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
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.
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.
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.
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.
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.
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.
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.
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 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: Wet, Sun Dried, Fired Brick Ratios | printed in | tcl wiki format | |||
|---|---|---|---|---|---|
| ratio | alternate ratio for base60 | decimal base10 | numerator | denominator | comment, if any |
| 3/2 | 90/60 | 1.5 | wet bricks | fired bricks | Old Babylonian |
| 2/3 | 60/90 | 0.666 | fired bricks | wet bricks | Old Babylonian |
| 6/5 | 72/60 | 1.2 | sun dried brick | fired bricks | Old Babylonian |
| 5/6 | 50/60 | 0.8333 | fired brick | sun dried bricks | Old Babylonian |
| 1/1 | 60/60 | 1. | fired bricks | fired bricks | Old Babylonian |
| 5/1 | 300/60 | 5. | price of fired bricks gur/sar | price of fired bricks gur/sar | more common, Old Babylonian |
| 10/1 | 600/60 | 10. | price of fired bricks gur/sar | price of fired bricks gur/sar | less common, redundant, Old Babylonian |
| 1/5 | 12/60 | 0.20 | market rate of fired bricks sar/gur | market rate of unfired bricks sar/gur | more common , Old Babylonian |
| 1/10 | 6/60 | 0.10 | market rate of fired bricks sar/gur | market rate of unfired bricks sar/gur | less common , redundant, Old Babylonian |
| 6.3/5 | 76/60 | 1.2666 | sun dried brick | fired bricks | modern estimate in analysis here |
| O.B. derived mostly from calculations in texts, not necessarily coefficient tables | |||||
| Alternate or redundant values intended for ranging calculations , not hard and fast coefficients by themselves |
| 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 |
| 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 |
| 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 |
| table 4 | printed in | tcl wiki format |
|---|---|---|
| quantity | value | comment, if any |
| testcase number: | 4 | |
| 3.53 : | pottery vessel volume liters (sila=liter) | |
| 2000.0 : | number of vessels, uncertain time? and multiple kilns? | |
| 0.85 : | constant2 green clay per vessel capacity kg/liter (optional) | |
| 4.2 : | convert applied megajoules routine MJ (supersedes if not zero) | |
| 35.300 : | answers:proportional vessel height to sila bowl cm | |
| 33.818 : | proportional vessel rim diameter to sila bowl cm | |
| 16.909 : | proportional vessel base diameter to sila bowl cm | |
| 6000.999 : | green clay mass | |
| 5700.949 : | soft fired pottery mass | |
| 25204.2 : | total applied heat from 6000.999 kg unfired clay |
| table 4 | printed in | tcl wiki format |
|---|---|---|
| quantity | value | comment, if any |
| testcase number: | 4 | |
| 0.666 : | pottery vessel volume liters (sila=liter) | |
| 15.0 : | 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) | |
| 6.66 : | answers: proportional vessel height to sila bowl cm | |
| 14.689 : | proportional vessel rim diameter to sila bowl cm | |
| 7.34479407471714 : | proportional vessel base diameter to sila bowl cm | |
| 10.019 : | total green clay mass kg for daily quota of one potter | |
| 9.5189 : | total soft fired pottery mass kg for daily quota of one potter | |
| 42.0838739 : | total applied heat MegaJoules for daily quota of one potter (15 bowls) | |
| 0.667998 : | green clay mass kg for one bowl | |
| 0.634 : | soft fired pottery mass kg for one bowl | |
| 2.8055916 : | 2.8 MegaJoules for one bowl |
+----------------------------------------------------------------------------------+ | CLAY MASS vs VESSEL CAPACITY: TWO REGIME CONSTANTS | | Developed from modern potter lore; green clay = unfired mass | | Includes trim waste, rim cuts, bottom cuts, and kiln stands | | | | +-------------------+------------------+--------------------------------------+ | | | vessel capacity | constant (kg/L) | notes | | | +-------------------+------------------+--------------------------------------+ | | | 1 to 2 liters | 1.00308 kg/liter | ~2.0154 manas per sila (1:1 ratio) | | | | > 2.5 liters | 0.8503 kg/liter | ~1.7086 manas per sila | | | +-------------------+------------------+--------------------------------------+ | | | | Why two constants? | | Larger pots have proportionally less trim waste | | Smaller pots: waste fraction is larger relative to vessel size | | Transition zone ~= 2 to 2.5 liters | | | | Green clay mass formula: | | total_green_clay = capacity_liters * clay_kg_per_liter * daily_quota | | | | Fired pottery mass (moisture and shrinkage loss ~5 percent): | | total_fired_clay = total_green_clay * 0.95 | | | | Mana and sila (Sumerian units): | | 1 sila ~= 1 liter (wet capacity measure) | | 1 mana ~= 0.5 kg (weight measure) | | 1.00308 kg/liter ~= 2.0154 manas/sila (small pot constant) | | 0.8503 kg/liter ~= 1.7086 manas/sila (large pot constant) | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | APPLIED HEAT: KILN ENERGY PER KILOGRAM OF CLAY | | Soft firing (Sumerian kiln estimate from MW124 potters report) | | | | Key data from MW124 potters report: | | 2000 vessels fired, 1800 kg of reed fuel (Su. gi bar) | | average fuel per vessel = 1800 / 2000 = 0.9 kg fuel/vessel | | | | British clamp kiln (1880s) reference: | | 1135 kg wood for 3800 kg green brick clay (1000 bricks * 3.8 kg each) | | scaling to MW124 reed fuel: | | green clay in MW124 = 3800 * (1800 / 1135) = 6026.4 kg | | average piece = 6026.4 / 2000 = 3.01 kg green clay | | average vessel capacity = 3.01 / 0.8503 = 3.54 liters | | | | Applied heat estimates: | | +-------------------------------+--------------------------------------------+ | | | method | result | | | +-------------------------------+--------------------------------------------+ | | | applied heat standard | 4.2 MJ/kg (soft firing, Sumerian kiln) | | | | reed fuel thermal (0.9 kg * | | | | | 17 MJ/kg per vessel) | 15.3 MJ per 3 kg vessel | | | | applied heat (3 kg * 4.2) | 12.6 MJ per 3 kg vessel | | | +-------------------------------+--------------------------------------------+ | | | | Note: reed thermal > applied heat (heat lost up chimney is accounted for) | | Total applied heat formula: | | total_heat_MJ = total_green_clay_kg * 4.2 MJ/kg | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | BEVEL RIM BOWL: REFERENCE VESSEL AND SCALING RULES | | Standard Sumerian bevel rim bowl (dug sila gal) used as scaling template | | Outer dimensions (1 sila = 1 liter): | | | | Top view: Side view: | | | | <---rim 180mm---> ^ | | +---------------+ | height | | | | | 100mm | | | | v | | +-----+---+-----+ <--base 90mm--> | | | | rim diameter = 180 mm | | base diameter = 90 mm | | height = 100 mm | | outer volume = 1484 ml (using outer dims) | | inner volume = 1000 ml (using inner dims, ~10mm wall thickness) | | | | Scaling to capacity V liters (experimental_dimensions proc): | | proportional_height = 100 * (V*1000 / 1000) * 0.1 cm | | proportional_mouth = sqrt(180^2 * (V*1000/1000)) * 0.1 cm | | proportional_base = sqrt(90^2 * (V*1000/1000)) * 0.1 cm * 0.1 | | | | Valid range: 0.5 to 4 liters (above 4L, calculator switches to sphere dim) | | Above 4 liters: diameter = (4*V*1000/pi)^(1/3) cm | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | TABLE: WET, SUN DRIED, FIRED BRICK RATIOS (Old Babylonian) | | Derived mostly from calculations in texts, not coefficient tables | | | | +--------+----------+---------+------------------+---------------------------+ | | | ratio | base-60 | decimal | numerator | denominator | | | +--------+----------+---------+------------------+---------------------------+ | | | 3/2 | 90/60 | 1.5000 | wet bricks | fired bricks | | | | 2/3 | 60/90 | 0.6666 | fired bricks | wet bricks | | | | 6/5 | 72/60 | 1.2000 | sun dried brick | fired bricks | | | | 5/6 | 50/60 | 0.8333 | fired brick | sun dried bricks | | | | 1/1 | 60/60 | 1.0000 | fired bricks | fired bricks | | | | 5/1 | 300/60 | 5.0000 | price fired gur/sar| price fired gur/sar | | | | 10/1 | 600/60 | 10.000 | price fired gur/sar| (redundant, less common)| | | | 1/5 | 12/60 | 0.2000 | market rate fired| market rate unfired | | | | 1/10 | 6/60 | 0.1000 | market rate fired| (redundant, less common) | | | | 6.3/5 | 76/60 | 1.2666 | sun dried brick | fired bricks (mod. est.) | | | +--------+----------+---------+------------------+---------------------------+ | | | | Key notes from tablets: | | Sun dried brick weight over wet brick weight = 40/60 or 48/60 | | Sun dried brick weight over baked brick weight = 50/60 | | Water content of wet brick ~= 12/60 of brick weight | | Weight loss (water) from dried to baked = 10/60 of dried brick weight | | Fraction 1/6 = mortar allowance for clay wall | | Factors 3/2 and 6/5 from BM36776 (Friberg and Robson) | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | CDLI DAILY POTTER QUOTAS (UMMA, UrIII period) | | Source: CDLI Equivalency list, R. K. Englund | | | | +-----+---------------+----------+--------+-----------+------+----------------+| | | QTY | vessel | capacity | green | fired | daily| heat MJ || | | | type | sila/L | clay kg| pottery kg| quota| total || | +-----+---------------+----------+--------+-----------+------+----------------+| | | 4 | 1-sila bowl | 1.0 L | 1.003 | 0.952 | 4 | 16.85 MJ/day || | | | (dug sila gal)| |each | | /day| (4*1.003*4.2) || | +-----+---------------+----------+--------+-----------+------+----------------+| | | 3 | 5-sila bowl | 5.0 L | 4.25 | 4.03 | 3 | 63.19 MJ/day || | | | | |each | | /day| (3*4.25*4.2+..) || | +-----+---------------+----------+--------+-----------+------+----------------+| | | 1 | 3-ban jar | 30.0 L | 25.5 | 24.22 | 1 | 107.1 MJ/day || | | | (storage?) | |each | | /day| (25.5*4.2) || | +-----+---------------+----------+--------+-----------+------+----------------+| | | | Potter clay range: 4.25 to 25.5 kg of green clay molded per day | | Suggested teams: 2 to 10 potters with a foreman (UrIII tablets) | | Proportion inference: spice bowl (15/day quota) ~= 2/3 sila capacity | | Note: "Gold's corollary -- any 3 items in a Sumerian trash bin likely | | associated with beer." 1L, 5L, and 30L all found cited for beer. | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | MW124 KILN RECONSTRUCTION: FIRINGS AND POTTERS (tentative planning) | | | | Given: 2000 vessels, 1800 kg reed fuel, 6026.4 kg green clay | | | | Small kiln (0.5 meter diameter, Ubaid era): | | fuel per firing = 85 kg | | number of firings = 1800 / 85 = 21 firings (rounded) | | | | Average loading per firing: | | pieces per firing = 2000 / 21 = 95 pieces | | green clay / firing = 6000 / 21 = 285.7 kg green clay | | | | Potters per firing: | | daily quota ~= 25 kg green clay per potter | | potters = 285 / 25 = 11.4 --> rounded up to 12 potters | | | | Fit analysis: | | Large 30-sila jar (98.6 cm rim): only 1-2 fit in 0.5 m kiln | | Bevel rim bowls: stackable (open-face) --> lower vertical profile | | advantage: more pieces per firing than closed vessels | | Inference: 0.5 m kiln supports 1-12 potters on smaller vessels | | 21 firings --> suggests a monthly report tablet | | | | eTCL calculator output for TC4 (2000 vessels, 3.53 L): | | total green clay = 6000.999 kg | | total fired clay = 5700.949 kg | | total applied heat = 25204.2 MJ | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | TESTCASE RESULTS SUMMARY (4 testcases) | | | | +----+--------+-------+-------+-------+------+--------+--------+-------------+| | | TC | cap. | quota | clay | fired | ht | rim | base | heat MJ || | | | liters | /day | kg/L | kg/L | cm | diam cm| diam cm| (if >0) || | +----+--------+-------+-------+-------+------+--------+--------+-------------+| | | 1 | 1.0 | 1 | 1.003 | 0.952 | 10.0 | 18.0 | 9.0 | 4.213 || | | 2 | 2.0 | 1 | 1.003 | 1.906 | 20.0 | 25.455 | 12.727 | 8.425 || | | 3 | 30.0 | 1 | 0.85 |24.224 | 300.0| 98.590 | 49.295 | 107.1 || | | 4 | 3.53 | 2000 | 0.85 |5700.9 | 35.3 | 33.818 | 16.909 | 25204.2 || | | sp | 0.666 | 15 | 1.003 | 9.519 | 6.66| 14.689 | 7.345 | 42.084 || | +----+--------+-------+-------+-------+------+--------+--------+-------------+| | | | sp = special spice bowl case (15-per-day quota inference, 0.666 sila) | | | | TC1 one-vessel check: 1.0 * 1.003 * 1 = 1.003 kg green, *0.95 = 0.953 kg | | TC3 one 30-sila jar: 30.0 * 0.85 * 1 = 25.5 kg green, *0.95 = 24.22 kg | | TC4 MW124 batch: 3.53 * 0.85 * 2000 = 6001 kg green, * 0.95 = 5701 kg | | | | Scaling note: TC3 rim diameter (98.6 cm) is a very large jar | | comparable to known Sumerian storage jars found in excavations | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+
| CALCULATE PROC: FORMULA FLOW (proc calculate {}) |
| |
| Inputs (global side1..side4): |
| side1 = liter_capacity pottery vessel volume in liters |
| side2 = daily_quota number of vessels per day (or batch) |
| side3 = clay_kg_per_liter constant (1.003 for small, 0.85 for large) |
| side4 = megajoules_per_kg applied thermal rating (4.2 MJ/kg if > 0) |
| |
| Step 1: Force float multiplication |
| side1..side8 = side1..side8 * 1.0 |
| |
| Step 2: Break flag routine (negative number guard) |
| if side(n) < 0: set side(n) = 0.000001, warn to console |
| |
| Step 3: Experimental dimensions (experimental_dimensions proc) |
| if capacity < 4.1 L: scale from bevel rim bowl (180mm rim, 90mm base) |
| if capacity > 4.0 L: use sphere diameter formula (4*V*1000/pi)^(1/3) |
| side5 = proportional_height (cm) |
| side6 = proportional_mouth (cm) |
| |
| Step 4: Green clay and fired clay totals |
| total_green_clay = capacity * clay_kg_per_liter * daily_quota |
| total_fired_clay = total_green_clay * 0.95 |
| side7 = total_green_clay |
| side8 = total_fired_clay |
| |
| Step 5: Applied heat (console only, if side4 > 0) |
| conversion = total_green_clay * side4 (MJ) |
| puts to console (not written to entry field) |
+----------------------------------------------------------------------------------++----------------------------------------------------------------------------------+
| EXPERIMENTAL DIMENSIONS PROC (proc experimental_dimensions {}) |
| Rescales bevel rim bowl dimensions to target capacity |
| |
| Reference bowl constants: |
| bevel_bowl_height = 100.0 mm |
| bevel_mouth_diameter = 180.0 mm |
| bevel_base_diameter = 90.0 mm |
| beveled_bowl_volume = 1000.0 ml (= 1 sila = 1 liter) |
| |
| Scaling formulas (capacity V liters --> V_ml = V * 1000 ml): |
| height = bevel_height * (V_ml / ref_vol) * 0.1 cm |
| = 100 * V * 0.1 cm |
| = V * 10 cm |
| mouth = sqrt(bevel_mouth^2 * (V_ml/ref_vol)) * 0.1 cm |
| = sqrt(180^2 * V) * 0.1 cm |
| base = sqrt(bevel_base^2 * (V_ml/ref_vol)) * 0.1 * 0.1 cm |
| = sqrt(90^2 * V) * 0.01 cm |
| |
| Sphere formula (V > 4 liters): |
| V_ml = liter_capacity * 1000 |
| diameter = (4 * V_ml / pi)^(1/3) cm |
| height = mouth = base = diameter (all set to same value) |
| |
| Validity note: |
| Reasonable between 0.5 to 4 liters |
| Questionable beyond 4 liters (sphere used as fallback, not realistic) |
+----------------------------------------------------------------------------------++----------------------------------------------------------------------------------+
| BREAK FLAG ROUTINE: NEGATIVE NUMBER GUARD (proc break_flag_routine {}) |
| |
| Purpose: prevent divide-by-zero and negative mass errors |
| |
| Step 1: Product check |
| product_entries = side1 * side2 * ... * side8 |
| if product < 0.0: puts warning to console (negative detected) |
| |
| Step 2: Individual entry check |
| if side(n) < 0.0: |
| set side(n) = 0.000001 (floor at near-zero positive) |
| set error1 = 1 |
| |
| Step 3: Warning report |
| if error1 == 1: |
| puts "warning flag! negative numbers detected, defaulted to positive" |
| prints testcase number (tc$t9) for traceability |
| |
| Fortran-style flag pattern: |
| error1..error10 all initialized to 0 at start of each check pass |
| set independently per entry field violation |
| global flag approach similar to old Fortran 77 error-flag convention |
| |
| Note: a negative mass or capacity has no physical meaning |
| The guard prevents TCL from propagating NaN or negative results |
+----------------------------------------------------------------------------------++----------------------------------------------------------------------------------+ | BEER JAR TYPES: SUMERIAN VESSEL SIZE ASSOCIATIONS | | All three testcase sizes (1, 5, 30 liters) associated with beer in texts | | | | +----------+----------+-------------------+----------------------------------+ | | | capacity | Sumerian | vessel type | beer association | | | +----------+----------+-------------------+----------------------------------+ | | | 1 sila | 1 liter | grain/beer ration | daily ration bowl; beer ration | | | | | | bowl | 2-liter ration also cited | | | | 5 sila | 5 liters | standard beer | standard beer bottle or beer jar | | | | | | bottle | | | | | 20 sila | 20 liters| delivery/mixing | beer delivery, fermenting, or | | | | | | container | mixing container | | | | 25 sila | 25 liters| delivery/mixing | same as 20-sila | | | | | | container | | | | | 30 sila | 30 liters| storage jar or | beer brewing vat or beer keg | | | | | | beer keg | 30 kg full = 1 manload (60 manas)| | | +----------+----------+-------------------+----------------------------------+ | | | | Drinking method: cane straws or ceramic drinking tubes | | Ceramic tubes occasionally mentioned in texts and illustrated on clay seals | | | | Gold's corollary: | | "Any three items in a Sumerian trash bin will most likely be | | associated with beer." | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+
| BABYLONIAN CARTAGE QUOTAS (from clay tablets) |
| Daily cargo limits from UrIII accounting tablets |
| |
| Quota 1 (short range): |
| 37_30 talents per us per day |
| = (37 + 30/60) * 30 kg = 1125 kg per 60*6 = 360 meters per day |
| One us = 4 minutes of arc = ~6 meters on the ground |
| 1 talent ~= 30 kg |
| |
| Quota 2 (long range): |
| 1_15 talent per danna per day |
| = (1 + 15/60) * 30 kg = 37.5 kg per 10.8 km per day |
| 1 danna = 10.8 km (approximately 1 Babylonian league) |
| |
| TCL checks: |
| expr {(37+30./60.)*30.} --> 1125.0 kg per short range day |
| expr {(1.+15./60.)*30} --> 37.5 kg per long range day |
| |
| Context: porter carrying bricks or grain sacks to kiln or storage |
| A full 30-sila jar = 30 liters * 1 kg/L ~= 30 kg = 1 manload (60 manas) |
| 1 Babylonian cubit { 1 kus ba.an.gi4 } = 1 cubit returned (brickwork term) |
+----------------------------------------------------------------------------------++----------------------------------------------------------------------------------+ | eTCL SLOT CALCULATOR: GUI LAYOUT | | Window title: "Sumerian Pottery Vessel Mass Calculator" | | Background: aquamarine4, border brown raised 30 | | | | .frame (left panel, 8 label+entry rows): | | +------------------------------------------------------------+ | | | pottery vessel volume liters (sila=liter): [________] | | | | quota of N1 vessels per day (optional): [________] | | | | constant2 green clay per vessel (kg/liter): [________] | | | | applied thermal rating MJ/kg (if >0 supersedes):[________] | | | | answers: proportional vessel height (cm): [________] | | | | proportional vessel rim diameter (cm): [________] | | | | green clay mass kg: [________] | | | | soft fired pottery mass kg: [________] | | | +------------------------------------------------------------+ | | | | .buttons (right panel): | | +--------------------+ | | | Solve | <-- runs calculate proc | | | clear | <-- clearx: wipes all 8 entries | | | report | <-- reportx: console show, wiki-format table | | | about | <-- tk_messageBox version info | | | exit | | | | Testcase3 (30L jar)| <-- clearx + fillup (30,1,0.85,4.2,...) | | | Testcase2 (2L bowl)| <-- clearx + fillup (2,1,1.003,4.2,...) | | | Testcase1 (1L bowl)| <-- clearx + fillup (1,1,1.003,4.2,...) | | +--------------------+ | | | | Applied heat (side4) conversion output: console only (puts), not in slot | | Proportional base diameter: in reportx console output only (not in slot) | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+ | PROPORTION INFERENCE: UNKNOWN VESSEL CAPACITY FROM DAILY QUOTA | | Applies rule of three to daily quotas when capacity is not cited | | | | Known: | | dug sila gal (1 sila): quota = 10 bowls per day | | dug-kur-KU.DU (spice bowl): quota = 15 bowls per day | | | | Assumption: quota is inversely proportional to labor | | more vessels per day --> smaller vessel size | | | | Proportion: | | 1 sila : unknown = 15 bowls/day : 10 bowls/day | | unknown = (1 * 10) / 15 = 0.666 liters = 2/3 sila | | | | eTCL verification (0.666 L, 15 per day, 1.003 kg/L): | | total green clay = 0.666 * 1.003 * 15 = 10.02 kg | | total fired clay = 10.02 * 0.95 = 9.52 kg | | total heat = 10.02 * 4.2 = 42.08 MJ | | single bowl green = 0.666 * 1.003 = 0.668 kg | | single bowl fired = 0.668 * 0.95 = 0.635 kg | | single bowl heat = 0.668 * 4.2 = 2.806 MJ | | rim diameter = 14.69 cm, height = 6.66 cm, base = 7.34 cm | | | | Historical note: bevel rim bowls 0.647-0.72 liter found in Ubaid period | | Cannot confirm in Neo-Sumerian (UrIII) period at this time. | +----------------------------------------------------------------------------------+
+----------------------------------------------------------------------------------+
| OVERALL PROGRAM FLOW (Sumerian Pottery Vessel Mass Calculator V4, gold 2014) |
| |
| package require Tk |
| namespace path {::tcl::mathop ::tcl::mathfunc} |
| | |
| v |
| Build .frame (8 label+entry pairs, grid layout) |
| Build .buttons (Solve, clear, report, about, exit, TC3, TC2, TC1) |
| grid .frame .buttons -sticky ns |
| | |
| v |
| User pushes Testcase(N): |
| clearx + fillup (capacity, quota, kg/L, MJ/kg, ht, rim, green, fired) |
| | |
| v |
| User edits entries 1-4 (capacity, quota, kg/L, MJ/kg) if needed |
| | |
| v |
| User pushes Solve: |
| break_flag_routine (negative number guard) |
| experimental_dimensions (rescale from bevel rim bowl template) |
| side5 = proportional_height, side6 = proportional_mouth |
| side7 = total_green_clay = capacity * kg/L * quota |
| side8 = total_fired_clay = total_green_clay * 0.95 |
| console puts: applied heat = total_green_clay * side4 (if side4 > 0) |
| | |
| v |
| User pushes report: |
| reportx --> console show (wiki-format table) |
| outputs: all 8 sides + proportional_base diameter |
+----------------------------------------------------------------------------------+ # 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"Please place any comments here, Thanks.
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