Basic stability calcs for school experiment?

[Highwayman]

Hi there, I would really like a little help, a nudge in the right direction, of how to approach this problem for a small school project: determining the static stability of a tupperware box and how it's stability is affected as a variety and combination of small weights are placed in it.

I've looked through various resources on the internet and some boat design books and pdfs floating about and have got an idea of the theories surrounding static stability but haven't got the foggiest of how to approach the problem, for example determining the waterline angle.

Any helps for a struggling high school student please?

Much obliged,

Richard.

[Guest625101138]

To understand it you need to understand second moment of area.

Do you know how to calculate the second moment of area - or should you know?

Can you do integration? Have you been given formulas for the second moment of area for a rectangle?

Rick

[Highwayman]

Hi there, thanks for the response.

Yes, I do indeed know how to deal with the centroids and the 2nd moment of area of both regular and irregular shapes and integration won't be an issue.

[Guest625101138]

Originally Posted by Highwayman

Hi there, thanks for the response.

Yes, I do indeed know how to deal with the centroids and the 2nd moment of area of both regular and irregular shapes and integration won't be an issue.

Then you have all the basic tools to determine the initial stability. This explains the relationships:
http://en.wikipedia.org/wiki/Metacentric_height

The most important is the equation:
BM = I/V

For a loaded box the I of the waterplane and immersed volume are quite simple calculations.

The box will be statically stable providing the centre of gravity of it and its load is lower than the height of M - the metacentre.

Rick W

[Highwayman]

Thank you for your help sir, I highly appreciate it.

[Ad Hoc]

Richard

What you need to do is place a vertical stick or pole of some kind in the centre of your Tupperware box, and another identical one at the edge, but also on the centre (fore and aft direction).

Firstly you need weighing scales, accurate ones.

Then place the box (with the two attached poles) in the water, and mark off the waterline, on the box.

You can then get the students to calculate the volume and hence demonstrate Archimedes principal.

Then using known weights (weigh them on your scales), of with holes in them which can then slide down the pole/stick, and any number off, onto the centre stick. And then mark off successive waterlines. Again demonstrating Archimedes principal, whilst noting the effects of the box with the increase in total mass.

Then move one of the weights (which is now on the pole/stick) from the centre pole, in the centre of the box, to the pole on the edge (on the centreline longitudinally). You will note that the box will list. You can either measure the new waterlines (on the port side and stbd side with marker pens again), by marking off, or use a simple protractor to measure the angle that the box is now listing at.

Knowing the mass of the box, the mass of the weights being used, the distance moved, and the volume and shape of the box, and now the angle the box takes up when listing, you can calculate the stability of the box.

This is a great fun experiment for students/kids. I have done similar to students in the past.

Good luck.