The Tyranny of the Rocket Equation (Encore)

Summary

Summary of "The Tyranny of the Rocket Equation (Encore)" Episode of Everything Everywhere Daily

Podcast Information

• Title: Everything Everywhere Daily
• Host: Gary Arndt | Glassbox Media
• Episode: The Tyranny of the Rocket Equation (Encore)
• Release Date: November 29, 2024

Introduction In this encore presentation of Everything Everywhere Daily, host Gary Arndt delves deep into the foundational principles that govern rocketry and spaceflight. The episode, titled "The Tyranny of the Rocket Equation," explores the pivotal role of Konstantin Tsiolkovsky's rocket equation and its enduring impact on modern aerospace engineering.

Konstantin Tsiolkovsky and the Rocket Equation The episode opens with a historical overview, highlighting Konstantin Tsiolkovsky's groundbreaking discovery in 1897—the rocket equation. Gary introduces Tsiolkovsky as the first recognized rocket scientist, emphasizing his profound influence on spaceflight:

“Tsiolkovsky realized that rockets worked because Newton's Third Law stipulated that for every action there is an equal and opposite reaction.” ([02:30])

Through a simple yet illustrative thought experiment involving a boat and heavy rocks, Tsiolkovsky elucidated the principle of momentum exchange, laying the groundwork for understanding how rockets propel themselves by expelling mass at high velocities.

Fundamentals of the Rocket Equation Gary and his co-host meticulously unpack the rocket equation, which quantifies the relationship between a rocket's velocity change (Delta V), exhaust velocity, and the mass ratio of the rocket. The equation is presented as:

"Delta V equals the exhaust velocity of the rocket engines times the natural logarithm of the final mass of the rocket over the initial mass of the rocket." ([03:38])

This formula underscores the inherent challenges in space travel, primarily the exponential increase in required fuel as payload mass grows.

Implications of the Rocket Equation

1. Mass and Fuel Constraints The discussion highlights the impracticality of launching large masses into space due to the "tyranny" of the rocket equation. As the fuel adds to the rocket's mass, more fuel is needed to propel the additional weight, creating a cascading effect:

   “The amount of fuel you use also has mass. And that mass would need fuel to launch it, and that fuel would need fuel to launch it, and so on and so on.” ([04:27])

2. Staging of Rockets To mitigate mass constraints, rockets are built in stages. By shedding lower stages once their fuel is depleted, the rocket reduces mass, thereby increasing its velocity more efficiently:

   “Rockets are built in stages. You want to shed as much mass as you can in order to increase your velocity.” ([06:54])

3. Fuel Proportion in Rockets vs. Other Vehicles The episode contrasts rockets with other modes of transportation, emphasizing the disproportionately high fuel mass in rockets. For instance:

   “A rocket is not dissimilar to a can of soda. An aluminum can of soda is about 94% soda and 6% can. The external fuel tank on the space shuttle was 96% fuel...” ([05:49])

Delta V and Spaceflight Delta V, representing the change in velocity needed for space missions, is a critical factor outlined in the episode. Achieving low Earth orbit requires approximately 8 km/s of Delta V, emphasizing that speed, rather than altitude, is paramount:

“Getting into orbit is more about speed than it is about altitude.” ([07:53])

Further destinations, such as the Moon and Mars, necessitate additional Delta V, illustrating the compounded challenges in interplanetary travel.

The Tyranny of the Rocket Equation Gary and his co-host coin the term "the tyranny of the rocket equation" to describe the dominant constraints imposed by this fundamental principle:

“The rocket equation rules everything when it comes to spaceflight. The design of rockets, spacecraft, satellites, and everything else has to take the rocket equation into consideration.” ([09:02])

This tyranny dictates not only current rocket designs but also future innovations aiming to push the boundaries of space exploration.

Overcoming the Constraints

1. Alternative Propulsion: Nuclear Thermal Rockets One proposed solution is the development of nuclear thermal rockets, which offer significantly higher exhaust velocities compared to chemical rockets:

   “A nuclear rocket would work by exposing gas, most probably hydrogen, to an extremely hot nuclear reactor.” ([09:49])

   With potential exhaust velocities surpassing 10 km/s, nuclear rockets could dramatically improve fuel efficiency and payload capacity.

2. Space Elevator Concept Another radical idea discussed is the construction of a space elevator—an extensive cable extending from geostationary orbit to Earth's surface. This infrastructure would allow payloads to ascend without the massive fuel requirements of traditional rockets:

   “A space elevator would be a long cable which extended from geostationary orbit down to the surface of the Earth.” ([11:44])

   By reducing the reliance on propulsion-based lift-off, space elevators could circumvent many limitations imposed by the rocket equation.

3. Future Physics Breakthroughs The episode also speculates on the potential discovery of new physics that could nullify gravitational effects, rendering the rocket equation obsolete. Although purely speculative at this stage, such breakthroughs remain a tantalizing possibility for future advancements in space travel:

   “If we learned of some way to nullify the effects of gravity, we could make the rocket equation moot.” ([12:00])

Conclusion: The Enduring Relevance of the Rocket Equation Wrapping up, Gary emphasizes the critical importance of understanding the rocket equation for anyone interested in spaceflight:

“Understanding the rocket equation isn't rocket science... It was engineered to perform within the laws of physics, which were outlined in the late 19th century by a Russian who lived in a log cabin.” ([12:24], [12:29])

The episode concludes by acknowledging the profound legacy of Tsiolkovsky's work and the ongoing quest to innovate within, and perhaps eventually beyond, the constraints of the rocket equation.

Notable Quotes

• Gary Arndt ([02:30]): “Tsiolkovsky realized that rockets worked because Newton's Third Law stipulated that for every action there is an equal and opposite reaction.”
• Co-Host ([04:27]): “The amount of fuel you use also has mass. And that mass would need fuel to launch it, and that fuel would need fuel to launch it, and so on and so on.”
• Gary Arndt ([06:54]): “Rockets are built in stages. You want to shed as much mass as you can in order to increase your velocity.”
• Co-Host ([09:02]): “The rocket equation rules everything when it comes to spaceflight. The design of rockets, spacecraft, satellites, and everything else has to take the rocket equation into consideration.”
• Co-Host ([12:29]): “It was engineered to perform within the laws of physics, which were outlined in the late 19th century by a Russian who lived in a log cabin.”

Final Thoughts "The Tyranny of the Rocket Equation (Encore)" offers a comprehensive exploration of the fundamental principles that underpin modern rocketry. By bridging historical insights with contemporary challenges and future possibilities, Gary Arndt provides listeners with a profound understanding of why rockets are designed the way they are and what innovations might one day transform space travel.

Transcript

[Host]

The following is an encore presentation of Everything everywhere daily. In 1897, the visionary Russian rocket scientist.

[Co-Host]

Konstantin Tsiolkovsky discovered an equation that governed how rockets worked. His equation, which was independently discovered by.

[Host]

Several other rocket scientists, immutably governs how we can send rockets into space.

[Co-Host]

The variables in his equation have determined.

[Host]

Everything surrounding spaceflight and rocketry since its.

[Co-Host]

Inception and will for the foreseeable future. Learn more about the tyranny of the.

[Host]

Rocket equation on this episode of Everything Everywhere Daily.

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[Host]

Rockets have been around in some form for centuries. If you remember back to my episode.

[Co-Host]

On Gunpowder, the Chinese were using rockets.

[Host]

And warfare and for fireworks for about a thousand years.

[Co-Host]

While rockets were a known thing, they.

[Host]

Left scientists baffled as to how they worked.

[Co-Host]

They weren't being pushed like a sailboat, and they weren't using friction with the.

[Host]

Ground like walking or a horse pulling a wagon.

[Co-Host]

The late 19th and early 20th centuries saw several people around the world independently tackle the problem. The first person recognized to have solved the physics behind rockets and therefore would get credit as the first rocket scientist, is Konstantin Tsiolkovsky.

[Host]

Tsiolkovsky realized that rockets worked because Newton's.

[Co-Host]

Third law stipulated that for every action there is an equal and opposite reaction.

[Host]

Rockets moved forward because they were expelling.

[Co-Host]

Something else from behind. The principle by which rockets moved was.

[Host]

Demonstrated by Tsiolkovsky with a simple thought experiment.

[Co-Host]

Suppose that you were in a boat in the middle of a pond. The boat had no sail or no oars to paddle. You were basically stuck in the middle.

[Host]

Of a pond with no way to move.

[Co-Host]

However, on the boat you did have.

[Host]

A pile of heavy rocks.

[Co-Host]

You could get yourself to shore by throwing the Rocks off the back of.

[Host]

The boat, not dropping them into the water, but throwing them horizontally.

[Co-Host]

This would give the boat momentum, which in theory, could get your boat to the shore. This is the same principle behind a rocket. Instead of rocks, however, you are expelling molecules of gas at very high speeds. Tsiolkovsky created an equation that explained everything, which is today known as the Tsiolkovsky equation, or more generally as the rocket equation. Without getting into the math too much, the equation is as DeltaV, or the.

[Host]

Change in the rocket speed equals the.

[Co-Host]

Exhaust velocity of the rocket engines times the natural logarithm of the final mass.

[Host]

Of the rocket over the initial mass of the rocket.

[Co-Host]

Tsiolkovsky recorded the date of his discovery of the equation as May 10, 1897. Other people, such as the English mathematician.

[Host]

William Moore, the American rocket pioneer Robert Goddard, and the German physicist Hermann Oberth, independently discovered the rocket equation as well.

[Co-Host]

And just as an aside, Konstantin Tsiolkovsky, the man who helped usher in the.

[Host]

Modern world of spaceflight, lived for most of his life in a log cabin.

[Co-Host]

Now, you might look at the equation and not think much of it, but it has several profound implications, implications that.

[Host]

Govern everything to do with rockets and spaceflight.

[Co-Host]

One has to do with mass.

[Host]

Suppose you wanted to put a 100.

[Co-Host]

Kilogram object into orbit. You would need a certain amount of.

[Host]

Fuel to do this.

[Co-Host]

However, the fuel you use also has mass. And that mass would need fuel to launch it, and that fuel would need fuel to launch it, and so on and so on. The amount of fuel isn't infinite, but it does mean that you need an enormous amount of fuel to launch something even quite small, because you're launching the fuel as well as the payload. And that's why rockets are so big.

[Host]

And why there are no small rockets.

[Co-Host]

There are no shoulder mounted or backyard.

[Host]

Rockets that could conceivably fly into orbit.

[Co-Host]

Moreover, the more mass you try to fly into space increases the size of a rocket exponentially. The Apollo program launched something smaller than.

[Host]

The size of a truck trailer into space, but required a rocket, the Saturn.

[Co-Host]

Vastly larger than one just carrying a small space capsule. So long as we're using chemical reactions, the exponential growth in the amount of fuel needed means that there is a limit to how large of something we can launch into orbit using conventional rockets.

[Host]

You couldn't, for all practical purposes, launch.

[Co-Host]

Something as large as a cruise ship.

[Host]

Into orbit all at once.

[Co-Host]

Another implication is the amount of fuel.

[Host]

That is part of any rocket.

[Co-Host]

Rockets are almost all fuel.

[Host]

It is common for the mass of.

[Co-Host]

A rocket sitting on a Launch pad to consist of 85 to 95% fuel. The actual amount of payload for a.

[Host]

Rocket is usually around 2 to 4%.

[Co-Host]

To put this into perspective, the mass of a large cargo ship may only be 3% fuel, and your car is.

[Host]

Around 4 to 5% fuel.

[Co-Host]

A freight locomotive may be 11%. And a commercial airliner might be as high as 35%. A rocket is not dissimilar to a can of soda. An aluminum can of soda is about 94% soda and 6% can. The external fuel tank on the space shuttle was 96% fuel, making it even more efficient than a soda can.

[Host]

So to use the soda can model, all of the soda is rocket fuel.

[Co-Host]

And the can is the apparatus of.

[Host]

The rocket, which is all necessary to put the pull tab into orbit.

[Co-Host]

This is why engineers have to worry so much about mass and efficiency when.

[Host]

Designing anything that's going into space.

[Co-Host]

Every kilogram has to be accounted for because it results in significantly more rocket fuel.

[Host]

And it's also why rockets are built in stages.

[Co-Host]

You want to shed as much mass.

[Host]

As you can in order to increase your velocity.

[Co-Host]

Getting rid of the lower stages of a rocket, when they aren't needed anymore, will help increase velocity. This is just dealing with the mass.

[Host]

Part of the equation. The other parts of the equation have limits as well.

[Co-Host]

In terms of the exhaust velocity of.

[Host]

The rocket, there are several different rocket fuels that can be used.

[Co-Host]

Solid rocket fuel can have an exhaust.

[Host]

Velocity of 3 kilometers per second, and a methane oxygen rocket can have an exhaust velocity of 4.5 kilometers per second.

[Co-Host]

All other rocket fuels are pretty much.

[Host]

Somewhere between those values.

[Co-Host]

So long as we're using rockets that are providing thrust from a chemical reaction, there's a limit to just how much.

[Host]

Exhaust velocity there can be.

[Co-Host]

You can't arbitrarily make it any larger.

[Host]

The final variable is Delta V. Delta V is one of the biggest factors in any orbital flight. And as far as launching from the ground is concerned, the initial point of DeltaV is 0.

[Co-Host]

In the case of launching something into space, it is indicative just how much.

[Host]

Velocity you need to get anywhere. Just to use approximate numbers, something has.

[Co-Host]

To go about 8km per second to get into low Earth orbit, which is only about 250 miles or 400 kilometers away.

[Host]

If you remember back to my episode.

[Co-Host]

On how satellites work, getting into orbit is more about speed than it is about altitude.

[Host]

We have to go that high to avoid atmospheric drag.

[Co-Host]

Without drag, you could orbit as high.

[Host]

As 1 meter off the surface.

[Co-Host]

Once you get into the Earth's Orbit, the hard part is done from there. The extra velocity needed to get to the Moon is only an additional 6 kilometers per second, and to Mars, an additional 8. This is why there has been talk of building a base on the Moon. The velocity necessary to escape the gravity of the Moon is much less than.

[Host]

That to escape the Earth.

[Co-Host]

If you want to explore the rest.

[Host]

Of the solar system, it's much easier.

[Co-Host]

To do from the Moon than it.

[Host]

Is from the Earth.

[Co-Host]

From an energy standpoint, the biggest leap in spaceflight wasn't landing on the Moon.

[Host]

It was just getting into orbit in the first place.

[Co-Host]

All of these constraints I've mentioned have led to engineers and physicists to coin.

[Host]

The term the tyranny of the rocket equation. The rocket equation rules everything when it comes to spaceflight. The design of rockets, spacecraft, satellites, and.

[Co-Host]

Everything else has to take the rocket equation into consideration. Even something novel like Starship by SpaceX.

[Host]

On which I did a previous episode.

[Co-Host]

And which just had its first test.

[Host]

Launch, is subject to the rocket equation.

[Co-Host]

Starship is more focused on reducing costs, but still doing so within the confines.

[Host]

Of the rocket equation. If the rocket equation has a tyrannical hold on travel by rockets, is there any way to break this tyranny? And the answer is sort of you can't break the laws of physics, but you can break the constraints around how rockets function today.

[Co-Host]

The first way would be to get.

[Host]

Rid of chemical reactions to provide thrust.

[Co-Host]

Chemical reactions have a maximum exhaust velocity.

[Host]

Of about 4.5 km per second, which is close to what some rockets are doing already.

[Co-Host]

A far more efficient rocket would be.

[Host]

A nuclear thermal rocket.

[Co-Host]

Uranium has an energy density a million.

[Host]

Times greater than hydrogen.

[Co-Host]

A nuclear rocket would work by exposing.

[Host]

Gas, most probably hydrogen, to an extremely hot nuclear reactor.

[Co-Host]

If the gas were heated to about.

[Host]

3,000 degrees Kelvin, it could have an exhaust velocity of 10 kilometers per second, more than twice that of a chemical reaction.

[Co-Host]

However, that's just the beginning. The theoretical maximum exhaust velocity for a.

[Host]

Nuclear thermal reactor is 5,000 kilometers per second.

[Co-Host]

The mere doubling of the exhaust velocity from a nuclear rocket would change everything, turning the fuel to mass ratio from.

[Host]

Something like a soda can to something perhaps more like an airliner.

[Co-Host]

NASA is already investigating nuclear rockets for.

[Host]

Use outside of the Earth's orbit. The other way around the rocket equation.

[Co-Host]

Is to cheat on the delta V. Earlier I said that going into orbit.

[Host]

Was an issue of speed, not altitude. And this is true mostly.

[Co-Host]

The higher the orbit, the longer it.

[Host]

Takes to go around the Earth.

[Co-Host]

In low Earth orbit, it takes about 90 minutes. However, if you keep going up, you.

[Host]

Will eventually reach a point where it.

[Co-Host]

Takes one day to go around the.

[Host]

Earth exactly the same as the Earth's rotation. This is known as geostationary orbit, a subject on which I've done a previous episode.

[Co-Host]

If you can get 22,236 miles or 35,786 kilometers above the surface of the.

[Host]

Earth, then you are traveling at orbital speeds.

[Co-Host]

Even though you just went straight up, it wouldn't even matter how long it took you to get to that altitude. The idea proposed to do this would.

[Host]

Be a space elevator.

[Co-Host]

A space elevator would be a long.

[Host]

Cable which extended from geostationary orbit down to the surface of the Earth.

[Co-Host]

A vehicle would then just need to climb the cable, which could be done.

[Host]

With significantly less energy than with a rocket.

[Co-Host]

A final way around the equation would.

[Host]

Just be the discovery of some form of physics that we currently don't know. If we learned of some way to nullify the effects of gravity, we could make the rocket equation moot. But as of now, that is only the realm of science fiction.

[Co-Host]

Understanding the rocket equation isn't rocket science.

[Host]

Well, ok, actually, I guess in this case it technically is rocket science, but.

[Co-Host]

It isn't difficult to grasp.

[Host]

The next time you watch a rocket.

[Co-Host]

Blast off into space, keep in mind.

[Host]

The rules that govern that rocket.

[Co-Host]

It was engineered to perform within the laws of physics, which were outlined in the late 19th century by a Russian who lived in a log cabin. The executive producer of Everything Everywhere Daily is Charles Daniel. The associate producers are Benji Long and Cameron Keever. I want to give a big shout out to everyone who supports the show over on Patreon, including the show's producers. Your support helps me put out a show every single day and also Patreon is currently the only place where Everything Everywhere Daily merchandise is available to the.

[Host]

Top tier of supporters.

[Co-Host]

If you'd like to talk to other.

[Host]

Listeners of the show and members of.

[Co-Host]

The Completionist Club, you can join the Everything Everywhere Daily Facebook group or Discord server. Links to Everything are in the show Notes.