Finding the Optimal Configuration of Three Weetabricks in a Low Milk

Finding the Optimal Configuration of Three Weetabricks in a Low Milk, Light Sugar, Hemispherical Bowl Environment 

Abstract

The stated problem of the optimal configuration of three weetabricks in a hemispherical bowl of radius r = 8cm was first treated analytically and a halfbrick stack was found to be optimal. An empirical investigation followed using a flatter based bowl and two configurations were found to be acceptable, the classic stack and the banana split.

 

1. Introduction

Weetabix are recognised as one of the pillars of modern society and are a regular, reliable and consistent staple breakfast. They are considered by most to be tasty, healthy, quick, convenient and just generally awesome [1]. However, one issue with this titan of cereals is the difficulty with adequately dealing with more than two bricks in one bowl. Four bricks leaves little option but the double stack (or jenga) which almost necessitates excessive milk and sugar to ensure even coverage. Three bricks are also best enjoyed with considerable milk however some poor unfortunates are unable to enjoy these delicious biscuits like normal human beings and insist upon the minimum possible amount of milk. In this instance three bricks presents a substantial problem as each brick must be adequately milked without leaving a pool at the base, implying that it must be poured onto directly. Further, milk cannot be relied upon as a sugar dispersal mechanism and the only recourse is again direct sugar application which is limited by surface area. Clearly then the traditional stack has some significant drawbacks for these pitiful creatures and so this study was undertaken to ascertain the optimal configuration of bricks in these limits.

For clarity, here is a statement of the original problem:

“I have Weetabix in the morning - for preference, 3 bricks. My bowls are internally-hemispherical, with a diameter roughly 1.7 times the length of the average Weetabrick. As for milk, I like there to be enough so that the bricks are not dry and dusty, but not so much that they become a sludge. If there is any milk left at the end, that is too much milk. I like sugar on my Weetabix, sprinkled after the milk has been poured, with a thin coating of sugar on one large face of each brick.
Question: What is the best way to arrange the bricks pre-milk so that I maximise my enjoyment of my cereal?” [1]

2. Theory

Modelling a brick as a 9 x 4.5 x 1.8 cm cuboid and a hemispherical bowl of radius 8cm (d~1.7*9) the lowest flat brick state is at θ=34.2°, with the flat square only possible at θ=52.65° which yields a ground clearance of 3.15cm.

This clearance was deemed unacceptable as it would lead to pooling of the meagre allocation of milk at the base of the bowl and consequently dry and crumbly bricks. The flat configuration is thus ruled out as an acceptable solution (even in a two brick case) which leaves only slanted or broken brick solutions.

Slanted solutions are tricky to solve analytically and the author feels that whilst this would be a more complete solution he is also extremely lazy and if any actual work was to be done it should probably be revision and so these solutions were only treated experimentally.

Broken brick solutions were restricted to halfbrick breaks only for two reasons. The first is the aforementioned lethargy of the author, the second is that further breaks lead to crumblage and the “mush” scenario which this project set out to prevent.

A halfbrick can be laid at the base of the bowl at an angle of θ=23.4°, leading to a ground clearance of 0.66cm which the authors consider acceptable. Furthermore the halfbrick reaches a height of just 2.46cm which means that the flat square can lie on top of the halfbrick, with the second half being placed on top. It should be noted that whilst this does not confer any advantage in surface area over the stack it does allow for bricks to be present at a greater depth would otherwise be the case. As such this is the preferred hemisphere solution.

It is worth noting that a full analysis of this problem probably involves minimising some differential equations but unfortunately maths makes the author cry (and salty tears do not good weetabix make).

 

3. Experiment

Empirical test were also carried out the closest bowl that the author could find in the kitchen, a tesco own brand white bowl with top diameter 15.5cm, a flat base of diameter 7.5cm and a height of 5.5cm. Whilst this is clearly not a hemisphere most bowls have a flat base and this was considered to be a better approximation to a real life situation.

3.1 The Classic Stack

Firstly, the baseline standard configuration, the stack. The great advantages of this configuration are simplicity and stability. The low ground clearance means that the milk is fully utilized and it has considerable surface area. It’s a classic for a reason. The one major disadvantage of this configuration is the lack of surface area for acceptable sugar distribution with a whole bricks worth of concealment. This configuration is successful and popular and is taken as the baseline for comparison.

 

3.2 Vertical stack

The vertical stack is the most obvious solution to the surface area problem with the stack. Ground clearence is low and surface area is almost completely maximised however stability and ease of milking are problems with this design. Sugaring is not as tricky as it appears but the milking issue makes it very difficult to achieve thorough milking, reducing average enjoyment and probably eliminating the vertical stack as the optimal configuration.

3.3 Banana Split

This novel design maintains the surface area advantage that the vertical stacked developed and the split design aids stability. Further the lower clearence of the centre brick leads to much improved milk distibution. Sugaring remains tricky however with practice a small spray on either side leads to satisfactory sweetening.

It would initially seem that the high clearance of the bricks from the side of the bowl would present a problem. This is not as large a drawback as it seems owing to the large area for pouring milk directlly onto the bricks.

If there was a criticism it would be that the central brick is sometimes under milked right in the center. The edges all recieve adequate milking but sometimes the very centre is a little on the dry side. Overall, this is an extremely succesful design and a strong contender to the stack.

3.4  The radiatior

 

This is an interesting configuration which maximises the surface area, however significant issues arise with the sugaring of the center brick and clear, consistent milking is borderline impossible without exceeding the meagre milk allowance that the study specified. Further, stability issues rendered the eating of the biscuits tricky and the hassle of carefully arranging the bricks might be beyond the early morning motor skills of the studies target demographic. In short, this configuration was quickly found to be completely unsuitable.

3.5 The Stonehenge

Given the brief to maximise enjoyment from the cereal I felt that this configuration should be considered. Whilst clearly wildly impractical and despite failing dismally when measured against any of the criteria we have been considering it is extremely enjoyable to destroy an ancient monument in your cereal bowl and the novelty factor was considerable. Whilst not an everyday solution the author believes that it is worth a try at least once. (Full disclosure: Cocktail sticks were used to contruct the stonehenge

3.6 The Colapsed Stonehenge

This is the flattest configuration of three whole bricks that could be achieved. Surface area is maximised and assembly is simpler than some. Ground clearence is a problem here as flat milk pouring is all that can be relied upon for milking and this leads to a highb risk of spillage over the side due to the high peak almost extending over the top of the bowl. This configuration is risky and inconsistent. Not recommended.

3.7 Halfbrick solutions

Halfbrick solutions were speculativly tried, however the author got hungry and ate his weetabix. Perhaps another day...

 

4. Extending the investigation

The main constraint on maximal enjoyment of three bricks is the combination of strick bowl and milk restrictions. It should be noted that the collapsed stone henge  can provide an extremely satisfactory breakfast experience when taken in a wider, shallower bowl such as a soup bowl .

It was also brought to the authors attention by Parks et al [3] that the stringent milk contraint might be better met by dipping the bricks into milk individually before placing in a milk free bowl. Sugar could then be applied on an individual basis and the classic stack, now individually milked and sugared, could be assembled and eaten with relish. This approach could cause unessessary mess when entrusted to neanderthals early in the morning however it offers significant hints at other non standard solutions.

5. Conclusion

It was pretty clear at this stage that the analytic solution was completely worthless and that most of the experiments tried were wildly (sometimes dangerously) impractical. Two configurations emerged as clear favourites: The classic stack and the banana split. Trading of simplicity of assembly against maximal area is a tricky problem that probably comes down to personal taste and time in the morning.

6. References

[1] Everyone, Cummon, they totally are, Since the beggining of time

[2] D. Gray, facebook wall post, 2011

[3] T. Parks, private communications, 2011

 

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