** 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]
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[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=12.9 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  17.85 MJ, 53.55 MJ, and 107.1 MJ 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.

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 6 liters capacity, but seemed questionable beyond 6 liters.

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.

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 was the standard beer bottle or beer jar size in modern terms. 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 Babylonian trash bin will most likely be associated with beer.

*** 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). 
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*** Pseudocode and Equations ***
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     #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?
====== 
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***Testcases Section***
**** Testcase 1 ****
%|table 1|printed in| tcl wiki 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  |  |&
&| 9.0 :|proportional vessel base diameter to sila bowl cm  |  |&
&| 1.003 :|green clay mass |  |&
&| 0.952 :|soft fired pottery mass   |  |&
 

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**** Testcase 2 ****
%|table 2|printed in| tcl wiki 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  |  |&
&| 12.727 :|proportional vessel base diameter to sila bowl cm  |  |&
&| 2.006 :|green clay mass |  |&
&| 1.9056 :|soft fired pottery mass   |  |&

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**** Testcase 3 ****
%|table 3|printed in| tcl wiki 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) |  |&
&| 300.0 :|answers: proportional vessel height to sila bowl cm |  |&
&| 98.590 :|proportional vessel rim diameter to sila bowl cm  |  |&
&| 49.295 :|proportional vessel base diameter to sila bowl cm  |  |&
&| 25.5 :|green clay mass |  |&
&| 24.224 :|soft fired pottery mass   |  |&

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***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, [http://xww.penn.museum ]
   * Planting and Growing Miscanthus Reed  [http://www.naturalengland.org.uk]
   * Brick and Ceramic Sectors  [http://www.faculty.ait.ac.th]
   * Energy Measurements and Conversions [http://www.agmrc.org]
   * Mani Kiln (google >> mani kiln efficient)
   * Village-Level Brickmaking  [http://practicalaction.org]
   * Technical problems of brick production, prepared by Kelvin Mason (June 1998) [http://practicalaction.org]
   * Energy Used to Fire Clay Bricks,  prepared by Kelvin Mason, June1998 [http://practicalaction.org]
   * Energy Used ...  good simple math for bricks, much used [http://practicalaction.org]
   * Building the Mani Kiln, Drawings by Manny Hernandez (google >> mani kiln efficient)
   * Ten Rules for Brick Firing,prepared by  Theo Schilderman (June 1998) [http://practicalaction.org]
   * 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[http://www.cdli.ucla.edu/cdlisearch]
   * Equivalency values page & CDLI MySQL search engine , CDLI Library [http://www.cdli.ucla.edu/cdlisearch]
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**Appendix Code**
***appendix TCL programs and scripts ***

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        # 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: }
        lappend names {soft fired pottery mass:}
        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 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 calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 side8
            global proportional_height proportional_mouth proportional_base
            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
            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 [* $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 side5 [* $proportional_height 0.1 ]
            set side6 [* $proportional_mouth  0.1 ]
            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 |  |&"
            puts "&| $side8 :|soft fired pottery mass   |  |&"
            }
        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   4.2 300.0 98.0 25.5 24.35 }
        ::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"
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[gold] This page is copyrighted under the TCL/TK license terms, [http://tcl.tk/software/tcltk/license.html%|%this license]. 

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