Sumerian Pottery Vessel & Clay Mass and eTCL Slot Calculator Demo Example , numerical analysis

Sumerian Pottery Vessel Mass & Clay and eTCL Slot Calculator Demo Example , numerical analysis

This page is under development. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Please include your wiki MONIKER in your comment with the same courtesy that I will give you. Its very hard to reply understandably without some background of the correspondent. Thanks,gold

• Sumerian Pottery Vessel Mass & Clay and eTCL Slot Calculator Demo Example , numerical analysis
• Introduction
  • Clay mass and capacity
  • Clay mass and applied heat
  • Rules of Thumb from Babylonian Tablets
  • Testcases
  • Beer and Jar Types
  • Uses of the eTCL calculator
  • Push Button Operation
  • Pseudocode and Equations
    • Table for Wet, Sun Dried, Fired Brick Ratios
  • Testcases Section
    • Testcase 1
    • Testcase 2
    • Testcase 3
    • Testcase 3
    • Testcase 4
  • References:
• Appendix Code
  • appendix TCL programs and scripts
• Comments Section

Introduction

gold Here is some eTCL starter code for calculating 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.

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 eTCL 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.

Testcases

As a an experiment for the eTCL 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.

Beer and Jar Types

Oops and double oops! After selecting the examples for a 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 eTCL calculator

As a example of using the eTCL 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 eTCL 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 eTCL 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 eTCL 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 eTCL 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 eTCL 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).

Pseudocode and Equations

     #pseudocode can be developed from rules of thumb.
     #pseudocode: some problems can be solved by proportions (rule of three), to some order of magnitude
     #pseudocode: enter quantity1,  quantity2, quantity3 and expected output (quantity4) for testcases.
     #pseudocode: enter time in years, number of remaining items
     #pseudocode: output fraction of (remaining items) over (items at time zero)
     #pseudocode: ouput remaining items as fraction or percent
     #pseudocode: output fraction of (quantity4 ) over ( quantity1 at time zero)
     #pseudocode: output fraction of (quantity2) * (quantity3 ) over (quantity1 at time zero)
     #pseudocode: outputs should be in compatible units.
     #pseudocode: rules of thumb can be 3 to 15 percent off, partly since g..in g..out.
     #pseudocode: need test cases > small,medium, giant
     #pseudocode: need testcases within range of expected operation.
     #pseudocode: are there any cases too small or large to be solved?

Table for Wet, Sun Dried, Fired Brick Ratios

Testcases Section

Testcase 1

Testcase 2

Testcase 3

Testcase 3

Testcase 4

References:

• Kenyan Ceramic Jiko cooking stove, by Hugh Allen
• DELCROIX, G. et HUOT, J.L., 1972, « Les fours dits « de potier » dans l’Orient ancien
• Michio: Anagama: Building Kilns and Firing
• Saraswati, B. and N.B. Behura. 1966. Pottery Techniques of Peasant India.
• Traditional Potters of India, [L1 ]
• Planting and Growing Miscanthus Reed [L2 ]
• Brick and Ceramic Sectors [L3 ]
• Energy Measurements and Conversions [L4 ]
• Mani Kiln (google >> mani kiln efficient)
• Village-Level Brickmaking [L5 ]
• Technical problems of brick production, prepared by Kelvin Mason (June 1998) [L6 ]
• Energy Used to Fire Clay Bricks, prepared by Kelvin Mason, June1998 [L7 ]
• Energy Used ... good simple math for bricks, much used [L8 ]
• Building the Mani Kiln, Drawings by Manny Hernandez (google >> mani kiln efficient)
• Ten Rules for Brick Firing,prepared by Theo Schilderman (June 1998) [L9 ]
• 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 Library[L10 ]
• Equivalency values page & CDLI MySQL search engine , CDLI Library [L11 ]

Appendix Code

appendix TCL programs and scripts

        # pretty print from autoindent and ased editor
        # Sumerian Pottery Vessel Mass Calculator 
        # written on Windows XP on eTCL
        # working under TCL version 8.6.x and eTCL 1.0.1
        # gold on TCL WIKI, 10nov 2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        frame .frame -relief flat -bg aquamarine4
        pack .frame -side top -fill y -anchor center
        set names {{} {pottery vessel volume liters (sila=liter) :} }
        lappend names {quota of N1 vessels per day (optional):}
        lappend names {constant2 green clay per vessel capacity kg/liter (optional):}
        lappend names {applied thermal rating megajoules per kg (optional, supersedes if not zero):}
        lappend names {answers: proportional vessel height to sila bowl cm:}
        lappend names {proportional vessel rim diameter to sila bowl cm: }
        lappend names {green clay mass kg: }
        lappend names {soft fired pottery mass kg:}
        foreach i {1 2 3 4 5 6 7 8} {
            label .frame.label$i -text [lindex $names $i] -anchor e
            entry .frame.entry$i -width 35 -textvariable side$i
            grid .frame.label$i .frame.entry$i -sticky ew -pady 2 -padx 1 }
      proc pi {} {expr acos(-1)}
      proc about {} {
            set msg "Calculator for Sumerian Pottery Vessel Mass
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg }   
      proc break_flag_routine {     } {
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global spares 
            global testcase_number
            set t9 $testcase_number
            set product_entries [* $side1 $side2 $side3 $side4 $side5 $side6 $side7 $side8] 
            if { $product_entries < 0.0 } { puts " warning flag! negative numbers detected in product entries ref. tc$t9" }
            foreach item { 1 2 3 4 5 6 7 8 9 10 } {
            set error$item 0 }
            if { $side1 < 0.0 } { set side1 .000001 ; set error1 1  }
            if { $side2 < 0.0 } { set side2 .000001 ; set error1 1  }
            if { $side3 < 0.0 } { set side3 .000001 ; set error1 1  }
            if { $side4 < 0.0 } { set side4 .000001 ; set error1 1  } 
            if { $side5 < 0.0 } { set side5 .000001 ; set error1 1  }
            if { $side6 < 0.0 } { set side6 .000001 ; set error1 1  }
            if { $side7 < 0.0 } { set side7 .000001 ; set error1 1  }
            if { $side8 < 0.0 } { set side8 .000001 ; set error1 1  } 
            if { $error1 == 1 } { puts " warning flag! negative numbers detected, defaulted to positive entries ref. tc$t9" }
            foreach item { 1 2 3 4 5 6 7 8 9 10 } {
            set error$item 0 }
            return 1 }
       proc experimental_dimensions {} {
            global proportional_height proportional_mouth proportional_base
            global liter_capacity
            set bevel_bowl_height 100.0
            set bevel_mouth_diameter 180.0
            set bevel_base_diameter 90.0
            set beveled_bowl_volume 1484.0
            set beveled_bowl_volume 1000.0
            set liter_capacityx 1.
            set liter_capacityx [* $liter_capacity 1000.0]
            set proportional_height [/ [* $bevel_bowl_height  $liter_capacityx ] $beveled_bowl_volume ]
            set proportional_mouth [/ [* $bevel_mouth_diameter $bevel_mouth_diameter $liter_capacityx ] $beveled_bowl_volume ]
            set proportional_mouth [sqrt $proportional_mouth ]
            set proportional_base [/ [* $bevel_base_diameter $bevel_base_diameter $liter_capacityx ] $beveled_bowl_volume ]
            set proportional_base [* [sqrt $proportional_base ] 0.1 ]
            set proportional_height [* $proportional_height .1 ]
            set proportional_mouth  [* $proportional_mouth .1 ]
            set proportional_base [* $proportional_base .1 ]
            if { $liter_capacity < 4.1 } { return 1 }
            if { $liter_capacity > 4.0 } {
            set exponent [/ 1. 3. ]
            set term1 [/ [* $liter_capacityx 4. ] [ pi ] ]
            set diameterx   [* [pow $term1 $exponent ] 1. ] 
            set proportional_height $diameterx
            set proportional_mouth $diameterx
            set proportional_base $diameterx }
            return 1 }   
       proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global proportional_height proportional_mouth proportional_base
            global liter_capacity
            global testcase_number
            incr testcase_number 
            set side1 [* $side1 1. ]
            set side2 [* $side2 1. ]
            set side3 [* $side3 1. ]
            set side4 [* $side4 1. ]
            set side5 [* $side5 1. ]
            set side6 [* $side6 1. ]
            set side7 [* $side7 1. ]
            set side8 [* $side8 1. ] 
            break_flag_routine
            set constant2_kg_liter 1.00308 
            set constant3_kg_liter 0.8503 
            set constant4_mana_sila 2.0154 
            set constant5_mana_sila 1.7086  
            set megajoles_per_kg 4.2
            set total_green_clay 1.0
            set total_fired_clay 1.0
            set proportional_height 1.0
            set proportional_width 1.0
            set liter_capacity $side1
            set daily_quota $side2
            set clay_kg_per_liter 1.
            set clay_kg_per_liter $side3
            set moisture_shrinkage 0.95
            experimental_dimensions 
            set side5  $proportional_height 
            set side6  $proportional_mouth  
            set total_green_clay [* $liter_capacity $clay_kg_per_liter  $daily_quota]
            set side7 $total_green_clay
            set total_fired_clay  [* $liter_capacity $clay_kg_per_liter $daily_quota $moisture_shrinkage]
            set side8 $total_fired_clay
            set conversion 0.0
            if { $side4 > 0. } { set conversion [* $total_green_clay $side4 1. ] ; 
            puts " conversion of green clay (if not zero) $side7 unfired kg to $conversion  megajoules"; }
                  }   
        proc fillup {aa bb cc dd ee ff gg hh} {
            .frame.entry1 insert 0 "$aa"
            .frame.entry2 insert 0 "$bb"
            .frame.entry3 insert 0 "$cc"
            .frame.entry4 insert 0 "$dd"
            .frame.entry5 insert 0 "$ee"
            .frame.entry6 insert 0 "$ff" 
            .frame.entry7 insert 0 "$gg"
            .frame.entry8 insert 0 "$hh" 
             }
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7 8 } {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 side8 
            global proportional_height proportional_mouth proportional_base
            global testcase_number
            console show;
            puts "%|table $testcase_number|printed in| tcl wiki format|% "
            puts "&| quantity| value| comment, if any|& "
            puts "&| testcase number:|$testcase_number | |&"           
            puts "&| $side1 :|pottery vessel volume liters (sila=liter)|   |&"
            puts "&| $side2 :|constant2 green clay per vessel capacity kg/liter (optional)  | |& "
            puts "&| $side3 :|applied thermal rating MegaJoules per kg (optional)| |& "
            puts "&| $side4 :|convert applied megajoules routine MJ (supersedes if not zero) |  |&"
            puts "&| $side5 :|answers: proportional vessel height to sila bowl cm |  |&"
            puts "&| $side6 :|proportional vessel rim diameter to sila bowl cm  |  |&"
            puts "&| $proportional_base :|proportional vessel base diameter to sila bowl cm  |  |&"
            puts "&| $side7 :|green clay mass kg |  |&"
            puts "&| $side8 :|soft fired pottery mass kg  |  |&"
            }
        frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 1.0  1. 1.003  4.2 10.0 18.0 1.0  0.95}
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 2.0  1. 1.003  4.2 20.0 25.48 2.0  1.9 }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 30.0 1. 0.85   4.2 33.1 33.1 25.5 24.2 }
        ::ttk::button .clearallx -text clear -command {clearx }
        ::ttk::button .about -text about -command about
        ::ttk::button .cons -text report -command { reportx }
        ::ttk::button .exit -text exit -command {exit}
        pack .calculator  -in .buttons -side top -padx 10 -pady 5
        pack  .clearallx .cons .about .exit .test4 .test3 .test2   -side bottom -in .buttons
        grid .frame .buttons -sticky ns -pady {0 10}
        . configure -background aquamarine4 -highlightcolor brown -relief raised -border 30
        wm title . "Sumerian Pottery Vessel Mass Calculator"

Comments Section

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