1. Maximal tipping angles of nonempty bottles ESSIM 2012, Dresden Group 12 NAMES

2. Outline Problem – Restrictions Creating bottle – Calculations Calculating the liquid mass centre – Monte Carlo method – Mesh method Results Conclusion

3. Problem Determine the maximal inclination angle and the corresponding fill quantity for various existing bottles. Figure sources: http://www.4thringroad.com/wp-content/uploads/2009/08/coca-cola-main-design.jpg http://s3.amazonaws.com/static.fab.com/inspiration/154695-612x612-1.png

4. Modelling ideas The bottle will fall when the system’s mass centre passes the tipping point. First, the problem was solved for totally full or totally empty cylindrical bottle, because it is easy to solve analytically. Only 2-dimensional case was considered because of the radial symmetry.

5. Problem restrictions Assumptions made: – Bottle density is homogeneous – Liquid density is homogeneous – Bottle has to be radial symmetric – Tilting point is fixed during inclination

6. Creating bottle For creating the bottle, coordinates of one edge are given Bottle mass is measured Next You will see the bottles we used!

7. Water bottle

8. Coke bottle

9. Cylinder

10. Fat wine bottle

11. Calculating the bottle mass centre Take the mass centre of each line between given coordinates Length of the line Mass centre of system of lines is

12. Calculating the mass centre of liquid Monte Carlo

13. Calculating the mass centre of liquid Mesh Calculate a triangular mesh Find the water level by minimizing the V-V(h) Use coarse grid, but refine in the water level Calculate the mass centre of every triangle

14. Will the bottle fall? Add mass centres of the whole system Has the mass centre passed the tipping point? Picture of a bottle on the edge of falling

15. Results Monte Carlo method

16. Results Mesh model

17. Conclusion Monte Carlo method is quite slow to use 3D would have been more accurate For cylindrical bottles, the maximum tipping angle is easily calculated