Shikashin also said:

"According to this cylinder and the formula you gave, the buoyancy of water is roughly divided into two parts;

The first part is the straight tube, the volume of the straight tube is the area of the straight tube, that is, the garden operator 3.14, multiply the radius of the straight tube by the square of 2 feet is 4, and then multiply the length of the straight tube is 4 feet, the number obtained is 50.24 cubic feet, and each cubic foot of water weighs about 72 catties, which is about 3,6107 catties.

The second part is the round ball at both ends, according to what you said, the volume is 4 divided by 3, and then multiplied by the garden operator 3.14, and then multiplied by the cubic of the diameter, the diameter is 2 feet, and the cubic of 2 feet is 8, so the volume number obtained is 33.5 cubic feet, which is about 2,411 ten catties.

If you want to add it twice, the volume weight of the discharged water is 6,000 and 3 pounds.

In this way, we need such a pontoon thirteen times larger in volume so that the submarine does not fall, is this too big? ”

Lin Xi suddenly felt that something seemed wrong, and hurriedly said to the copper and iron master Liu Ziming: "Master Xuanyuan, is there any mistake in your calculation just now?" ”

Liu Ziming, a master copper and iron maker, said: "Three or four of us have checked the calculations. ”

Lin Xi felt that it was impossible to judge based on this alone, so he said, "You bring the paper, and I will calculate it myself." ”

The copper and iron master Liu Ziming's face turned a little red, Lin Xi saw it in his eyes, and said:

"Master Luxin, although you are craftsmen, but now if the project starts, you are the commander of a project, and you are in a high position, and the weapons you make will determine the life and death of the enemy or our own people.

At the moment, we don't have a process for setting up a project, but if you care a lot about your words and don't care about your responsibilities, I don't think it's appropriate.

At least, in the future, you must sign and pledge the project proposal, success is your credit, failure is your responsibility.

In the future, when the weapons leave the factory, you project leaders and commanders must personally use the weapons you are responsible for!

This is the iron law for the future!

Marshal Tu Xicai, Qingxu Pope, Jiang Chen, you have to record it, and in the future, you will make a name with the Academy of Engineering! ”

And they all said no.

Lin Xi took the pen and paper and began to check:

"The cross-sectional area of the cylinder is a garden, and the area formula is the garden operator 3.14, multiplied by the square of the radius of the garden;

The cylinder is a large garden for the outer diameter, a small circle for the inner diameter, only between the inner and outer diameter is the barrel wall;

So the area of the outer circle is equal to 3.14 times the square of 2 feet is equal to 4, so the area is 12.56 square feet,

The area of the inner circle is equal to 3.14, multiplied by the square of 1 foot 9 inches and 7 minutes is equal to 3.88, so the area is 12.18 square feet.

Therefore, the copper cross-sectional area is equal to 12.56 minus 12.18, then it is equal to 0.38 square feet;

The length of the straight package is 4 feet, so the volume is the cross-sectional area multiplied by the length, which is 1.52 cubic feet.

The approximate weight of copper per cubic foot is 638 catties.

Therefore, the weight of copper at the straight tube is about 97 ten catties.

Let's count the two ends again;

At both ends is a sphere, and the volume formula of the sphere is 4 divided by 3, multiplied by the park operator 3.14, and multiplied by the cubic of the radius.

The volume of the wall thickness is also approximately equal to the difference between the volume of the large sphere and the volume of the small sphere.

The cubic of the large sphere is 2 feet to the third of 8, the cubic of the small sphere is 1 foot 9 inches and 7 minutes to the third of 7 minutes is 7.65, and the difference between the two is 0.35;

Multiply 4 by 3 by 0.35, which is about 1.47 cubic feet, and the weight of copper per cubic foot is about 63 108 catties.

Therefore, the two end hemispheres are combined into a round ball, which consumes about 9318 catties of copper.

The sum of the two items is 97 ten catties plus 93 ten catties, which is 1,908 catties.

There is a lot of wear and tear in casting, and we round up 2,000 catties or a little more.

Only then did it be calculated that the volume weight of the discharged water was 6,000 and 3 ten catties.

We took it and counted it six thousand pounds.

It can be seen that there is a load of 4,000 catties inside, and with 1,000 catties of batteries, three people are counted as 200 catties each, which is only 600 catties, and there are 2,600 catties that can hold things.

Masters, do you see if the calculations are correct? ”

Lu Xin, copper and iron master Liu Ziming, and a few other children also began to calculate, but they basically used an abacus, which was much more dexterous than Lin Xi's freehand calculation.

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[Note: Abacus, also known as the abacus, abacus is a simple calculation tool created and invented by our ancestors, although other countries in the world also have similar things, but China's abacus is the most advanced.

At the end of the Eastern Han Dynasty, the mathematician Xu Yue's "Chronicles of Mathematics" contained: "Abacus controls four times, and longitude and latitude are three talents." "Northern Zhou Zhen Luan Zhuyun:" The stereotype is three points, each with five beads, the upper bead and the lower four beads are different in color, the upper pearl is different from the other, and the lower four beads are each one. Therefore, there was an abacus in the Han Dynasty, but the shape was different from today.

However, one bead above the middle beam is five, and each bead below the middle beam is one, which is the same as in modern times, and according to Xu Yue, his teacher Liu Hong once asked the Taoist Mr. Tianmu, Mr. Tianmu explained 14 calculation methods, one of which is the abacus, which shows that the abacus has appeared in the Eastern Han Dynasty at the latest.

Some historians believe that the name abacus first appeared in the Yuan Dynasty scholar Liu Yin (1249-1293) in the Collected Works of Mr. Jingxiu. In "Yuan Qu Xuan", the anonymous "Pang Jushi mistakenly released the debt", the abacus is also mentioned. There is such a sentence in the play: "Idle hands, go to the abacus and dial my age." In 1 274 A.D., Yang Hui recorded the "Nine Dividing Method" about the abacus in "Multiplication and Division" and Zhu Shijie in "Arithmetic Enlightenment" in 1299. In 1450 A.D., Wu Jing in the "Nine Chapters of Detailed Annotations and Analogous Algorithms", the use of the abacus is described in more detail, Zhang Zerui painted an abacus in the "Qingming Riverside Map", it can be seen that as early as the Northern Song Dynasty or before the Northern Song Dynasty, China has widely used the abacus as a calculation tool.

China's abacus evolved from the ancient "calculation". "Calculation" is the use of a bamboo stick as a chip to calculate. At the end of the Tang Dynasty, the improvement of multiplication and division had been seen, and the division song of calculation was produced in the Song Dynasty. In the mid-15th century, there were specifications for making an abacus in the Lubanmu Sutra. Due to the popularization of the abacus, works on the abacus were also produced, and the most popular abacus book was the "Algorithm Tongzong" compiled by Cheng Dawei in the Ming Dynasty in 1593. "The Algorithm of Mathematics" is an arithmetic book focusing on the application of abacus. The book consists of 17 volumes and 595 practical problems, most of which are taken from other arithmetic books, but all calculations are made using abacus. The book contains an abacus schema and an abacus formula, and examples of how to perform calculations on the abacus according to the formula. Among them, the bead algorithm of opening square and opening square was first proposed by Cheng Dawei. The appendix at the end of the book, "The Source of the Arithmetic Classics", records 51 titles of mathematics books since the Song and Yuan dynasties, most of which have been lost, and this appendix has become a valuable historical material for mathematics. Because the abacus formula is easy to memorize and simple to use, it is widely used in China, and has also spread to Japan, North Korea, India, the United States, Southeast Asia and other countries and regions.

With the use of abacus, people have summed up many calculation formulas, making the speed of calculation faster. This method of calculating with an abacus is called abacus. In the Ming Dynasty, abacus has been quite popular, and many books about abacus have been published, among which the most influential one is Cheng Dawei (1533~1606)'s "Zhizhi Algorithm Tongzong" (1592).

China is the hometown of the abacus, and today, when computers have been widely used, the ancient abacus has not only not been abandoned, but has been in the ascendant in many countries because of its advantages such as convenience and accuracy. Therefore, people often compare the invention of the abacus with the four great inventions of ancient China, and there is an abacus painted in the cabinet of Zhao Taicheng's pharmacy in the famous painting of the Northern Song Dynasty "Qingming Riverside Picture". Because the abacus is convenient and fast to calculate, it has been a common calculation tool used by the working people in ancient China for thousands of years, and even the most advanced electronic calculators in modern times cannot completely replace the role of the abacus. UNESCO has officially recognized the abacus as an Intangible Cultural Heritage of Humanity. 】

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Lu Xin was the first to complete the calculation, because the formula provided by Lin Xi is very simple, and the addition, subtraction, multiplication and division in it is not difficult, so it does not take long for everyone, and because of carry and rounding, there are still differences in the calculation of each person, but when the third person calculates it, the difference with Lin Xi is less than 100 catties, which is obvious, the copper and iron master Liu Ziming must have miscalculated before.

Copper and iron master Liu Ziming's face was black and red and purple, the green tendons were exposed, sweat was like rain, maybe it was calculated for the third time, the number was different this time, but the error was not more than 200 catties with Lin Xi's maximum.

Liu Ziming, a master copper and iron craftsman, was stunned and tears fell like rain, and he fell to his knees: "Today, villain, villain, when calculating, miscalculated, and as for the result is a hundred times different, if it is not for the Venerable Master's eyes like a torch and find out the mistake, it is really a great crime, please punish today!" ”

Lu Xin also hurriedly knelt down: "Today, the copper and iron master Liu Ziming is noble and proud, never pretends to be a color, he is actually a loyal man, the work in his hands, has never been improving, it is a new law today, he is not skilled, I beg forgive the copper and iron master Liu Ziming, we are willing to take responsibility as a whole, he did not check, I did not audit!" Today, now is the time to employ people, and please forgive me today. ”

The Qingxu Pope said: "Today, fortunately, it is only under discussion, and it has not caused major mistakes and impacts, so it is better to set rules in the future to prevent the slightest problem, and now it is important to make war weapons." ”

Tu Xicai said: "Today, this, my opinion is the same as that of the Qingxu Pope, the copper and iron master Liu Ziming is certainly suspected of arrogance, if it is not for the insistence of today, the consumption of 100,000 catties of copper, we will naturally die down, but when Lu Xin calculated, there was no mistake or omission, it can be seen that they are not sincere." It's not weak, and I'll send it for the time being......"

Lin Xi sighed: "Okay, you need to know that the lives of the soldiers are in our hands, they are desperate in front, we have our lives to fight for in the back, this time there is no major responsibility, copper and iron master Liu Ziming recorded a punishment, you have to report to the Engineering Institute, not to approve people, but to improve the process and system, so that everyone is willing to try, try is to explore, there must be a situation of unclear direction, which requires trial and error, there may be trial and error, there may be trial and error."

Trial and error, we also know that this direction or method will not work, we correct it to the right direction, and this is right.

If you make a mistake and do not correct it, or even conceal it, or if you find a mistake and try your best to cover it up, this is making a mistake, and you will suffer a big loss and make a big mistake.

We must understand the importance of this point from the perspective of world view and methodology, and we will suffer in vain today!

Get up."

Everyone hurriedly thanked them, and then sat down.

Lu Xin wanted to change the atmosphere quickly, so he immediately said:

"Today, even if it is a 2,000-pound cavity, our previous process can't be poured, and this is an empty thing, only the top hatch and the bottom of the sea valve can be opened to support, and we can't do it."

Here we need to make an explanation in order to understand that the model of modern Chinese is an example worthy of learning or taking the Fa, and it also refers to the meaning of taking the Fa and imitating it.

But the original meaning of the model is a casting method, also called the model method, is the Xia Dynasty has adopted the model casting method, generally using the stone fan and pottery fan casting process, this process is to first use the clay to mold out the real sample of the utensils to be cast, the surface is carved out of the ornament, that is, the commonly known mold, the mold is dried on it with mud repeatedly pressed into the outer fan. Scrape off a layer of mold, that is, the inner fan, and the distance between the inner and outer fan is the thickness of the object to be cast. Finally, the bronze solution is injected from the pouring hole, and the solution is cooled, and the inner and outer fans can be broken and the bronze utensils can be taken out.

Both the inner and outer models of the model method need their own support to stabilize the cavity, which is to cast mostly open utensils.

But now the submarine is a large cavity with a closed mouth, there is no place to support the inner fan, and the inner fan cannot be put in from the outer fan.

Liu Ziming, a copper and iron master, said: "In fact, there is still a lost wax method, but the size of the instrument is too large, and we really have no good plan in a hurry." ”

Liu Ziming's lost wax method is to use wax to make a casting mold, apply modeling materials externally, and become an overall casting mold, and then heat the casting mold to remove the wax to form a cavity casting model, pour liquid metal, and cool down to obtain a molded casting.

In ancient times, it was mostly used to cast castings with complex shapes, and the utensils cast by the lost wax method can be exquisitely clear, with a hollow effect, and the words and patterns of casting can be very delicate.

The earliest known lost-wax castings in China are copper cup parts and copper mirrors from the late Spring and Autumn period excavated in Xichuan, Henan Province.

After the Warring States Period, the application scope of the lost wax method gradually expanded, in addition to the Ding and Yi, it was also used to cast seals, music bells, Buddha statues and shellfish storage vessels and ornaments in ethnic minority areas. In modern times, the lost-wax method is still used to cast metal castings, called investment casting.

The history of the dewaxing method in China can be traced back to the Spring and Autumn Period and the Warring States Period, and the earliest bronze ware cast by the dewaxing method is the Xiong Shenyu of the King of Chu, in addition, the cloud pattern copper ban unearthed from the Chu tomb of Xichuan Xia Temple in the middle of the Spring and Autumn Period and the bronze plate of the tomb of Zeng Marquis B in the Warring States period unearthed from the Suizhou drum pier are also typical artifacts made by the lost wax method.

Large chimes are also made using the lost-wax method.

Nevertheless, the lost wax method still needs an inner and outer fan, and the inner fan also needs support.

Lin Xi thought for a while and said:

"I'll have an idea, and you can discuss it.

This cylinder consists of two valves on the sea surface and the bottom of the sea, the upper valve has a two-and-a-half-to-three-foot opening, and the lower valve also has a two-and-a-half-to-three-foot opening. ”

Liu Ziming said: "Logically, it makes sense. But what about the distance between the outer and inner fan? ”

Lin Xi said:

"So let's make some short brass posts on the inner fan, three minutes away, with a crown, and then apply three points thick yellow wax, and cover them with iron sheets, which are perforated on the top of the brass columns.

In this way, if the yellow wax is baked outside the iron sheet, the yellow wax will be lost, and the space between the inside and outside will be freed up, right? ”

Lu Xin said: "That's the reason, Lao Liu, everything has its own uses and tricks, the submarine is a drawing given by today, and it must be the most precise, although this method is special, it is reasonable." ”

Liu Ziming said: "Yes, Liu didn't expect that since this is the case, some copper strips and copper pillars can be poured out on the iron sheet of Neifan first, and the structure will be enclosed, so that the fixation of the iron sheet will be convenient." ”

Another master craftsman, Yi Leshui, said: "Every three inches square hit a copper hat top, and then painted with yellow wax, the iron sheet outside the fan to make two layers, the first layer with a very thin iron sheet to paste on, the second layer with a slightly harder, the third layer with a relatively hard one, and then welded with solder, copper water poured down, less than a word of effort, the copper juice sticks to the outer layer of the iron sheet, it is coagulated, the copper juice inside slowly solidifies, it will not destroy the iron sheet, and so on, the iron sheet is broken, it doesn't matter.

The temperature dropped, and when I went inside, I pulled out the iron sheets and brackets one by one, and the ship was completed. Surely, it's foolproof."

Liu Ziming also said: "Lao Yi said it well, there is another section, the top of the copper hat is stained with wax, so when pouring, the copper juice needs to be extremely hot and completely fused with the top of the copper hat." In this way, the temperature of the copper juice should be extremely high, the pouring should be fast, and it will not explode at that time, and the air port will be left in the middle of the pouring mouth every foot.

Today, we can handle everything else, but how about high-temperature melting and large-capacity crucibles? ”