V3 · Sonnet

Winter stored until September

Ice before the refrigerator

In winter, ice was cut from ponds and stored underground. By summer the same chamber became an account: how much ice was used, and how much simply melted.

February 60.0 m³

After the winter harvest: chamber full.

September

After seven monthly steps of the model.

  • remaining
  • withdrawn for use (useful cold)
  • melted (losses)
  • cover (schematic)

One cell is 1 m³ of ice. The two-chamber layout (ice above a sunken store) is described by Pietrzak in his article on the icehouse of the “Konsum” shop in Łódź; the water outflow in the drawing is a symbol of the diagram, and whether this detail comes from the source needs checking (context and caveat).

A model, not a measurement. Harvest of 60 m³, cover A, moderate withdrawal, a synthetic temperature series. The drawing is a diagram, not the plan of any structure.

Change the assumptions and compare the covers

The winter account

The same stock, three covers

The three chambers get the same ice, the same withdrawal plan and the same temperature series. They differ in one parameter: the cover coefficient k — conventional, not a ranking of materials. Move the month and see where the loss comes from: withdrawal or melting.

Scale and rules of the model

Why a block lasts for months

Heat enters through the surface, while the ice lies in the volume. Doubling the side of a cube gives four times the surface but eight times the volume, so each m³ of ice has less and less surface.

Ratio of the surface to the volume of a cube: S/V = 6 / side. One linear scale for all bars.
  • Cube with a 5 cm side120 m⁻¹
  • 1 m cube (1 m³)6 m⁻¹
  • 60 m³ cube (side c. 3.9 m)c. 1.5 m⁻¹

The difference is of the order of 80 times. For comparison: 60 m³ of solid ice is c. 55 t (ice density c. 0.92 t/m³); in a real chamber the blocks were stacked with gaps, so this figure is only an order of magnitude.

The model also contains the opposite effect: as the block shrinks, the surface decreases more slowly than the volume (V2/3 versus V), so melting eats an ever larger fraction of what is left. A cooler September weakens it.

Rules of a single step (month)

melting [m³] = k · 5 · V2/3 · T · 0.00847
  1. V is the stock at the start of the month in m³, T is the temperature of the step from the synthetic series in °C, k is the cover coefficient (0.22 / 0.42 / 1.45, conventional, dimensionless). The constant 0.00847 and the geometry A = 5·V2/3 are assumptions carried over from V2 — with no documented origin.
  2. Melting comes first, limited to the whole stock. Then withdrawal: the smaller of the plan and what is left. The stock does not fall below zero.
  3. What fell short of the plan is counted separately as unmet withdrawal. It enters neither withdrawal nor losses, so nothing is counted twice: remaining + withdrawn + melted = harvest.
  4. February is the starting state after the harvest. The step is calculated from March to September. We assume no temperature for February.
Step parameters (conventional, in m³ of ice planned for withdrawal in the month)
MonthT [°C]Moderate withdrawalSummer peak
Februaryinitial state——
March32.51.0
April83.01.5
May143.02.5
June173.55.0
July193.56.5
August183.56.0
September132.53.0
Plan total21.525.5

The “Losses only” profile has a plan of 0 in every month. The temperatures are synthetic series A, not readings from any station.

Historical context

From pond to cellar

Descriptions carried over from V2 — to be checked against the source
Four stages of the seasonal cold chain. They replace the tabs from V2: everything is on the page at once, also without JavaScript.

  1. Winter

    Cutting on the pond

    Artificial ice ponds were set up next to breweries. In winter, ice was cut from them. It was needed in large quantities, because fermenting and maturing beer require low temperatures.

    Muzeum Browaru [Brewery Museum], “Piwo lubi chłód” [Beer likes the cold]

  2. Winter

    Every block has to get inside

    An archival photograph shows a conveyor used to direct the blocks into the store; according to the description, workers guided them between the cross slats of the chain. This is an American example — the way of transport in a given brewery has to be established separately.

    Photo: Brown Bros., “The New Student’s Reference Work”, 1914 (Wikimedia Commons)

  3. Spring

    Delaying the inevitable melting

    In brewery cellars, ice went into narrow, tall chambers. The blocks were layered with straw to limit the inflow of heat; the description of the American photograph mentions packing in sawdust. The cover was part of the storage technology.

    Muzeum Browaru (straw) · photograph description (sawdust)

  4. Summer

    The winter stock works for people

    Ice cooled the small cellars with barrels at places where beer was served, as well as the wagons used to transport beer, known as piwiaki. The cold served both production and everyday storage.

    Muzeum Browaru

A Polish trace

Ice above. Store below.

2015rescue investigation of the remains of an icehouse in Łódź
1883/84–1889the period in which the structure was built

The icehouse of the housing-estate shop “Konsum” was investigated at Księży Młyn in Łódź. Janusz Pietrzak describes a two-chamber layout: an above-ground ice store and a cool shop store sunk into the ground. The ice and the goods did not have to occupy the same space.

V2 added that cold air flowed down from the upper chamber and that meltwater was carried away by drainage. The drawing shows this detail schematically; whether it follows directly from the article needs checking.

The author of the research finds no basis for dating the structure’s decommissioning precisely. Archaeology uncovers the technology of everyday life, but does not always preserve a document that closes the history of a building. Study in Folia Archaeologica.

How we know this — and what we do not know

  1. Muzeum Browaru [Brewery Museum] — “Piwo lubi chłód” [Beer likes the cold]
    https://muzeumbrowaru.pl/pl/piwo-lubi-chlod/
    According to the description in V2: artificial ice ponds beside breweries, winter cutting, straw in narrow cellar chambers, cooling of serving-house cellars and of piwiak wagons. To be checked against the source.
  2. Janusz Pietrzak — Lodownia sklepu „Konsum” na Księżym Młynie w Łodzi [The icehouse of the “Konsum” shop at Księży Młyn in Łódź]
    Folia Archaeologica 31, 2016
    According to the description in V2: rescue investigation in 2015, construction dated to 1883/84–1889, a two-level layout of chambers, no basis for precise dating of the decommissioning. To be checked against the source.
  3. Brown Bros. — photograph of a mechanical ice conveyor (1914)
    The New Student’s Reference Work, Wikimedia Commons
    In V3 the photograph is not embedded; there is only a link to the file description. The public-domain status given in V2 needs checking on the file page.

Limits of this page

  • The temperature series (0–19 °C) is synthetic. The coefficients k = 0.22 / 0.42 / 1.45, the constant 0.00847 and the geometry A = 5·V2/3 are conventional — they are not measurement results or a ranking of straw, sawdust and bare masonry.
  • The model ignores the ground, ventilation, opening of the chamber, gaps between blocks, the density of ice and heat gains from the lower chamber. It gives no uncertainty interval: the figures in m³ are the result of a calculation, not a forecast.
  • The drawings of the chambers are the author’s own diagram, not a map or a plan. The barrels and drainage are symbols.
  • The historical descriptions were carried over from V2; the sources were not reopened in this batch. The editors check that the links work and that the text matches the source.
  • Removed from V2: the saving of results in the browser, the worksheet of one’s own trials with an ice cube, and static panels with hard-coded numbers (some did not match the code). The worksheet could not confirm the parameters of an icehouse, and the comparison is now calculated live.

This page is not advice on food storage, nor permission to go onto ice. The model shows only how the stock shrinks under the assumptions adopted.