The brutality of the formula Tsiolkovsky
The cruel laws of the nature around us can only be called in a figurative sense. We have created machines that can free us from the bonds that hold all of humanity in the gravity well, but the management of some of their aspects remains beyond our power. If we want to start our journey around the solar system, then these restrictions will have to somehow be circumvented.
Modern missiles discard some of their own mass in the form of gas from engine nozzles, which gives them the opportunity to move in the opposite direction. This is real thanks to the third law of Newton, which was formulated in 1687. We owe the whole of our rocket movement the Tsiolkovsky formula of 1903.
There are only four variables in the formula (from left to right): the final speed of the aircraft, the specific impulse of the rocket engine (the ratio of engine thrust to second mass fuel consumption), the initial mass of the aircraft (payload, design and fuel) and its final mass (payload and design).
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How can I change one of the variables if the other three are already set? It is simply impossible, no form of desire, desire, or request will help here.
It is the gravity losses that determine the limits of human space exploration, and we have to take them into account when we choose the place where we want to go. Today, these places are not so much. From the Earth’s surface, we can be in Earth’s orbit, from Earth’s orbit we can go to the surface of the Moon, or to the surface of Mars, or into the space between the Moon and the Earth. Various combinations are possible, but with the current development of technology these are the most likely destinations.
The values below do not take into account any losses on, for example, the resistance of the atmosphere, but the values are close enough to illustrate what should be taken for granted. This is in some way the cost of the flight.
As you can see, the path from Earth to orbit, these miserable 400 kilometers is the most expensive part of the flight. This is a whole half of the "cost" of the flight to Mars, even to the moon to get "worth" less. All this is connected with the gravitational attraction of our cosmic house.
And we have to fly on a rocket with chemical engines; Although there are promising developments, the traditional engines that have been used for more than 60 years in manned cosmonautics remain real. Chemical fuel imposes a limit on the amount of energy that can be extracted from them, and thus invested in a rocket, and we use the most effective reactions known to humanity. And again we have to come to terms with some value of a variable that we cannot change.
Below are presented as some types of rocket fuel, which at least once were used to propel vehicles with a person on board or are planned to be used, and their specific impulses. Methane-oxygen is under consideration for future expeditions to the Moon and Mars. The self-igniting two-component liquid rocket fuel was used for the Apollo landing module of the lunar module because of its simplicity.
The most effective pair is oxygen-hydrogen, and chemistry cannot give us more. In the late 70s of the last century, a nuclear rocket engine with hydrogen as a working medium, which accelerated the heat of a controlled nuclear reaction, produced 8.3 km / s.
So, the only thing that we can now change in the Tsiolkovsky formula is the ratio of the masses of the aircraft. The rocket must be built in such a way that this relationship has any given value, otherwise it simply will not achieve its goal. Something can be done if we add some ingenious solutions to the design, but in general this will have little effect on the result - the chemistry of the fuel and the gravity of the celestial bodies cannot be changed.
So what do we have? Here is the percentage of fuel of the total mass of the rocket, necessary for the rocket to hit the Earth's orbit.
The figures do not take into account the diverse losses of atmospheric resistance, incomplete combustion and other negative factors, so the real ratio is slightly closer to 100%. Excellent engineering solutions such as separation into stages, several types of fuel (for example, kerosene or solid fuel for the first stage, hydrogen for the others) are very helpful in a situation where only about 10% of the mass of the device remains on the rocket itself. Mass payload sometimes literally goes to its weight in gold.
The characteristics of real rockets do not differ much from these ideal ones, obtained without taking into account the many factors of values. The largest Saturn-5 rocket in the history of mankind at the launching table had fuel at 85% of its entire mass. She had three steps: the first worked on kerosene and oxygen, the second and third - on hydrogen and oxygen. The same indicator for the "Shuttle". Soyuz uses kerosene in all its stages, so its fuel mass is 91% of the total mass of the rocket. The use of hydrogen-oxygen vapor is associated with a large number of technical difficulties, but this combination is more effective; kerosene paired with oxygen provides the ability to use more simple and reliable solutions.
15% of the mass of the rocket is much less than it seems. A rocket must have tanks, pipes leading to engines, a body that must be able to withstand both supersonic flight in the atmosphere after the inhuman heat of the launch pad, and the cold of airless space. The rocket needs to be led, controlled by supersonic steering wheels and shunting engines. The fragile bodies of people in a spacecraft need to be provided with oxygen, as well as remove carbon dioxide, they need to be protected from heat and cold, to enable them to safely return to the surface of their home planet. Finally, people are not the only load of the rocket: we do not launch people just for fun, or rather, we can launch a person for the sake of the fact, but only once. A variety of equipment for conducting experiments also flies into space with people, as flights into space are aimed at scientific research.
The real mass of payloads of rockets is much less than these 10% —15%. “Saturn-5”, the only rocket that helped a man to set foot on the Moon, delivered only 4% of its total mass to Earth orbit, while 120 tons were delivered to orbit. "Shuttles" could deliver about the same (100 tons), but the real payload was about 20 tons, 1% of the total mass.
Compare rocket with our usual vehicles. (Of course, the rocket has tanks with oxidizing agents, and the earth transport uses air oxygen for this.)
It is easy to see how the materials and design of the vehicle differ depending on the relative mass of the fuel. Vehicles with a fuel mass of less than 10% of its total mass are usually made of steel, and above its structure there is no need to think too much: attach this part to the body and the body where intuition requires. The ten-ton truck can be overloaded, but it will continue to move, albeit slowly.
Air transport requires a more serious approach and lightweight structures made of aluminum, magnesium, titanium, composite materials. There is simply nothing to change, and over any small detail you need to think twice. Machines of this kind cannot work so far beyond their load limits. 60% —70% of the mass of these vehicles is the actual weight of the vehicle with a payload, and with the use of some engineering solutions, comfortable, safe and profitable operation is possible.
And rockets, where 85% is fuel, are at the limit of our engineering capabilities. We can hardly produce them, they require constant improvement in order to be able to use them. Externally, small changes require a huge amount of varied analysis and testing of prototypes in wind tunnels, vibrostands, and for a test run, personnel should be removed to a bunker a couple to three kilometers from the launch pad - even after all these checks, incidents are possible. It is often impossible to exceed the load by more than 10% of the specified technical requirements. This is similar to the situation when, after acceleration to 44 kilometers per hour, the bike will fall apart into the smallest cogs simply because the speed limit is 40 km / h.
A miracle of mass production, about 94% of aluminum beer can consists of its contents, and only 6% is on the hull, but somehow this indicator is better for the shuttle’s external tank, despite the fact that it does not contain a drink a little colder than room temperature. temperatures, and highly active liquids with temperatures of about 20 degrees above absolute zero, compressed to terrible pressure. At the same time, this fuel tank can withstand an overload of 3 g, keeping the flow of oxidizer and fuel at 1.5 tons per second.
Don Pettit describes the details of the expedition STS-126 November 2008. Shuttle engines should have shut off at a speed of 7824 m / s, but if it had happened at 7806 m / s, the spacecraft would have become a satellite of the Earth, but would not have fallen into the target orbit. Simply put, the Endeavor would not have reached the ISS. Is this a big difference? This is about the same situation as when you need to pay 10 dollars, and for this you need only two cents (0.2%). Well, in this case it would be possible to use part of the fuel for orbital maneuvers. If the speed was only 3% lower, then these reserves would not be enough, and the shuttle would have to be planted somewhere in Spain. This 3% could have been lost if the main engine had turned off just 8 seconds earlier.
Imagine the best combination of circumstances: the Shuttle tank (we drop the mass of the engines) and hydrogen-oxygen fuel. If we substitute the values into the Tsiolkovsky formula, then it becomes clear that with the radius of our planet one and a half times its current size, we would never have reached space only due to the technology of chemical rocket engines .
And all this - the consequences of the formula Tsiolkovsky. If we want to get rid of its cruel domination, we will have to create working versions of fundamentally new engines. Perhaps then the missiles will become as safe, familiar and reliable as jet passenger aircraft.
Based on the materials of the National Aeronautics and Space Administration .
Modern missiles discard some of their own mass in the form of gas from engine nozzles, which gives them the opportunity to move in the opposite direction. This is real thanks to the third law of Newton, which was formulated in 1687. We owe the whole of our rocket movement the Tsiolkovsky formula of 1903.
There are only four variables in the formula (from left to right): the final speed of the aircraft, the specific impulse of the rocket engine (the ratio of engine thrust to second mass fuel consumption), the initial mass of the aircraft (payload, design and fuel) and its final mass (payload and design).
')
How can I change one of the variables if the other three are already set? It is simply impossible, no form of desire, desire, or request will help here.
It is the gravity losses that determine the limits of human space exploration, and we have to take them into account when we choose the place where we want to go. Today, these places are not so much. From the Earth’s surface, we can be in Earth’s orbit, from Earth’s orbit we can go to the surface of the Moon, or to the surface of Mars, or into the space between the Moon and the Earth. Various combinations are possible, but with the current development of technology these are the most likely destinations.
The values below do not take into account any losses on, for example, the resistance of the atmosphere, but the values are close enough to illustrate what should be taken for granted. This is in some way the cost of the flight.
| Destination point | Cost of speed |
|---|---|
| From the Earth’s surface to the Earth’s orbit | 8 km / s |
| From the Earth's orbit to the Lagrange points of the Earth-Moon system | 3.5 km / s |
| From the orbit of the Earth to the low orbit of the Moon | 4.1 km / s |
| From Earth's orbit to near-Earth asteroids | > 4 km / s |
| From the orbit of the earth to the surface of the moon | 6 km / s |
| From the orbit of the Earth to the surface of Mars | 8 km / s |
As you can see, the path from Earth to orbit, these miserable 400 kilometers is the most expensive part of the flight. This is a whole half of the "cost" of the flight to Mars, even to the moon to get "worth" less. All this is connected with the gravitational attraction of our cosmic house.
And we have to fly on a rocket with chemical engines; Although there are promising developments, the traditional engines that have been used for more than 60 years in manned cosmonautics remain real. Chemical fuel imposes a limit on the amount of energy that can be extracted from them, and thus invested in a rocket, and we use the most effective reactions known to humanity. And again we have to come to terms with some value of a variable that we cannot change.Below are presented as some types of rocket fuel, which at least once were used to propel vehicles with a person on board or are planned to be used, and their specific impulses. Methane-oxygen is under consideration for future expeditions to the Moon and Mars. The self-igniting two-component liquid rocket fuel was used for the Apollo landing module of the lunar module because of its simplicity.
| Type of fuel | Specific impulse |
|---|---|
| Solid rocket fuel | 3.0 km / s |
| Kerosene oxygen | 3.1 km / s |
| Self-igniting fuel | 3.2 km / s |
| Methane-oxygen | 3.4 km / s |
| Hydrogen-oxygen | 4.5 km / s |
The most effective pair is oxygen-hydrogen, and chemistry cannot give us more. In the late 70s of the last century, a nuclear rocket engine with hydrogen as a working medium, which accelerated the heat of a controlled nuclear reaction, produced 8.3 km / s.
So, the only thing that we can now change in the Tsiolkovsky formula is the ratio of the masses of the aircraft. The rocket must be built in such a way that this relationship has any given value, otherwise it simply will not achieve its goal. Something can be done if we add some ingenious solutions to the design, but in general this will have little effect on the result - the chemistry of the fuel and the gravity of the celestial bodies cannot be changed.
So what do we have? Here is the percentage of fuel of the total mass of the rocket, necessary for the rocket to hit the Earth's orbit.
| Type of fuel | The mass of fuel from the mass of the rocket |
|---|---|
| Solid rocket fuel | 96% |
| Kerosene oxygen | 94% |
| Self-igniting fuel | 93% |
| Methane-oxygen | 90% |
| Hydrogen-oxygen | 83% |
The figures do not take into account the diverse losses of atmospheric resistance, incomplete combustion and other negative factors, so the real ratio is slightly closer to 100%. Excellent engineering solutions such as separation into stages, several types of fuel (for example, kerosene or solid fuel for the first stage, hydrogen for the others) are very helpful in a situation where only about 10% of the mass of the device remains on the rocket itself. Mass payload sometimes literally goes to its weight in gold.
The characteristics of real rockets do not differ much from these ideal ones, obtained without taking into account the many factors of values. The largest Saturn-5 rocket in the history of mankind at the launching table had fuel at 85% of its entire mass. She had three steps: the first worked on kerosene and oxygen, the second and third - on hydrogen and oxygen. The same indicator for the "Shuttle". Soyuz uses kerosene in all its stages, so its fuel mass is 91% of the total mass of the rocket. The use of hydrogen-oxygen vapor is associated with a large number of technical difficulties, but this combination is more effective; kerosene paired with oxygen provides the ability to use more simple and reliable solutions.
15% of the mass of the rocket is much less than it seems. A rocket must have tanks, pipes leading to engines, a body that must be able to withstand both supersonic flight in the atmosphere after the inhuman heat of the launch pad, and the cold of airless space. The rocket needs to be led, controlled by supersonic steering wheels and shunting engines. The fragile bodies of people in a spacecraft need to be provided with oxygen, as well as remove carbon dioxide, they need to be protected from heat and cold, to enable them to safely return to the surface of their home planet. Finally, people are not the only load of the rocket: we do not launch people just for fun, or rather, we can launch a person for the sake of the fact, but only once. A variety of equipment for conducting experiments also flies into space with people, as flights into space are aimed at scientific research.
The real mass of payloads of rockets is much less than these 10% —15%. “Saturn-5”, the only rocket that helped a man to set foot on the Moon, delivered only 4% of its total mass to Earth orbit, while 120 tons were delivered to orbit. "Shuttles" could deliver about the same (100 tons), but the real payload was about 20 tons, 1% of the total mass.
Compare rocket with our usual vehicles. (Of course, the rocket has tanks with oxidizing agents, and the earth transport uses air oxygen for this.)
| Vehicle type | Mass of fuel from the total mass |
|---|---|
| Big ship (water transport) | 3% |
| Pickup | 3% |
| Ordinary car | four% |
| Locomotive | 7% |
| Fighter | thirty% |
| Cargo airplane | 40% |
| Rocket | 85% |
It is easy to see how the materials and design of the vehicle differ depending on the relative mass of the fuel. Vehicles with a fuel mass of less than 10% of its total mass are usually made of steel, and above its structure there is no need to think too much: attach this part to the body and the body where intuition requires. The ten-ton truck can be overloaded, but it will continue to move, albeit slowly.
Air transport requires a more serious approach and lightweight structures made of aluminum, magnesium, titanium, composite materials. There is simply nothing to change, and over any small detail you need to think twice. Machines of this kind cannot work so far beyond their load limits. 60% —70% of the mass of these vehicles is the actual weight of the vehicle with a payload, and with the use of some engineering solutions, comfortable, safe and profitable operation is possible.
And rockets, where 85% is fuel, are at the limit of our engineering capabilities. We can hardly produce them, they require constant improvement in order to be able to use them. Externally, small changes require a huge amount of varied analysis and testing of prototypes in wind tunnels, vibrostands, and for a test run, personnel should be removed to a bunker a couple to three kilometers from the launch pad - even after all these checks, incidents are possible. It is often impossible to exceed the load by more than 10% of the specified technical requirements. This is similar to the situation when, after acceleration to 44 kilometers per hour, the bike will fall apart into the smallest cogs simply because the speed limit is 40 km / h.
| Container | Useful content |
|---|---|
| Aluminum beer can | 94% |
| External Shuttle Tank | 96% |
| Molotov cocktail, incendiary bottle | 52% |
A miracle of mass production, about 94% of aluminum beer can consists of its contents, and only 6% is on the hull, but somehow this indicator is better for the shuttle’s external tank, despite the fact that it does not contain a drink a little colder than room temperature. temperatures, and highly active liquids with temperatures of about 20 degrees above absolute zero, compressed to terrible pressure. At the same time, this fuel tank can withstand an overload of 3 g, keeping the flow of oxidizer and fuel at 1.5 tons per second.Don Pettit describes the details of the expedition STS-126 November 2008. Shuttle engines should have shut off at a speed of 7824 m / s, but if it had happened at 7806 m / s, the spacecraft would have become a satellite of the Earth, but would not have fallen into the target orbit. Simply put, the Endeavor would not have reached the ISS. Is this a big difference? This is about the same situation as when you need to pay 10 dollars, and for this you need only two cents (0.2%). Well, in this case it would be possible to use part of the fuel for orbital maneuvers. If the speed was only 3% lower, then these reserves would not be enough, and the shuttle would have to be planted somewhere in Spain. This 3% could have been lost if the main engine had turned off just 8 seconds earlier.
Imagine the best combination of circumstances: the Shuttle tank (we drop the mass of the engines) and hydrogen-oxygen fuel. If we substitute the values into the Tsiolkovsky formula, then it becomes clear that with the radius of our planet one and a half times its current size, we would never have reached space only due to the technology of chemical rocket engines .
And all this - the consequences of the formula Tsiolkovsky. If we want to get rid of its cruel domination, we will have to create working versions of fundamentally new engines. Perhaps then the missiles will become as safe, familiar and reliable as jet passenger aircraft.
Based on the materials of the National Aeronautics and Space Administration .
Source: https://habr.com/ru/post/362721/
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