A Treatment of Central Nugg Theory – or – Taking the Limit of Sugar-Butter Divinity

Avecilla, et al.

1. Nug / Spiral / Outer Edge Preferences in the General Population and Preference Optimization Functions

Human taste preferences play a role in cinnamon roll consumption patterns, roll per capita volume, and general attitudes toward cinnamon rolls. Sub-optimal roll structures are hypothesized to contribute to interpersonal strife, disappointment with the state of the universe, and susceptibility to neo-dadaist cults.

In order to investigate these phenomena, we pursue an experimentalist approach, varying the internal fine-structure of the dough, cinnamon filling, and frosting. In addition, we refine the cinnamon roll as a modern meta-material, incorporating meso-scale patterning that is shown to focus the pleasure wave experiences.

Situating our study in the cultural context, we note that 75% of the cinnamon roll consuming population prefer the very middle of the roll as the most exquisite part, while 25% prefer the outer crust. It has been shown that no one prefers the long spiral wrapping as their favorite [9]. In order to pursue a more perfect union of middle, here termed “Central Nugg”, with outer crust, we create a series of rolls having ever more refined implementations of “All Central Nuggs”.

2. Modeling the Spiral

The spiral roll can be approximately modeled as an archimedian spiral (1) r = a + bθ having uniform layer thickness where θ is sufficiently large. Thickness of the dough layer is 3 to 6 mm in the unrisen state, and 6 to 9 mm in the risen, baked state. The expansion is due primarily to increasing gas fraction of CO2 during rising, from 5% to 50% by volume, isobaric expansion due to heating from 300K to 373K, and evolution of H2O vapor during baking. Thickness of the filling layer is 0.5 to 3 mm unrisen, and may decrease during rising and baking as the filling melts. A typical roll may be approximated as r = 5θ / 2π for θ from 0 to 8π

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Complicating this picture, the dough is formed from a sheet of constant thickness, and cannot reduce its dimension in the limit of θ -> 0. This produces discontinuities in the form of the dough-filling spiral, which are what ultimately give rise to the desired phenomenon of the Central Nugg. A more complete model of the roll is given by 5/(2π)*θ-4 < r < 5/(2π)*θ, θ from 2π to 9π Notice that due to the terminus of the dough rollup, there is a filling enriched region at the middle, contributing to the enhanced cinnamonyness of the Central Nugg.

3. Heat Transfer and Deliciousness Diffusion

Another component of the deliciousness of the Nugg is its slight underbake, relative to the more external parts of the roll. It is baked by conduction from below, and radiation from above, but it temperature curve is retarded by the surrounding roll, and it is steamed and braised by the filling it is surrounded by.

According to Matz (1972), conduction and radiation tend to localize heat differentials, with conduction acting to raise the temperature of the loaf bottoms and sidewalls of pan bread, and radiation that of exposed loaf surfaces; convection, on the other hand, tends to create a more uniform heat distribution within the oven.

Sluimer (2005), however, stated that conduction contributes only a small part of the heat transport of baking, and the greater part of the heat required to bake a product originates from condensation of steam within the product. Bakery engineers and bakers alike (Sievers 1978, Lanham 1994) have observed that the cellular structure of dough makes it a poor conductor of heat.  

Baking Business
https://www.bakingbusiness.com/articles/47205-pyler-says-three-ways-heat-is-transferred-to-dough

4. Definition of a Central Nugg

In order to pursue the Central Nugg, we must understand what is its essential quality and how to recreate that. Preceding sections have hinted at its geometric and thermodynamic qualities.

4.a Geometric Definition

Intuitively, the Central Nugg is at the center. But we hypothesize that this is merely a coincidental correlation, and the Nugg can be recreated in other locations. It must contain sufficient filling to provide for excess cinnamon, and enough surrounding dough to provide moderated baking conditions.

There is however, an additional ineffable geometric component to the Nugg. Consider the following three cross sections of candidate Nuggs, all having equal area:

Intuition and psychometric data from cinnamon roll users suggest that not all of these are considered equal as Central Nuggs. The candidate on the left is too flat; it doesn’t enrobe a soft chewy center. The candidate on the right is a recapitulation of the entirety of a roll. It may contain a central nugg, but it not one in and of itself. The candidate in the center, is the epitome of the nugg. Using the model established previously, we see that the nugg should contain approximately the first 3π/2 to 5π/2 radians worth of dough spiral.

In Section 6. Results, you will see a variety of spiral morphologies in the realized Nuggs. This was due to experimental tolerances, and deliciousness metrics were performed across the various nuggs to compare the resulting output.

4.b Definition from Bending Stress and Tensile Strength

Finally, we should not simply accept the intuitive definition, but we should determine why it is so. An analysis of the nugg from material science and statics suggests an answer. During the unwinding and consumption process, much of the roll may be smoothly unrolled, experiencing elastic deformation. However, a point is reached at which any further attempted unwinding results in tensile rupture of the inner dough surface, and the central nugg is reached.

The tensile strength of bread is given as 1 to 11 kN/m^2, [M.G Scanlon, H.D Sapirstein, D Fahloul, Journal of Cereal Science, 2000], while the classical beam strength equation is given by:

As the unwinding proceeds down the spiral, the fulcrum distances continually decrease, until a point is reached at which no further unwinding can occur without tensile rupture. At this limit, the Central Nugg has been reached.

5. Implementation

The desired implementation will achieve a rich buttery dough, fluffy with a medium grained crumb. The volumetric porosity should have an RMS scale on the order of 1 mm. Starch carmelization and mailliard reactions contribute to palatable color and rich flavor. Protein and sugars carmelization in the filling enrich and stabilize the sugary goo. Proper candida growth parameters and protein cross-linking through mechanical strain accumulation must occur in order to support rise and porosity. The filling requires a blend of butteryness, tanginess, and fluff.

Shaping is a precision process to create the “All Central Nuggs” rolls. Divide the dough in to 4 equal portions. Roll out one portion of dough into a 10×15″ rectangle. Coat with 1/2 the filling. Slice into 7 strips, cutting parallel to the short edge. Roll these tightly and freeze. Repeat with another 1/4 of the dough.

Roll another portion into a 10×10″ rectangle. Cover in filling, leaving 1″ uncovered along one edge. Array 7 of the frozen nuggs on the dough, in a hexagonal-close-packed arrangement. As you are stacking the nuggs, spread cinnamon filling on and between them so that each one is completely surrounded by filling. Failure to do this will result in unacceptable results. Roll the hexagonal close packed nuggs up in the dough rectangle and immediately slice into 1.25″ thick rounds with the sharpest available knife. Repeat with the other set of frozen nuggs and remaining quarter of dough.

Cinnamon Roll dough (makes about 12)

• 3 large eggs, room temp
• ¾ C buttermilk, room temp
• 2-¼ t yeast
• Mix
  • ¼ C Sugar
  • 1-¼ t salt
  • 4-¼ C Flour
• Extra flour  (1 C) for adjustment and rolling
• 6T butter, melted and cooled

Proof yeast in buttermilk

Mix in eggs, followed by flour mix in two additions

Knead 10 min with dough hooks, 1 min more by hand, add more flour halfway through if still quite sticky. rise oiled and covered in a warm place until double

Filling:

• 1/2 C Butter
• 1/4 t salt
• 1 C packed light brown sugar
• 2 T cinnamon

Make 12 many-eyed rolls

rise 20min or until nearly double (can rise overnight)

bake 375 for 20-27m

Frosting

• 8 oz Cream Cheese
• 4 oz cool soft butter
• 1.5 C pwd sugar
• ⅛ t salt
• 1 t vanilla
• Fold in ½ C heavy cream, whipped to soft peaks

6. Results