A math book for "Journey to the West" Yuhuazhou blacksmith proves innocence

  Although wrought iron can be forged, its internal structure is loose and its texture is soft, and it needs to be further forged into steel to make high-quality weapons.

Repeated heating, forging and folding can remove impurities containing magnesium, aluminum, silicon, calcium and other elements in iron as much as possible, so that its quality will become better and better and eventually become steel.

From pig iron to wrought iron, and from wrought iron to steel, the forging process reduces its weight.

  Archimedes is famous in the history of science for his discovery of the law of buoyancy, which is said to have originated from the king of Syracuse who doubted the purity of a golden crown and commissioned Archimedes to find out.

Ultimately, Archimedes, using the newly discovered law of buoyancy, determined that the craftsman who made the crown stole the gold and replaced it with impurities.

From "Journey to the West", we can also see a quite similar case.

It happened in the 88th to the 90th. The general plot is that the three Wukong brothers accepted three little princes as apprentices in Yuhua Prefecture, Tianzhu, and taught them martial arts respectively. The princes organized blacksmiths to imitate Wukong and others' weapons and make them. During this period, Huang Shijing stole the golden hoops, etc., and the blacksmith was once suspected of being a thief.

After some twists and turns, the golden hoop rod and other magical soldiers were recovered.

Although the blacksmith's suspicion of theft was cleared, the two sets of figures disclosed in the book made them suspect of corruption:

  The prince also summoned a blacksmith along with the announcement, comprador thousands of kilograms of steel, and set up a factory in the front yard of the palace, supporting the furnace for casting.

One day, the steel was cooked, and the next day, the three people were asked to take out the golden hoop rod, the nine-toothed palladium, and the demon-subduing staff, and put them between the tent factories.

  Seeing that the blacksmith and the others had made three kinds of weapons, he kowtowed to the walker and said, "Grandpa, the little ones are all finished." He asked, "How much does each weigh?" The palladium and the demon-subduing staff each weigh 800 catties."

  At the beginning of making the weapon, there were ten thousand jins of steel. After it was made, the total weight of the three weapons was only 2,600 jin, and the difference between the two was 7,400 jin.

After reading this, some readers can't help but wonder, does this disparate figure mean that the blacksmiths secretly removed the iron materials and enriched their pockets?

  What is the consumption of raw materials

  To judge whether the output ratio from raw materials to products is reasonable, it is necessary to know how much raw materials were usually consumed from ironmaking to ironmaking in ancient times.

  It can be seen from the original text that the blacksmith would spend a day refining the iron before making it, so the first ten thousand catties that the prince bought were pig iron.

Pig iron is a product with a carbon content greater than 2% obtained by mixing pulverized iron ore with pulverized coal that acts as a reducing agent.

It can only be cast but not forged. To make weapons, mature iron must be refined.

Wrought iron is traditionally obtained in China using the "fried steel method", in which pig iron is melted by blasting air in a frying furnace and decarburized by stirring.

  Take the "floor-stove-type" frying stoves that were still circulating in Shanxi and other places before and after the founding of New China as an example. The operator first put charcoal, firewood, etc. into the hearth, ignited the blast, and then added pig iron. It is just smelted from ore, or it can be scraps of recycled cast iron pots.

The operator blocks the furnace door and continues to blast heating, and the pig iron will gradually burn into red. At this time, start stirring with an iron rod. When the pig iron is further burned and turns white, stir vigorously to make it form a semi-molten agglomerate. Stirring allows the carbon contained in the pig iron to combine with the oxygen in the air to escape, thereby reducing its carbon content.

Subsequently, the operator uses tongs to take out the agglomerates, forging to extrude impurities, and after several times of reheating and heavy beating, iron ingots or slats are finally formed.

  Although wrought iron can be forged, its internal structure is loose and its texture is soft, and it needs to be further forged into steel to make high-quality weapons.

Repeated heating, forging and folding can remove impurities containing magnesium, aluminum, silicon, calcium and other elements in iron as much as possible, so that its quality will become better and better and eventually become steel.

The idiom has the cloud "a thousand tempering", which originates from this process.

From pig iron to wrought iron, and from wrought iron to steel, the forging process reduces its weight.

In this regard, Shen Kuo of the Northern Song Dynasty recorded: If there is steel in iron and steel, if there are tendons in the noodles, if you wash the noodles softly, you will see gluten, and the same is true for steelmaking.

But take the more than one hundred fires of fine iron forging, and each forging is called, one forging and one light, until the forging is exhausted and the jins are not reduced, then pure steel is pure steel.

  Regarding the loss of steelmaking, we can get a glimpse of it from the extant Xiahou Yang Suanjing, which was written at the end of the 8th century.

The wrought iron fried in this book is called pyrite, and there are two questions related to it: today there are 6281 catties of pig iron, if it is to be smelted into pyrite, it will cost 5 taels per catty.

The answer: 4,318 catties and 3 taels of yellow iron.

Now there are 4,318 jin and 3 taels of yellow iron. To be smelted into steel, 3 taels are consumed per jin. What is the geometry of steel?

Answer: steel 3508 catties, 8 taels, 10 baht and 5 ha.

  "Xiahou Yang Suanjing" divides steelmaking into two steps. The first step is to make wrought iron from pig iron, with an output rate of 11/16. The second step is to make steel from wrought iron, with an output rate of 13/16. To steel, the yield is about 55.9%.

  "Xiahouyang Suanjing" is a mathematical book. Can the numbers in it reflect the actual efficiency of ironmaking?

Judging from the process survey and historical records, it is almost the same.

For example, in the 1950s, scholars investigated in Yunnan for frying steel in a wool iron furnace. After frying mature iron from pig iron, the loss was one-third, which was close to the consumption of 5 taels per catty (16 taels).

Song Yingxing of the late Ming Dynasty said in "On Qi", "Fan iron... When it first entered the raw and cooked furnace, the iron and the iron fell by one third." "When wrought iron is released, it is called wool iron, and when it is forged, it consumes three out of ten".

Its proportions are close to the previous ones.

If the survey data of Song Yingxing and Yunnan are taken, the loss of 1/3 of wrought iron for making wrought iron and the loss of 30% for making steel of wrought iron, the output rate is about 46.7%.

  From 46.7% to 55.9%, it can be regarded as the range of pig iron production rate of traditional steel frying process.

Substitute into the situation of Yuhua Prefecture in "Journey to the West", the craftsman can obtain about 5,000 catties of steel from 10,000 catties of pig iron.

  If a weapon is made of wrought iron, it needs to be folded and forged repeatedly to make the structure denser and increase its strength.

If good steel is prepared, the forging process can be simplified.

The loss of materials in this link is mainly due to the removal of the oxide skin on the surface of the steel during forging, that is, the dark small pieces that were dropped by the hammer when we watched the forging.

Of course, the quality of the product does not necessarily have to be reduced, not increased. For weapons that have been severely worn, the blacksmith can also take other steel materials and smash them together again. Over time, repeated folding and forging may cause bending on the weapon. A beautiful pattern that turns.

  The loss caused by this process depends on the type of product.

For example, the planing blade used in woodworking needs to take advantage of the looseness of wrought iron. The number of times of forging is small, the texture of chisels and knives is much denser, and the swords can reach "nine refining", "seventy-two refining" and even "hundred refining". .

The more times of forging, the more oxide skin is smashed, and the greater the loss.

According to experienced masters, to get a high-quality sword, it may cost about 20% of the materials on the basis of the previous step.

That is to say, the total weight of a weapon made of 5,000 catties of steel should be around 4,000 catties.

  From this point of view, the products given by the blacksmiths in Yuhua Prefecture are indeed not enough, about 1,400 jins less than the reasonable situation.

Maybe they returned the remaining raw materials to the government, but the author did not write down this trivial matter that had little to do with learning from the scriptures, and then contacted the craftsmen to warn the craftsmen of the twists and turns of the theft of weapons.

  Why is the iron bar so heavy?

  If we collect the relevant data in the book "Journey to the West", we will find that the iron rods made by craftsmen exactly correspond to the commonly used sizes of Monkey King's golden hoop rods.

  How heavy is the golden hoop?

The third time in "Journey to the West" mentioned that the inscription on it recorded "13,500 catties". The book did not say any changes in Wukong's use experience. We can think that its weight remained constant.

The material of the golden hoop rod is "shenzhen iron", which means that the density can be large or small while the volume can be expanded and contracted according to the owner's wishes.

So what kind of iron rod does Sun Wukong use?

In the fifth chapter of "Journey to the West", it is said that Sun Wukong fought against Jiu Yao Xingjun, shaking the iron rod, "the thickness of the bowl, the length of two feet".

On the eighty-eighth time when he demonstrated martial arts to the little princes, it was also "the thickness of the bowl and the length of two or three feet." It seems that this is the size of the golden hoop stick in Wukong's actual combat.

  It is worth mentioning that Wukong is usually only 4 feet tall, and "zhang two" is 12 feet. Wukong can only hold one end of the stick when he stands on the ground, so he will not stand on the dance stick like in operas and TV series. Eighty-eight times, he was in mid-air "about three hundred paces off the ground", and he spread his stance to perform.

  One zhang is 10 feet, and the commonly used construction ruler in the Ming Dynasty was 32 cm, and "zhang two" is equivalent to 3.84 meters.

How thick is "the thickness of the bowl"?

There are many Ming Dynasty bowls handed down and unearthed in museums all over the world. From the collection materials such as the Palace Museum, it can be seen that the diameter of the large bowls in the Ming Dynasty was 27-30 cm, and the diameter of tea bowls or small bowls was about 10 cm. The diameter is mostly 15-20 cm.

If we take 16 cm as the "thickness of the bowl", then we can calculate the volume of the whole bar is about 77.2 cubic decimeters.

  The iron rods imitated by Yuhuazhou are not divine iron, and their density can only be close to dense pure iron or steel, that is, about 7.8 grams/cubic centimeter. The total rod weight is approximately 602 kg.

How much is a pound in Ming Dynasty?

According to the research of weights and measures historians, its weight is equivalent to the current 596.8 grams, so the imitation iron rod weighs 1009 jin, which is almost the same as the "qianjin" mentioned in the book.

  (The author is an associate researcher at the Institute of History of Natural Sciences, Chinese Academy of Sciences)

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