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Stone Shifting 2
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Steve Gray
Steve Gray
931 posts

Re: Stone Shifting 2
Aug 27, 2003, 11:08
Ok, I've just about finished the computer model. There are a few loose ends to tidy up before I post it on the web for you.

Nigel, I have some difficulty with your descriptions when you refer to left or right because I haven't seen the picture that you have in your head. In my model the tower is on the left and the A frame would be on the right (the model doesn't bother with the A frame). The stone initially rotates clockwise. I have not really programmed the hole. What I do is to assume that when the top right corner of the stone passes below ground level, that corresponds to the right hand side of the hole and that the sloping side of the hole will be wherever the left slope of the block is. I then stop the base of the block from rotating any further (as the ground would do) so that the rotational momentum now carries the block into a clockwise rotation.

I will need some of you practical guys to verify the model with some tests. Put in the figures for the objects you are experimenting with and see if the model predicts their behaviour correctly. If not, I may have to tweak some of the maths.

Based on the current (untested) behaviour of the model I have drawn the following conclusions:

1. Using a low tower helps to prevent slip, but the entry angle into the ground is far from upright so the block needs lots of momentum to get upright.

2. A high tower almost inevitably causes the block to slip, but it is nearer to vertical when it enters the hole.

3. If the centre of the block is close to the pivoting point the block rotates slowly and does not build up so much momentum. (I had mistakenly assumed otherwise at first).

4. If the centre of the block is further from the pivoting point there is much more momentum and the block is more likely to overshoot.

5. A long (and hence large) block gains momentum better than a short block and can therefore be launched from a low tower and still achieve upright.

The model suggests that a 9.75m (32 feet) x 1m block can be launched from a 3m tower with a 1.3m overhang (pivot to centre) and its momentum will just carry it to an upright position. The angle of entry into the ground is 39 degrees.
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