Traveling Back to the 1960s: The Entire Internet Teaches Me How to Build Missiles

Testing missiles is no child's play.

Once this thing is ignited and launched, it's like a wild horse that's been unleashed.

If you misjudge the target, it's not just a matter of making a fool of yourself.

Therefore, in the last two days of the scheduled test, all three teams worked through the night to check the plan to ensure there were no oversights.

Although Zhou Yunxiao's group was small, they were all shrewd and capable. Baoqiang flipped through a thick stack of data files and could almost recite the fuse test records of a certain month, day and time from memory.

College student A, holding a slide rule, hunched over the table, deriving the equations handed to him by Xiao Su, and calculating the impact range of the missile's terminal fragments. Draft papers were scattered all over the floor.

While calculating the parameters of the fragmentation cone, college student B used a T-square to draw the trajectory intersection diagram and handed it to Zhou Yunxiao for review.

Zhou Yunxiao himself paced back and forth in front of the blackboard with his hands behind his back, occasionally stopping to add one or two new constraints, or overturning the formula he had just written and starting over.

His unpredictable changes would have driven anyone else crazy, but Comrade Xiao Su followed his line of thought without complaint.

Whenever Zhou Yunxiao proposed a macro-level direction, Xiao Su would transform it into a quantifiable mathematical theory and write out the equations for each step by hand.

Her notebook was filled with neat handwriting. Sometimes, algebra alone couldn't solve these problems, so she had to rack her brains and use all the knowledge she had learned in geometry, calculus, complex functions, and other subjects.

Zhou Yunxiao walked over, watched the girl writing calculations furiously on the draft paper, and nodded in satisfaction.

The lines of equations and text on the draft paper actually constitute a set of guidance commands for the surface-to-air missile.

Xiao Su needs to indicate the relationship between the equations before and after, and make the execution of this complex set of commands as simple as possible.

To those who don't understand mathematics, this is just a bunch of boring, meaningless numbers, but those who do understand mathematics will find a subtle elegance in it.

Each command is interconnected and ultimately points to a precise target.

The circles surrounding the numbers allow the analytical solution of the equation to be substituted into the next command line, making the overall structure look concise and clear.

Some inexperienced calculators often write a lot of redundant equations on the draft paper, which ruins the simplicity of the guidance command and makes verification troublesome.

But Xiao Su seems to have a natural talent for simplification. She's like someone building a skyscraper, immersed in the world of calculation, combining these command lines one after another, sometimes not even looking up at the clock all day.

If it weren't for the programmers in the live stream reminding him, Zhou Yunxiao wouldn't have even realized that these familiar draft paper command lines were actually the earliest form of programming.

It is the precursor to computer programs.

[Isn't Comrade Zhou the wicked product manager who changes requirements every day and comes up with macro concepts on a whim?]

[A bad-tempered programmer, faced with a client like this who changes requirements every day, would have already slammed their keyboard down. Not only did Xiao Su not get angry, but she also managed to keep her logic so clear—that's true pampering!]

Wait a minute! Guys, look at those circles and arrows Xiao Su drew. Don't they look a bit like a control flow diagram in a program? Does anyone understand them?

[Constraints, logical branches, loop iterations... My goodness, is she writing pseudocode for a guidance algorithm on scrap paper? Were computer scientists this skilled back then?]

[Wow, that's impressive! Without any prior knowledge of C or Python, they managed to compile guidance logic into machine-understandable instructions using only calculus and algebra?]

[Who says there was no software engineering in the 60s? Comrade Xiao Su is the patriarch of the sect! Quickly offer incense!]

Zhou Yunxiao couldn't help but smile as he listened to the gossip from netizens.

Xiao Su certainly never imagined that the bunch of equations and command lines she painstakingly wrote on draft paper would one day be easily compiled and executed smoothly using computer code.

However, she only has paper and pen, and has never seen what a computer looks like.

"What are you laughing at?" Xiao Su suddenly looked up at him.

Zhou Yunxiao quickly suppressed his smile and, following Professor Hou's words in the live stream, gave her some pointers.

"You can solve the equation for this step in a different way."

Xiao Su looked down at the spot she was pointing to, pursed her lips, and said, "This is the relative motion equation for the terminal intersection. Since both variables are performing three-dimensional maneuvers, if we only consider the ultimate escape overload, this is a nonlinear system of differential equations."

If we force an analytical solution, it will lead to elliptic integrals of the second kind, and then the slide rule will not be able to be used...

Zhou Yunxiao shook his head, took the pen from her hand, found a blank piece of draft paper, and wrote down a few lines of equations.

"Don't worry too much about precise analytical solutions; engineering mathematics isn't pure mathematics. Look here, the rendezvous time of the end fuse is only a fraction of a second. Here, we reduce the target's acceleration to a constant. Then, by performing a Taylor expansion, we can eliminate more than two truncation errors!"

Xiao Su thought for a while and said, "Linearization is indeed possible... but in that case, the boundary conditions of the fragmentation cone will be distorted, the integration domain will no longer be a regular shape, and the area integral will not be calculated."

"Wrong, didn't you just use complex functions?"

Zhou Yunxiao continued to guide him, "After this formula, make a conformal transformation."

Xiao Su was taken aback. "Conformal mapping?"

"That's right." Zhou Yunxiao drew a simple mapping topology diagram and explained:

"After establishing the complex plane of the missile, the center of mass of the missile body is set as the origin. Then, through analytical continuation, the irregular discrete cone integral domain can be directly mapped to the unit circle."

"Once the boundary of the integral reverts to a standard circle, there's no need for calculations; simply consult the Bessel function table in the *Bradius's Handbook of Mathematical Functions*. If you only consider the first three orders, you'll get the result very quickly!"

Upon hearing this, Xiao Su's eyes lit up. He immediately crossed out half a page of equations on the draft paper with his pen, turned over a new page, and wrote down the new transformation matrix.

After a moment, she looked up in surprise and said, "I knew it! Comrade Yunxiao, I didn't expect you to be so good at math! You figured out the solution to such a complex calculation in just a few words..."

Zhou Yunxiao waved his hand dismissively, "It's just that we've encountered similar cases before. When it comes to mathematical skills, you're still the strongest in our group!"

This idea was proposed by Professor Hou during the live broadcast, and he dared not take credit for it, so he could only vaguely change the subject:

"Alright, it's getting late. If the calculations are all correct, let's do a live-fire test tomorrow using these guidance offset parameters. Everyone should go home and get some rest."

Xiao Su happily hummed in agreement, then playfully pressed the pen to her lips and made an "OK" sign with both hands.

……

The next morning.

Early in the morning, the soldiers of the Third Division began their training with great enthusiasm.

Three missile transport vehicles pulled three modified Hongqi-1 test missiles out of the warehouse and slowly drove them along the cement road into the No. 17 test range.

Target Range No. 17 can be said to be the cradle of all future surface-to-air missiles of the East Country. It is located on a flat Gobi Desert five kilometers east of the headquarters.

The range is divided into two positions, north and south, each capable of deploying six launchers, and can launch up to 12 surface-to-air missiles simultaneously.

The two workstations are 300 meters apart, and each workstation has a 50-meter-long and 50-meter-wide cement floor.

In the middle of the field is a large concrete platform covering ten square meters, poured with special refractory cement. This is where the launch pad is deployed.

At this moment, only three launch pads have been deployed, with a ten-meter-long launch rail formed by a huge steel structure base.

From a distance, it looks like a giant steel rail pointing diagonally towards the sky.

Beneath the steel rails are densely packed cables and gas supply pipes, connecting directly to the bunker and launch control room behind the launch pad.

Unlike the underground command post used during the Dongfeng-1 test, the control room here is built on the ground, with walls made entirely of reinforced concrete, and the roof alone is seven meters thick with concrete.

Even if the Red Chess No. 1 falls from the sky, it can still protect the operators hiding inside.

In addition, more than a dozen bunkers were built around the two work sites.

When Zhou Yunxiao and Xiao Su arrived, they were immediately drawn to the proudly standing Red Chess Number One on the field.