse; uhm, that would require an absurdly large shaped charge jet.

Are you telling me shaped charges are 100% efficient in terms of how they work? I find that hard to believe.

Moreover, he energy in the "jet" will not just "magically" vanish if the jet dissipates, particularily given the obscene yields I am talking about (which are in fact conservative, as they assume circumstances comparable to what you find in modern cremation furnaces.) At worst, we're simply talking a VERY inefficient way to cremate someone which will just up the calcs even FURTHER.

On the other hand, given the minimum energies I'm estimating, I imagine the parameters of the "jet" are going to be qutie different from modern explosives, so that is bound to have an impact as well.)

Pic of Krak Grenade

More likely, the "bumps" along the grenade are filled with prometheium, so that you can have a two-fer-one inciendary/Anti-armor grenade in one.

Which may not be accurate, as it looks like a fansite.

[Starglider]

Won't the track weight be rather lower if the tracks are made out of plassteel instead of normal steel? That'd give you leeway for more armour. The suspension, engine and fuel weights are presumably different with 40K materials and power technology as well, but that's less significant than the 10.8 tonne track+road wheels weight. Is it reasonable to model the engine as a modern gas turbine? The 620hp seems like a lower limit at best for 40K tech.

[Winston Blake]

Incidentally, when this calc has come up in the past, some people (or idiots) inssited it wasn't a kinetic impactor, but rather an explosion shoving the tank. How would that affect the calcs? (I doubt it could be omnidirectional, so it would probably have to be a shaped-charge, like a krak shell.)

Well we could assume that all of the shaped charge's jet hit perpendicularly, so the jet must have had the necessary momentum to cause the lurching. There's some unknowns here, like how much of the shell's mass is the shaped charge liner, and what fraction of the charge's energy goes into the jet.

Assuming a 50kg round with 5% liner mass, you'd have a 2.5kg jet (I have absolutely no idea how reasonable those values are). Let's assume for now that it had negligible speed when it hit. From before, it must have 250e3 Ns of momentum, meaning a velocity of 100 km/s. That gives an energy of 12.5 gigajoules.

If the jet carries 60% of the charge's explosive energy (pure guess), then the total charge had to be 20.8 GJ. That's almost 5 tonnes of TNT! For my anally-derived values here, that would mean the shell's explosive is over 100 times as energetic as TNT.

Now to take into account the shell's velocity, we're faced with another unknown - how much of the lurch was caused by the blast and how much by the impact? Since it's a shaped charge, it might be alright to assume that the detonation caused everything except the liner to scatter laterally and rearward. That would mean the impact doesn't contribute much momentum at all. Assuming a shell velocity of 3km/s, the jet now only needs 97 km/s from the explosive. That still means a total explosive yield of 4.7 tonnes. So velocity is practically irrelevant.

Based on these guessed values, I think we're faced with four choices:

• The shell is a shaped-charge with low-end nuclear yield (and consequently, the target armour is mind-bogglingly strong).
  
  It's mostly solid metal (and needs a speed of over 5 km/s).
  
  It's got a lower speed and it's filled with HE (and I don't know how to calculate the pressures/etc necessary to estimate the yield).
  
  It's a HESH-type shaped charge and the shell has effectively stopped relative to the armour before detonation.

For that last one, it means we can use the full 50kg mass for the impact instead of just the 2.5kg jet. Assuming an impact velocity of 3km/s again, that's 150e3 Ns of momentum from the impact. The explosive only has to supply 100e3 Ns now.

Assuming it's squashed flat, we might assume that 45% of the blast will be directed against the armour. I don't think this is the right way to do it, but let's assume 45% of the mass is thrown at the target. It would need 4.44 km/s to make up that 100e3 Ns, giving an energy of 222 MJ. This means a total yield of 490 MJ, or 118 kg of TNT.

So based on all these guesses, I think it could work if it was a HESH shell fired at about 3 km/s with an explosive that is about 2.5x as powerful as TNT.