29 July, 2009

Horse vs Car

Data:
(a) For pulling carts, four Mongolian horses can pull 2000 kg between 50-60 km a day. (See source).

(b) Average mass of horse is 500 kg. (see source).

(c) For each kg of body-mass a body needs on average 40 calories. (see source).

(d) Grass, the primary food of horses contains 2.0 calories per gram. (see source. See also here and here).

(e) Each 1k acre on average produce 1600 kg grass-hay per acre per year. (see source).

(f) One liter of petrol contains 33.2 million joules. (see source).

(g) One calorie = 4200 joules. (see source).

(h) A 1.25 tons car has 28 mpg mileage. (see source. See also here).

Working:

From the data:
"For pulling carts, four Mongolian horses can pull 2000 kg between 50-60 km a day"
means 4 horses, 2 tons, 50 km
= 4 horses, 100 km-ton
= 1 horse, 25 km-ton.

1 horse = 25 km-ton/day x 300 days = 7500 km-tons/year. Mass of horse is 500 kg, energy intake is 40 calories/kg. Total energy intake is 20,000 calories/day or 8 million-calories/year or 923 liters petrol.

A horse fully grows up at age 3 and work till age 15 therefore 20% of its life time is spent in childhood when it not work. A mare also has average life 15 years but in addition of 3 years childhood it also has to raise (feed & take care of) two ponies each of whom need full attention in first 1.5 years of life so 3 years needed for that per mare. Therefore the mare works for 9 years.
Out of total 30 years average lifetime available to the couple the horse works 12 years and mare 9 years total 21 years. Divide 30 by 21 and we gets 1.43 herd-mass for each working-mass. Total food energy consumed by the 500 kg working horse is equivalent to energy in 923 liters petrol, multiply that by 1.43 and we get 1318 liters. Total work done by the working horse is 7500 km-tons/year so 5.69 km-tons per liter petrol.

Lets compare that with engine:
1.25 tons, 28 miles, 1 gallon.
= 1.25 tons, 28 miles, 3.75 liters
= 1.25 tons, 44.8 km, 3.75 liters
= 1.25 tons, 11.95 km, 1 liter
= 14.93 km-tons per liter of petrol.

A car takes almost as much energy in completion as it consume in its life time. Lets assume that the making of engine and related body parts takes half the energy and the remaining luxury stuff like seats, air conditioner, tape, speakers etc takes the other half energy. Since in making of a loading truck we can avoid or drastically decrease the amount of energy consumed in making of luxury stuff we have to reduce the work done per liter of petrol in our calculation only by 75% instead of 50%. 14.93 x 0.75 = 11.2 km-tons/liter-petrol. Comparing this with horse's work done per equivalent liter petrol of 5.69 km-ton we find that horse has 50% efficiency of a car engine.

1 1k acre of pasture produce 1600 kg hay which is equal to 404.8 liters of petrol.

World oil production is 30 billion barrels. Oil provides 40% of energy. So total energy usage is equal to 75 billion barrels. In a population of 6 billion it means 12.5 barrels which means 2000 liters petrol. So that means 5 1k acres or 1 modern acre. Modern acre is one on which agriculture is done in modern way that is by using artifical fertilizers, pesticides and tube wells. Since although 1 1k acre can produce equivalent of 400 liters of petrol the using of horses reduces the efficiency to half so 10 acres are needed per person to feed horses to maintain the current world average life style.

We can use donkeys in place of horses. Infact donkeys are atleast 33% more efficient in work and 25% efficient in food. So double efficient. The higher efficiency in work is due to working larger number of hours per day and larger delivery-load to body-mass ratio. The higher efficiency in food is due to eating many side things in crops that horses don't eat.

In terms of power 2000 liters of petrol means 2104 watts of continuous power in form of primary energy. Lets round that to 2000 watts. In developed countries the average is 10,000 watts and in developing countries the worst is 200 watts. Note that we are not counting food energy consumed by people which for a 2000 calories/day average diet is 100 watts. In countries like Pakistan the non-food energy consumption per capita is just 200 watts which means only 1 pasture 1k acre would be enough to maintain the current life style post peak oil.

28 July, 2009

Protest

House Plan



This is a middle class house plan. It has four bedrooms. There is a large open place at middle, the waranda. The passage behind medium bedrooms is half yard wide, it is only for air means it is not a walkable place due to extension of windows. The corridors are 1.5 yards wide including 0.5 yards taken occassionaly by round pillars. There are 4 attached baths one with each bedroom.

The plot is a square of 484 sq yards or 400 sq meters. Two outer walls are 6 inches wide and six inner walls are 4 inches wide, total 1 yard width is given to walls in both north-south and east-west dimensions. The place to map is therefore 21 yards x 21 yards.

The house is made by keeping ventilation in mind so that the inhabitants are not dependent on electricity for cooling. Enough space is given both in front and back of each room for crossing of air. The drawing room, dining room, toilet, study, kitchen and garage also have cross ventilation. The bedrooms are given one additional window each for more air.

A very large open space is left in front of house wide enough for a truck to come in if inhabitants wishes so. The total opening is 27 ft divided into two equal halves by a central 9 ft wide pool. The space around pool is 9 ft wide at north-south and 10.5 ft wide at east-wide directions, wide enough for a truck to roll around the pool.

Both the lawn and open place at entrance is 9 ft wide.
Dimensions in yards are:


Bedrooms 4.0 x 3.0 = 12.0 sq

Living Room 4.0 x 3.0 = 12.0 sq

Waranda & pool 9.0 x 9.0 = 81.0 sq

Toilet 3.0 x 2.0 = 6.0 sq

Study 4.6 x 3.0 = 13.5 sq
Kitchen 4.6 x 3.0 = 13.5 sq
Garage 4.6 x 3.0 = 13.5 sq
Drawing Room 4.6 x 3.0 = 13.5 sq

Dining Room 4.0 x 3.0 = 12.0 sq
Store 4.0 x 3.0 = 12.0 sq

Corridors 1.5 x 6.0 = 9.0 sq

Lawn 20.0 x 3.0 = 60.0 sq
Front Place 20.0 x 3.0 = 60.0 sq

Yields

The following data is based on 1k Land. It is land that gets either 10 inches of rain water 80% of which falls in crop season or 1 acre-ft/acre water 33% of which may evaporate in transit, effective water that is actually used by land is therefore 800 cubic meters per acre per year. The land gets no ground water. There is no spreading of artificial fertilizers. No pesticides are used. The seeds are traditional/pre-green-revolution. Only one crop per year happen, planted in spring and cultivated in autumn.


Yields Water Need Total Water Need
(kg/acre/yr) (cu-meter/kg) (cu-meter/yr)
X Y XY

GRAINS:
Wheat 400 1.00 400
Rice 1000 5.00 5000
Millet 600 0.70 420
Barley 600 0.70 420
Pulses 250 1.40 350

Veg-Oil 250 2.80 700
Spices 250 2.80 700
DryFruits 250 2.80 700
Sugar 500 1.40 700

Tea/Coffee 500 1.40 700
Cotton 250 10.00 2500

Grass-Hay 1500 0.70 1050

Fruits 1000 0.70 700

Veg 1000 0.70 700

Notes:

(i)In some crops not all of the effective water is used. Such crops includes wheat, millet, barley, pulses etc, the so-called dry crops. Due to their less use of water these crops can sometimes be planted in dry weather of winter where rainfall is less than summer. These crops can also be planted in poor land having only 400 cubic meters water. It not means that the yield would be same in poor quality lands. The traditional seeds of dry crops unlike the green-revolution seeds are not capable of using all of the available water.

(ii)In case of fruits 700 cubic meters water is used out of the available 800 cubic meters, the rest is used by grass and weeds that grows in places between trees.

(iii)In case of grass more than 800 cubic meters of effective water is used. Due to the typical net-like pattern made by grass roots underground water absorption in ground is reduced.

27 July, 2009

Types of Land


We can divide land on the basis of the amount of water it receive. The underlying assumption is that upto a certain extent fertility of land grows with amount of water available to it. Desert having little water has little fertility whereas deltas of nile, euphrates, ganges and indus have high fertility due to water availability.

There are infact three sources of water, primary which is rain, secondary which is canal, teritiary which is ground water. I would not consider the teritiary source in this article for land classification because it is energy intensive.

On the basis of quantity of rain it gets a land can be divided into 7 categories:

>80 inches
as good as desert for food production

80 inches
not so fertile due to excess water, can only grow a few crops like rice, grass, poor quality

40 inches
average land

20 inches
the most fertile land

10 inches
average land

5 inches
poor quality land

<5 inches
desert

On the basis of canal water available the land can be divided into 3 categories:

0 acre-ft/acre

1 acre-ft/acre

2 acre-ft/acre

What is "inches of rain" and "acre-ft/acre" anyways?

Lets consider the middle case of 10 inches of rain falling on one acre. Since there are 2.54 cm in each inch therefore it means 25.4 cm tall water column standing on one acre. Lets round that off to 25 cm for easy calculation and understanding. One acre is 4840 sq yards which is equal to 4047 sq m. Lets round that off too to 4000 sq meters. So, 10 inches of rain roughly means 25 cm water standing on 4000 sq m. The volume is 1000 cubic meter water. I call this 1k land because it gets 1000 cubic meter water in a year. In my calculations 1k land can be any land that gets 1000 cubic meter water irrespective of the source of water, it not always have to be rain water to call it "1k land".

One acre-ft/acre canal water means 1 ft tall water column standing on 1 acre of land. Acre-ft is the general unit of measurement of canal water. 1 ft means 12 inches and one inch means 2.54 cm, so 1 ft means 30.48 cm. Round that to 30 cm. Multiply that with 4000 sq m as before and we get 1200 cubic meter water per acre.

Before ending this discussion lets find the cost of rounding. In case of rain water, if we multiply the actual 4047 sq m with the actual 25.4 cm we gets 1028 cubic meter water instead of the round off value of 1000 cubic meter. In case of canal water, if we multiply the actual 4047 sq m with the actual 30.48 cm we gets 1234 cubic meter water instead of 1200 cubic meter.

Effective Water

In addition of knowing how much water is available per acre one must also know how much water getting to land is actually available for crops. Ofcourse not all of it is, some rain fall in off season when its of no use to crops, water flowing in canals and before that in rivers get evaporated on their long (hundreds of miles) journey to farm etc. Lets calculate the effective water in both cases of rain water and canal water one by one.

In my part of world, that is, in south asia, 80% of all rain water falls in two months of sawan and badho, that is from 16th july to 15th september. This also used to be the time when the crops need water in the traditional one-crop-per-year farming. So, 80% of all rains gets to land when the crops need them. I assume for simplicity the same for the rest of the world. It means that the average case of 10 inches rain water per year which is roughly translated to 1000 cubic meters water per acre per year is 800 cubic meters effective water.

In case of canal water, in Punjab due to relatively cooler weather and more fertile land the evaporation rate of canal water is 25%, in Sindh due to relatively hotter weather and generally less fertile land and also due to longer distance the canal water has to travel to farm the evaporation rate of canal water is 33%. I, for simplicity, takes the general rate of evaporation 33% so that 1 acre-ft/acre water which is roughly translated into 1200 cubic meters water above means 800 cubic meters effective water to equate with 10 inches rain. Note that there is no off-season canal water distribution because canal water is essentially the rain water stored in dams and barrages distributed only when needed, so all of it gets to land when needed there is no discount of off-season water, the only discount is evaporation.

Lets go back to the discussion of categories of land. Excluding desert and desert-like lands where rain water is less than 5 inches or more than 80 inches, we get five categories of land on basis of rain water. We also have 3 categories of land on basis of canal water. So, taking union, we have 15 categories of land as follows:


5 inches rain = 400 cu m effective
5 inches rain + 1 acre-ft canal = 1200 ditto
5 inches rain + 2 acre-ft canal = 2000 ditto

10 inches rain = 800 ditto
10 inches rain + 1 acre-ft canal = 1600 ditto
10 inches rain + 2 acre-ft canal = 2400 ditto

20 inches rain = 1600 ditto
20 inches rain + 1 acre-ft canal = 2400 ditto
20 inches rain + 2 acre-ft canal = 3200 ditto

40 inches rain = 3200 ditto
40 inches rain + 1 acre-ft canal = 4000 ditto
40 inches rain + 2 acre-ft canal = 4800 ditto

80 inches rain = 6400 ditto
80 inches rain + 1 acre-ft canal = 7200 ditto
80 inches rain + 2 acre-ft canal = 8000 ditto


So, in short, the amount of effective water available vary between 400 cu m to 8000 cu m, a factor of 20. What we need is not the average case but the typical case. The average case is useful when the good, fair and worst are all in the same proportion which is not a real life situation.

So what is a typical case? A typical case is the mode as in statistics, that is the most common situation. It not need be the mathematical average. Its the case which you are most likely to encounter in a given situation.

How to find the typical case in a exponential situation? Well, first what is the exponential situation? Exponential situation is the situation where the numbers vary in multiples, like a sequence of 1,2,4,8,16. Here the typical case is 4 which is the middle value. It is the situation which you are most likely to encounter.

In the discussion of category of land, the best approach is to combine the case of 10inches of rain with 1 acre-ft/acre canal water. Result is 1600 cu m effective water per acre per year. For a deeper discussion, in order to get a sustainable agriculture it is unwise to use the canal water on regular basis. The agriculture should be primarily based on only the rain water, keeping the canal water as a safety valve in case of emergencies. Emergencies in this case includes droughts, pest attacks etc. If we embed the safety valve, the reserve troops in the normal operations where would we fall in case of failures? It sure is inefficient but it is indeed very resilient. All the world agriculture before the 1950s was infact based on only rain water, canal water was used only in emergencies, in years when rainfall is less than normal. Other disadvantages of canal water would be discussed in a separate article.

In summary, in absence of canal water, the average effective water available is 800 cu m, the lower value is 400 and the higher value is 1600, so we get the simple pattern of 3 values.


Worst: 5 inches OR 0.5 acre-ft = 400 cu m eff

Typical: 10 inches OR 1.0 acre-ft = 800 ditto

Best: 20 inches OR 2.0 acre-ft = 1600 ditto
OR
10 inches + 1.0 acre-ft = 1600 ditto

Average: 40 inches OR 4.0 acre-ft = 3200 ditto
OR
20 inches + 2.0 acre-ft = 3200 ditto

Worst: 80 inches OR 8.0 acre-ft = 6400 ditto
40 inches + 4.0 acre-ft = 6400 cu m ditto


Note that 3200 cu m case is taken as average because after a certain level excess water actually reduce fertility instead of increasing it.

Only a few of the possible combinations are given above for 3200 cu m and 6400 cu m.

The point is hidden in the amount of effective water available, not on the source of water.

For simplicity, some new terms are introduced, 2k means 2000 cu m nominal and 1600 cu m effective, 3k means 3000 cu m nominal and 2400 cu m effective and so on. In that sense, land types varies between 1k and 10k, 2k being most fertile, both 1k and 4k being average, both 8k and 0.5k being poor. More than 8k are extremely unlikely to be of any value to agriculture.

Another important thing to consider is the relation between intensity of rain water and availability of canal water. At fertile land, for example in punjab, both the availability of canal water and intensity of rain is higher than that in sindh. An increased amount of canal water applied to land increase the humidity of air which inturn results in more rain fall. Considering the feedback loops would increase complexity so are not discussed in detail in this article. Only take-home message from this is that it is more likely to get 2 canal water in a land that already has 20 inches rain than in land that has 5 inches rain because that would be a desert already having little or no access to any kind of river or canal.

24 July, 2009

Calories Part 2 - Diet Plan


Following is a daily balanced diet plan for an average 2000 Calories food requirements:



ITEM GRAMS CH P F Calories

Wheat 100.00 66.67 12.10 2.70 339.92
Rice 62.50 43.75 6.25 2.72 225.02
Millet 37.50 8.88 1.32 0.37 44.20
Barley 75.00 55.12 9.38 1.72 273.82

Milk 250.00 12.20 8.30 9.10 165.72
Butter 5.12 - - 4.10 37.72
Ghee* 4.55 - - 4.10 37.72

Mutton 31.25 - 8.10 0.27 34.88
Beef 31.25 - 25.00 - 100.00

Fats** 7.81 - - 6.25 57.50

Veg 62.50 3.91 - - 15.63
Veg Oil 31.25 - - 31.25 287.50
Sugar 31.25 31.25 - - 125.00
Spices 31.25 15.63 6.25 - 87.50

Fruits 250.00 31.25 - - 125.00

SUM 971.50 268.66 76.70 62.58 1957.15




*Ghee is fats taken out from milk. In the above diet plan 125 grams of milk is dedicated to make ghee. 125 grams milk contains 4.55 grams fats but only 90% of them is taken out, rest is lost in the process. Ghee itself contains 90% fats, rest is water. Therefore 4.55 grams fats in original milk results in 4.55 grams ghee. In the same way 125 grams milk is dedicated to make butter, the 4.55 grams fats present results in 4.095 grams fats in butter after 10% loss of fats. Butter is 80% fats so 5.12 grams butter.


**Animal fats is the fats available in the fats in the skins and other organs of animals. They make up 20% of the body mass of animals. Assuming that it is not desirable to use all of these fats we go for only 7.5%. Since animals are by mass 60%meat therefore animal fats are 1/8 of the meat.

Note:

The figures may look odd for daily requirements but if multiply by 8 they become more easy to comprehend. For eg vegetable oil 31.25 grams daily means 250 grams per 8days. The figure 8 is to roughly calculate for a week 10 being so far from 7. It is assumed that the food buying is done once per week. The oddness of figures should also get removed in next article about land requirements for growing the stated food items, the figures being tuned to yields.

Calories Part 1 - Basics


There is a unit of energy called "calorie" which is equal to enough heat energy needed to raise temperature of 1 gram of water 1 degree centigrade. In diet calculations a higher unit of energy "Calorie" (with capital C) is used which is equal to 1000 calories, enough heat energy to raise temperature of 1 kg water 1 degree centigrade.

In diet requirements, an organism needs 30 to 50 Calories per kg body mass. This is true for all animals and humans. A person doing light work such as table work needs just 30 Calories whereas a farmer or a carpenter needs 50 Calories. For our calculations we take the average 50 Calories.

Other than noting the overall energy need its also important to know the components of food needed. There are seven components of food: Carbohydrates, Proteins, Fats, Minerals, Vitamins, Fiber and Water. The last two, Fiber and Water, contains no energy at all, fiber is needed to rest the system as system not have to digest the fiber, water is needed to keep the digestive system clean. Minerals and Vitamins also contains no energy but are needed to rebuild the body after daily wear and tear. The only energy contents are first three, in this article we discuss only them.

Each gram of Carbohydrate contains 4 Calories, each gram of Protein also 4 Calories, each gram of Fats 9.2 Calories. For a balanced diet, 56-60 percent of energy must come from Carbohydrates, 12-15 percent from Proteins and the rest 25-32 percent from Fats.

The amount of diet energy needed depends of level of activity which is constant for a given person. A farmer remains to be a farmer and a clerk clerk. The other thing energy depends on is body mass which in turn depends on height which in turn depends on age if the body is growing.

Lets take the simple case of an adult who have reached the maximum height it would acquire in his/her lifetime. This adult would have in most cases also fixed its activity level by choosing a profession and gain enough mass appropriate to height. In most cases the optimum mass of 5'8" to 6' man is 75 kg and a naturally shorter woman of equal age 62.5 kg. For the population as a whole the average ideal mass is 50 kg, that is, if you consider children too.

Lets take 50 kg average mass and average activity level, that translates into a 2000 Calories daily energy need. Note that even for a 75 kg adult mass if doing office work the energy requirement is close to 2000 Calories, actually 2250 Calories. For a 2000 Calories, 1200 Calories must come from Carbohydrates (60%) which means 300 grams of it and 300 Calories from Proteins (15%) which means 75 grams and 500 Calories from Fats (25%) which means 55 grams.

So, in short, for an average person, the need is 300 grams Carbohydrates, 75 grams Proteins and 55 grams Fats. Each of these components of food available in different food items is given below in percentages:



ITEM CH P F Calories

Honey 80.00 - - 3.20
Milk 4.88 3.32 3.64 0.66
Wheat 66.67 12.10 2.70 3.40
Rice 70.00 10.00 4.35 3.60
Millet 23.68 3.51 0.98 1.18
Barley 73.48 12.50 2.28 3.65
Pulses 50.00 26.00 6.00 3.60
Fruits* 12.50 - - 0.50
Others 25.00 - - 1.00
Veg 6.25 - - 0.25
Mutton - 26.00 0.87 1.12
Beef - 80.00 - 3.20
Fish - 18.00 - 0.72
Butter - - 80.00 7.29
Sugar 100.00 - - 4.00
Oil - - 100.00 9.20
Spices 50.00 20.00 - 2.80



*This is an average calculation for different types of fruits not including those having a higher sugar amount such as banana/mango etc

Another thing to consider in getting the food is how much load it put on soil, in short how much land is needed to support an average person.

Why Empires Collapse?


An empire, country or even a city or village is not roads, factories, farms and houses. It is the trust people have in each other to become a coherent mass to achieve common goals. The key is gain sharing. Once the powerful become too powerful and too selfish to think themselves above the law, to stop contributing in common good through paying taxes, community services and military services the trust is gone. The weak justifiably start thinking themselves as mere beasts of burden, draft animals to drag the huge loads of wasteful and unjustified life styles of the elites. The coherence is lost. Whenever a chance comes the weak becomes allies with the enemies of empire and give easy back doors and corridors for the military, economic and idealistic invasion. When an outsider is not present or is not willing to mess up with empire, the weaks on the least loose efficiency and start ignoring the maintenance, the result is lost of output and unreplaced accumulated depreciation of infrastructure that exponentially increase the speed of collapse. Once things are visibly getting out of hand of the elite they first press the weaks further by taxing-to-death but even that not safe the empire. The next stage is a war between elites who already have developed hatred for each other in their greed of acquiring resources now blame each other for the cause of collapse each posing itself the most loyal to the empire. Even in this condition the empire continue to drag on because the constituents of empire, the people, both weak and strong have vested interests in empire, the strong ones obviously find the only way of continuing their life styles in the existence of empire and the weaks propagandized by the elite the "barbarism" of outsiders and due to fear-of-unseen keeps their heads down. This not continue forever, at some point in time an outsider becomes both strong and brave enough to invade the empire, first at outskirts/borders/battlefields of empire, then at established colonies and finally at the core country and the capital. The weaks generally either welcome the invaders or remains nuetral, the strongs do fight and do their best in saving the empire but its too late. The empire finally falls. After that one of the two things can happen, the invaders might not feel it desirable to rule the empire go back to their strongholds and the empire or the individual provinces of empire might have a chance to rebuild on the ashes with a significant lower level of complexity and injustice but even if the empire do get a chance it would eventually collapse by a new invasion a few decades or centuries later. The second thing that might happen is that the invaders make their own empire on the ashes of the fallen empire. That empire too would at some point face the same collapse.

Lets take a few examples. British empire was made when due to improvements in judicial system in early 18th century lead to an increased level of justice and gain sharing. The british gets a very loyal public that work and fight for the empire. Once the elites gets too strong and too rich, especially the govt servants sent to colonies like india, the injustice increase. The wwi was a major blow to the british empire which though unlike wwii win it on its own and collapse former enemies/threats such as turkish empire, russian empire and austria-hungary empire become very weak. The british empire did got a chance to correct its errors after wwi, to redistribute wealth and increase gain sharing but it lost its chance. When the second blow came in wwii in Battle of England the empire could hold no more. The russians in the eastern front and to some extent americans in norway invasion saved the british isles from falling into outsiders' hands but the real chance for the empire was long gone. The british were wise to let go the colonies and settle on a much smaller population, territory, wealth, power and resources.

The turkish empire was built on the basis of tribal justice and equality and the life styles of the first emperors was not that high of those in the middle (Sulaiman the magnificient) and later (Abdul Hameed) ages. The first attempts of introducing high levels of injustice was blowed by the outsiders' invasion in mid 16th century when tamerlane invaded from east and imprisoned Sulaiman the magnificient in a cage even when the Sulaiman had already conquered the heart of europe in france and italy and had "tied his horse where the pope lives". The turkish empire collapsed but the persians after tamerlane had no interest in ruling the provinces of former empire so the empire got a second chance. The empire got its former glory and power very very soon and continue to exist for almost 4 more centuries. The final blow came in the wwi.

The point is, we should not just see the history of rise and decline of empires on basis of resource depletion. Classic (pre christ) empires like Akkad, Egyptian, Babylon, Chinese and Indian were built on very sustainable resource base, especially the agricultural practise was very sustainable, the mineral resources also continue on to exist to be taken out later in middle ages and modern ages by almost similar technology. The only true reason for collapse of empires, countries and city-states that is sufficient enough to explain the rise and collapse of ALL empires is injustice.