The roar of rockets going into space, giant pillars of fire, a colossal force that exceeds the force of gravity. The afterburner roar of combat aircraft. The loudest and most powerful human power device. All of this is a channel of a special form and special properties that radically changed humanity. What is its essence and how is the difficult birth of supersonic - read in our material.
Evolutionary history of the nozzle
When did a person first use a nozzle? Already in the 1st century, Heron of Alexandria proposed a jet nozzle for his "eolipil". In it, two oppositely directed steam nozzles rotated a hollow metal ball with reactive force. After 1200 years, China was making powder rockets - for fireworks and military ones - having mastered jet propulsion in practice. In the Middle Ages, combat missiles began to fly in Europe. In the nineteenth century Russian army, rocket weapons grew to regular foot and mounted rocket teams, launching rockets from special launchers; massive missiles in the fleet, large rocket factories such as the largest plant in Europe in Nikolaev. The first launch of combat missiles from a submerged missile submarine took place during Pushkin's lifetime, on August 29, 1834, on the Neva, 40 versts above St. Petersburg.
Nozzle - a device for accelerating the flow of liquid or gas. Why overclock it? In some cases, the fast stream itself is needed, which is used further. In others, it is not the flow that is needed, but the force that arises when it is ejected - reactive. Such a power nozzle is called a jet nozzle. It was jet nozzles that were practically mastered by the first with the emergence of the first missiles.
Simultaneously with the widespread exploitation of rockets, steam technology at the end of the nineteenth century reached steam turbines, which rotated the propellers of ships. A high-speed jet was required to flow around the turbine blades, and the faster the speed of the steam jet, the more force it created on the turbine blades, increasing its power. The nozzle was required here not for the reactive force (which, of course, also arose, but as a side, unused effect), but for creating a high-speed flow. Through it, the energy thrown by the nozzle in the form of a mass of steam will fall on the blades and perform work on them, spinning with force. The total force of the blades is transmitted to the propeller.
Working on a high-speed steam turbine nozzle, the Swedish engineer Carl Gustav Patrick de Laval proposed a fundamentally new type of nozzle in 1890. It was able to accelerate the flow to supersonic speeds, which had never been possible before. So the supersonic Rubicon was crossed, which immediately doubled the speed of the outflow.
And at the nozzles of Heron's eolipil, and at the tip of the fire hose (and this is a nozzle for accelerating a stream of water), the flow channel narrows. In such a channel, the flow of the working fluid - steam, gas or liquid - is accelerated. Why? The flow rate (the amount of the working fluid passing through the section per second) is the same anywhere in the channel - how much flows in through the initial section, so much should exit through the final section. After all, the substance flowing through the channel does not decrease or increase, there are no holes in the walls that supply or discharge it. And the law of conservation of mass makes the consumption of matter the same through any place of the nozzle.
Both the liquid and the subsonic gas flow practically do not change their volume; therefore, they are approximately considered as incompressible when the speed of sound is still far away. The constant consumption of their mass means the constant consumption of their volume. The stream has to hurry to drive the same volume through the narrowed space. The gas is forced to accelerate.
The pressure difference makes it flow - the flow flows in the direction of low pressure, pushed from behind by a high one. In the narrowing channel, the pressure and temperature of the flow are continuously decreasing, but its speed increases. The potential energy of pressure and temperature of the gas is pumped into the energy of motion, into its acceleration. The higher the pressure difference between the beginning and the nozzle exit, the greater the acceleration and flow rate. For its growth, the pressure in front of the nozzle is raised. The same is true for temperature differences, and they try to heat the gas more by burning the fuel components.
But the rate of expiration turned out to have its own fundamental limit. This is an outflow at the speed of sound. It is not overcome by any increase in pressure at the inlet to the nozzle. No matter how much it is raised, two, four or ten times, within the limits of the converging nozzle, the flow will not exceed the speed of sound.
Let us recall what subsonic and supersonic motion is. The speed of sound (weak wave seals in a gas) depends on many factors - the composition of the gas, its density and pressure. But most of all, it depends on the temperature. Under specific conditions, the speed of sound takes on a specific local value. Compares the speed of the flow with the local speed of sound, the Mach number, dividing the speed of the flow by the speed of sound. Its value is denoted M and shows how many times the speed of the current is greater or less than the speed of sound. When M is less than unity, the flow is slower than sound - subsonic. At M = 1, the flow flows exactly at the speed of sound. For M> 1, the flow is supersonic.
It is possible to overcome the sound boundary only by using a special principle. It is called the principle of influence reversal.
In gas dynamics, there is the concept of impact. This is the effect on the gas flow, which changes its parameters, including the velocity. The narrowing of the channel is a geometric effect, a change in the geometry of the flow. And there is the principle of reversal of impact. According to him, one and the same action can change the speed of the current only up to the speed of sound. Moreover, this is true for both acceleration and deceleration (if the flow is supersonic). The maximum achieved by the same impact will always be the speed of sound, M = 1. Becoming an insurmountable sound barrier for this impact. More than this limit, the impact of any power will not be able to do anything.
To step over M = 1 and continue accelerating or decelerating the flow, you need to change the effect to the opposite. With a geometric effect (narrowing of the channel), its sign must be changed. For overclocking, this is a change of narrowing for expansion. Where to change when? After the stream reaches the speed of sound. In the expanding part, the flow will become supersonic and accelerate further. Why?
After becoming supersonic, the flow acquires critically different properties. Subsonic incompressibility is replaced by greater compressibility and expandability. The expansion of the gas is so great that it overtakes the geometric expansion of the channel. The swelling gas is forced to flow faster and faster even through the growing cross-sections of the channel. Therefore, the flow velocity in the supersonic expansion of the nozzle increases and the gas density decreases. Laval proposed this nozzle shape and obtained a supersonic flow at the exit. A nozzle with a contraction-expansion geometry was called a Laval nozzle.
Ways to achieve supersonic sound
Note that it is not only the changing geometry of the Laval nozzle that can accelerate the flow to supersonic. Supersonic nozzles with constant channel geometry are possible, just with a straight pipe. There are three types of them: mass, thermal and mechanical. And they all work on the principle of reversal of impact. The mass nozzle has perforated walls. In the subsonic part of the pipe, gas is pumped inward through the perforations of the walls. To pass an increasing amount of gas through the pipe, the gas is accelerated, reaching the speed of sound. And after the speed of sound, the effect changes to the opposite - the gas is pumped out of the pipe through the holes in the walls. What causes expansion (there is much after pumping out) and acceleration of the gas remaining in the pipe. To accelerate the flow, the gas mass flow rate changes - therefore, the nozzle is called mass.
The other two are purely theoretical. Heat nozzle - when moving through a constant pipe, the gas heats up, reaching the speed of sound. And after that, the gas is cooled with supersonic acceleration. The mechanical nozzle supplies energy to the gas by mechanical force, and behind the speed of sound it also mechanically removes energy to accelerate the supersonic flow.
The Laval nozzle is a special case of the principle of reversal of influence, its geometric avatar. Two opposite funnels with a common bottleneck. It is such a nozzle that is widely used in practical matters. Since reaching the speed of sound radically changes the behavior of the flow, the speed of sound has been called the critical speed. And the section of the nozzle (always the smallest), in which the speed of sound is achieved, was called the critical section of the nozzle.
In the converging subsonic part of the nozzle, the gas density changes insignificantly, it expands slightly. But its pressure and temperature are significantly reduced - the speed increases mainly due to them. These parameters fall most steeply in the critical part of the nozzle, in the zone of the speed of sound. The change in action keeps these flow changes further in the supersonic section by adding gas expansion. Therefore, the flow rate continuously increases in both parts of the nozzle - both subsonic and supersonic.
A subsonic gas flow behaves like a river flow, an incompressible liquid that retains its volume. Absolutely? No, as the speed increases, the air flowing around the body is gradually compressed, but insignificantly; the compression ratio does not exceed the first tens of percent. This does not fundamentally change the flow pattern, leaving it within the framework of hydrodynamics, or "hydrodynamics for air" - aerodynamics. The picture remains this way until the sound Rubicon.
Gas dynamics lies behind the speed of sound. Here the compressibility of the gas is fully manifested: it contracts and expands many times, many times and tens of times. This radically changes the flowing volumes and creates critical changes in the picture.
A supersonic flow behaves in the opposite way to a subsonic flow - it slows down in contraction, and accelerates in expansion. If it slows down, it does it abruptly and instantly, always with compression of the volume and heating, forming sharp boundaries of compaction inside itself. And finally, supersonic flow can flow towards high pressure - for example, into this very seal.
Another nature of the driving force allows the supersonic flow to flow against the pressure drop. The prevailing is not the gas pressure, as in a subsonic flow, but the force of inertia of motion. The behavior of the subsonic flow is controlled by the thermal essence - the potential energy of the gas pressure, and the supersonic properties of the flow are created by another form of energy - the kinetic energy of motion.
Wasp waist and overexpansion
Classic rocket engine nozzles are funnel-shaped tapers and flares with a narrow wasp waist between them. It is narrow due to the high density in the combustion chamber. The compressed gas can expand many times, while still maintaining a tangible impact on the nozzle walls and creating thrust. The main expansion begins when approaching the speed of sound and continues throughout the supersonic part of the nozzle. In which the ratio of the final area to the initial, that is, the area of the nozzle exit and the throat section, was called the expansion ratio of the nozzle. How much can you expand (and therefore accelerate) the gas inside the nozzle? In space, the rarefaction of the flow at the nozzle exit is brought to a practically recoverable benefit - as long as the addition of thrust on the extension of the nozzle justifies the increase in its mass. Unused residual pressure is dumped into the void of space.
When starting from the surface of the Earth, the atmosphere presses into the nozzle, preventing the outflow. The jet flies out from the nozzle of the atmosphere expanded more strongly - the density and pressure of the jet are lower than atmospheric. Such a jet is called overexpanded, and the nozzle operates in overexpanded mode. The more rarefied the flow at the nozzle exit, the greater the pressure drop with the atmosphere and its counteraction to the jet. The overexpanded supersonic jet, due to its high speed, leaves the nozzle against a drop of half the atmosphere, or even more. And it is inhibited by the atmosphere behind the nozzle.
Here it is, the working property of a supersonic flow to move towards higher pressure. If this difference grows even more, atmospheric pressure will squeeze into the nozzle and begin to squeeze the jet away from the walls, “turning off” this section of the nozzle. Thus, to slow down the jet while still in the expansion of the nozzle, not allowing the thrust to grow - the mode of blocking the nozzle by external pressure will begin. Why expand the flow at the nozzle exit below the atmospheric pressure? Because its pressure drops rapidly with an increase in altitude, to which everything impetuous will leave the rocket.
The first fifty kilometers of the vertical will smoothly zero the atmospheric backpressure.
The flow at the nozzle exit will become denser than the decreasing atmosphere, throwing out excess pressure to no use. The stream, compressed more densely than the atmosphere, is underexpanded to equality with it. He would expand his smog more, making the thrust a little stronger. This is the underexpansion mode. To reduce unnecessary discharge of unused nozzle pressure, the expansion ratio is optimized. That is, it is calculated so that the integral losses during the operation of the ascending nozzle are minimal, and the work done by the reactive force is greatest for the entire flight segment.
For this, the pressure at the nozzle exit is calculated to be equal to atmospheric pressure at altitudes of 8-12 km. Here, the operation of the nozzle is optimal - there are no pressure drops with the atmosphere, and there are no losses. The initial overexpansion smoothly decreases with height, zeroing in the optimal outflow mode by 10-12 km, after which the underexpansion will gradually increase. So the nozzle, as the rocket rises, goes through three modes of its operation. And the choice of pressure at the nozzle exit gives the smallest integral losses all the way to the shutdown point.
In the second and third stages of intercontinental and space rockets, the engines are launched in the absence of perceptible atmospheric pressure. Therefore, the expansion of their nozzles makes a noticeable b Olighter than the first stage. Space rocket engines also have large expansion ratios - orbital maneuvering, orientation. Their supersonic parts resemble large goblets with a small critical section eye.
Large family, or Variety of nozzle gas dynamics
The principle of the presence of a critical section is implemented in a huge variety of forms. The classic two funnels, transmitting the flow to one another through the merging of vertices, can change beyond recognition. The slotted nozzle is a flat channel with contraction and expansion. Central body nozzles can barely change the outer diameter; the inner central body defines the channel geometry. It can be conical or bullet-shaped, and ends at the nozzle exit, and the critical part turns out to be annular. The central body can vary widely, completely changing the shape of the nozzle.
The nozzle can consist of one central body, which is enclosed along the base by an annular slot. The compressed stream from the slot flows through the central body, expanding on it. Such a nozzle has the form of a backward-directed concave cone. The concavity works in the same way as the cup-shaped bulge of the wall of a conventional nozzle. Only the nozzle with its wall compresses the edges of the diverging flow into an even flow, and the central body forms a straightened core of the flow.
This is how a wedge air motor works. Its nozzle is linear - the central body is elongated horizontally and forms an inverted wedge, similar to a saber blade with two sides converging to the blade. On these working concave sides, the supersonic flow expands, creating thrust. Functionally, the sides are the wall of a conventional nozzle, unfolded in a line, creating thrust in the same way.
This wedge is flowed from top to bottom by a supersonic stream from small combustion chambers mounted in a close row at the top. Each side of the wedge becomes one nozzle wall for the flow from the chambers. The other wall is the atmosphere, which compresses the flow from the side and regulates its expansion with its pressure. Therefore, the flow on the surfaces of the wedge-air-wedge nozzle expands optimally, adapting to changes in atmospheric pressure.
The central body can become flat, like a plate, and be located at the depth of the nozzle, at the beginning of its expansion. Like the head of a nail, not completely driven into the middle of the critical section. The space under the cap will be the subsonic part of the nozzle. And the edges of the disc-shaped body will become the inner part of the critical section. The flow spreads radially from under the plate and turns around its edges towards the nozzle exit, being squeezed by the walls and accelerating into a supersonic jet. The poppet nozzle is much shorter than the conventional nozzle and therefore lighter. Its peculiar gas dynamics is fully consistent with the Laval nozzle.
Less pressure, more power from record giants
High pressure requires strong and thick walls of the combustion chamber, it is easier to lock it in a small chamber. The mass of a large structure with high pressure will also be large. In solid fuel engines, the entire body is a combustion chamber. Therefore, the pressure in them is lower than in liquid-propellant rocket engines, reaching only the first tens of atmospheres. Since the pressure in front of the nozzle is lower, it means that the degree of expansion of the nozzle and the narrowing in the throat section are less. For example, a teenager can freely pass through the throat of the nozzle of a solid fuel accelerator SLS. With a nozzle exit diameter of 3, 8 m and a critical section of 1, 37 m, the expansion ratio is about 7, 7. The average pressure level of 39 atmospheres does not allow setting a large expansion ratio.
The thrust is created not by the flow rate itself, but by the flow rate at this speed. Solid propellant engines can create a huge flow rate of the working fluid through the nozzle. They have no fuel supply - all of it is still supplied at the plant along the entire length of the engine, sometimes reaching tens of meters. Such a fuel massif has a huge combustion area and a corresponding flow rate, which creates a very large jet thrust.
The most powerful engines ever created by man in history are solid-propellant rocket engines. Of the serially produced boosters for the SLS launch vehicle, the former Space Shuttle boosters with an added fifth fuel section. With a total length of 54 m (this is the height of an 18-storey building), a diameter of 3.7 m and a mass of 726 tons, their thrust is 1620 tons, and the consumption is 6 tons per second. The nozzle of such an accelerator is today the most powerful serial nozzle in the world.
The experimental solid propellant engines were even more powerful. The Aerojet AJ-260 SL-1 tested in 1965 showed a thrust of 1,800 tons, and the Aerojet AJ-260 SL-3 engine was supposed to produce 2,670 tons of thrust. Their single nozzles remain the most powerful Laval nozzles ever made by humans.
Variable geometry in the thunder of afterburner
Nozzles with even lower pressure, with a difference of only a couple of atmospheres and a very small constriction, have become widespread in aviation, becoming an indispensable solution for a whole class of engines. Since it is impossible to store a lot of energy in a small pressure, here they go by the thermal path - they pump gas with the heat of a powerful kerosene fire.
Afterburners are used primarily in combat aircraft. They use the afterburner when flying at supersonic, to reduce the takeoff roll, rapid climb, and intense maneuvering. Afterburner is almost a twofold increase in thrust, with a manifold increase in fuel consumption. It is burned in the general flow behind the turbine, in a piece of the flow path before entering the nozzle, called the afterburner. Its nozzles form a huge kerosene burner that heats the flow in front of the nozzle by a thousand degrees.
The nozzle, being a heat engine, converts an increase in heat into an increase in speed.
Such a strong additional heating of the gas will increase the pressure in front of the nozzle. This will reduce the speed of the turbine and compressor, which will immediately reduce the air flow to the nozzle. To avoid a collapse of the engine operation, the critical section of the nozzle is expanded, "dumping" the growing pressure into it. This is done by fifty movable elements - sashes. Trapezoidal cast plates of heat-resistant and heat-resistant (these are different properties) steel overlap, like scales or tiles, forming the working surface of the nozzle. Moving in concert by hydraulic cylinders, they change the internal constriction, while simultaneously changing the nozzle cut. Thanks to such a movable design, the nozzle keeps the gas expansion close to optimal and adapts to the engine operating mode, allowing a strong increase in thrust during afterburner. And after switching off the afterburner, the nozzles are displaced back, reducing the critical section and the size of the nozzle exit.
The Laval nozzle is used in a myriad of jet devices. In all types of missiles flying in the air - from space and intercontinental to anti-aircraft and anti-tank missiles, salvo shells, rocket-propelled grenades, and an endless variety of other rocket-propelled flying bodies. There are also known jet bullets, and of different types - for example, experimental underwater bullets for the APS submarine machine, similar to thick green spokes with a jet engine with a diameter of 5, 45 mm. Or the half-inch (12.7 mm) rotating Gyrojet rocket bullets with four tiny oblique nozzles, tested in Vietnam in the early 1970s, along with a special pistol for them. These were the smallest combat missiles in history.
The nozzle block can consist of one channel, or several, or dozens of nozzles. The dimensions, shape, number, location, inclination, thrust, purpose of these nozzles vary over the widest range. The jet nozzles divert the ejection pilot seat from the aircraft, gently land the landing equipment and descent vehicles, accelerate the illumination rockets and signals, reduce the recoil of recoilless guns, throw detonation cords for demining, set aside the launch yokes during the mine launch of ICBMs, and perform a host of other tasks, reactive force.
A person produces supersonic flow with a Laval nozzle almost everywhere he uses it. In turbines, slotted Laval nozzles accelerate the flow to be supplied to the rotor blades. In supersonic jet turbines, the channels between the blades of the movable disk are also slotted Laval nozzles, which accelerate the gas to supersonic speed. Each two adjacent blades form with their surfaces a channel of a flat Laval nozzle bent backward at an angle. The flow in it is accelerated and flows back to the motion, creating a reactive force for the blades. Supersonic turbines are used in aviation and astronautics, ground technology and navigation, energy and energy production.
It is possible to grind the material with a supersonic flow, obtaining a fine mill. Bulk material enters the supersonic jet. It is captured and accelerated by a jet that hits a solid barrier, and breaks against it at a speed of many hundreds of meters per second. High purity of grinding - the material itself pricks against the obstacle - allows you to grind medicines or highly purified chemicals.
Supersonic wind tunnels also use a Laval nozzle. The most common type of supersonic tube is balloon. In a large room, there are two or three rows of thick steel cylinders of two-storey height, covered by a rack second floor (to get to the top of the cylinders when needed). A couple of days before purging, the cylinders are pumped all day with air under the hum and vibration of the compressor. Their bodies are very hot from compression far beyond a hundred atmospheres, then they cool down overnight.
Purging takes place in a separate box with steel doors. All the air stuffed into the cylinders is discharged in thirty seconds. The nozzle converts the compressed air of the cylinders into a supersonic flow flowing in the working part of the pipe. Small in cross-section, it is assembled from strong steel elements that enclose the flow with the blown model. A bonus is the simulation of a supersonic flight at high altitude with its frost - from the expansion of the flow, the temperature in the test section is minus 80 degrees. The Mach number of the flow in the pipe can exceed 5, then the pipe becomes hypersonic.
In one of the Moscow universities with a vast but intricate courtyard, in one of its nooks, there was a lattice booth that looked like a kiosk. The auditoriums of the English language department went into this part of the courtyard. Once a week, classes were interrupted for half a minute by a wall of continuous rumble, which completely drowned out any attempts to speak by teachers and students. The lattice booth hid the outlet channel of the supersonic pipe of this university, flooding the courtyard with a roar during the purge. Thus, supersonic aerodynamics invaded all areas of science that came out as auditoriums to this booth.
Ludwig Prandtl, the pioneer of supersonic calculations and the founder of supersonic aerogasdynamics, was able to calculate the nozzle giving the required Mach number at the available flow rate. In 1909, he built in Germany, in Göttingen, where he worked, the world's first supersonic tube. Today all nozzles are counted according to his method of calculating a supersonic nozzle.
Calculations allow you to profile the nozzle. Profile is the curvature of the nozzle shape, which distinguishes it from a simple cone, the exact geometry of the nozzle. In the critical section, the expansion of the gas is the most intense, and immediately after it it is necessary to quickly give the gas a volume for expansion. The walls of the nozzle here diverge to the sides with a steeply expanding bell. At the end of the nozzle, when the expansion work is done, the flow is directed by the cylindrical edge of the nozzle into an almost parallel stream.
The smooth transition from the sharply expanding part to the almost cylindrical edge makes the nozzle convex, similar to a glass or a bell. This will be the profiled nozzle. Correctly chosen curvature of the walls will expand the gas optimally, with the greatest acceleration of the flow at the shortest length of the nozzle. These are the minimum weight, cooling surface, material and processing volume, and cost. Therefore, almost all nozzles are profiled today. Their profile is calculated according to the given parameters of the source gas and the desired flow, making it possible to mold the best curvature of the vessel for supersonic sound.
Potential Key to Full Rocket Reusability
The nozzle can also become the main solution to the complete reusability of launch vehicles. The problem of returning the second stage of the rocket is due to its high orbital speed. The stagnation temperature of the flow at this speed, which occurs at the stage at the entrance, reaches several thousand degrees.
You can make a nozzle that takes up the entire bottom end of the step. Then its fire-resistant surface can act as a heat shield. In this case, the metal nozzle is actively cooled by the fuel component flowing in the channels of its walls. And the component itself, flowing out through the nozzle without combustion, will squeeze the pillow of hot, shock-compressed air from the end of the stage. The edge of the step wall can also be occupied by the cooled edge of the nozzle. Thus, strategically integrating the nozzle into the base of the step. Then the nozzle will be able to solve two tasks separated in time - both the creation of thrust and the thermal protection of the stage when entering the atmosphere. Probably, having formed a new type - a reactive heat-shielding nozzle.
Such a nozzle will add a heat-shielding task to its basic gas-dynamic function (flow acceleration), increasing its value.
It takes a lot of calculations that will find the optimum of one design for both problems. With such a large nozzle diameter, a conventional elongated supersonic glass becomes too bulky and heavy. A nozzle with a central body or a poppet nozzle will turn out to be much easier. Their area is several times smaller, requiring less cooling. You can give the "saved" cooling to the adjacent step walls. Evaluation of such decisions will be given by the calculation of specific projects.
In 2020, the American firm Stoke Space Technologies received two grants through SBIR (Small Business Innovation Research). It is a US government research and development (R&D) program to help small businesses. The nine-member team is led by Andy Lapsa, director and co-founder of Stoke, who has been building engines at Blue Origin for ten years. His team is focused on the development of a reversible upper stage engine.
An SBIR grant of $ 225,000 was issued by the National Science Foundation for "an integrated, reusable upper stage power solution." The grant summary “proposes to develop a new technology to allow space launch vehicles to re-enter the atmosphere and land at a given point with reuse. Technical challenges include a combination of a highly efficient propulsion system, reliable thermal protection and a lightweight structure.” The article considers "a new technical solution that combines the main characteristics of a stage with the efficiency of a separate system (talking about a cooling system. - Author's note), which allows reuse of the second stage."
Another SBIR grant of $ 125,000 was received from NASA for "a new rocket engine configuration for booster stages and planetary landing modules." The grant summary speaks of “a new geometry for the rocket nozzle, which has not been previously considered and on which the focus of the first phase. The nozzle provides a high expansion ratio with dimensions ten times shorter than traditional bell-shaped nozzles, and allows for deep throttling at atmospheric pressure. When integrated into the base of the stage, the engine nozzle serves as an actively cooled metal heat shield during reentry. The first phase includes the development of the nozzle design methodology, forecasting of the nozzle performance and the manufacture of equipment for parameter testing."
Time will tell how fruitful Stoke's efforts will be. But the formulation of the tasks speaks of an urgent need for a breakthrough to a reusable second degree. And the nozzle is a possible key solution for fully reusable rockets.