The Logic of Reusable Rockets: How can its feasibility be proven through the three first principles of materials, fuel, and mechanics?

Alright, let's talk about this. This is quite an interesting question. The idea of rocket recovery has been around for a long time, but why has it only been realized recently? It's because the "three brothers" – materials, fuel, and mechanics – have finally matured.

Let's break it down and explain it in plain language.

1. Mechanics: How do you make an "iron can" descend steadily from the sky?

This is the most crucial and counter-intuitive part. When we throw something into the sky, it falls back down in "free fall" and smashes. Rocket recovery is about making it "anti-free fall."

First Principles: Newton's Third Law (Action and Reaction) + Gravity

• Going up is easy: It expels fire downwards, and the immense thrust (action) propels the rocket (reaction) into the sky. Simple and crude.
• Coming down is hard: When it falls, Earth's gravity continuously accelerates it, making it extremely fast. What to do?
  • "Air braking": When it descends to a certain altitude, the engines are reignited, but this time they fire in the direction of the fall. This creates an upward thrust to counteract the downward velocity. It's like when you're driving and approaching your destination, instead of hitting the brakes, you shift into reverse and hit the gas to slow down – requiring extremely precise control.
  • "Attitude control": When the rocket descends, it's nose-down, like a javelin. But for landing, it must be tail-down (engines first). So, it needs to perform a graceful "flip" maneuver in the air. This process requires extremely precise calculations and control.
  • "Control surfaces": You might have seen several waffle-like grid wings on top of SpaceX rockets, called "grid fins." As the rocket descends through the atmosphere, air flows over them. By changing the angle of these "fins," the rocket's flight attitude and direction can be precisely controlled, much like steering a ship, ensuring it accurately flies towards its designated landing spot.

In essence, mechanics solves the "how to do it" problem. It proves that as long as I can precisely control the engine's thrust and direction, combined with aerodynamic control surfaces, theoretically, I can make a colossal object descend gently like a feather under gravity.

2. Fuel: Where does the "gas" come from for "air braking"?

The mechanics solution sounds perfect, but there's a fatal flaw: where does the fuel for "braking" come from?

First Principles: Tsiolkovsky Rocket Equation (simply put: the greater your change in velocity, the higher the proportion of fuel required)

• Traditional rockets (expendable): Their design philosophy is "all in." Every drop of fuel is used for the single goal of "sending satellites into space." Thus, their payload capacity is maximized.
• Reusable rockets: They must act like a thrifty traveler. They can't use up all the fuel in the tank when departing; a portion must be reserved as "capital" for the "return trip" and "landing."
  • What is the "cost"?: This reserved fuel itself has weight. This means that for a rocket of the same size, a reusable rocket can carry less "cargo" (satellites, etc., i.e., payload). For example, an expendable rocket might carry 10 tons of cargo, but for reusability, it might only carry 7 tons, because the "capacity" for the other 3 tons is taken up by the reserved return fuel.
  • Key to feasibility: The logic of feasibility lies in a simple economic calculation. Although I earn less this time (due to reduced cargo capacity), I save the manufacturing cost of a brand-new rocket. As long as the "saved rocket cost" is significantly greater than the "lost revenue from reduced cargo," the business is worthwhile. Elon Musk and his team figured out this equation and, through technological optimization, reduced this "loss" to an acceptable range.

In essence, fuel addresses the question of "is there the capital to do this?". It proves that although reserving fuel for landing sacrifices some payload capacity, as long as the technology is efficient enough, this sacrifice is worthwhile and economically viable.

3. Materials: How many times can this "iron can" endure the abuse?

Alright, we can control its landing, and we have the fuel for it. But if repairing the rocket after landing costs more than building a new one, or if it's simply a "single-use recoverable item," then recovery becomes meaningless.

First Principles: Material Strength, Fatigue Resistance, High-Temperature Resistance

• One trip to space, covered in wounds: Rocket launch and atmospheric re-entry are extremely harsh processes.
  • Launch: Immense acceleration and violent vibrations put the rocket body structure to an extreme test.
  • Re-entry: High-speed friction with the atmosphere generates temperatures of hundreds or even thousands of degrees Celsius. Although the first stage rocket's speed isn't as high, the heat generated is still very substantial.
• Material challenges:
  • Light and strong: Rocket materials must first be light, because every extra gram requires additional fuel to propel it. At the same time, they must be extremely robust to withstand the immense pressure during launch.
  • High-temperature resistance: Components like the rocket body, engines, and grid fins must be able to withstand the high temperatures during re-entry without melting or failing.
  • Fatigue resistance: This is the most critical aspect of "reusability." Just like a wire that breaks after being bent repeatedly, this is metal fatigue. Rocket materials must be able to withstand multiple "launch-recovery" cycles of pressure and extreme temperature changes without developing microscopic cracks or structural weakening. If it requires major overhaul or even scrapping after just one flight, then it's not truly "reusable."

In essence, materials address the question of "is it worth doing?". It proves that the alloy materials (such as aluminum-lithium alloys) and composite materials we now possess are strong and durable enough to allow a rocket to fly again with only minor inspection and maintenance. This transforms "recovery" from a technical demonstration into a truly commercially valuable endeavor.

To summarize:

• Mechanics says: "I have a way to bring it down."
• Fuel says: "I have the resources (energy) to bring it down."
• Materials says: "After it comes down, it can still be used."

When the technologies in these three areas all developed to break through a certain critical point, they fit together perfectly like three puzzle pieces. The logic of rocket reusability thus transformed from a theoretical "possibility" into an engineering and commercial "reality."