Topic: Design and the Centre of Gravity

[Bernard C]

If you have an asymmetric object like a fish / animal / boat / &c. posy trough supported by four fins / feet / wheels / &c., where do you put them?   It seems to me more important to maximise stability when the object is in use than when it is not.  So, a designer might experiment to find or calculate the centre of gravity of the object when filled, and then locate the feet so that the centre of gravity is exactly above the centre of the rectangle formed by where the feet rest on the underlying surface.   Subsequently a check should be made on the object when empty to ensure that it is still reasonably stable, starting all over again with the feet further apart if it's not.

There is one simple flaw in this.   I've assumed that the maximum stability of an asymmetric object is when its centre of gravity is directly above the centre of the foot rectangle.   Is this assumption justified?

One other query.   Imagine a fairly standard Murano fish, standing on four fins, weighing 1kg.   The front fins are 10" from the back fins.   If I put the front fins on one set of digital scales and the back fins on another, I get readings of 400g at the front and 600g at the back (because of the tail).   Is the Centre of Gravity 6" back from the front fins and 4" forward from the back fins, or is the calculation more complicated?

Thanks for your interest,

Bernard C. 

[Ivo]

I was always taught that the essence of any object is that it does not topple over. If it does, the design is flawed.

[jsmeasell]

Stability all comes down to physics, doesn't it? That's why lots of glass pieces have a wide, round base or foot. I don't see many pieces with four toes or pegs, etc. because you usually get a wobble (or "wonky") effect. Three toes work just fine because of the way the weight is distributed.

[johnphilip]

Thats why fish have a swim bladder to keep them the right way up , if they get swim bladder problems they look like me after a couple of bottles . :ho:

[Paul S.]

I had half a dozen of these large Murano fish, and my wife said the best place to put them was in someone else's house - so that's where they went (via a charity shop).   Holding one carefully, try placing the index finger various at various positions under the belly and look for the (approximate) point of balance.   Being a bit of a dimbo at physics, I don't know the correct answer, but would have thought that the fish would never over-balance provided the point of balance remained somewhere within the distance between the supporting fins (that prop the thing up).      Of course, these fish remain always at the same weight (they are never filled with anything)- and must admit that the few I did have never gave the impression that they might fall over.   I don't think it would matter whether the point of balance was nearer the front or the back with a fish - they always seemed very stable.
Modern designs (i.e. C20 examples) may well have been made in the knowledge that we all now have dead flat window sills - so no problems with four supports.

"Three toes work just fine because of the way the weight is distributed".       I don't think the distribution of weight is the reasoning behind 'three supports'.      The iconic example of three legs is, of course, the milk-maids stool  -  and the reason why this was designed with three legs is to accommodate 'uneven' ground, not to solve a weight issue (although it has to be admitted that there may well have been some chunky milk maids around in past centuries).   A design with three supports will remain stable always, whether the ground is flat or not.

[Paul S.]

meant to say Bernard, I never had you down as a collector of these tacky/touristy/garish/kitsch/cheap looking/dust collecting fish  -  thought you went in for quality Britsh glass

[Lustrousstone]

Three feet will also allow the feet themselves to be uneven, as four will not.

[dirk.]

Hi Bernhard,
I missed this interesting topic, when you posted it. Quite fascinating, how those
seemingly simple questions can occupy your thoughts for days. IĀ“ve thought about
it and phoned my friend Oliver yesterday to see if he would come to the same conclusions.
HeĀ“s always been best in class for maths and physics in our schooldays and has a
remarkable intuition, when it comes to questions like these.

I've assumed that the maximum stability of an asymmetric object is when its centre of gravity is directly above the centre of the foot rectangle.   Is this assumption justified?

Yes, in any case. IĀ“ll make some further explanations later.

If I put the front fins on one set of digital scales and the back fins on another, I get readings of 400g at the front and 600g at the back (because of the tail).   Is the Centre of Gravity 6" back from the front fins and 4" forward from the back fins, or is the calculation more complicated?

This one was really hard. Oliver gave the final thought for this. We didnĀ“t exercise a
waterproof arithmetic for this problem, so there may be some doubt left. The problem
however becomes more transparent, when you picture this as a special case of the lever
principle. The weight on the scales should be regarded as a force(?) then; just picture the
centre of gravity as the pivoting point.
force (a) x length of lever (a) = force (b) x length of lever (b)
We need to assume this assumption applies, even if the pivoting point isnĀ“t fixed. Further this
will only be true, if the four feet form a rectangular with right angles, as otherwise we canĀ“t
determine the centre of the force for each pair of the feet. Also the feet must be absolutely
horizontal, when put on the scales while measuring.

Subsequently a check should be made on the object when empty to ensure that it is still reasonably stable, starting all over again with the feet further apart if it's not.

Now we come to the problem of toppling over. WeĀ“ve so far missed an important component in
this discussion. Surely any object will only be stable as long as the centre of gravity is over the
base, but the danger of toppling over will be determined by the angle, which is formed between
a line from the centre of gravity to the edge of the stand. Speaking of two objects with the
same stand this will mean: The one with the centre of gravity closer to the base will be more
stable. A coin might be good example: Lying flat the angle between the line from centre of gravity
to the edge and a horizontal line will be ~1Ā° - close to zero danger of toppling over (turning upright
in this case). Put on itĀ“s rim the angle will be ~89Ā° - just the opposite.
If you apply these thoughts to water-filled objects it will come apparent, that their stability when
filled will change proportional to the height of the centre of gravity. So some may even become more
stable, when filled.
Phew - this was most exhausting for me. Hope I didnĀ“t write a lot of inapprehensible nonsense...  

[Paul S.]

my admiration for your ability to write like this in a language other than your own, is boundless.   You are indeed clever Dirk