Open an aircraft carrier to fight against Japan

Several people looked at Lin Yuan intently, and Lin Yuan said: "I saw the book "Introduction to Naval Weapons" on your desk, who will tell me what is in this book?"

Liu Guang raised his hand, Lin Yuan nodded, Liu Guang said: "This book is about the weapon system of warships, including naval guns, torpedoes, propellant powder, shells, etc."

Lin Yuan said: "Then I believe everyone is familiar with all kinds of shells in naval battles, so who can tell me, what shells are there in naval battles?"

Liu Guang raised his hand again, and Lin Yuan motioned for him to answer. Liu Guang said, "There are armor-piercing bombs, high-explosive bombs, and armor-piercing explosive bombs."

Lin Yuan asked again: "Okay, please explain to me the purpose of these types of shells."

Liu Guang said: "Let's talk about armor-piercing projectiles first. Because the warships of navies all over the world use relatively thick armor, they must penetrate their armor if they want to seriously damage enemy warships. In this case, high-speed armor-piercing projectiles are required; From a structural point of view, since the trajectory of the artillery shell is relatively straight, the probability of being hit on the side of a warship is the highest, so the armor of a warship is generally laid on the side.”

"A battleship has three elements: firepower, armor, and maneuverability. These three elements restrict each other. If the armor is thicker, the mass of the warship will increase, so the maneuverability will decrease. In order to maintain the balance of the three, the weight of the armor cannot be adjusted. In this case, the navies of various countries have arranged heavy armor on the side, while decks and bridges have no armor or only a small amount of armor.”

"High-explosive bombs are specially designed to deal with the superstructure of enemy warships. When high-explosive bombs explode, although the fragments produced are not enough to penetrate the armor of the ship's hull, they can cause great damage to the personnel on the deck, and the damage The force does not only come from the shrapnel, it will generate a strong shock wave when it explodes, and after the shock wave hits the human body, it can cause the internal organs to vibrate and rupture the internal organs.”

"The power of armor-piercing blasting bombs is even stronger. This kind of bombs can explode after penetrating the opponent's armor. The interior of the enemy's hull is a very critical part. If these parts are damaged, the battleship is not only lost. The problem of combat effectiveness, and more importantly, the loss of vitality."

"However, the production design of this kind of armor-piercing explosive bomb is also very difficult. One of them is the design of the fuze. The timing of the fuze must be well controlled. There is no explosion during the armor-piercing process, and the book says that only our country can develop this kind of artillery in the world today."

Lin Yuan nodded and said with a smile: "You are very good, then my question comes."

When everyone heard that Lin Yuan was about to ask a question, they all looked at Lin Yuan, wanting to show off their skills. Lin Yuan said: "You will all be commanders of warships in the future. Although it is impossible to be the captain or chief of staff from the beginning, you will also be the commander of the warship from now on. The staff will do it, so my question has to do with making a battle plan."

Lin Yuan went on to say: "For the convenience of describing the problem, we introduce a concept of lethality index. We don't need to consider how this index comes from, we just need to simply understand that the higher the lethality index, the greater the lethality. Now we set the lethality index of armor-piercing shells at 2, high-explosive shells at 1.5, and armor-piercing explosive shells at 3."

"We are now imagining such a tactical environment. You need to lead your warship to attack the enemy's fleet. Suppose your warship can only carry one hundred kilograms of shells. Here we do not consider the authenticity. The weight of each armor-piercing explosive shell It is five kilograms, the weight of the armor-piercing shell is four kilograms, and the high-explosive shell is two kilograms, now you can only choose two kinds of shells, how do you choose to maximize the lethality index?"

After everyone listened to it, they were all thinking about it, and Lin Yuan said, "You can also discuss it, it's okay, just let me know when you're done thinking about it."

Several people immediately began to discuss: "How should this be calculated?" "I think it is more similar to the linear programming mentioned above. Is it possible to use linear programming to solve it?" "Yes, that's right, it should be done using linear programming. .”

Several people discussed for a while, and then began to write on paper, Lin Yuan smiled and said: "The specific calculation process is unnecessary, just tell me the idea."

Liu Guang said: "This should be abstracted into a linear programming problem. In this problem, the objective function is the lethality index, and the constraint condition is the sum of the masses. Therefore, we express the quantities of the two types of bombs as unknowns, and we can list a When solving an equation and an inequality, draw the straight line represented by the equation and the inequality in the coordinate system using these two unknowns as the horizontal axis and the vertical axis.”

"On the graph, these two lines will have an intersection point, and the intersection point may be the point you want to select. Choose two of the three types of bombs and combine them. There are three types in total. Calculate these three situations separately, and then Then compare and see which group maximizes the objective function and which group can be selected."

Lin Yuan nodded and said: "Very good, the idea is good, but I haven't calculated the numbers in detail, and there may be problems, but your thinking is correct, and now the real difficulty is coming—" Lin Yuan looked They looked at them and said: "Now that we have improved the technology, these three types of shells can be equipped together. Tell me how to choose this response?"

Liu Guang said: "It used to be two variables, but now it's just three variables."

Lin Yuan smiled and said, "That's right, it has become three variables, but how do you solve it this time?"

Everyone frowned when they heard Lin Yuan's question. Indeed, the linear programming problem with two variables can be calculated using the graphical method, but there is no way to draw a picture with three variables. Lin Yuan looked at their silence and said: "Now We only have three types of shells, but in actual combat we still have torpedoes? Four variables! If we use other weapons, there will be more variables, how should we deal with it then?"

Everyone shook their heads, Lin Yuan turned around and took the book of linear algebra from the shelf, and said, "The method of solution is in it, but looking at your linear algebra, even if I tell you how to solve it, you won't be able to solve it." Yes, study hard, the answer is in it.”

Lin Yuan went on to say: "In the future, you will encounter many such situations in actual combat. There is a special discipline called military operations research. This discipline will guide you on how to choose the most optimal parameters in actual combat. What do you say? Is this subject useful?"

Everyone heard that the selection of optimization parameters is also a science, and they couldn't help but nodded. Lin Yuan said: "Although this course is useful, it is based on what you are learning now, so you should learn what you are now."

After Lin Yuan finished speaking, he said to everyone: "Actually, the courses you are studying now can be used in the future. Many people think that they can't use those things because they haven't learned them well. When you reach a certain level, you will I discovered that everything is useful, but you don’t know how to use it and where to use it.”

Several people nodded their heads. Lin Yuan looked at Liu Guang and asked, "What do you think about geometry?"