Back in July 2014, whilst on a day trip to Whitby, I ate at **the Angel Wetherspoons’ pub**. I sent this tweet.

@jdwtweet I generally love your food but this at Angel Whitby is a little stingy!! pic.twitter.com/YRtkWct19O

— Doug Paulley (@kingqueen3065) July 16, 2014

Wetherspoons responded by **pulling the CCTV** of our meal and **interviewing the waitress**. They indicated that the portion size was **within one standard deviation of the mean** of their standard so they were **content** with the size of the portion. They accounted for my disapproval with the observation that I **had been eating for precisely 2 minutes and 17 seconds** when I took the photo, and stated that the waitress had testified that I had **not indicated any displeasure** to her at the time of the meal.

I was **impressed** with this commitment to **customer satisfaction**, so when I attended *The Corryvreckan* (Wetherspoons’ pub in **Oban**) whilst on holiday last week, I decided to support their analysis with the **provision of data from another sample**. This is therefore a **comparative study** of the size of Wetherspoons’ **Steak and Kidney pudding meal**.

The diameter of the meal is approximately 18cm, on a patterned plate of approximately 25cm. The surface area of a plate of diameter d is approximately (πd^{2})/4, or in this case 490cm. Of that, approximately ^{2}250cm was obscured by food or by the gravy pot, that being an occlusion of approximately ^{2}51% of the plate. This appears to be roughly equivalent to that of Whitby in 2014; though I note that the practice of providing a gravy boat may give the impression of more food than previously. | |

The chips appear to be distributed on the plate in a pseudo-random distribution. The average depth of food on the plate is therefore difficult to estimate, but is perhaps a mean of 1 or 2 centimetres from the deepest point. | |

The pudding varies in diameter between 7cm at its “base” (the top in this picture) to 10cm at its “top” (the bottom in this picture.) The pudding is approximately 6cm in height. Using the reasonable approximation of a cylinder of diameter 8.5cm, its volume can therefore be approximated using the formula volume=(πd^{2}h)/4=340cm. The density of cooked ground beef is approximately ^{3}1.03gcm, essentially indistinguishable from the density of distilled water at standard temperature and pressure (1gcm^{-3}^{-3}), so I estimate the mass of the pudding is approximately 340g. Comparative research of other single portion steak and kidney pies reveals that this is within an order of magnitude of expectation. | |

There were precisely 30 chips, varying in length between 2cm and 12cm, with a median length of perhaps 8cm. There was therefore approximately 2.4m of chip on the plate. | |

The average thickness of each chip was 0.64mm. Given the presence of some outliers with tapered ends, I am estimating the total volume of the chips on the plate as being 240cm x 0.6cm x 0.6cm or 86.4cm. Fried potatoes have a density of ^{3}449Kg/m3, or approximately 0.5gcm-3, so I estimate the total mass of chips to be approximately 43g.Research indicates that the average portion of cooked chips is | |

There were 169 peas. They averaged 0.45cm in diameter. The volume of a sphere of diameter d is (πd^{3})/6, so each pea measured approximately 0.047cm. The total peaage was therefore approximately ^{3}8cm^{3}.The NHS states that the “ The density of cooked peas is 5.5g. | |

The gravy boat is a new addition since 2014. The depth of the gravy is approximately 3.5cm.The average individual portion of gravy is approximately 14cm. I estimate that the surface area of this gravy portion exceeds this and therefore we are on the up.^{2}But not all the gravy got eaten, as I was not furnished with a spoon. | |

The total mass of the pudding, the peas and the chips was therefore approximately 390g.The average eating rate varies substantially by individual, food type and circumstances but is approximately Of course, because I was being | |

My blackcurrant and soda was approximately 11cm in height and the glass was approximately 5.5cm in diameter. Its volume = (πd^{2}h)/4 = 260ml, or just less than half an imperial pint. | |

But, of course, some of that was taken up by ice cubes. There were 5, with an average size of 1.5cm. The total volume of ice was therefore 5 x 1.5 x 1.5 x 1.5 = approximately 17ml.In approximately half of cases, restaurant ice has over 1,000 colliform bacteria per cube (i.e. faecal bacteria) and is thus more contaminated than toilet water. On average, there was therefore probably | |

The receipt varied from 19cm in length to 20.5cm, at a width of 8cm. The total surface area of the receipt was therefore 164cm. At an assumed weight of ^{2}58gm, the paper weighed approximately ^{-2}9mg – or approximately a billionth of the mass of this European oak tree. |

## Conclusion

I hope that this **comparative study** of the **dimensional composition** of my meal is to the **exacting standards** of **Wetherspoons** and **contributes** to their **body of statistical analysis** of their meal – and I look forward to their prompt analysis as to whether their Oban staff complied with **Wetherspoons’ evil corporate penny-pinching control-freak bollocks. **

I think you need to investigate packing of spheres, in particular, the packing of spheres in a pseudo-spherical open container (e.g. a “Spoon”). Mathematically, this is a complex matter:

https://en.wikipedia.org/wiki/Sphere_packing

I also think that an investigation into the range of sizes of peas is in order: variation within the pea world may not be obvious to the human eye but is an important aspect of pea volume estimation.

Natural variation in pea size is something that botanists have studied, and there is an extensive literature on this e.g.:

http://www.ncbi.nlm.nih.gov/pubmed/17727416

However for the purposes of Wetherspoon evaluation, might I respectfully suggest an empirical study? It would require some peas, and a tablespoon. My guess is that three heaped tablespoons of peas is not as large as you estimate, and that the portion provided does fall with the government recommended 5-a-day range. I look forward to reading your followup post on the empirical distribution of peas when measured using a tablespoon, in terms of mass, volume, and number, both within and between spoon-samples.

Sometimes I really worry about you Doug!