**Sumerian Construction Rates and eTCL Slot Calculator Demo Example**

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 intelligibly without some background of the correspondent. Thanks,[gold]
----

<<TOC>>

[gold] Here is some eTCL starter code for calculating materials and dimensions of ancient Sumerian buildings. The impetus for these calculations was checking reed and mud brick construction in some excavation reports and modern replicas. Most of the testcases involve replicas or models, using assumptions and rules of thumb. 

In the Sumerian coefficient lists on clay tablets, there are coefficients which were used in determining the amount of construction materials and the daily work rates of the construction workers.  In most cases, the math problem is how the coefficient was used in estimating materials and work rates. One difficulty is determining the effective power of the coefficient in base 60. For example, 20 could represent either 20*3600,20,20/60, 20/3600, or even 1/20.  The basic mud wall dimensions and final tallies were presented in the Sumerian accounts on clay tablets, but the calculations were left off the tablet. At least one approach for the modern reader and using modern terminology is to develop the implied algebraic equations from the Sumerian numbers. Then the eTCL calculator can be run over a number of testcases to validate the  algebraic equations. 

In Sumer of the Ur III dynasty, there were canal regulators at Girsu, Lagash (2), Umma, Larsa,Kilmah, Shurruppak, Isin, and elsewhere. The canal regulators were used to channel water into the canal bed, moderate the channel stream level, and  divide offshoot canals  into  several streams for irrigation. Usually at the site of a major regulator along a navigable canal, there was a rest house and kitchen for transferring travelers and canal workers, as well as a military depot to defend the instillation. From the remains of the Amar-Suen canal and voyager logs, there were Rest Houses along the Amar-Suen canal about 10 to 20 km apart. The Umma texts suggested that canal boats were available at Umma of 5-60 gur capacity, equivalent to modern cargo ratings of  0.35 to 40 cubic meters.
From the remains and excavations at Girsu, the sluice of the canal regulator was 11.4 meters long and 3 meters wide. 

From remaining extant walls of the Girsu canal regulator, the sluice was about 5 meters depth. The canal downstream was about 16 meters wide (in ancient times). The immediate area was has been dry in modern times. At least in modern thinking, the difference between the Girsu sluice width (3 m.) and the canal width (16 m.) would preclude efficient operation of the regulator. At Lagash, the sluice of the canal regulator was 3 meters wide and 18 meters long. The Lagash canal regulator has reinforced brick fans  to channel the ancient canal flow, of 24 and 27 meters length respectively (on the sides of the regulator). The Lagash canal downstream from the regulator was about 6 meters wide (in ancient times). The immediate area was has been dry in modern times. The Kimah agricultural regulator was 6 meters wide and was led into 4 channels for agriculture. Possibly the smaller channels of Kimah were 6/4 or 1.5 meters wide. At least, irrigation canals of 1.5 meters width would be compatible with the smaller irrigation canals with square cross sections (1.5 m. sides)  mentioned in the math texts. From the Girsu remains, coefficient lists, and math problems, the depth of a regulator sluice was usually 5 meters (rounded).

In the coefficient lists and math problem texts, there are canals and canal regulators discussed with some dimensions, although no one to one correspondence can be concluded. The math constant IGI.GUB sa3  ID2  he-ri-im (constant of the width of an excavated river ) was 30/60 ninda in s. notation or about (30/30)*6, 3 meters. The math coefficient IGI.GUB sa3 PA5.SIG (constant of a small canal,  side or depth) was 48/60 ninda in s. notation or about (48/60)*6, 4.8 meters depth. There were math problems listed for  small canals of length/width/depth of  1800/1.5/1.5 meters and other problems for small feeder canals of 1800/0.5/0.5 meters. There was  a corrupted math problem about a canal regulator ( Akk. tarahhu) with  possible  length of 1800? meters and possible canal  upper width of 10? meters. Generically, the width of a regulator sluice was usually 3-6 meters,  the width of the main canal was 6-16 meters, the width of small square irrigation canals was 1.5 meters, and the smallest square canals mentioned were 0.5 meters (from the math problems). 
                             
For simple order of magnitude calculations, the governor of Umma controlled 40 plowteams which were assigned 3.88 sqkm to plow for a total of 40*3.88 or 155.2 sqkm of state arable land. If the small feeder canals ran for 2*1800 meters on both sides of the Umma canal, then one side of the state property was 2*2*1800, 7200 meters, or 7.2 km. The state land along the Umma canal would be 155.5 sqkm/7.2 km or 21.6 km. Hence for simple calculations, the state land need only extend for 21.6/2  km, or roughly 10.8 km along the canal from the capitol Umma to account for the estimated state land.

The supportable population of Umma can be estimated from the barley yield of the arable land. In recent times, the Iraqi government has a figure for average barley yield of  800 kg/ha, equals 425 gurs per sqkm. If all the state land was planted to barley, the maximum yield was 425 gurs/sqkm *155.5 sqkm or 6.6E4 gurs. In the good times of King Amar-suen, the   records show the Umma land was from 1/3 to 1/2 fallow. In recent times, the traditional Iraqi farmers would have half (1/2) the land fallow. Records of the prior reign indicate King Shulgi taxing 1/2 grain harvest for royal use, so the full potential harvest of Umma must have been discounted  to some extent.  Making simple assumptions,  the supportable population of the Sumerian city of Umma can be estimated. The 6.6E4 gurs of barley could be converted into 6.6E4*300 liters of barley, where each adult consumed 2 liters of barley a day or (2*365) liters of barley over a years time. The supportable population would be from (6.6E4*300/(2*365)*(1/2) to (6.6E4*300/(2*365))*(2/3), from 13500 to 18000 people. Also the state records show the city of Umma exporting grain to Susa or loaning grain shipments to other cities (in the good years). That is, the city of Umma was usually a net exporter of grain, so the lower figure of 13500 inhabitants is the most likely.

For another rough check on the inhabitants of Umma city, the "6 for 6" rule can be used. For subsistence farmers producing on half the land with the other half fallow, a family of six inhabitants will need 6 hectares of arable land. For the 155.2 sqkm or 1.552E4 hectares of state arable land, there should be 1.552E4/6 or 2586 families. The 2586 families times 6 in family should give 15,500 inhabitants. This rule has the advantage indicating subsistence adults and children. Given 2 adults per family, the the number of adults should be 2586*2 or 5172 adults. The number of children would be  2586*4 or  10300 children. 

The population density of Umma can be estimated in the reign of Amar Suen. The elevated area of the Umma tell is about 1500 meters in diameter. The city area was 3.14*1500*1500/4, 1.76E6 sqmeters, 1.76 sqkm, or 176 ha.  Taking the lower population figure, the population density was 13500/176 or  77  inhabitants per ha. The higher population estimate of 18000 people would lead to 18000/176 or 102 i/ha. This sounds low density,  but the city of Umma was host to two large temples, a harbor with quay, and state government buildings (low density areas).    


The scale or order of magnitude of the Lagash regulator can be estimated from the Lagash inscriptions and Sumerian coefficients. The boulder indicated 648,000 fired bricks and 1840 gurs of bitumen. Gurs are volumes of 0.3 cubic meters, so one can start  with  volume computations. Since the larger Sumerian canal ships were rated at 60 gurs, the number of shiploads could have been  1840 gurs/60, 30.66, or rounded 31 ships. In modern units, the volume of bitumen used was 1840*.3 or  550 cubic meters. The typical fired brick of the 2/3 cubit type was length/width/depth was 0.33/0.33/0.8 meters. From the average density of fired brick at 2000 kg/c. meters, the total  mass of the bricks was 6.48E5*0.33*0.33*0.8*2000    or 1.129E7 kilograms. Since bitumen is about the density of water(1000 kg/c.m.), the 60 gur capacity of a Sumerian ship would be equal to a cargo of 60*.3*1000.,18000, or 1.8E4 kilograms. Converting into shiploads of brick, the project would be equivalent to 1.129E7 / 1.8E4 ,0.6272E3, or rounding 627 shiploads of brick. From the British clamp kilns of the 1880's, a British clamp kiln would need 1135 kg wood for 3800 kilograms of green clay for soft fired bricks. Using similar proportions, the Sumerians would need  1135*1.8E4/3800 or 5.376E4 kilograms of wood or reeds. Using the Sumerian coefficients, some limits on the workdays needed to make the bricks is possible. As a first cut, the number of workdays would be 648,000/240 or  2700 workdays for making brick.
   
It is very difficult to get a handle on the numbers of workers and duration of the project.  The population of Lagash about 2300 BCE  is estimated to be from 10,000 to 30,000 inhabitants. On a seasonal basis, team of workers could be brought off the farmland,  and probably Lagash had a pool of skilled workers that was about 1/4 the population. King Enmetena of Lagash reigned from 2404-2375 BCE. Although are no explicit texts on the duration of the canal building, the building or restoration of the canal probably took place between 2004 and 2000 BCE, a period of four years. There are a lot of iffy's here. If all the bricks were made in a single  "month of making bricks", then the needed brickmakers would be  2700/30 or 90 brickmakers . If the project was spread over 5 years, then estimated workdays making bricks would be 2700/5 or 540 workdays per year. If on a one month assignment during the "month of making bricks" (over extended 5 years, the required brickmakers would be 540/30 or 18 brickmakers.  After the crops were planted, perhaps 2500 workmen would be available for digging, porting clay, and collecting reeds (for building material and fuel) for a period of 60 days. The ratio of about one foreman for 40 workmen gives 2500/40 or rounded,  60 foremen.

Some commodity price records are known for various eras in Sumerian accounts, Babylonian astronomer tablets, and partly in the coefficient lists. One piece of silver bought 288 bricks. If bought separately, the bricks on the project would  cost  648,000/288 or 2250 silver pieces. One piece of silver bought (2/5) gur of bitumen, so the bitumen would cost 1840/(2/5)  or  4600 silver pieces. Craftsmen were normally paid 1 ban or 10 liters of grain. The craftsman and other wages can be calculated in terms of silver. One silver piece bought a gur or 6 ban of grain. In terms of accounting, a craftsman could be paid in 1 ban of grain, 10 liters of grain, 1/6 gur of grain, or 1/6 silver piece. Generally, workmen, field labor, or hirelings were paid on  the books in 2 bowls or 1 liters of grain, 1/5 ban of grain, 1/30 gur of grain, or 1/30 silver piece. On the books, the foreman would be paid 5 ban, 50 liters of grain, 5/6 gur of grain, and 5/6 silver piece. From some accounts, the foreman was responsible was responsible for accounting for the labor, and for arranging distribution of grain to the higher status workers, and for furnishing bowls of gruel or hot mutton soup to the lower status workers. The labor of 2500 workmen for two months would cost 2500*30*2*(1/30) or 5000 silver pieces. However, traditionally about 1/10 workmen labor or more was taxed to the King. So probably only the brickmakers and foremen received a salary. In fact, the boulder inscription could imply forced or unpaid labor.

With the possible exception of fan walls to channel water into the sluice, the bulk of the regulator was underground and probably can be considered an excavation,  at first. From the coefficient lists and the average excavation rate,  the workdays of excavation would be roughly 6.48E5*0.33*0.33*0.8/3, 1882 workdays. The workdays of digging mud for bricks would be roughly 6.48E5*0.33*0.33*0.8/3, 1882 workdays. The task of gathering sufficient reeds and firewood would be 5.376E4 kilograms of wood/250, or 179 workdays. 2700 workdays for making brick was previously figured. Though no coefficients, laying a reed mat foundation might be 500 workdays. The workdays of laying brick would be roughly 6.48E5*0.33*0.33*0.8/3, 1882 workdays. The workdays of plastering  the completed brick surface would be 700 workdays. Suggest that making the wooden gates might be another 500 workdays. So far the total is 9705 workdays. With 90 brickmakers and assistance of the 500 workmen, the project would take about 9705/90 or 108 days. The remaining 2000 workmen would clearing and digging the extended canal. If materials and labor are accounted, the price of the Lagash regulator and canal improvements might be 2250 bricks + 4600 (bitumen) + 5000 (labor workmen) + 1620(brickmakers/craftsmen) + 4500 (foremen), as 18000 silver pieces.

In planning any software, it is advisable to gather a number of testcases to check the results of the program.With back of envelope calculations,  a number of peg points were developed to check output of program. The math for the calculations were confirmed by pasting statements in the TCL console. Also, some of the pseudocode statements were checked in the google search engine which will take math expressions. Aside from the TCL calculator display, when one presses the report button on the calculator, one can develop a more detailed report.

Using the eTCL calculator, a single brick wall of L/W/T 27/2/0.66 meters can be extimated.  On the eTCL calculator, set the temple width to zero and the thickness to half the wall. The eTCL calculator (27/0/2/.33) gives 35.64 cubic meters. For comparison, hand calculations give L/W/T , 27*2*.66 or 35.64 cubic meters. A square brick column or rubble filled wall can be figured with a similar scheme. One can also use the eTCL calculator for a rectangular construction of 4 walls and subtract a wall or doorway of known dimensions.

The eTCL calculator made some order of magnitude calculations for a trial Sumerian house with some assumptions. The Orchard House was 30.11 meters long, 11.5 meters wide, and walls 3 meters high with a surface area of 30.11*11.5, or 346.6 square meters.  As constructed, the front wall was 10.45 meters and back wall was 11.5 meters, presumably the difference of (11.5-10.45) or 1 meter was the threshold or entrance. One side of the house was extended as a garden wall. For the Orchard House, the ratio of wall length to width was 30.33/11.5  , 2.618:1, or rounding 3:1. For an initial cut of the wall volume using hand calculation, the total wall volume would be the sum of the front wall L*H*T (11.5*3*0.33), the rear wall(11.5*3*0.33), side wall (30.11*3*0.33), and second side wall (30.11*3*0.33). The eTCL calculator makes the assumption that all bricks are of the "2/3 cubit" burned brick type. The garden wall would enclose 60*60 sq. meters or 4*60 perimeter of square iku, based on modern assumptions. Using an assumption that the wall thickness of the Orchard House was 0.33 meters, the eTCL calculated a wall volume of 77.7 cubic meters. If  the "2/3 cubit" burned brick was used, the  total number was  8924 bricks. The estimated workforce was 2 foremen (salary of 50 liters), one junior scribe (10 liters), 56 craftsmen (10 liters), and 16 subsistence men (0.5 liter). While the number of bricks has not observed on any receipt, the estimated workdays for making bricks would be 8924/240 or 37.2 workdays, within the nominal workforce for one day. The estimated workdays for digging clay for bricks would be 77.7/3 or 25.9 workdays, within the nominal workforce for one day. Presumably, the bulk of the bricks were made on site, but the available text doesn't state so. For comparison, the average Sumerian mudbrick house was about 90 sq. meters, and the average room size was  3 meters width by 3.65 meters length,3* 3.65, or about 10.95 square meters. The Sumerian mudbrick houses generally contained rooms of 11 square meters built around a central courtyard. For the Orchard House, the general guidelines suggest about 6 rooms (3*3.6 m.) on both sides of a central courtyard about 5 meters wide.  

For a more substantial project with the eTCL calculator, consider building or repairing an orchard wall of 306 rods or 3672 meters. Such a mudbrick wall would be L/W/H 3672/0.5/1.5 with sun dried bricks of the one cubit sides, 0.5*0.5*.0.08 meters. The volume of the mudbrick wall would be 3672*0.5*1.5 or 2754 sq meters (by hand calc). Setting for single wall, the eTCL calculator setting (3672/0/1.5/.25) calculates a volume of 2754 sq. meters. The eTCL calculator does not use the sun dried bricks, but the number of bricks should be wall volume over brick volume, 2754 over (0.5*0.5*.08) or 1.377E5  sun dried bricks. Using the coefficient lists, the estimated mandays digging clay for the bricks would be wall volume 2754/3 or 918 mandays. The task of making bricks would be 1.377E5/240 or 573.75 mandays. For a tentative budget on the orchard wall, the sum of 189*0.5(subsistence men)+378*10 (craftsmen) + 2*10(junior scribes)+10*50 (foremen) would cost 4394 liters of grain.  

For the testcases, one would like to get realistic testcases from the ancient sources. The gist of a model document or scribal copy exercise (2300 BCE.) formulates the wall and foundations of the two temples of Sara and Ninurra at the city of Umma of Ur III. The model document gives some dimensions and numbers of bricks in Sumerian units. Other cuneiform documents from various eras give estimates for manhours for  tasks like canal digging and hoeing weeds, as foremen tally the labor and supplies for the  accountants. The eTCL calculator or similar modeling calculations can give some idea of the scale of the Sumerian public works. Aside from the large temples, the Sumerian canal regulators and canals are of historical interest. In the modern era, ship canals and water irrigation systems are still being planned at great expense. So it is worthwhile to compare the modern canal solutions and fees with the Sumerian solution.





*** Pseudocode and Equations using coefficients   ***
%|   Pseudocode with some Equations   |   |%
&|namespace path {::tcl::mathop ::tcl::mathfunc} ||&
&| pseudocode: mortar = vol of walls times 1/6 , 144. c.m.* (1/6) or 24 c.m.   | |&
&|  pseudocode: brick volume = 0.33*.33*.08, or 0.0087 cubic meters  | |&
&|  pseudocode: answer is mandays of labor or silver pieces +- error   | |&
&|      workdays on foundation  = vol of foundation / coefficient  | |&
&|         =  36 / 3  or  12  workdays  | |&
&|      workdays making bricks = number of bricks / coefficient1   | |&
&|                =  1.65E4   / 240  or  69  workdays  | |&
&|       workdays digging  clay    =  vol of walls / coefficient2     | |&
&|       =   144. c.m.  / 3 c.m. or  48  workdays  | |&
&|       workdays porting  clay    =  vol of walls / coefficient3  | |&
&|     =   144. c.m.  / 4 c.m. or  36  workdays  | |&
&|    workdays mixing  clay    =  vol of walls / coefficient4    | |&
&|        =   144. c.m.  / 3 c.m. or  48  workdays | |&
&|        workdays making bricks = number of bricks / coefficient5      | |&
&|       =  1.65E4   / 240  or  69  workdays  | |&
&|           workdays laying bricks =  vol of walls / coefficient6     | |&
&|               =  144. c.m.  / 3  or  48  workdays   | |&
&|          workdays making 3 doors =  3 doors * coefficient7     | |&
&|       =  3 doors /   (2/3)  or  4.5  workdays     | |&
&|        workdays making reed thatch =  roof area /coefficient8     | |&
&|         =  5*10 sq.m. / 1.125  or 44.4 workdays     | |&
&|      workman wages = total workdays times  1/30 silver piece       | |&
&| mass of bricks times 1/6 = mass of mortar   | |&
&| mass of bricks + mass of motor = amount of clay needed.   | |&
&| length wall of bricks times 1/5 = extension or footing of foundation     | |&
&| dimension of bricks times density of clay = mass of clay      | |&
&| 454 kilograms coal over 1000*3.8 kilograms of clay, 454/3800     | |&
&| 1135 kg wood for 3800 kg of clay      | |&
&| 32001 kg wood for 107160 kg of clay.     | |&
&| 2001 kg wood./ 600 = 53.5 workdays of firewood collection      | |&
&| workman wages = total workdays times  2 liters of grain         | |&

***Table 1, Sumerian coefficients for Canal Excavation rates***

%| canal excavation| coefficient| daily workload cubic meters |Sumerian tablet. 1  | Akkadian? tablet. 2    |  comment |%
&| first level  | 20/60| 6   | silutum|    il-lum  |   first level is easiest, (20/60)*18= removing 6 c. meters  from canal       |&
&|       second level | 10/60| 3  |  dusu  |  obscured   |  dusu is construction basket or  yoke-of-2-buckets, (10/60)*18= lifting 3 c. meters  from canal         |&
&|      third level    |  6/60+40/3600 |  3600/400 |  dusu  |   had/talum ihd/til      |  dusu is construction basket or  yoke-of-2-buckets , (400/3600)*18= removing  2 c. meters from canal    |&
&| These rates are primarily from math problems, but are partially included in some Sumerian Coefficient Lists | | |&

***Table 2, Sumerian Canal Regulators, known***
%| location of canal regulator | canal and modern river, if known | est.  number of bricks     |  est barrels of bitumin    |  Est. arable hectares   | year before common era  |  comment    |%
&| Isin.| Isin canal and Euphrates  river|  1.3E6 bricks.  |    7971               | 2700???| 1881 BCE     |     King   Sumuel  of  Larsa   |&
&| Girsu | Id-Nina-Gina canal and east branch Euphrates river|  68.6E3 bricks |    420         |    10E4 ha     |  2150     |  King Gudea, ref foundation cones     |&
&| Kimah  | Id-Nina-Gina canal and east branch Euphrates river|  bricks |       |    2E4   ha           |   2150?    |  King Gudea?      |&
&|   Umma|  Iturungal  canal and east  Euphrates delta  |   |  |  1.55E4 ha   |     |    |&
&|   Lagash First      |  Lumagimdu canal |   6.48E5 bricks |1840  | 27200         | 2400???       | King Enmetena of  Lagash, ref dedication boulder       |&
&|  Lagash Second |  Lumagimdu canal    |4.32E5 bricks  | 1840|  27200                     |     2350         |  King Uru-inimgina  of Lagash   |&
&| Note, Several kings claimed authorship of the same canal or restored the same canal, so attribution is tricky.  | | | |   |&


***Table 3, Sumerian and Akkadian Canal Terms***
&|   adug  |  irrigate with canal water |  literally < water pot< , Akk.  saqu sa eqli   |&
&|   aigidu  |  canal water | literally < <i see water<, Akk.  sekiru|&
&|   bala-ak |   reposition boat over canal (weir?)   | listed on voyage records, literally <unload crossing<, Akk. nabalkutu or nabalkat |&
&|   bur |   canal depth   | ref math problems,  Akk. buru |&
&|   dagal-an-ta  |  upper canal width, width at top| ref math problems, literally < side large upper >  |&
&|   dagal-ki-ta  |  lower canal width, width at bottom| ref math problems, literally < side large earth > |&
&|   durum.tus.tus | regulator type, another word|   literally  <wet small small<  |&
&|   dusu  |  third level of canal | ref coefficient lists and math problems, literally <basket<, Akk.  tupsikku |&
&|   egir|second wooden wall | egir or egar means wall, Akk. igaru , literally <from the earth< |&
&|   ges kes.du  |regulator    |   literally  <wood bind  built <, kes means gather, bind  |&
&|   gugal  |  canal inspector |  literally < great man or foremost man<  , Akk.  gugallu|&
&|   hirim |  (general)    ditch  |   Akk. mitru             |&
&|   id |  (general)    river  |   Akk. naru             |&
&| id he-ri-im  | river canal path  | cited coefficient lists,  literally < river path high mud <, Akk.naru or mitru |&
&|   igi    |   first wooden  wall   |  igi means watcher or (i see)         |&
&|  iku | field, area unit     |   field surrounded by irrigation ditch, 60*60 sq meters, Akk. iku (sic) |&
&|   ka-i7-dat  |  lift canal boat bow into different (or higher?) channel | ref voyage records, literally < open mouth support >, Akk. nabalkutu or nabalkat|&
&|   kab-kud | divisors breaking into smaller streams| literally  <measure cut <  |&
&|   kun | outlet  |    literally < animal tail<  Akk. zibbatu             |&
&|   kun.zi.da | regulator type,  another word | ref voyage records, literally  <outlet cut side drain<   |&
&|   mehru | M.B. (general)  weir | ref Middle Babylonian |&
&|   mitru  |  (general)   canal or watercourse|   Akk. mitru              |&
&|   na |  river level, canal level  | units of level change, equal to 4 susi, records of Babylonian Astronomers |&
&|   nari |  canal  |   Akk. naru             |&
&|   nag-kud |narrow basin or reservoir near canals |possible agricultural basins for watering vegetables and herds, literally <  drink cut<, Akk. butuqtu |&
&|   natbaktu | M.B.  canal regulator  |   ref Middle Babylonian |&
&|   pa | (general)  small canal, ditch  |   Akk. palgu  |&
&|   par | small canal, ditch  |   Akk. palgu  |&
&|   pa.sig |    small canal, ditch  | literally < little canal<, ref coefficient lists  Akk. palgu            |&
&|   pa.sig.libir.ra |  old small canal, ditch  | ref math problems. literally < old little canal<,   Akk. palgu |&
&|   pi natbakti | M.B.  first gate of canal regulator  |   ref Middle Babylonian |&
&|   silitum   | first level of canal |ref math problems,  silum meant depression or concavity ,  Akk. silu |&
&|   sepit natbakti | M.B. second gate of canal regulator |   ref Middle Babylonian |&
&|   sur |  small canal, ditch, foundation drain  |   Akk. suru  |&
&|   ta.ra.ah.hi.im.mi | regulator type, another word|   literally  <cut stream mudwall<  |&
&|   talum til? |  second level of canal |ref math problems,  til means broaden, expansion  |&
&|   tarkullatum | removable wooden beams    |  literally  < cut stream < , epic of Gilgamesh   |&
&|   tarkulli    | removable wooden beams   |  literally  <cut stream <,   epic of Gilgamesh |&
&|   tarkullum | removable wooden beams   |  literally  < cut stream <,  epic of Gilgamesh |&
&|   tul |   water   cistern |ref math problems, Akk. burtu  |&
&|   u-tir       |   water  bridge?   | literally <forest  bridge<   |&
&|   us          |  canal length      |ref math problems, literally <measure<   |&
&|   zubi  |  (general)    canal or watercourse|   Akk. mitirtu  |&
&|   Table includes compound words and phrases in Sumerian or Akkadian.|||&
&|   These are technical (math) terms which may not be found in dictionaries of single root words and |&
&|   conventional literature. |&
&|   Table includes cuneiform words of rare citation or even one single instance on a clay tablet, |&
&|   which increases the uncertaincy of meaning. |&

***Table 4, Sumerian coefficients for daily work rate, supplements etc  ***
%|Sumerian coefficients for daily work rate,  etc |  |   |   |    |% 
%|daily work of one man etc in base 60 | transliterated name | english |decimal /fraction |reciprocal |comment|% 
&|12| u4, u4-1-se |  hours of workday  | 12| 1/12 |12 hours, common to several accounts and math problems  |&
&|3:45 | sa pi-ti-iq-ti |coefficient wall high manlife | 3/60+45/3600 | 16 | raising mud wall, 3/60+45/3600 surface a day |&
&|30 |IGI.GUB sa3  ID2  he-ri-im   | constant of the width of an excavated river| 30/60 | 2 | literally ( river, plenty,  pour out, mud ), 30/60 ninda conv. to  3 meters width  |&
&|48 |IGI.GUB sa3 PA5.SIG |coefficient small canal side depth | 48/60 | 60/48 |  literally ( canal side depth), 48/60 ninda conv. to  4.8 meters depth  |&
&|7:30 |i-za-ab-bi-il |coefficient canal  labor | 7/60 + 30/3600 | 3600/450|  ( 450/3600) vol.sar.  conv. to  2.25 cubic meters   |&
&|48 |a. sa3  |coefficient water of field| 48/60 | 60/48 |   possibly daily rate for dipping water on field,  48/60 volume sar, conv to14.4 c. meters  |&
&|   48 | igigub sig2 hi.a      |coefficient wool     |  48/60 | 60/48 |   possibly daily rate of loom, conv to (48/60)*6, 4.8 meters length  |&

&|   40 |    igigub sig2 hi.a  |coefficient wool     |  40/60 | 60/40 |   possibly daily rate of loom, conv to (40/60)*6, 4.0 meters length of spun wool  |&
&|   18 |   im-la |coefficient cone?   |  18/60 | 60/18 | ref  grain heap problems, Sum. imla,   Akk. imlum |&


----
***Testcases Section***

In planning any software, it is advisable to gather a number of testcases to check the results of the program. The math for the testcases can be checked by pasting statements in the TCL console. Aside from the TCL calculator display, when one presses the report button on the calculator, one will have console show access to the   capacity  functions (subroutines). 

**** Testcase 1 ****
%|  Four walled first temple|    |       |%
%|   quantity         | value | units       |%
&|   temple length | 20.  | meters |&
&|  temple width | 10. |  meters |&
&|  temple height | 5.  | meters  |&
&|  temple  wall thickness | 1.2 | meters   |&
&|  length    brick   |  .33| meters  |&
&|  width  brick   |   .33  |  meters  |&
&|  height brick   |  .08  |   meters  |&
&| answer: material volume |  144. | cubic meters |&
&| answer: brick volume |   0.0087 | cubic meters |&
&| answer:number of bricks| 1.65E4   | bricks |&
  
**** Testcase 2 ****
%| 4 Walled Temple || |% 
%|   quantity         | value | units       |%
&|   temple length | 20.  | meters |&
&|  temple width | 20. |  meters |&
&|  temple height | 5.  | meters  |&
&|  temple  wall thickness | 1.2 | meters   |&
&|  length    brick   |  .33| meters  |&
&|  width  brick   |   .33  |  meters  |&
&|  height brick   |  .08  |   meters  |&
&| answer: material volume |  192. | cubic meters |&
&| answer: brick volume |   0.0087 | cubic meters |&
&| answer:number of bricks| 2.2E4   | bricks |&


**** Testcase 3 **** 
%| Single Wall |||%
%|   quantity         | value | units       |%
&|   temple length | 27.  | meters |&
&|  temple width | 0. |  meters |&
&|  temple height | 3.  | meters  |&
&|  temple  wall thickness | 0.5 | meters   |&
&|  length    brick   |  .33| meters  |&
&|  width  brick   |   .33  |  meters  |&
&|  height brick   |  .08  |   meters  |&
&| answer: material volume |  71.28 | cubic meters |&
&| answer: brick volume |   0.0087 | cubic meters |&
&| answer:number of bricks | 8.181E3   | bricks |&
**** Testcase 4 ****
%| mw 124 tablet,  potters report |  | Ur III  |%
%| quantity  | values  | units   |comment |%
&|  reeds as fuel | 1800 | kilograms |   potters report |&
&|  pottery vessels | 2000 | vessels | potters report   |&
&| clay objects | 12  | objects | potters report   |&
&| workdays at pottery shop| 3604  | workdays | potters report   |&
&|1135 kg wood for 3800 kg of clay|   |  | 1880's clamp kiln|&
&|1135/1800 = 3800/x | | |proportions |&
&|x= 3800*1800/1135, 6026.4 kg of clay | | |modern equation estmating clay |&
&|days digging clay 6026.4 kg of clay /6 1004 days| | |coefficient equation|&
&|days forming clay 6026/(288*.33*.33*.08) = 2401 days | | |coefficient equation |&
&|3404 days total re reported 3604  | | |comparison|&

**** Testcase 5 ****
%|   trial Sumerian "Orchard House"  with some assumptions   |   |%
%|  quantity etc | length cubits | width cubits| height cubits| length meters | width meters | height meters| comment |%
&| back wall | 23| 1/2| 3 | 11.5 | 0.249 | 1.493| back wall|&
&| front wall | 21| 1/2| 2 | 10.45| 0.249 | 0.995| front with door opening,3 m. finished?|&
&|  side wall | 60+1/2| 1/2| 3 | 30.11| 0.249 | 0.995| back wall |&
&|  combo side wall & garden wall |255| 2/3| 3 | 126.9| 0.3314 | 1.49| combo, "2/3c" probably baked brick|&
&|  end of day totals | quantity    | value  |  | | | | comment  |&
&|                             |workers   |  74 +5/6 for 1 day   |  | | | | turned in day one |&
&|                             | its grain  |598+ 2/3 liters |  | | | | turned in one day one |&
&|                             | food wages| 8 [liters] |  | | | | turned in one day one |&
&|  running eTCL calculator & assumptions| quantity    | value  |  | | | | comment  |&
&|                             | house front meters | 11.5 | | || | modern estimate|&
&|                             | house side meters|  30.11| | | | |modern estimate|&
&|                             | house wall thickness| 0.3114| | | | |assuming all baked, modern estimate|&

&|                             | house surface area | 346.26 sq. meters|  | | | | modern estimate|&
&|                             | wall volume of 4 walls| 77.7 cubic meters | | | || modern estimate|&
&|                             | number of baked bricks| 8924 | | | || assuming all baked  (2/3c) type, modern estimate|&
&| | orchard size |60*60 meters ||||| garden wall would enclose 60*60 sq. meters or 4*60 perimeter of square iku, modern assumption|&


----
***Screenshots Section***
****figure 1.****
[http://s26.postimg.org/5g6hl47mh/Image250.gif]
----
***References:***

   * Cities of the Ancient World: [https://faculty.washington.edu/modelski/WCITI2.html] 
   * Canal regulators in Ancient Sumer [www.aulaorientalis.org/AuOr%20escaneado/AuOr%2020-2002/1/6.pdf] 
   * Geometrical coefficients [http://www.helsinki.fi/~whiting/coefficients01.pdf]
   * Problem texts F-J: Excavations   [http://www.helsinki.fi/~whiting/problems03.pdf]
   * Problem texts N-Q: Bricks [http://www.helsinki.fi/~whiting/problems04.pdf]
   * Cuneiform mathematics [http://www.helsinki.fi/~whiting/math.html]
   * Mesopotamian units [https://en.wikipedia.org/ wiki/ Ancient_Mesopotamian_units_of_measurement] 
   * triangle rule [akira.ruc.dk/~jensh/publications/Pythrule.pdf] 
   * The Ricardian Trade Model [www.econ.iastate.edu/classes/econ355/choi/ric.htm]
   * History of Old Babylonian mathematics[www.mpiwg-berlin.mpg.de/Preprints/P436.PDF]
   * Friberg [eprints.soas.ac.uk/10098/29/16_Friberg-George.pdf]
   * Yale University Tell Leilan Project [leilan.yale.edu/pubs/files/Ristvet2007PowerArch.pdf] 
   * Project Documentation [research.ncl.ac.uk/forum/v5i1/gelder.pdf] 
   * Accounting for Change in Early Mesopotamia,Eleanor Robson,All Souls College, Oxford

----
**Appendix Code**

***appendix TCL programs and scripts ***

======
        # pretty print from autoindent and ased editor
        # Sumerian construction  calculator
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 24mar2014
        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 {{} {length meters:} }
        lappend names {width meters:}
        lappend names {hieght meters : }
        lappend names {wall thickness meters: }
        lappend names {answer: material cubic meters}
        lappend names {vol of Sumerian bricks meters**3:}
        lappend names {number of Sumerian bricks: }
        foreach i {1 2 3 4 5 6 7} {
        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 volx { aa bb cc } {
         set volem [* $aa $bb $cc ]
         return $volem
          }
        proc about {} {
            set msg "Calculator for Sumerian Construction  
            from TCL WIKI,
            written on eTCL "
            tk_messageBox -title "About" -message $msg } 
        proc calculate {     } {
            global answer2
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number 
            global tlength 
            global tlengthsq surfacearea  
            global tlengthx
            incr testcase_number
            set tlength $side1
            set twidth  $side2
            set theight $side3
            set tthickness $side4 
            set brickl 0.33
            set brickw 0.33
            set brickt 0.08
            set brickvolx [volx 0.33 0.33 0.08]
            set wallside [volx $tlength $theight $tthickness]
            set wallfront [volx $twidth $theight $tthickness]
            set totalvolx [+ [* $wallside 2. ] [* $wallfront 2. ]]
            set brickvol [* 0.33 0.33 0.08]
            set bricknumx [/  $totalvolx $brickvol ]
            set side5 $totalvolx
            set side6 $brickvol 
            set side7 $bricknumx
            }
        proc fillup {aa bb cc dd ee ff gg} {
            .frame.entry1 insert 0 "$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"}
        proc clearx {} {
            foreach i {1 2 3 4 5 6 7} {
                .frame.entry$i delete 0 end } }
        proc reportx {} {
            global side1 side2 side3 side4 side5
            global side6 side7 testcase_number 
            global tlengthsq surfacearea
            global tlength
            console show;
            puts "testcase number: $testcase_number "
            puts "temple length: $side1 "
            puts "temple width meters: $side2 "
            puts "temple height meters: $side3 "
            puts "temple thickness meters: $side4 "
            puts "material volume meters**3: $side5 "
            puts "brick volume meters**3: $side6 "
            puts "number of bricks: $side7 "
            }
         frame .buttons -bg aquamarine4
        ::ttk::button .calculator -text "Solve" -command { calculate   }
        ::ttk::button .test2 -text "Testcase1" -command {clearx;fillup 20. 10. 2. 1.2 144.  .0087 16500. }
        ::ttk::button .test3 -text "Testcase2" -command {clearx;fillup 20. 20. 2. 1.2 192.  .0088 22000. }
        ::ttk::button .test4 -text "Testcase3" -command {clearx;fillup 30. 10. 2. 1.2 192.  .0087 22000. }
        ::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 Construction Calculator "       
======
*** Pushbutton Operation***

----
For the push buttons, 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, but takes away from computer "efficiency". 

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 (which numbers will be cleared on the next solve button.)  The command { calculate; reportx  } or { calculate ; reportx; clearx  } can be added or changed to report automatically, but is not recommended as computer efficiency is impaired. Another wrinkle would be to print out the current text,  delimiters,  and numbers in a TCL wiki style table as
======
  puts " %| testcase $testcase_number | value| units |comment |%"
  puts " &| volume| $volume| cubic meters |based on length $side1 and width $side2   |&"  
======

----
*** Initial Console Program ***

====== 
        # pretty print from autoindent and ased editor
        # Sumerian bricks for
        # special project of King Amar Suen
        # written on Windows XP on eTCL
        # working under TCL version 8.5.6 and eTCL 1.0.1
        # gold on TCL WIKI , 24jul2014
        package require Tk
        namespace path {::tcl::mathop ::tcl::mathfunc}
        console show
        set diameter .5
        set height .08
        set length .66
        set length .66
        set bricknumber 4.32E5
        set brickmass [ * $bricknumber .66 .66 .08 ]
        set pitchmass [ / $brickmass 6. ]
        set workdays [ / $bricknumber  288. ]
        puts "brick mass $brickmass"
        puts "pitch mass $pitchmass"
        puts "man workdays   $workdays"      

   
======

----
**Comments Section**

<<discussion>>
Please place any comments here, Thanks.


                              
<<categories>> Numerical Analysis | Toys | Calculator | Mathematics| Example