Buoyancy of a to-be-immersed tunnnel element
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Hi you all,
First post on this forum, so please correct me if i'm violating any rules.
I'm using SU8PRO and recently installed SP3.2. Now my challenge is to model a tunnel element for a to be immersed tunnel and sea of salt water and check if it floats and if it's stable. FYI an immersed tunnel is built by shipping floating tunnel elements to the right location en let them sink onto the right place on the bottom of the sea by making them heavier.
Now the density (or the weight) of water is app. 1.025 and the density of armored concrete is 2.500. Because the tunnel element has got closed hollow spaces it's supposed to float. I modeled these hollow spaces as groups with a density of 0.000, placed inside the tunnel element.
By my calculations the weight of the tunnel element is less then the weight of the displaced water, so the tunnel should float. But in Sketchup, it doesn't. Not even close. See my attached model.
Has someone any clue on where i'm going wrong? How SHOULD I model a heavy object with air inside?
Off course what I can do is add up the volume of the concrete and the hollow spaces, divide them by the weight of the concrete and give the complete tunnel element that weight. Actually that's not what I want, because that eliminates the differences in thicknesses - and thereby the weight - of each wall or roof.
Hope to get some help.
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Your objects are non-solid groups.
Therefore their volume is unlikely to be reported properly.You don't need SP to do this ?
Try making the concrete part one simple solid box, and the hollow parts one solid of several individual.
They'll both then have proper volumes - reported in Entity Info...Get the volume of the concrete and subtract the volume of the hollow parts - you now have the volume of total 'sealed assembly', and of the 'concrete' and the 'hollow parts'... let's invent some values:
20 m3 and 80 m3 respectively - where the 'sealed assembly' totals 100 m3...
Use the concrete density to calculate the assembly's weight [we'll ignore what's in the hollow parts!].
For simplicity we'll assume 2.5 tonnes/cu3.
Then the concrete [and the assembly ignoring what's in the hollow parts] weighs 2.5 x 20 = 50 tonnes
The total volume is 100 m3 so the assembly's density is 50 / 100 = 0.5 tonnes/m3 - the water's density is just over 1.0 tonnes/m3, so the assembly should float.
The upward force of buoyancy is equal to the weight of the displaced water.
To float the 'sealed assembly' the displaced water needs to weigh at least the weight of the 'sealed assembly' = 50 tonnes, or more - i.e. be ~50 m3 or more.
The 'sealed assembly' is actually 100 m3 so it should float with the water-line at ~50% sides.
If you have proportionally more concrete in the 'sealed assembly' then it will ride lower in the water, until you have its density at > ~1.0 tonnes/m3 - at which point it will sink as it is denser than the water.
If it's safer if it floats lower in the water then allowing some water into the hollows will increase it's combined density and thereby the water-line will be higher up the sides
If you have proportionally less concrete in the 'sealed assembly' then it will ride higher in the water, if that is 'safe' - but it can never float on the very top surface, because it must displace some water to provide the upward force of buoyancy... -
Hi TIG,
Thanks for your quick reaction. Though I'm not sure what you're saying :O.
"Your objects are non-solid groups."
My solids tool says they are."You don't need SP to do this ?"
I'll admit I don't need SP for the calculation, but it would be great to test my calculations with SP.I understand your calculation with the result of app. 50% draft and i know how the system works with ballast water tanks to get the result of no pitch or roll or a preferred draft. But as mentioned in my first post, I don't want the 'sealed assembly' to have a homogeneous mass. I want to see if there is any roll while floating. With the given model I know there is, so now I'm trying to simulate that with SP. I guess it's not jet bug free.
When I just tried again, the 'air volumes' just went trough the roof of the tunnel.
I don't know how to glue two groups together with both of them with there own density..
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I'm no SP expert.
Although the individual 'pieces' might be 'solids', when you assemble them like you have, then they are no longer 'manifold solids', but nested groups.
You can't get a reliable volume unless the selected group/instance is a real 'solid'...
That's why I suggested you make an overall 'box' get its volume and subtract the volume of the 'air' - you could combine all of the separate 'air cavities' groups [exploded] into one solid 'air' group that would still return its true volume...You could try using my CenterOfGravity tool to find the CofG of the 'assembly' concrete-parts-group and air-parts-group... then combine them into a third CofG- their different densities will be reflected in the CofG location
If the CofG/side-SPs are much above the water-line then it might float but be top heavy and therefore prone to capsizing...I don't know how you combine different density solids into one SP object...
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When it comes to "complex solids" like pipes or things with holes or voids in them it is best to think how the object can be subdivided into convex hulls (though not always necessary you can use boxes, cones, etc) and then you group the convex hulls together in a group. For instance a hollow ball would be modeled by a set of elements that would almost approximate truncated prisms for each little subelement. Smaller and smaller elements means the "shell" in terms of displacement volume will approach the actual value volume. Looking at this model I think a total of 16 subshapes (some of them repeated) will do the trick.
While the above paragraph is true for things like interactions between objects, this doesn't seem to solve the buoyancy problem. Perhaps someone else can shed some light in the murky waters.
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@TIG: I actually do use your CoG tool! I like it a lot. I used it already to check my calculations for the center point and the weight of the concrete shape and used this weight to calculate the volume of the displaced water. Then again I used your tool to find the buoyancy point.
I'm now thinking of the right way to make one group of concrete with one rectangeled shape cut out and make one group of air. What I've tried already was to have separate groups of air in the hollow spaces of the concrete element. To bad it resulted in up flying air groups and a falling concrete tunnel element. Somehow I can't get the air groups to be enclosed in the tunnel. The just fly through the roof..@mptak: Thanks for your input. I've already tried to make separate groups, but I can't find a way to make torque tightened connections between these objects. They just fall apart.
Does someone know how to solve this?
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You might try using fixed joints (the round ball one) though up to now I have had the most luck in just changing the overall density (specific gravity). I suppose the problem with adding "air groups" is that one then cannot run cars through the tunnel. Overall the buoyant functionality seem a little less than predictable even with the most simple of objects as is evidenced in this attached file.
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hmmz.. Based on your example, it seems that the laws of physics of buoyancy haven't been programmed quite flawless yet. I think I'll wait voor SP4.0. Maybe things have changed by then
Thnx both of you for your time and help.
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