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A Rocket's common purpose is to deliver it's Payload in Orbit around the Earth.To take a Payload around the Earth requires a lot of Energy.The Energy is stored Chemically as a Fuel or Oxidizer that can be found in Two Large Separate Tanks.Both of them are stored in Extremely Low Temperatures to make them Dense as Possible.

When Both are combined and burnt in the Combustion Chamber,Energy is released in a form of a gas.
A hole in the Combustion Chamber allows the Gas to be expelled and accelerate the Rocket.The Goal of the Rocket is to provide necessary change in velocity the Payload requires to get into it's Orbit.

This Change in Velocity is called Delta-V

The Rocket accelerates due to the conservation of the Momentum Law.When some amount of Mass times some Velocity is ejected from the Rocket,the Rocket gains an equal Momentum in the opposite direction.As the Rocket burns Fuel and Oxdizer,it's mass decreases.This means that it's Acceleration must increase because the Thrust is about constant.

At Lift-off the Rocket Accelerates slowly but as it’s about to run out of Propellant,the Accelration is at it's Maximum.At the Very End, the Acceleration is limited to the Mass of the Rocket without the Fuel and the Oxidizer.

this is also known as Dry Mass

and Most of this Mass is useless.

The Huge Tanks aren’t needed if there’s only a few Thousand Liters of Propellant left and who needs Huge Rapidly Burning Engines when you’re about to run out of Propellant? That’s a lot of unnecessary mass and because of this, a lot of Delta v is missed out on.

How Do you solve this Problem?
By using a Second Stage.

Using a Second Stage means that once the Huge Tanks are no longer useful, they are jettisoned.Now a Smaller Rocket is ignited.One with Smaller Tanks and a lighter, more efficient engine providing less thrust.Now, as the Second Stage is about to run out of Propellant, the Dry Mass is quite small.The result is that not so much of that Velocity is missed out on.

By using two stages, the Delta v is dramatically increased without adding too much weight.The Energy expelled from the Rocket comes mostly in the form of Kinetic Energy.This is the Energy the Exhaust Gas has due to its Velocity.Notice how the Kinetic Energy is proportional to Velocity squared, while Momentum is proportional to only velocity.

The Gas is accelerated to a High Velocity,a huge amount of Energy is required, and only a reasonable amount of Momentum is gained.This is not efficient.The Velocity should be minimized, so that a large change in Momentum is possible with the available Energy.However, minimizing the Velocity means that
more Mass is required.So, even though it seems inefficient, the Engine should Accelerate the Gas to a Huge Velocity.

Source


4 Comments

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    121 LiamW

    The other benefit of staging is that you can have a booster that's extremely efficient at low-altitudes pushing a second stage into space that's far more efficient in a vacuum. You end up with much, much higher efficiency. SSTOs with aerospikes are cool too but they're much harder to build due to limitations mentioned by the OP.

    5.0 years ago
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    5.0 years ago
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    @KraZIvan Planning for More Parts

    5.0 years ago
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    11.7k KraZIvan

    Very informative, thank you for posting this

    5.0 years ago

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