10 July, 2010

Fief

Its a piece of land given to a person in medeival society to rule on and to raise a small army to help the king of the country. I made a standard for the size of land that is suitable for one such unit. I named it estate or village. 1 estate is a square 1 mil long and 1 mil wide. Note that 1 mil is equal to 2 km. 1 estate is therefore equal to 4 sq km or 1000 acres. It means its enough for growing food for 1000 people traditionally if all of it is arable. Usually only 80% of it would be arable, so 800 people. There can be 16 farmers, each using 40 acres of arable land and leaving 10 acres in form of a forest.

One acre requires 40 hours of farm work right at farm. Other related works take:

5 hours for milking - 156.25 kg @ 31.25 kg/hour
5 hours excretions processing - 800 kg @ 160 kg/hour
2.5 hours taking out vegetable oil from seeds using bulls - 12.5 kg @ 5 kg/hour
2.5 hours cleaning grains
2.5 hours animal care including preparing meal, feeding, taking out
2.5 hours butchering including slaughtering, cutting meat, mincing etc

These extra works are 20 hours. So, a farmer have to work 60 hours per crop per acre. In our calculations its 1 crop per year, so 60 hours per acre per year.

Ideal time for a farmer to work per year is 2400 hours. It make him work at 40 arable acres.

There are 365 days a year. Take out 15 days for gazetted holidays. The remaining 350 days means 50 weeks. Give an off day per week. 300 working days. Give 30 days leave per year for sickness etc. 270 working days a year. If the farmer works 6 hours of actual work (no talking, resting, eating, drinking etc during that) then per year per farmer 1620 hours of work. If work 8 hours a day actual work then 2160 hours a year per farmer. There is 1.25 males of working age in a family of five (explained below). If each worker works 7 hours a day actual work then 2362.5 hours work per family of five per year.

Lets keep work day 6 hours long per worker and 270 working days a year, so per worker 1620 hours of work per year. Lets suppose a woman can work 2 hours a day doing things like milking cow, cleaning grains etc, then its 2160 hours. Lets keep a family's total working hours at 2160 hours a year. To help the prime male worker, either a female work, or a sub-prime male worker works, or the prime male worker himself works the extra 2 hours.

The family still have 40 acres farm to work on. To make this happen we have to cut time spent at each acre, see below:

Actual farming, per acre, 36 hours, not 40 hours, because at 80% of farm the farmer have to grow the crop too and cut it too, so 32 hours for that, for the rest 20% of farm the farmer only have to cut, the crops there grow naturally because its a pond, forest, natural grass land for bulls etc, half effort there, so 4 hours there. 18 hours for other works as animal caring, feeding, food preparation have to be done by farmer in his own time. So, 54 hours per acre, 2160 total hours, 40 acres.

800 arable acres per fief. Keep 200 arable acres for thick forests where people don't go and are reserved for wild life. Keep 200 acres for thin forests, lake and natural grass land where people go to cut trees, to feed war horses and to collect honey. So, 400 arable acres given to farmers, 10 farmers in each fief.

Note that for each person there is a need of 144 hours of work, details are:

54 hours - farming and related works (discussed above)
27 hours - cloth, shoes, dye, herbs etc industry
27 hours - metal, construction, pottery, furniture etc industry
18 hours - commercial services such as trade, hair cutters, dentists etc
18 hours - govt industries such as military, police, judiciary, rulers, spies, record keepers etc

That is approx 25 families per fief. 20% population of empire lives in cities, 80% in villages, so 100 people per fief.

Acre

An acre is amount of land that one person can plow once in one day using one pair of bulls pulling a plow. It is standardized as 4000 sq meters.

One meter is also the amount of land that is needed to support one person for one year, if:

(1) There is only one crop per year.

(2) Land is average (grow 400 kg of wheat a crop for example).

(3) Rain is the only source of water that is used, that is, canal water is not used, also no well water is used (no tube wells, pumping water from ground etc).

(4) No chemical fertilizer is used. Excretions of farm animals and humans are put in soil.

(5) No pesticides are used.

(6) No tractor is used.

(7) The diet of supported person is balanced, that is, get 55% calories from CH, 15% from proteins, 30% from fats, also get all needed minerals (majority from honey) and vitamin and fibers.

(8) From this one acre all needed categories of food (fruits, honey, milk, meat, fish, vegetable oil, grains, vegetables, dry fruits etc are grown).

(9) Within this one acre, other than supporting the person, the farm animals needed to work on farm (such as bulls) are also supported.

(10) Clothing for the person (basically in the form of cotton) is also supported within this acre.

(11) Medicines for the person (the herbs) as well as wood to burn and also flowers for fragrance products are also grown from this one acre.

Note that, traditionally, an acre is a very long, rectangular shape of land. Its length is 200 meters and breadth just 20 meters. This long shape made it easy for the farmer to plow it on a straight path and u-turns are very much reduced. The square shape is beegha or square furlong which is 200 meters x 200 meters, so there are 10 acres in a square furlong. Traditionally, land was bought and sold only in multiples of beegha as land was cheap and people few, also 10 acres used traditionally hardly support a farmer's family with no extra to give in taxes.

1/100 of begha is 400 sq meters, a piece of land ideally suited to make a house for a nuclear family, a store house, a small market for a village, a small masjid in a village, a small school, a small hospital etc. In my opinion, ideally no building should be lesser than 400 sq meters in area. I have also named this area, I call it "qita" which means plot in urdu.

Some lands need to be plowed twice, some thrice before any crops can be grown on it. So, if it need to be plowed thrice, the farmer needs 3 days to plow one acre and 30 days to plow one beegha. A farmer should not spend more than a month in plowing because there are only 6 months available in all to have a crop, one consumed in plowing, one must be there for harvesting and 4 months are the minimum one should reasonably give to plants to grow. Note that seeding is an easy activity and can be done while plowing, by a woman who simply walks behind the farmer spreading seeds as land is being plowed. Ideally, a farmer should have 40 acres to work on, 10 acres to have a crop such as grain, dry fruit, vegetables etc, 10 acres orchard, 10 acres hay land where hay is grown by farmer that is its not a natural grass land, 10 acres for miscelleanous including cotton, wood, herbs, flowers, pool for fishes, hay for bulls etc. Other than these 40 acres used by farmer, there should be a 10 acres for natural forest, grass land, lake etc. So, 50 acres land is arable which is 80% of village, that means for each farmer we should have 62.5 acres of land.

There is an issue in above, if one farmer have to work at 40 acres then he would be just a farmer, he would have no time or energy left to do anything else, things like milking cows, butchering cows, cleaning grains, putting excretions of farm animals back to farm after processing etc.

Unit of Mass - Wasq

On the basis of unit of length "zira", we can have a unit of mass too. Mass of one cubic zira water is 125 kg, this is a traditional arabic unit of mass, its called wasq. One wasq is equal to 1000 oqia where one oqia is equal to 125 grams.

Wasq and oqia can easily be seen in daily life. Some examples are:

(1) One wasq is the maximum weight a man, usually a wrestler can have with health.

(2) One wasq is about the maximum mass a man, usually a body builder, can lift.

(3) One wasq is about the mass of grains an average person usually eat in a year, considering 2000 calories per day diet.

(4) One oqia is about the average size of an apple.

(5) One oqia is the maximum amount of grapes a person should eat in a day.

(6) Two oqia is the amount of water/milk/tea/juice/soda etc in an average glass/cup.

(7) One oqia is the mass of a large bullet, the kind that is fired from an airplane.

(8) One oqia by volume, that is, 125 cubic cm, is the volume of one mouth full of a man.

Unit of Mass

Importance of Zira in Islam

Many laws in islam have lengths measured in zira. Some examples are:

(1) Distance between wells must be atleast 40 zira.

(2) If some nijasat (excretions, alcohol, blood) falls in a pool/pond etc of water and neither of color, smell, taste of water change then water still becomes nijasat, unless the size of pool/pond etc is 10 zira x 10 zira or 20 zira x 5 zira.

Zira is also used in some arabic units of measurement, such as

(1) Mil. 1 mil = 4000 zira. Note that the term "mile" in english is derived from arabic "mil". One mile = 1600 meters, One mil = 4000 zira = 2000 meters.

(2) 1 farsukh = 3 mils = 12,000 zira.

The Basic Unit - Zira

SI system is based on seven basic, independent units, one of them, "meter" for length is also used to find unit for mass (1 cubic meter contains 1000 kgs of water).

The unit "meter" has no fundamental justification. Its hard to approximate for a layman what a meter is. There is another unit called "zira" which is far more understandable and easy. Infact, "zira" is the unit of length which is the first unit of anything ever used in any human civilization. For example, egyptians built pyramids using this unit, greeks used it extensively and so did romans. Perhaps great wall of china is also built using "zira" as a measuring ideal.

So, whats so special in "zira"? It is that one zira is equal to distance between the tip of middle finger and elbow of a man. Ofcourse that varies with height of people but still its an easy approximate that can be taught to a layman. Ofcourse zira has a specific length which do not vary with the peron using it, it is about 50 cm or 20 inches. Note that a person's height is equal to four time the distance between his middle finger and elbow (lets call that distance one "hand"). Therefore, a 6 ft tall man has one hand equal to 18 inches or 45 cm. It means that for a 10 inches hand the person's height need to be 80 inches or 6 ft 8 inches. Since almost all men are under that height (the exceptio would be less than 5% of population) so for almost every person his one hand is somewhat less than one zira.

The level of variation is like +/- 33% because men's heights vary between 5 ft and 8 ft 4 inches in different races. The 33% seems like a lot but atleast a person has a general idea of what a zira is, such an idea is totally absent for a meter.

Note that romans called zira a cubet and so do english speakers, although a cubet is now considered as 18 inches. That variation may be because romans standardized it for a 6 ft tall man's hand.

06 July, 2010

Ideal Size For Bedroom

The task here is to find the most appropriate size for a bedroom. This could be a bedroom for one person or for two. The inhabitant(s) of said bedroom can be children or adults.

We should start with finding furniture that we want in the bedroom. All of these furnitures must take a maximum of 25% area of the bedroom. Another 25% area of bedroom must be kept aside for walking and standing space such as at both sides of bedroom and in front of the doors of the cupboard. The rest half area of bedroom must be left empty, in which some carpet can be placed or left uncovered for ground sitting.

We should begin with a bed, since by defintion a bedroom must have a bed. The calculations we are making here works for both a wooden bed and a mattress or blanket put on ground. Most adults are under 6 ft height, the bed must be long enough to hold full body of an adult. Some space must be given to pillow, that space is around 4.5 inches more than the end of head. At foot too, a 4.5 inch long space must be kept extra to provide some flexibility in moving a little up and down while sleeping. Therefore, a bed must be 6 ft and 9 inches long.

Now we should put our focus on desired width of a bed. A person on average needs 18 inches wide space just to get tightly packed in with 27 inches providing some place to move hands. Therefore 27 inches is the least acceptable width of a bed. Note that 27 inches is very much like the width of a train berth, where you can sleep for a night or two but don't want that on permanent basis. On the other extreme, a maximum 54 inches or 4.5 ft width is the most that is acceptable. I have personally used a 3.5 ft wide bed and its a little more than what I am comfortable with and I never got to use the full space in one night even after enough rolling and stretching. Therefore, a 3.375 ft wide bed is the most appropriate for most people.

An appropriate bed (actually mattress size) is therefore 6.75 ft x 3.375 ft.

I should use better units here, then things can be clearer. The oldest unit of measurement used by humans is zira. One zira equals about 20 inches or 50 cm. An appropriate bed is 80 inches x 40 inches (6 ft 8 in x 3 ft 4 in) mattress size.

I have used a bed that is less than 1 inch thick at borders and its a strong bed. Lets have a stronger bed with 2 inches thickness at each size. These extra 2 inches are visible only at front (pillow size) and rear (legs side). At the rolling sides (left and right) only 1 inch thickness is visible because the other inch of wood would be covered by mattress. In any case, these 2 or 1 inch are not important for our calculation because we plan to leave 20 inches walking space at both sides of bed, since most adults' bodies needs only 18 inches so the thickness of wood of bed is easily absorbed. The bed can also be placed close to a wall to get extra space in room.

I like the door of room to be at center of wall, this wall should be where the rear of bed is pointing. The door should be 18 inches wide, with 1 inch each side of fixing support of door in wall. The door must have two slides, each one providing a walking space 9 inches wide, therefore both slides must be open for a person to enter. At the left and right of the door, after one inch support, the wall must be 60inches wide at each side (left & right). Since 60 inches is 5 ft therefore other than door the wall is total 10 ft wide. To make it 12 ft we can have the door 2 ft or 24 inches wide. In that case, the door itself should be 20 inches wide and its support in wall at each side should be 2 inches wide. A 20 inches wide door almost guarantee that even a strong muscled man can comfortably enter.

At each side, which as discussed above is 60 inches wide, the middle 20 inches wide place is given to a window. Therefore we have 2 windows on this wall and on each side of each window a 20 inches wide wall exists. Since each window is 20 inches wide and since each window has two slides (like the door) therefore each slide is 10 inches wide, therefore a 10 inches wide space must be there after the rear of bed. Another 20 inches must be there for a person to stand.

The room is decided to be 12 ft wide. Length wise we have 80 inches long bed, then inches of standing space, then 10 inches of slide space, total 110 inch. If we add in 10 inches then it becomes 10 ft. The room therefore becomes 12 ft x 10 ft.

Another way is to have a 40 inches wide door and keep 40 inches wide wall at each side of door. The room then is 120 inches or 10 ft wide. The length is 80 inches for bed, 10 inches for window slide and may be 30 inches more, total 120 inches or 10 ft.

Given that an ideal bed is 80 inches x 40 inches, minimum walking space needed for a fat or muscled person is 20 inches wide and there are about 40 inches in a meter and 20 inches in the oldest measurement tool used by humans, the most appropriate bedroom size is 4 m x 4 m or 8 zira x 8 zira or 160 inches x 160 inches. Note that this is the internal area of room. Ideal wall thickness is 20 inches, therefore including that too the space for room becomes 5 m x 5 m or 10 zira x 10 zira or 200 inches x 200 inches. Keeping a room this big, we can put at maximum 4 x 2 = 8 mattresses in the room.

The door is planned to be 40 inches wide, each slide being 20 inches wide a 20 inches space is left empty (that is, without furniture at each side) of door. The door therefore gets half of the width of the wall at maximum leaving 40 inches at each side. If door don't go fix at sides then each side is 60 inches wide. At the middle of that a 20 inches wide window is put for ventilation. Another window is put at its opposite end, at the front of bed for example for cross ventilation. The room therefore have 4 windows.

The height of the room have to be 4 meters, with roof and floor 0.5 meter thick each. The whole complex with walls therefore is 125 cubic meter or 1000 cubic zira. Internal area is 64 cubic meters. Since one mole of air at STP needs a volume of 22.4cubic dm therefore 64 cubic meters means 2857 moles. Since air is 21% oxygen by volume therefore 600 moles of oxygen are present in the room. Since molecular mass of oxygen (O2) is 32 amu therefore, 600 moles means 19200 grams of oxygen.

The equation of digestion of glucose is given by:

C6H12O6 + 6O2 -> 6C02 + 6H2O

therefore 180 grams glucose needs 192 grams oxygen for digestion. One gram of glucose means 4 calories and a healthy average person needs 2000 calories a day, therefore 500 grams of glucose therefore 533 grams oxygen. There is sufficent oxygen in room to last for 36 days for an average person. Note that an adult female on average needs 2500 calories therefore 1.25 times more therefore for her its oxygen for 28.8 days, for an adult male daily consumption is 3000 calories, therefore there is oxygen supply of 24 days for him in the room.

Note: I have over simplified food requirements. Human body needs proteins and fats too but for simplicity I ignored that for now and assumed that all food is carbohydrate.

So, we have 40 inches wide door and 60 inches wide place at each side. Height of room is 160 inches. I like to have the window at height of 60 inches so that I be visible from outside the window only when I am standing, this means privacy when I am sleeping or doing some table work etc. The window should have a height of 40 inches and therefore above it there is a 60 inches high wall again. In the middle of that 60 inches a 20 inches high small window (roshan-dan) is very appropriate. These small windows are ofcourse supported by same size and location small windows at opposite end to ensure ventilation.

The window scheme is explained again: in the wall that contains door, leaving a space of 20 inches at both ends, there are two windows each 20 inch wide and 40 inch long and each of these windows start at a height of 60 inches. Above them at a distance of 20 inches height wise there is one small window for each large window which as the same width as the large window but half height.

Below the large window, a cupboard can be placed. Total space taken by this cupboard could be 40 inches width, 20 inches length (towards the leg side of bed) and 60 inches height. Inner space is much less due to thickness of wood.

Its better to place two people in each such room instead of one. This is for better utilization of space, to avoid night fear and for security. Two beds can be placed width wise adjacent to two walls with each bed's leg side facing a large window. A cupboard can be placed under one large window and a table (writing or dressing) under the other large window.

Note that there should be two doors in each room. We have discussed only one door so far. The other door should be directly in front of the entry door and should be rarely used. The need for two doors is to have an alternate way of escaping the room in case one door is jammed by an enemy, by earthquake etc. For proper ventilation and escape passage the front and back of each room must have corridors. Each such corridor must be atleast 2 m wide and atmost 4m wide.