Sumerian_Pottery_Vessel_Mass_calculator_numerical_analysis

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Preface

gold12Dec2018. Here are some calculations for Sumerian Pottery Vessel Mass using TCL expressions.


Introduction

Here are some TCL calculations for the clay mass of Sumerian pottery vessels. The impetus for these calculations was checking daily quotas as N1 pots per day in the CDLI Equivalency list. Most of the testcases involve replicas or models, using assumptions and rules of thumb. The units can be changed in the internal calculator formulas as TCL code. Any convenient and consistent output units might be used like millimeters, inches, feet, or dollars to donuts.


In the cuneiform math problems and coefficient lists on clay tablets, there are coefficient numbers which were used in determining the amount of materials and the daily work rates of the workers. In most cases, the math problem is how the coefficient was used in estimating materials, work rates, and math problems. One difficulty is determining the effective magnitude or power of the number coefficient in the base60 notation. In cuneiform, numbers in base60 are written using a relative place notation. For example, 20 could represent either 20*3600,20,20/60, 20/3600, or even 1/20. The basic dimensions and final tallies were presented in the cuneiform accounts on clay tablets, but some calculations, some units, some explanations, and some problem answers (aw shucks!) were left off the tablet. The Babylonians did not use algebra notation, decimal notation, errors in percent, or modern units of measurement. So the reader will have to bear some anachronisms in the initial pseudocode preparations and final TCL code. At least one approach for the modern reader and using modern terminology is to develop the implied algebraic equations and decimal equivalents from the cuneiform numbers. Then the TCL calculator can be run over a number of testcases to validate the algebraic equations.


Revision text. The TCL calculations for Sumerian pottery vessels involve estimating the clay mass required for various types of vessels based on their dimensions and capacities. These calculations can help potters determine the amount of materials needed to produce a specific number of vessels within a given timeframe. The coefficients used in cuneiform math problems and coefficient lists on clay tablets provide valuable insights into the methods and calculations employed by ancient Sumerian potters. Understanding the effective magnitude or power of these coefficients in base60 notation can help modern readers decipher the math problems and work rates described in these ancient texts. One challenge in interpreting cuneiform numbers is determining the relative place notation used, as numbers could represent multiples, divisions, or fractions of different units. However, by developing the implied algebraic equations and decimal equivalents from the cuneiform numbers, modern readers can gain a better understanding of the calculations and processes used by ancient potters. By running the TCL calculator over a number of testcases, it is possible to validate the algebraic equations and gain a deeper appreciation for the methods and techniques employed by Sumerian potters in producing their clay vessels


Clay mass and capacity


The following relations between pot capacity and clay mass was developed from modern potter lore. For 1liter>pots< 2 liters, the constant is 1.00308 kilograms green clay/wet liters, 2.0154 manas/sila, almost 1:1 kg green clay to wet liters. For pots > 2.5 liters, the constant is 0.8503 kilograms green clay/wet liters or 1.7086 manas per sila. Larger pots have proportionally less waste. Also, some large storage pots have been found intact under the ancient floors but were designed without bottoms, apparently to allow complete drainage of contents. Green clay mass here includes the unfired green pot, plus the potter's trim waste, rim cuts, bottom cuts, and kiln stands. Capacity refers to vessel wet capacity after firing (no heaped grain above rim). Clay loses about 5 percent weight in moisture from drying and firing. Tentatively from the quotas in CDLI Equivalency list, the potter molded between 1 to 25 pieces using 4.25, 12.75, and 25.5 kg of green clay in a day.


Clay mass and applied heat


The potters report in MW124 showed 2000 vessels fired with 1800 kilograms of reed fuel (usually Su. gi bar) . The average fuel rate was 1800 kg /2000 vessels, 0.9 kilograms fuel per vessel. The British clamp kiln of 1880's used 1135 kg of wood for 3800 kg of green brick clay for soft fired bricks (1000 bricks*3.8 kg). Setting proportions, green clay in MW124 was 3800*1800/1135, 6026.4 kg of green clay. Average green piece in MW124 was 6026.4 kg / 2000 vessels, 3.01 kg. Averages can be deceptive, but the average vessel in MW124 would be about 3/0.8503 or 3.53 liters capacity.


The applied heat can be estimated from the potters report MW124 and modern kilns. From study of traditional kilns and the British clamp kilns, the applied heat in the Sumerian kilns was about 4.2 MegaJoules per kilogram for a soft firing. The thermal estimate from burning reeds is about 0.9 kg*17MJ/kg=15.3 MJ per (3kg) vessel and in order of magnitude agreement with 3 kg*4.2MJ/kg=12.6 MJ, applied heat estimate. Since a good bit of heat is lost up the chimney, the thermal estimate from burning reeds should be higher than the applied heat to the clay. The gist is that pot and brick quotas in CDLI Equivalency list imply an energy use quota also. The potters quota of 4 1_sila_bowls, 3 5_sila_bowl, and 3_ban_jar per day convert to 16.85 MJ, 63.19 MJ, and 107.1 MJ per day.


Time period, number of kilns, and firings is uncertain in MW124. For tentative planning, the most common small kiln (from the Ubaid era excavations only) of 0.5 meter diameter would take 85 kg of fuel. Using the cited reed fuel of 1800 kgs for 2000 pieces, the number of firings would be 1800 kgs fuel over kgs kiln fuel, 1800/85, rounding 21 firings. The TCL calculator returned 6000 kg of green clay and total applied heat of 25204.2 MegaJoules for the 2000 pieces. The average loading of green clay pieces would be 2000/21, rounding 95 pieces and 6000/21, average 285.71 kgs of green clay. The nominal number of potters or potters daily quotas in the kiln would be 285 kg over tentative 25 kg daily clay molded, 285/25, 11.4, rounded up 12 potters. Most of the Sumerian potters worked in teams of 2 to 10 potters with a foreman (tablets from UrIII). It is clear that only one or two of the larger known 30-sila jars would fit in the small 0.5 meter kiln, if not stacking or placing small pieces inside the jar during firing. The bevel rim bowls are open faced and very stackable in a kiln, stackable into a lower vertical profile than a closed vessel or bottle, and that is a considerable advantage to the bevel rim bowl. The inference is that the 0.5 meter kiln could support 1 to 12 potters on the smaller vessels. The 21 firings would suggest a monthly report. Ref. Sumerian Pottery factory on this wiki.


Rules of Thumb from Babylonian Tablets


Here are some rules of thumb from Babylonian brick constants and Babylonian math problems. A sun dried brick has water content and also as hidden water. Some sun dried bricks have straw content. Straw content should not be a factor in fired bricks. Sun dried brick weight over wet and heavy brick weight equals 40/60 or second try equals 48/60. Sun dried brick weight over baked brick weight equals 50/60. Fraction 1/6 is mortar for clay wall. Weights of wet and sun dried bricks in table BM36776 have factors 3/2 and 6/5, per Friberg and Robson. Second and third section of factor equals 3/2. Fourth section has factor equals 6/5. Water approximates 12/60 weight of wet brick. Weight loss (water) is 10/60 of dried brick to baked brick. { 1 kus ba.an.gi4 } means 1 cubit returned or 1 cubit back, used in brickwork. The daily cartage quota is 37_30 talents per us per day equals expr {(37+30./60.)*30.} or 1125 kg per 60*6 meters per day. The daily cartage quota is 1_15 talent per danna per day equals expr {(1.+15./60.)*30} or 37.5 kg per 10.8 kilometers per day.


In ancient times, potters and brick makers relied on simple rules of thumb to estimate the materials needed for their creations. These rules were derived from practical experience and were often based on the capacity of their vessels or the weight of their bricks. For pottery, a constant of 1.00308 kilograms green clay per wet liter was used for pots with a capacity between 1 and 2 liters. For larger pots, a constant of 0.8503 kilograms green clay per wet liter was used. This constant accounts for the potter's trim waste, rim cuts, bottom cuts, and kiln stands. The capacity refers to the vessel's wet capacity after firing, without any heaped grain above the rim. Potters also had to consider the weight loss during the drying and firing process, which was around 5%.


The potter's daily quota was estimated to be between 4.25 and 25.5 kilograms of green clay. In Babylonian brick construction, the weight of sun-dried bricks was compared to that of wet and heavy bricks, as well as baked bricks. The ratios between these weights were used to estimate the amount of mortar needed for clay walls. The water content of wet bricks was also taken into account, as well as the weight loss during the drying and firing process.


Bricklayers used various factors to estimate the weight of wet and sun-dried bricks, such as 3/2 and 6/5. The daily cartage quota for bricks was also calculated, with quotas varying based on the distance to be covered. These rules of thumb provided a practical framework for potters and bricklayers to estimate the materials needed for their work, ensuring that they could produce enough vessels and bricks to meet the demands of their communities.


Testcases


As a an experiment for the TCL calculator, the entered capacity in liters is used to rescale a beveled rim bowl or cereal bowl of 1 liter. The outer dimensions of the bevel rim bowl are bowl rim diameter = 180 mm, bowl base diameter =90 mm, and bowl height = 100 mm. Using the outer dimensions, the bowl volume is 1484 milliliters. If the walls or sides of the bowl are somewhat less than 10 mm thick, the inner volume is about 1000 ml. The rescaled vessel dimensions in rim,base, and height are included in the report.


The grain bowl of 1 sila capacity should weigh 1*1.00308, 1 kg of green clay. The fired bowl should weigh about 1kg*0.95, 0.95 kg of fired clay. The CDLI quota at Umma of 4 bowls of 1 sila a day would effectively be 4*1 kg of green clay and 4*0.95 or 3.8 kg of fired clay. The grain bowl of 5 sila capacity should weigh 5*0.85, 4.25 kg of green clay and 5*0.85*95, 4.03 kg of fired clay. The CDLI quota at Umma of 3 bowls of 5 sila a day would effectively be 3*4.25 or 12.75 kg of green clay and 3*4.03 or 12.09 kg of fired clay. The 3 ban or 30 sila storage? jar at Umma might weigh about 30*0.8503, 25.5 kg green clay, as one per day quota. Tentatively, the potter molded between 4.25, 12.75, and 25.5 kg of green clay in a day.


Revision text. The TCL calculator involves rescaling a beveled rim bowl or cereal bowl of 1 liter to match a desired capacity. The outer dimensions of the original bowl are used as a reference to calculate the rescaled vessel dimensions in rim, base, and height. This process allows for the creation of custom-sized bowls with specific capacities. The weight of the green clay needed to create a grain bowl of 1 sila capacity is approximately 1 kilogram, while the weight of the fired clay is about 0.95 kilograms. The CDLI quota at Umma, which required 4 bowls of 1 sila capacity to be produced daily, would effectively result in the use of 4 kilograms of green clay and 3.8 kilograms of fired clay. For a grain bowl of 5 sila capacity, the required green clay is 4.25 kilograms, and the fired clay is 4.03 kilograms. The CDLI quota at Umma for 3 bowls of 5 sila capacity would result in the use of 12.75 kilograms of green clay and 12.09 kilograms of fired clay. The 3 ban or 30 sila storage jar at Umma might weigh about 25.5 kilograms of green clay, with a daily quota of 1 potter molding between 4.25, 12.75, and 25.5 kilograms of green clay. This experiment demonstrates the practical considerations involved in pottery production, such as estimating the materials needed based on the desired capacities and shapes of vessels, as well as the weight loss during the drying and firing process. These calculations help potters to manage their resources efficiently and produce the required number of vessels within a given timeframe.


Beer and Jar Types


Oops and double oops! After selecting the examples for a random and wide range of capacity sizes, it was found that all vessel sizes of 1,5, and 30 liters have been associated with beer in the cuneiform texts. The 1-liter is both the size of a common grain ration and the common beer ration, although a beer ration of 2-liters is also cited in the texts. The 5 sila, 20, and 25 sila jars were the standard beer bottles or beer jars in modern terms. The 20 and 25 sila jars were used to deliver beer, but were also used as fermenting containers or mixing containers. What is sometimes called a storage jar of 30 silas was also used as a beer brewing vat or beer keg. Cane straws or drinking tubes were used to sip the beer. The potters made a sort of ceramic drinking tube. The ceramic tubes or cane straws are occasionally mentioned in the texts and illustrated on the clay seals. Note that the 30 sila or 30 liter capacity in beer would weigh 30 liters*1 spg. or 30 kilograms and match the full manload (60 manas). This brings us to Gold's correlary; any three items in a Sumerian trash bin will most likely be associated with beer.


Uses of the TCL calculator


As a example of using the TCL calculator, the potter should enter the capacity and daily quota for the vessel. The applied heat is normally 4.2 MJ/kg from the Sumerian kiln, but can be changed. The answers are total mass of green clay for the day, total mass of fired pottery, and total applied heat. Estimated bowl dimensions are rescaled from the bevel rim bowl of 1 sila capacity. The rescaled bowl dimensions seemed reasonable between 0.5 to 4 liters capacity, but seemed questionable beyond 4 liters.


Not all bowls (dug) in CDLI Equivalency list have a cited capacity, so proportions using the CDLI daily quotas have some potential. For example, the spice or spice-dough bowl known as dug-kur-KU.DU or dug sila ku-du had a quota of 15 bowls per day. The dug sila gal (lit. pot bowl great, 1 sila) had a quota of 10 bowls per day. Perhaps the spice bowl and sila gal are inversely proportional to labor in the daily quotas, 1 sila : unknown silas = 15 bowls per day:10 bowls per day. Resolving the proportions, the spice bowl would be (1*10) /15, decimal 0.666 liter or 2/3 sila. After loading the TCL calculator as 0.666/15/1.003 for the 15 bowl quota, the calculator reported total green clay mass as 10 kg for the daily quota, total fired pottery as 9.5 kg, and total applied heat as 42 MJ (for the daily quota of one potter). The individual pot weighed 0.66 kg of green clay and fired to 0.63 kg of fired soft pottery. The TCL calculator returned experimental dimensions as rim diameter of 14.68 cm, height of 6.66 cm, and base diameter of 7.34 cm. After loading the TCL calculator as 0.666/1/1.003 for 1 bowl, the calculator reported green clay mass as 0.667 kg for one bowl, fired pottery as 0.63 kg, and applied heat as 2.8 MJ. There were bevel rim bowls very close to these specs (0.647 to 0.72 liter) in the Ubaid period, but this posting can not confirm these bowls in the Neo-Sumerian period.

Push Button Operation

For the push buttons in the TCL calculator, the recommended procedure is push testcase and fill frame, change first three entries etc, push solve, and then push report. Report allows copy and paste from console. For testcases in a computer session, the TCL calculator increments a new testcase number internally, eg. TC(1), TC(2) , TC(3) , TC(N). The testcase number is internal to the calculator and will not be printed until the report button is pushed for the current result numbers. The current result numbers will be cleared on the next solve button. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the functions (subroutines).


Testcases Section


Testcase 1

table 1printed in tcl format
quantity value comment, if any
testcase number:1
1.0 :pottery vessel volume liters (sila=liter)
1.0 :constant2 green clay per vessel capacity kg/liter (optional)
1.003 :applied thermal rating MegaJoules per kg (optional)
4.2 :convert applied megajoules routine MJ (supersedes if not zero)
10.0 :answers: proportional vessel height to sila bowl cm
18.0 :proportional vessel rim diameter to sila bowl cm
0.9 :proportional vessel base diameter to sila bowl cm
1.003 :green clay mass kg
0.952 :soft fired pottery mass kg

Testcase 2

table 2printed in tcl format
quantity value comment, if any
testcase number:2
2.0 :pottery vessel volume liters (sila=liter)
1.0 :constant2 green clay per vessel capacity kg/liter (optional)
1.003 :applied thermal rating MegaJoules per kg (optional)
4.2 :convert applied megajoules routine MJ (supersedes if not zero)
20.0 :answers: proportional vessel height to sila bowl cm
25.455 :proportional vessel rim diameter to sila bowl cm
1.272 :proportional vessel base diameter to sila bowl cm
2.006 :green clay mass kg
1.905 :soft fired pottery mass kg

Testcase 3

table 3printed in tcl format
quantity value comment, if any
testcase number:3
30.0 :pottery vessel volume liters (sila=liter)
1.0 :constant2 green clay per vessel capacity kg/liter (optional)
0.85 :applied thermal rating MegaJoules per kg (optional)
4.2 :convert applied megajoules routine MJ (supersedes if not zero)
33.677 :answers: proportional vessel height to sila bowl cm
33.677 :proportional vessel rim diameter to sila bowl cm
33.6778 :proportional vessel base diameter to sila bowl cm
25.5 :green clay mass kg
24.224 :soft fired pottery mass kg


Screenshots Section

figure 1. Calculator Screenshot

figure 2. Console Screenshot


References:

  • google < clay vessels Wikipedia >
  • Wikipedia search engine < Texas Poker algorithm >
  • Wikipedia search engine < multiplication algorithm >
  • Wikipedia search engine < Texas Poker Math >
  • Wikipedia search engine < Texas Poker lograrithms >
  • Wikipedia search engine <Texas Poker >
  • Wolfram Alpha search engine < Texas Poker >
  • Kenyan Ceramic Jiko cooking stove, by Hugh Allen
  • DELCROIX, G. et HUOT, J.L., 1972, « Les fours dits « de potier » dans lÂ’Orient ancien
  • Michio: Anagama: Building Kilns and Firing
  • Saraswati, B. and N.B. Behura. 1966. Pottery Techniques of Peasant India.
  • Traditional Potters of India, 1
  • Planting and Growing Miscanthus Reed 2
  • Brick and Ceramic Sectors 3
  • Energy Measurements and Conversions 4
  • Mani Kiln (google >> mani kiln efficient)
  • Village-Level Brickmaking 5
  • Technical problems of brick production, prepared by Kelvin Mason (June 1998) 6
  • Energy Used to Fire Clay Bricks, prepared by Kelvin Mason, June1998 7
  • Energy Used ... good simple math for bricks, much used 8
  • Building the Mani Kiln, Drawings by Manny Hernandez (google >> mani kiln efficient)
  • Ten Rules for Brick Firing,prepared by Theo Schilderman (June 1998) 9
  • CFD Simulation of Flue Gas Flow in Traditional Pottery , Cecilia Schotte, thesis
  • CFD Simulation of Flue Gas Flow in Pottery Furnace, Kristina Nilenius, thesis
  • Equivalency values of the UR III period, Robert K. Englund, CDLI Library10
  • Equivalency values page & CDLI MySQL search engine , CDLI Library 11

Pseudocode & Equations Section

        more than one formula for 1) tables and 2) calculator shell
   

Appendix Code

Trial GUI Shell




Comments Section

Please place any comments here with your wiki MONIKER and date. Thanks.12DEC2018gold