What is the weight of an AT-AT?

[Alyeska]

Just a thought, but doesn't Ice have a threshold as to how much pounds per square inch it can survive before deforming?

[Connor MacLeod]

ACtually I'm wondering neccesarily if we can make calcs at all from the footfalls on the basis of the planetary shields covering the base. As is established in TPM, matter under a shield tends to exhibit weird qualities (like bolts bouncing off of grass in TPM).

Given that blaster bolts from speeders and such are able to hit the frigging snow without evidently melting or vaporizing it in any noticable way, I'd hardly be surprised to learn that the same is true at Hoth either.

(For that matter, the shields might be making the snow/ice better able to stand up to the Walkers if that is a problem.)

A crazy questio nthere too.. would the existence of shields (or rather, particle shielding) possibly influence the "shaking" we see from the At-AT footfalls?

[Crayz9000]

The only problem with that is that now we're bringing more variables into the equation, which, by Occam, we should not do.

Unfortunately my head is fuzzy from the late hour (funny... used to be crystal clear now... must be the damned job making me wake up early ) so I can't think very well of how to calculate the mass.

[Winston Blake]

A crazy questio nthere too.. would the existence of shields (or rather, particle shielding) possibly influence the "shaking" we see from the At-AT footfalls?

Maybe the shaking at Echo Base was from the AT-ATs tranferring force into the shield as they penetrated it, which was transferred through the shield back to the nearby shield projector, which is attached to the ground. We know from TPM that shields exert a force on battledroids trying to push through - the converse could hold true for very large vehicles like AT-ATs.

[Bounty]

Couldn't the shaking have been stray AT-AT shots hitting the ground, or blowing up off-screen gun batteries? It seemed a bit random for footsteps, to be honest.

Would it be more useful to determine how heavy it can possibly be and not sink into the ground without antigrav fields? Unless it is made of aluminum I think it would need such fields anyway, so it might have an effective weight close to the maximum anyway.

But what's the point of the legs then? Purely a psychological trick? I thought the walkers were the answer to environments where antigrav didn't work properly, but if the thing can't stay upright without them it sorta defeats the purpose, doesn't it?

[Wyrm]

If one assumes a class three earthquake, the energy release appear to almost exactly 2 GJ...

Does it make much of a difference that we're not measuring an "earthquake" in the strictest sense of the word, but a "snowquake"? Snow would transmit vibration differently from rock.

I'm no expert but I expect such a 'snowquake' would require more initial energy as snow is more compressable than rock and might absorb the impact energy instead of sending it away as a wave. I've heard extremely cold ice can become hard like rock, but I don't expect Hoth is cold enough as human life is possible without sealed environment suits.

Remember that snow compactifies under pressure. Particularly, the snow underneath miles of more snow settles and hardens to be able to support the weight of snow sitting atop it; the snow would have to get stiff just to support its own weight. Ice Ih, the major component of normal snow, exists up to 10⁸ Pa at temperatures colder than -20°C, and has a bulk modulus of 7.81 GPa at -13°C (steel has a bulk modulus of ~160 GPa). Typical rock has a bulk modulus of about 100 GPa, so ice is not bad, but ~10 more compressible than rock.

[The Silence and I]

Remember that snow compactifies under pressure. Particularly, the snow underneath miles of more snow settles and hardens to be able to support the weight of snow sitting atop it; the snow would have to get stiff just to support its own weight. Ice Ih, the major component of normal snow, exists up to 10⁸ Pa at temperatures colder than -20°C, and has a bulk modulus of 7.81 GPa at -13°C (steel has a bulk modulus of ~160 GPa). Typical rock has a bulk modulus of about 100 GPa, so ice is not bad, but ~10 more compressible than rock.

Neat info, but doesn't that just about entirely back up what I suspected? Ice is elastic while under very high rates of strain, such as while an AT AT foot decelerates from the contact force, (Here) but becomes inelastic under sustained loads, and AT AT feet are not swift. As I understand this I think it will absorb much of the impact energy and keep it too. Your numbers are also for highly compact ice, which you won't likely find at the top few feet of Hoth's surface.

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Bounty: A 23 meter tall metal walker with what, 4 meter wide circular feet? More or less? Thats 4*PI*2^2 = 50 meter^2. Just eyeballing the main body (sans head and legs) I guesstimate 12 x 16 x 8 meters. That's 1536 m^3. If it is 80% empty air that's still 300 m^3. If it's materials were as dense as water (HA!) it would mass 300 tons without head, legs, and feet. That puts a pressure of 6 tons on the ground per square meter of foot. Humans have around 2 tons per square meter and cattle have about 15 tons per square meter. So far it can walk on most surfaces, but consider a steel construction: it'll mass roughly 8 times more! Now the ground has to support 48 tons per square meter (470 kPa)! Even a brontosaurus only put 29 tons per square meter on the ground and they certainly were extremely limited in their choice of terra firma. (foot pressures found in Chris Lavers' book 'Why Elephants Have Big Ears')

Now add the mass of the legs and the head and it gets heavier still. If you want super dense armor plating, same thing. How about it's cargo?

Wyrm claims ice can support 100 MPa while I found ice to have a compressive strength of around 9 MPa. In either case solid ice can support the steel AT AT. However it can't easily walk on soft ground with so much pressure. I can believe such a device can walk on hard ice without antigrav, but it cannot be called 'All Terrain' by any stretch of the imagination unless it is very lightly built or uses antigrav technology. I'm willing to believe either case as I could care less about the EU, but... *shrug*

*********************

By the way, assume my figures are extremely rough because they are. I only eyeballed and someone else is welcome to make a more precise attempt.

[Major Maxillary]

Maybe the AT-ATs just stepped lightly? you know, like you do when you don't want to alert the cat you're about to play "fluffy tail" with?

[Batman]

Maybe the AT-ATs just stepped lightly? you know, like you do when you don't want to alert the cat you're about to play "fluffy tail" with?

The fact that that's not physically possible above a certain weight/contact area ratio comes to mind. As does the fact that as per the movie the AT-ATs didn't bother to.

[Darth Wong]

Maybe the AT-ATs just stepped lightly? you know, like you do when you don't want to alert the cat you're about to play "fluffy tail" with?

If they stepped lightly, then they wouldn't shake the ground.

The ground-shaking is a real conundrum. If the AT-ATs are light or they're using anti-grav technology, then they shouldn't make the ground shake like that. They are hitting the ground hard enough to make the ground shake; this is an observation, not speculation. So these are not feather-light footsteps we're talking about, or anti-grav floated vehicles.

Instead, we have to explain why the ground was not compacting under them. I've long suspected that they're intended more as self-propelled artillery than mobile combat vehicles; their abysmal handling of close-in foes is consistent with this. The heavy feet would allow them to "set" into the ground for firing heavy weapons at long ranges.

[Wyrm]

Remember that snow compactifies under pressure. Particularly, the snow underneath miles of more snow settles and hardens to be able to support the weight of snow sitting atop it; the snow would have to get stiff just to support its own weight. Ice Ih, the major component of normal snow, exists up to 10⁸ Pa at temperatures colder than -20°C, and has a bulk modulus of 7.81 GPa at -13°C (steel has a bulk modulus of ~160 GPa). Typical rock has a bulk modulus of about 100 GPa, so ice is not bad, but ~10 more compressible than rock.

Neat info, but doesn't that just about entirely back up what I suspected? Ice is elastic while under very high rates of strain, such as while an AT AT foot decelerates from the contact force, (Here) but becomes inelastic under sustained loads, and AT AT feet are not swift. As I understand this I think it will absorb much of the impact energy and keep it too. Your numbers are also for highly compact ice, which you won't likely find at the top few feet of Hoth's surface.

Quite right. The firn-glacial ice transition occurs about 100 m below the surface snow.

Bounty: A 23 meter tall metal walker with what, 4 meter wide circular feet? More or less? Thats 4*PI*2^2 = 50 meter^2.

Um, 4πr² is the surface area of a sphere. The area of a circle is A = πr². This means that a four-meter wide cicle (radius: 2 m) has an area of 12.5 m² for each foot, or for all feet together, 50.2 m².

Just eyeballing the main body (sans head and legs) I guesstimate 12 x 16 x 8 meters. That's 1536 m^3. If it is 80% empty air that's still 300 m^3. If it's materials were as dense as water (HA!) it would mass 300 tons without head, legs, and feet. That puts a pressure of 6 tons on the ground per square meter of foot. Humans have around 2 tons per square meter and cattle have about 15 tons per square meter. So far it can walk on most surfaces, but consider a steel construction: it'll mass roughly 8 times more! Now the ground has to support 48 tons per square meter (470 kPa)! Even a brontosaurus only put 29 tons per square meter on the ground and they certainly were extremely limited in their choice of terra firma. (foot pressures found in Chris Lavers' book 'Why Elephants Have Big Ears')

300 m³ of water would be 3e5 kg (density of water: 1 Mg/m³). 300 m³ of steel would be 2.358e6 kg. Under 1 g (9.8 m/s²), this would make 58.489 kPa of ground pressure for the AT-AT of water, and 459.727 kPa for the AT-AT of steel. Only now are we encroaching on impossibility here.

Now add the mass of the legs and the head and it gets heavier still. If you want super dense armor plating, same thing. How about it's cargo?

Wyrm claims ice can support 100 MPa while I found ice to have a compressive strength of around 9 MPa.

No. Compressive strength is how much pressure the material can stand without inelastic deformation, not how much pressure the material can stand, period. After all, water yields readily to stress, but it can still support a lot of weight (the bulk modulus of water is about 2.15 GPa; it only deforms a small amount in response to stress). It'll only fail to support weight if the water has somewhere to yield to.

Sure, the ice will start yielding at 9 MPa, but that doesn't mean it has anywhere to go, or that it will get their particularly quickly. Ice sheet flow is measured on the order of 1-2 cm/day.

Just a thought, but doesn't Ice have a threshold as to how much pounds per square inch it can survive before deforming?

Snow certainly does. I sink an inch or two into old snow and I'm only ~130 lbs. Snow only gets strong when it gets compact.

With that in mind, I've gone back to TESB and made a few observations. However much the AT-AT actually masses, it's quite apparent that the amount of weight borne by each the feet isn't all that much. I call your attention to two scenes.

In the scene where Luke's speeder gets crushed by the AT-AT's foot, the non-crushed portions of the frame sink no further than a foot (depending on how big those canons are), and possibly only a few tens of centimeters. Since the speeders have a relatively small footprint (I get 5.3 m in length and about the same in width, so not more than 28.09 m² in area), the actual weight bearing down on the speeder cannot be much larger than can be supported by crushing snow by about 30 cm over that area.

I make a similar observation in a scene where Luke is running along underfoot of an AT-AT. I note these feet have sunk no more than a foot into the ground, over about 12.5 m² of foot area (Assuming feet ~2.5 m in radius; how big are they?). Compare this to Luke sinking no more than halfway up his shin (~6 in) in the exact same snow. If we assume maybe 250 lb of Luke in full flight gear and that rocket winch, and about half a square foot of foot area per stride, this is about 3.5 lb/in² (23939.75 Pa) at ~6 in of compression.

Hmmm...

Wasn't the run in question completely contained between the lift and fall of an AT-AT step, though?

We don't actually see the AT-AT's foot falling, but we can clearly hear it falling in a scene with a man running at a normal gait throughout. In Luke's run to catch up to the AT-AT, we have Luke running with one of the AT-AT's feet striding forward. Then we have a short shot of Luke only, running along, with the distinctive *WHOOMPH* *whoosh* of the AT-AT's footfall clearly audiable. And he's not knocked down by the tremors, nor is he even thrown off balance.

If they stepped lightly, then they wouldn't shake the ground.

The ground-shaking is a real conundrum. If the AT-ATs are light or they're using anti-grav technology, then they shouldn't make the ground shake like that. They are hitting the ground hard enough to make the ground shake; this is an observation, not speculation. So these are not feather-light footsteps we're talking about, or anti-grav floated vehicles.

Instead, we have to explain why the ground was not compacting under them. I've long suspected that they're intended more as self-propelled artillery than mobile combat vehicles; their abysmal handling of close-in foes is consistent with this. The heavy feet would allow them to "set" into the ground for firing heavy weapons at long ranges.

Sooo... if the AT-AT's footfalls are making the ground tremble with every footfall, then they are coming down heavily. But feet coming down heavily means that these feet are going to require a lot of give in the snow pack, given the rather poor compressive qualities of snow and firn; by all rights the feet should be burying themselves in the snow if they are coming down that hard, much more than the measily foot they seem to be doing in the film. The fact that the footfalls are causing tremors in Rebel base implies that the tremors should be knocking Luke to the ground every time the AT-AT he's underfoot puts a foot down. These two facts seem to imply that the AT-AT is treading lightly, in contradiction to the tremors.

I can't seem to find my way out of this contradiction. Help?

[Howedar]

Bounty: A 23 meter tall metal walker with what, 4 meter wide circular feet? More or less? Thats 4*PI*2^2 = 50 meter^2.

Um, 4πr² is the surface area of a sphere. The area of a circle is A = πr². This means that a four-meter wide cicle (radius: 2 m) has an area of 12.5 m² for each foot, or for all feet together, 50.2 m².

Yeah. Uh, that's what he did.

4 feet, each at A=Pi*R^2, with R=2m (assuming d=4m).

Hence 4*Pi*2^2.

[Shroom Man 777]

(For that matter, the shields might be making the snow/ice better able to stand up to the Walkers if that is a problem.)

I think it'd be profoundly stupid if the AT-ATs blew up the shield generators and then ended up sinking into the snow.

[Cykeisme]

Maybe the shaking at Echo Base was from the AT-ATs tranferring force into the shield as they penetrated it, which was transferred through the shield back to the nearby shield projector, which is attached to the ground. We know from TPM that shields exert a force on battledroids trying to push through - the converse could hold true for very large vehicles like AT-ATs.

This makes a lot of sense. Anyone find a problem with this hypothesis?

Sooo... if the AT-AT's footfalls are making the ground tremble with every footfall, then they are coming down heavily. But feet coming down heavily means that these feet are going to require a lot of give in the snow pack, given the rather poor compressive qualities of snow and firn; by all rights the feet should be burying themselves in the snow if they are coming down that hard, much more than the measily foot they seem to be doing in the film. The fact that the footfalls are causing tremors in Rebel base implies that the tremors should be knocking Luke to the ground every time the AT-AT he's underfoot puts a foot down. These two facts seem to imply that the AT-AT is treading lightly, in contradiction to the tremors.

I can't seem to find my way out of this contradiction. Help?

Regarding the observation (assuming the Echo Base tunnel tremors were caused by footsteps from mile off, and not momentum transferred to the shield generator) that Luke didn't seem to be thrown, shaken, or even caused to stumble by the AT-AT footfalls makes me think it would have been really cool if, while Luke escaped his wrecked T-47 and then chased the AT-AT, he was thrown and stumbled about with each heavy footfall. Would make the AT-ATs seem that much more badass.

The only thing I can think of is that the composition (and thus compactability) of the terrain varies across different locations. The AT-ATs may have been crossing exposed (or at least shallowly snow-buried) rock when Echo Base trembled, and the snowspeeder must have landed over the peak of a rocky outcropping. Perhaps the rocky terrain is wildly uneven, but completely hidden and buried by the layers of ice and snow?
This is, once again, not taking into account Winston Blake's idea, which I like.


Regarding the compressibility of ice and snow that was brought up several times.. wouldn't water ice (and snow) return to liquid state when compresed, due to trying to reach equilibrium? Since water is more dense than ice, and all that.

Bounty: A 23 meter tall metal walker with what, 4 meter wide circular feet? More or less? Thats 4*PI*2^2 = 50 meter^2.

Um, 4πr² is the surface area of a sphere. The area of a circle is A = πr². This means that a four-meter wide cicle (radius: 2 m) has an area of 12.5 m² for each foot, or for all feet together, 50.2 m².

Yeah. Uh, that's what he did.

4 feet, each at A=Pi*R^2, with R=2m (assuming d=4m).

Hence 4*Pi*2^2.

lol@silly wyrm

[nightmare]

Those AT-ATs were moving very slowly when Luke could catch up to one just by running. I don't think he was making more than 25 kph or so. Maybe the answer is so simple that the AT-ATs were, in fact, "treading lightly" when traversing less dense terrain. In order to move in towards the base so quickly, they had to move much faster when they started out.

Then there's the Snowspeeder getting crushed without massive deformation, but that could be a combination of snow under it and strong materials. Mostly the latter, I think. The snow/ice on Hoth really behaves more like armored concrete than anything else.

[Turin]

I've long suspected that they're intended more as self-propelled artillery than mobile combat vehicles; their abysmal handling of close-in foes is consistent with this. The heavy feet would allow them to "set" into the ground for firing heavy weapons at long ranges.

In fact, we see this one of the shots (I think its the one where they take out the power generator). The walker clearly firms up its stance and by spreading its legs out, providing a wider more stable firing platform, before taking the shot.

Those AT-ATs were moving very slowly when Luke could catch up to one just by running. I don't think he was making more than 25 kph or so. Maybe the answer is so simple that the AT-ATs were, in fact, "treading lightly" when traversing less dense terrain.

What does "treading lightly" mean in this case? In the earlier example of a person trying to sneak up, treading lightly means that the lead foot is lightly placed while more weight ends up on the other leg. Then the person shifts their weight. If the walker is treading lightly in this fashion, it actually makes the problem worse, not better.

[nightmare]

Those AT-ATs were moving very slowly when Luke could catch up to one just by running. I don't think he was making more than 25 kph or so. Maybe the answer is so simple that the AT-ATs were, in fact, "treading lightly" when traversing less dense terrain.

What does "treading lightly" mean in this case? In the earlier example of a person trying to sneak up, treading lightly means that the lead foot is lightly placed while more weight ends up on the other leg. Then the person shifts their weight. If the walker is treading lightly in this fashion, it actually makes the problem worse, not better.

Not necessarily true in the case of ice. A quick step imparts more kinetic energy by hitting the ground harder, where a slow step means hitting the ground less hard. While you get more weight on each step, your chance to traverse ice - or a hard snow/ice crust - successfully, increases. An AT-AT also has four legs and they moved by placing one foot at a time when walking so slowly, maximising ground contact. It's quite plausible, by the way, that they would have a different gait when speeding up. I suppose I could verify that, but it doesn't matter.

[LadyTevar]

From the 'Making of', Lucas explains how they used an Elephant to model how the Walker should move. If you've ever paid attention to Discovery Channel, you'll have seen that Elephants run not by breaking into a galloping run, like a horse or camel, but by speeding up their normal gait. (IE: Elephant legs always move in the same pattern, while horses and camels have different patterns for walk, trot, and run.)

It would make sense, if the Imperials also based it off a living creature and wanted the Walkers to have a 'cruise' and a 'flank' speed, for the difference to be merely in how fast the legs move.

[Turin]

Not necessarily true in the case of ice. A quick step imparts more kinetic energy by hitting the ground harder, where a slow step means hitting the ground less hard. While you get more weight on each step, your chance to traverse ice - or a hard snow/ice crust - successfully, increases. An AT-AT also has four legs and they moved by placing one foot at a time when walking so slowly, maximising ground contact.

I was totally neglecting the kinetic energy of the footfalls. Nevermind.

It's quite plausible, by the way, that they would have a different gait when speeding up. I suppose I could verify that, but it doesn't matter.

Plausible, but it seems overly complicated to engineer when you can, as Lady Tevar has suggested, build a workable system just by changing the speed of the leg movement, rather than the pattern in which they move. A lot of the "high speed" gaits for animals require the spine to bend quite a bit, which obviously is unworkable with the AT-AT as it's constructed.

[Pint0 Xtreme]

I've long suspected that they're intended more as self-propelled artillery than mobile combat vehicles; their abysmal handling of close-in foes is consistent with this. The heavy feet would allow them to "set" into the ground for firing heavy weapons at long ranges.

I brought up this idea awhile back noting that the AT-AT fire at Hoth appeared very much like artillery fire considering the ranges it fired at. The use of their heavy feet to implant themselves into the ground certainly adds to this speculation.

[Wyrm]

Um, 4πr² is the surface area of a sphere. The area of a circle is A = πr². This means that a four-meter wide cicle (radius: 2 m) has an area of 12.5 m² for each foot, or for all feet together, 50.2 m².

Yeah. Uh, that's what he did.

4 feet, each at A=Pi*R^2, with R=2m (assuming d=4m).

Hence 4*Pi*2^2.

lol@silly wyrm

Duly razzed.

ADDENDUM:

Regarding the compressibility of ice and snow that was brought up several times.. wouldn't water ice (and snow) return to liquid state when compresed, due to trying to reach equilibrium? Since water is more dense than ice, and all that.

Not if it's cold enough. Ice melts when compressed because the increased pressure shoves the water from the solid phase to the liquid phase through adiabatic compression. (The work on the ice mass heats it a bit, raising its temperature.) This is easily believable if the AT-AT's footfalls are causing Echo Base to shake from several km away, but if the feet are only sinking a foot into the ground, this is more difficult to believe. (The sinking of Luke's feet into the same snow is about the same order.)

[Connor MacLeod]

[
I think it'd be profoundly stupid if the AT-ATs blew up the shield generators and then ended up sinking into the snow.

Yeah, ,because there was nothing keeping them aloft but the shield generators, and without it they would have fallen into a sixty-foot deep snowdrift.