Mathematical formulae reveal how to make the perfect donut every time

  • Mathematician Dr Eugenia Cheng used calculus to study ring doughnuts
  • She found that the perfect doughnut has an 0.4-inch (11mm) hole
  • This gives it an optimum ‘squidgy to crispy’ ratio of 3.5 to 1
  • A total of 5.8g of sugar is then needed to evenly coat the doughnut
  • The bigger the hole, the crispier the crust and the smaller the hole, the softer the inside 

Victoria Woollaston for MailOnline

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The best tasting ring doughnuts are said to be those straight from the fryer with just the right level of softness, a crispy crust and a light dusting of sugar.

And now a mathematician has established the formulae needed to create these perfect doughnuts every time.

Dr Eugenia Cheng found that a ring doughnut with a 0.4-inch (11mm) hole has the best ‘squidgy to crispy’ ratio of 3.5 to 1 – and 5.8g of sugar is needed to add the right amount of taste.

To get the optimum level of softness to crispness, a ring doughnut should have an average hole size of 0.4-inches (11mm). This gives it a 'squidge to crisp' ratio of 3.5 to 1. Its diameter should be between 2.8-inches and 3.2-inches (72mm and 82mm), and then a total of 5.8g of sugar is needed to evenly coat the doughnut

To get the optimum level of softness to crispness, a ring doughnut should have an average hole size of 0.4-inches (11mm). This gives it a ‘squidge to crisp’ ratio of 3.5 to 1. Its diameter should be between 2.8-inches and 3.2-inches (72mm and 82mm), and then a total of 5.8g of sugar is needed to evenly coat the doughnut

‘The doughnut, aka torus, is an important mathematical object, as well as being delicious,’ explained Dr Cheng, a senior lecturer of Pure Mathematics at Sheffield University.

Commissioned by Domino’s Pizza, Dr Cheng devised formulas to find the volume and surface area of doughnuts, the sugar to doughnut ratio, the mass of sugar and the ‘squidge to crisp ratio.’

THE PERFECT RING DOUGHNUT 

The optimum 'squidge to crisp' ratio of a ring doughnut formula is pictured

The optimum ‘squidge to crisp’ ratio of a ring doughnut formula is pictured

To get the tastiest level of softness to crispness, a ring doughnut should have an average hole size of 0.4-inches (11mm).

This is a ‘squidge to crisp’ ratio of 3.5 to 1. 

Its diameter should be between 2.8-inches and 3.2-inches (72mm and 82mm). 

A total of 5.8g of sugar is then needed to evenly coat the doughnut. 

All being equal, the bigger the hole, the crispier the crust and the smaller the hole, the softer the inside. 

While the sugar to doughnut ratio was established as two over r.

Dr Cheng identified the ‘squidge to crisp ratio’, confirms that, all else being equal, the bigger the hole, the crispier the crust. 

While the smaller the hole, the softer the inside.

To get the tastiest level of softness to crispness, a ring doughnut should have an average hole size of 0.4-inches (11mm).

This gives it a ratio of 3.5 to 1. 

Its diameter should be between 2.8-inches and 3.2-inches (72mm and 82mm). 

‘This relatively small hole means that the doughnuts are 78 per cent squidge and 22 per cent crisp,’ explained Dr Cheng.

‘You imagine that as the doughnut grows, it has to keep adding on an infinitely thin surface area amount of doughnut, like putting on extra layers of clothing.

‘Of course, there’s no such thing as an infinitely thin layer of doughnut around the outside – in reality it has some thickness. 

‘This is the crispy part around the outside.’

She took the overall volume of the doughnut and then subtracted the volume of the soft part on the inside, which is itself in the shape of a doughnut.

The radius of the doughnut is denoted by R, measured from the centre of the hole to the middle of the dough.

While the smaller radius of the dough inside is shown as ‘r’, measuring the thickness of the dough.

Starting with a circle of 5g of caster sugar, Dr Cheng found it covered a radius of 70mm.

She then worked out the mass of sugar needed to cover an average doughnut with an R of 30mm and a r of 15mm, before using the ratio to determine 5.8g of sugar is need to evenly coat the Domino’s doughnut.

The radius of the doughnut (pictured) is denoted by R, measured from the centre of the hole to the middle of the dough. While the smaller radius of the dough inside is shown as r, measuring the thickness of the dough

The radius of the doughnut (pictured) is denoted by R, measured from the centre of the hole to the middle of the dough. While the smaller radius of the dough inside is shown as r, measuring the thickness of the dough

Dr. Cheng's formulas for the volume of doughnut, surface area, sugar to doughnut ratio, the mass of sugar needed for the doughnut and the 'squidge to crisp ratio' are pictured

Dr. Cheng’s formulas for the volume of doughnut, surface area, sugar to doughnut ratio, the mass of sugar needed for the doughnut and the ‘squidge to crisp ratio’ are pictured

The sugar to doughnut ratio was established as two over r.

‘Admittedly if we fix the volume of dough, the amount of sugar we get is proportional to the square root of the size of the hole.’

But Dr Cheng concluded: ‘It’s easy to get carried away messing around with calculus.

‘Go ahead and eat your doughnuts however you like them.’

FORMULA FOR THE PERFECT PIZZA 

Dr Cheng recently calculated (pictured) while smaller pizzas have more topping per bite, there is a larger risk of the pizza having a soggy bottom

Dr Cheng recently calculated (pictured) while smaller pizzas have more topping per bite, there is a larger risk of the pizza having a soggy bottom

Dr Cheng recently calculated that in relative terms, the average bite taken from an 11-inch pizza has 10 per cent more topping than the average bite from a 14-inch pizza.

Her formula also reveals that while
smaller pizzas have more topping per bite, for home cooks seeking lots of extras on their creations, there is a
larger risk of their pizza having a soggy bottom.

She created another formula, alpha, divided by the radius of a pizza, squared to work crust sizes for pizzas of different diameters.

She explains the size of the pizza’s crust is proportional to the thickness of the pizza – the larger the pizza, the thinner the base, so the smaller the crust. 

Dr. Cheng has found that the secret lies in proportions of the 14 inch pizza as it cooks just as evenly as the smaller version but the topping is spread over a larger area and goes close to the edge of the pizza.

However, technically, pizza lovers in search of the most topping per bite should opt for the 11-inch classic version, based on the research. 

 


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