Rocket from Amperka, part 1: Theory of rocket engines. Caramel fuel

8 min


Hello! We are the team of YouTube channel Amperka, in the studio and we are filming videos on projects and pieces of iron. However, at some point, everything changed.

Under the cut – the story of the construction of our rocket.

It was spring 2020 and quarantine self-isolation did not spare anyone. Including us, excommunicated from the studio, so as not to be at risk of infection with an overseas bacillus. It was during this period that the old ideas began to become more active in my head to do what I had wanted for a long time, but what had been put aside in the long box “when the time will be”. Finally, that_time came, and from that very box the idea of ​​building our own rocket was extracted, also spurred by the recent successful launch of the “trampoline” from SpaceX.

Since such a serious project cannot be done in one go, we will divide it into components for convenience (the list will be replenished as it works):

  1. Part 1. Theory of rocket engines. Caramel fuel

Rocket science, as a whole, is a complex, complex and multifaceted science. We didn’t have any relevant experience, we didn’t graduate from institutes in this direction, but we have hands, a head, a desire — and this is a lot, so, as Yuri Alekseevich used to say, let’s go.

Theory of turbojet engines

What is jet propulsion (for those who are suddenly not in the know) we won’t talk much: in a nutshell, this is a movement due to the rejection of mass in the opposite direction from the direction of motion. We will not talk about all kinds of exotic designs of engines such as nuclear, ionic and others like them – one is not designed to work in the atmosphere, the other is too complex and cannot be reproduced in amateur conditions, etc., therefore, we will focus on simple but affordable designs for the average man , which, if desired, can be repeated almost at home, namely, chemical. In such engines, a jet stream is obtained due to the chemical reaction of the fuel and the oxidizing agent (in some cases, atmospheric oxygen can play the role of the oxidizing agent).

So, chemical engines (RRL), according to the state of aggregate fuel, are classified as liquid (LRE) and solid fuel (TRE), so we will choose from them. LRE are very convenient because they allow you to control the thrust, but require the use of complex nozzle systems in the combustion chamber and no less complex fuel supply systems in their design. Designing a rocket engine, even the most primitive one, will take months, and therefore this is not our option. An alternative can be a turbojet engine due to the simplicity of its design and significantly lower fuel requirements. Yes, we won’t be able to accurately dose traction. More precisely, we will not be able to dose it at all. However, there are some aspects on which we can play, and this will be discussed further.

Types of mixed fuel

The very first, and, accordingly, primitive fuel for missiles was gunpowder: first smoky, and then smokeless. The Chinese, having invented this combustible mixture, quickly realized that it could not only make a bang and a lot of light, but also push a shell, gradually burning inside it. Of course, there is little sense from him, it is suitable only for fireworks, and the specific impulse leaves much to be desired. Smokeless gunpowder evolution has become a homogeneous (single-component) nitrocellulose-based compounds. They are quite unpretentious in storage and operation, and also quite environmentally friendly, but they still have the same drawback in the form of a weak specific impulse.

Much better results are shown with mixed formulations of fuel and oxidizer. Most often, oxidizing agents made of perchlorates with fuel from powder of metals and polymers or “caramel fuel”, widely known among amateur modellers, are used as such a pair, where nitrates (nitrate) and complex carbohydrates (sugar, sorbitol) are used as oxidizing agents as fuel . Here are just the last two options (perchlorate and caramel) fuel we chose as experimental for our rocket.

Engine calculation

The most important characteristic of solid fuel is its burning rate, often this value is a constant for a certain fuel composition. Burning spreads over the surface. If you simply set fire to the end of a cylindrical fuel checker, we will get end combustion, which will give a long, uniform burnout, however, at the same time, getting enough traction to lift the rocket into the air will not work. To increase efficiency, it is necessary to make a channel in the fuel through which combustion will spread, thereby increasing its area. It should also be borne in mind that as the burnout occurs, the channel profile will change, therefore, the effective area will change. You can, of course, experiment for a long time with various profiles, however, all this has already been done before us and packaged in a convenient software tools.

In the program, you can enter all the necessary parameters and get the graphs of thrust that the rocket will develop. In the Grain configuration column, under the question mark, there is a descriptive manual for various channel profiles.

Empirically, using various channel configurations, we found the optimal parameters for our rocket. To obtain the same indicators, you need to enter the following values:

We chose the Moon burner channel shape. Smart Meteor, taking into account the entered data, built us such a graph:

We understand from this diagram that the engine will get a good kick from the start and will develop very good traction throughout the entire operation time. According to the program calculations, the peak thrust value was obtained at almost 312 N at a peak pressure of 24.5 bar. The average values ​​were about 265 N and 19.5 bar, respectively.
Another indisputable advantage of the program is the ability to directly export the calculated values ​​to another program no less useful to us – Openocketwith the help of which we will calculate rocket stability, plumage, balancing and other important indicators, but this will be in the next series.
However, not a single fuel alive beginner rocket. Nozzle is equally important. According to this principle, RDs are divided into nozzle and non-nozzle ones. The latter, technically, have a subsonic nozzle, which, in fact, is simply a hole or cone in the lower part of the engine. It is called Subsonic because the gases flowing through it cannot reach, let alone exceed the speed of sound, no matter how much pressure builds up in the combustion chamber, hydrodynamics tells us this. And as you know, you can’t argue against physics. However, such nozzles due to their simplicity are used in small amateur rockets, as well as in fireworks. But we are making a rocket, which means that subsonic nozzles are not our way.
An alternative solution is a supersonic nozzle or, as it is also called by the name of the inventor, a Laval nozzle. In a simplified version, it is two truncated cones, conjugated with narrow ends. The interface is called the critical point.

The principle of its operation resembles the principle on which a refrigerator works: gases passing through a “narrow neck” and falling into a large volume are rapidly cooled, due to which their volume decreases, which leads to an increase in their flow rate. As a result, due to the difference in the diameter of the outlet, we get a stream of gas moving at supersonic speed at the outlet. Thus, using the Laval nozzle, we significantly increase the efficiency of the rocket.
By the way, Meteor carries out calculations, implying that the engine has just a supersonic nozzle, the calculation and manufacture of which will also be left for the next release.
So, we have the characteristics, parameters and dimensions of the engine, you can start cooking fuel.

Making fuel drafts

The first fuel we will have is caramel, we will cook from sorbitol and potassium nitrate. Sorbitol can be bought at the pharmacy, it is used as a sweetener. Potassium nitrate can be found in the garden department, but there it is quite dirty, so they bought b / w in Ruscheme.
The simplest way is to grind the components to a state of fine powder and mix, but then the fuel remains loose and will not keep its shape. It was decided to fuse the components together. We will have to make a temperature-controlled heater and a sand bath, for which we need:

We throw out its native controller from the plate and put in the section a solid-state relay, which we will control through Arduino, to which we will connect the display and potentiometer to see the current temperature and be able to set it. In the baking dish, make a hole and insert a thermocouple. Fill the form about halfway sand salt (there was no sand at hand, but there was a grocery store nearby, this will not affect the quality). This is necessary to create an environment with high thermal inertia. By the way, it is better to take “extra” salt, as the larger salt begins to crack and shoot in different directions when heated, arranging Stalingrad. In the center of the salt bath, we establish an evaporation cup, after having previously placed a thermocouple probe under its bottom. We will control the process through the first relay controller for Arduino. We check with a pyrometer the temperature difference between the thermocouple readings of the temperature of the bowl, we make the appropriate adjustments.
Meteor carefully calculated the mass of fuel, which amounted to 838g, take with a margin, it’s still useful. It was decided to make a fuel charge of several checkers for ease of manufacture. Then it will be possible to simply glue them together and insert them into the engine housing.
Take 65% potassium nitrate and 35% sorbitol by weight, carefully pour into the bowl and add a little water. This will calm the nerves, and eliminate the need to grind the components into dust, since in water they already dissolve and mix well. We put on fire, set the temperature and wait, constantly stirring. Gradually obtained porridge will melt and become like oatmeal. It is necessary to wait for the evaporation of all excess water (this can be understood by the ceased release of boiling bubbles).
Then we must act decisively: we will press the fuel into the pre-prepared PVC water pipe fixed in the holder with an internal fastening under the round axis. After removing the axis, we will just have a fuse channel along the entire length of the checker. It is convenient to press in with the holder for a drill, which was very successfully found in the studio. It is important to press the fuel in such a way that there are no bubbles or cavities inside the checker, otherwise it will negatively affect combustion.
We postpone the pipe with fuel and leave it to cool. Then it will be possible to saw it and get a checker. We made several pieces, we’ll burn one of them for the purpose of the experiment.

In the next issue, we will deal with the engine block, nozzle, and test bench.
In the meantime, we are preparing it, I recommend reading the following a book about the design of missiles. Most of the information was drawn from it.


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