How do things that spew fire and fly at hundreds of miles per hour not get anyone's attention. But more
recently, SpaceX and their attempt to bring down 10 story high rocket stages weighing 4 tons on
autonomous
sea fairing landing platforms did the trick for me to try and make my own flying flame farters.
Project Plan
1. Watch some rocket launches on YouTube.
2. Build a rocket.
3. Be temporarily known as the rocket guy.
If above mentioned goal is not reached, proceed to call myself the rocket guy.
Project Scope
Get a thing as high as possible only using materials available to me in my immediate vicinity.
Do so without posing a (majour) risk to anything other than the thing being launched.
Single Most Basic Applied Principle
Things that push get pushed.
To push a thing
the difficulty in pushing it depends on đź”˝
how heavy it is
and how fast you push it. "PUSHDNESS" = heavyness X fastness
(momentumnity).
Since
relativity is impartial
There's no difference between
pushing yourself off of something or
pushing something off of you
— either action makes you both move apart.
This is how the rocket do
The rocket pushes gas away very, very fast,
therefore pushes itself away from the gas.
How to make fast gas
Exploding Sugar
Imagine sugar molecules as magnetic
balls separated by sticks. If you bump the stick hard enough, the balls fly toward each other, releasing
their pent up anger like two boets that eyed the same bint in a bar fight.
Note the red arrows show where they are being pulled to, and how the mass of balls fly off like a mouse
trap woken from its tensioned slumber.
A molecule hitting a thing is a small push to that thing
Now imagine we have a container full of these balanced but angry lumps of stick
magnets. As soon as one is bumped hard enough, it flies off in a direction, hitting another
one and setting it off.
A chain reaction of pent up anger like the French when a politician so much as breathes releases
the energy only the mating rituals of covalent and ionic bonding can offer.
Organizing the Chaos
We need to get all these molecules to push in the same direction.
We need to ensure the gas particles are only pushed backwards so that we only get pushed forwards, sideways
push is wasted push.
Right before the particles explode out the hole, notice the arrows that shows in which direction they're
about to fly off to.
Imagine we can put a plate in the way of each of those sideways flying particles and bounce them
straight
backwards.
Introducing the Nozzle
The nozzle
bounces sideways-moving
gas particles
backward ,
increasing forward push.
Don't make your gases fight, send them out right
We stopped almost all of the sideways push and made it into a lot of foreward push.
Here's another very important thing to understand about the nozzle, it will require you to keep two
things in mind:
1) Temperature is how fast the gas particles are moving, how much pushness have they got.
2) Pressure is how often a particle hits the inside of a container and how fast it was when it hit.
Every time a particle bounces and it pushes a thing, some of its energy goes to that thing and it slows
down
(pressure drops). And as the nozzle gradually expands, the volume also decreases. Like when you hit one
pool
ball into another one, the first one practically stops, having given all its energy to the one that
speeds
away. But if the thing the gas is pushing is a lot heavier, it needs to bounce against it a lot more to
get its
energy out.
This means every time a particle hits the nozzle and bounces backwards, it slows down a little because
it sped
up the casing and nozzle by pushing against it. With these two concepts, we can see how the pressure and
temperature of the gas decreases as it flows down the nozzle. Remember that the air in the atmosphere is
also
made of particles that bounce and jiggle like the ones we made inside the rocket casing, even though
they're
much more relaxed and cooled down.
Now you have to ask what happens when:
The gas pressure is lower than the atmosphere pressure.
SpaceX Falcon 9 at sea Level
In this case the nozzle should have been made shorter or narrower so that the gas ends at atmospheric
pressure.
Just on an interesting side note, if the section above made sense to you, think about how a rocket gets
affected by the decreasing pressure in the atmosphere as its altitude increases. Look at these two pictures
as a hint:
The gas pressure is higher than the atmosphere pressure:
SpaceX Falcon 9 high altitude
If the gas coming out of the nozzle is still at a higher pressure than the surrounding atmosphere,
it will expand quickly until the pressures equalize, wasting a lot of potential thrust. This is similar to
just opening a hole in the back of a container, where the gas escapes in all directions. Using a nozzle is
still better than a simple hole, though, since it recovers some of the sideways push from the chaotic gas
particles.
To fix this, the nozzle should be larger or shaped differently so that the gas exits at the same pressure as
the atmosphere.
On the flip side, if the nozzle expands the gas too much, the pressure can drop below atmospheric pressure.
This is bad because atmospheric particles start pushing back on the outside of the nozzle,
counteracting the rocket’s thrust. The blue arrows show the atmosphere pushing against the rocket,
while the red arrows represent the thrust from the rocket gas. As the gas pressure drops too low,
the red arrows shrink, and the atmosphere starts to win the push-and-pull battle, effectively dragging the
rocket backward.
Making the rocket fuel (AKA Explodable sugar)
Here I will be a bit more specific as to what will happen to the sugar. Sugar consists of
oxygen, carbon, and hydrogen particles. The amount of each or how they stick together to make sugar is not
important here. Instead, what I want to focus on is where all that jumpy spring energy is
stored that we will release.
They're placed together in such a way that they're not as close to each other as they could be, and bumping
the arrangement hard enough sends the molecules crashing into and sticking to molecules which allow them to
be closest to one another. After being burned, they get to pair up with each other into groups of
water and carbon dioxide, which is the closest they can stick to other
molecules.
You break up the sugar molecule, which takes a little work, but when you bring the parts back together they
will fly at each other into their burnt configuration with more force than it took to pull them apart,
therefore releasing their stored spring energy.
Why burn sugar?
It might seem odd since we usually think of sugar in chocolates and sodas.
But sugar is packed with energy—the same energy our bodies use.
In fact, sugar has so much energy that our bodies often can't use it all, and the extra gets stored as
fat!
We need to bring oxygen with.
Sugar alone isn't enough. To release all its energy, sugar needs more oxygen than it
already contains.
Without enough oxygen, the sugar molecules can't fully react and settle into a lower-energy state.
No air inside the rocket. Since the sugar is sealed in the rocket, we can't supply it
with air from the outside.
Plus, even if we could pump air in, it wouldn’t be nearly enough to create the explosion we need—it
would just burn like a candle.
Solution: Add an oxidizer. An oxidizer is a chemical that releases oxygen when it’s
heated.
Think of it as sugar’s partner in combustion. Heat it up, and it breaks apart, releasing lots of oxygen
to fuel the reaction.
Together, sugar and the oxidizer create the energy needed for the rocket to work.
Burn rate:
Imagine we had a very long narrow hall full of mousetraps, or those magnet balls and sticks. If we triggered
the one side, we would see a wave of propagating chaos move
down the hall as the traps or magnet balls trigger each other—like a Mexican wave of woken-up spring energy.
If we could measure how far that wave traveled per second we'd have the Burn Rate
This wave of breaking up and flying off particles can be slow, as in the case of paper
burning, or fast, like a match head.
If you can control how fast it burns, and control how much burns at the same time, then you can control how
much hot, speedy gas you make per second, and therefore control
how much push your rocket gets.
If we produce too much gas at a time, it may not be able to escape the nozzle fast enough and could cause
the rocket to become over-pressurized and explode.
Even if the rocket could handle the pressure, we mentioned that we want the final pressure of the gas to
match that of the atmosphere.
Otherwise, we’d just be wasting good push if too much fuel burns at once.
Predicting how high it will go
Rockets Get Lighter as They Burn:
There's an interesting thing to note about rockets: they get lighter and lighter as they burn and push away
their fuel.
Think about it—most of the rocket starts off filled with whatever you're going to turn into hot gas, and as
it burns, you blow it out the back.
Here’s an example: Imagine a rocket that weighs 0.5 kg and has 1 kg of
fuel, which it burns at a rate of
0.1 kg per second.
- The rocket starts off with a total mass of 1.5 kg.
- Since fuel is burned and blown out at 0.1 kg per second, it takes 10
seconds to use all the fuel.
- By the end of the burn, all that's left is the 0.5 kg casing of the rocket, which is now
(hopefully) going very fast after pushing all that other mass away.
If you understand what's happening above, think about what will happen to the acceleration
(how fast the rocket picks up speed).
You’d agree that it’s easier to make a light object go faster than a heavy object when you push just as hard
on both, right?
Since we burn the same amount of fuel through the same nozzle until all the fuel is gone, the amount
of push stays constant.
But the rocket gets lighter and lighter, so in the beginning, the push from the nozzle makes it pick up
speed more slowly. By the end of the burn,
the rocket will pick up speed much more quickly.
Here’s another graph to show how mass, acceleration, and speed are related:
If you know something about integration—or if you're just good at playing with quantities in your
head—you’ll realize that the
area under the acceleration line on the graph up to a certain time is equal to the
speed at that time.
Now that we understand hot gases and high pressures, we need to find materials and parts that can handle
these violent conditions.
But exactly how much pressure and heat should they handle? While these are critical questions, another
factor makes the answers much less dramatic: time.
If we ask, "how much pressure for how long?" or "how much heat for how long?" the answers can be drastically
different.
For example, if you Frisbee-throw a piece of bread through a bonfire's flames, it won’t toast—maybe just
slightly seared edges at most.
So, can we find things in my kitchen and backyard that will withstand rocket fire explosions? Most likely.
But to be sure, we need math. So, let's make some!
​
The following section contains some complex and incomplete explanations of
thermodynamic concepts. If the term "thermodynamics" scares you, then this warning probably applies
to
you. It's not necessary to understand everything in blue, but it's here for those interested in
seeing
all the steps.
First, what temperatures (remember this is just fancy for how fast the molecules are moving) will
a sugar and saltpeter mixture reach?
To work this out, we need two things:
How much energy is released when we burn an ideal sugar and saltpeter mixture?
How much does the temperature rise for every bit of energy we release?
Energy and Molecule Bond Analogy:
To answer the first question, think of the bonds between the particles like a stretched bungee cord. When
the molecules are in the sugar structure, they are stretched far apart, storing energy like the elastic
of the bungee cord. To release the energy from the cord, you must stretch it a little to unhook it (add
some energy), and then let it go. It will spring back to a shorter length, releasing the energy and
shooting off particles like a rubber band gun.
To do the energy release calculations, we have to take all the molecules into account. It may seem
complicated because we have to deal with the saltpeter, which is made of potassium, nitrogen, and
oxygen. But having different molecules is like having different types of elastic bands—everything adds
up, but you just have to do a few more sums.
When we start, we have sugar and saltpeter. When we end, we have water, carbon dioxide, nitrogen, and
salt. The salt is just made from the leftover potassium and some carbon and oxygen. Don’t worry about
it, it’s like any other molecule, and it has an enthalpy of creation. All that complexity is summed up
into one number that can be added and subtracted.
Reference: I got all my chemical properties like enthalpy of formation and specific
heats from the NIST website: NIST Webbook.
Additional Credit: Richard Nakka did amazing work in calculating these values, including
cool graphs that show the velocity, pressure, and thrust ratio through the engine. You should check it
out here: Richard Nakka's engine calculations.
What needs to be noted here is that this is the absolute ideal reaction and circumstances for that
reaction. In reality, not all the molecules of sugar will react with the other molecules they should.
Some molecules may not form their lowest possible energy state and form complex molecules, taking some
of the energy away. The whole burning process is chaotic, uncontrollable, and dirty.
Understanding Energy in Molecules:
To answer the first question, we can think of the bonds between particles like a stretched bungee cord. When
molecules are part of the sugar structure, their bonds are stretched far apart, storing energy like the
elastic of a bungee cord.
To release this energy, you first have to stretch the cord a little to unhook it (add some energy), then let
it go. The cord snaps back to a shorter length, releasing energy in the process. Similarly, breaking the
bonds in sugar releases the stored energy, shooting off particles like a rubber band gun.
Just as you can release energy by breaking sugar into carbon dioxide and water, you can also add energy to
carbon dioxide and water to make sugar again—just like stretching the bungee cords and hooking them on
again. In fact, this is what plants do through photosynthesis. They take carbon dioxide and
water, add energy from sunlight, and carefully arrange the molecules so they don’t snap back down.
The energy it takes to create a molecule is called its enthalpy of formation. The energy we
can release is simply the difference between the molecule’s initial energy state and its final energy state.
Using Oxygen and Hydrogen as an Example:
Before we dive into the energy and heat involved in sugar and saltpeter, let’s look at a simpler example:
oxygen and hydrogen—the same chemicals used by the space shuttle.
The high-speed particles that shoot around and push against the rocket nozzle are water particles. That
white trail behind the space shuttle? It’s just steam—normal water vapor, like the steam coming out of your
kettle.
Energy Release Calculations:
To calculate the energy released during a reaction, we have to account for all the molecules involved. While
this may sound complicated—especially when dealing with saltpeter, which contains potassium, nitrogen, and
oxygen—it’s not as bad as it seems.
Think of it as dealing with different types of elastic bands. Each has its own amount of stored energy, but
in the end, everything adds up. You just need to do a few more calculations to account for the different
molecules.
In our case, we start with sugar and saltpeter. By the end of the reaction, we have water, carbon dioxide,
nitrogen, and salt.
The leftover potassium combines with some carbon and oxygen to form the salt. While it might seem complex,
the energy stored in the salt is accounted for through its own enthalpy of formation. This means all the
complexity can be boiled down to a single number that can be added or subtracted in the overall energy
calculation.
SpaceX Falcon 9 at sea Level
SpaceX Falcon 9 high altitude
