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Tallinn University of Technology. Introduction to Astronautics Sissejuhatus kosmonautikasse. Vladislav Pust õnski 2009.
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The rocket is a device that should deliver its payload to the target. It should follow the right path, often guided by its own systems, and should maintain stability so that it do not wander off its trajectory. Let us look in detail how these issues are addressed.Navigation, guidance & steering of rockets
Stabilization and steering
The thrust produced by the engines is applied to the rocket in points different from the center of mass. According to the laws of mechanics, it gives rise to torques (moments of force) in the general case. These torques try to rotate the rocket around its center of mass faster and faster. There are no torques only if the center of mass lies on the line of the resultant force. The rocket should move along the path defined by the flight profile, so the rotations of its body are predefined as well; these rotations should be provided by the guidance system. This means that torque should be controlled and the guidance system should be able to change it.
However, steering is unavoidable in the simplest case as well, when the rocket should fly along a straight line (for example, performing an orbital change maneuver). The problem is that a rocket device is unstable in the general case. Even with a fixed-mass device it is impossible to ensure that the center of mass lies exactly on the line of the resultant force. Tolerances at installation of engines and other devices would necessarily create some moment arm. The real situation is even worse, since the forces and the position of the center of mass change in flight. During the flight in the atmosphere, varying lift forces act to the body of the rocket, and the mass of the rocket changes along the trajectory. The level of the propellant drops, large amounts of liquids in the tanks wave, the propellant sloshes, the body of the rocket is subject to various oscillations, separation of parts like nose fairings and interstages occurs, etc. These factors lead to quick shifts of the center of mass.
Due to these factors the rocket body is subject to variable torques, so its flight would be unstable without steering. A popular misconception exists that rockets are unstable since their center of mass is placed in front of their engines, and the forces are applied in the tail. Even Goddard built his first rockets so that the engines were placed in front of their center of mass. This misconception arises from the wrong analogy of such rocket (with engines in front) with a suspended pencil which is stable, while a standing pencil (analogous to a rocket with engines in the tail) is unstable. However, a suspended pencil is stable due to the reaction of the suspension: small angular deviation from the equilibrium position gives rise to the reaction force that returns the pencil to the equilibrium. In the case of a standing pencil, the reaction of the support forces the pencil to deviate more and more from the equilibrium. As for a rocket, the reaction force of exhaust gases does not depend on the rocket attitude, so small rotations do not lead to appearance of any change of this reaction. That means that the rocket is indifferent to angular deviations: they are not amplified nor dampen, and the rocket simply continues to rotate if there is some torque. By the same reason, a rocket with multiple engines in the back is not more stable in the least than a rocket with one engine, as one may think taking as an analogy a one-legged and a four-legged chair. It is the support reaction force that makes a four-legged chair stable, since if the chair is inclined, the reaction of the support on the lower side increases and returns the chair to stability. No reaction force changes in the case of an inclined rocket, thus it does not become stable if it has more engines in the back.Rocket rotations
The angular motion of a rocket may be represented as rotation about three independent axes which are mutually perpendicular (as for each 3-dimensional body). The choice of these axes is natural for a launch vehicle, since it has a “nose” and a “tail”, and it is also possible to distinguish “up” and “down” (although sometimes it is done by convenience only, since the
rocket may be axisymmetric or have nothing to distinguish the “upper” and the “lower” side). For a satellite distinguishing between the “nose” and the “tail”, the “up” and the “down” may be even more conventional, but it is always done someway.
A natural choice of axes is “nose – tail”, “up – down” and “left – right”. The nose-tail axis is called the roll axis, the up-down axis is called the yaw axis and the left-right axis is called the pitch axis. The corresponding rotations are called rolling motion, yaw motion and pitch motion, or simply roll, yaw and pitch. These are so-called Tait-Bryan rotations. The positive direction of rotation is clockwise if looked from the tail, from the downside and from the left side.Stabilization & steering methods
The above-mentioned arguments demonstrate that rocket devices need stabilization for a normal flight. Rockets may be compared to a pencil on the finger tip: it may stand only if the hand reacts to each deviation from the equilibrium and returns it back to its unstable equilibrium position. In general, rockets should by stabilized by all three axes. Yaw and pitch stabilizations are unavoidable since otherwise the rocket would deviate from its path. However, in some cases roll stabilization may be avoided. This is the case of spin stabilization (when the rocket is intentionally wound round the roll axis, see further) or if rolling motion is slow enough not to destabilize the rocket by other two axes (body rotation is described by Euler’s equations, rotation around one axis may give rise to complicated angular motion around another axes). There is a number of practical methods used for stabilization. They may be divided into passive and active methods.
Passive methods include aerodynamic stabilization and spin stabilization. Aerodynamic stabilization is realized by placing fins in the tail part of the rocket, so that
aerodynamic pressure could orient the rocket axis along the air flow. For that, the center of pressure should be placed behind the center of mass, and the area of the fins should be sufficient for aerodynamic forces to overcome perturbational torques. This method is feasible only for the first stages of rockets which fly in dense atmospheric layers. Upper stages fly in very rarified atmosphere or nearly in vacuum and cannot be aerodynamically stabilized. Aerodynamic stabilization is also limited by the rocket size. The rocket mass grows as cube of its linear dimensions, so does the thrust. However, aerodynamic forces, being proportional to the area of the rocket, grow as square of the linear dimensions, thus efficiency of aerodynamic stabilization drops off with linear dimensions of the rocket, and the fins become too large and drastically increase the weight of the stage. The problem of this method is also that most of launch vehicles are aerodynamically unstable. They have heavy first stages with high mean density (due to kerosene and/or solid propellants), while the upper stages are ordinarily of lower mean density due to hydrogen fuel and voluminous nose fairing under which the payload is placed. These factors place the center of mass of the launch vehicle quite low, and it is generally below the center of pressure. To shift the center of pressure below the center of mass, large fins would be required. In the early era of rocketry, aerodynamic stabilization was the only stabilization method. The first ballistic missile V-2 also had large fins. Nowadays passive aerodynamic stabilization is rarely used on launch vehicles, since it mostly should be aided with other steering methods (to provide motion along the predefined curved path) and because of large weight of aerodynamic surfaces; however, even giant Saturn V had small fins to make the rocket a little bit more stable. However, the smallest launch vehicle, the first Japanese Lamda-4S rocket, had a fully aerodynamically stabilized first stage.
Another passive stabilization method is spin stabilization. The idea of this method is that the rocket is stabilized by rotation around the roll axis. If the rocket rotates quickly enough,
pitch and yaw torques try to incline the rocket in different directions in different moments of time, so the resultant deviation averages to zero. This method is often applied on small solid upper stages of launch vehicles because of its simplicity. A stage may be wound before launch on the launch vehicle, in this case the stage sits on a special spin table mounted on a bearing on the lower stage, like it was done on the Juno I and on the Payload Assist Module (PAM) based on the Star 48 solid rocket motor on the Space Shuttle, the Delta and the Titan launch vehicles (rotation frequency is about 60 rpm). A stage or a spacecraft may be also spun by motors, the thrust of whis is directing out of the plane of the roll axis (like historical Hale rockets in the 18th century). After launch the spacecraft rotates with the spin-stabilized stage and may need to be de-spun. Motors may be used, but enother mechanism known as yo-yo de-spin is also applied if the rotation frequency is too high and the attitude control system cannot cope with it. To cables with weights (yo-weights) are wound round the payload and fixed. For de-spin they are released. Angular momentum transfers to unwinding weights and spinning slows down. Sometimes only one yo-weight is used. Its release forces the spent stage to tumble, and the impulse of aftereffect (that may cause the spent stage slam into the payload) averages over different directions, so the stage cannot come closer to the payload. Spinning of a spacecraft may play other roles as well, like uniform exposition to the Sun to avoid excessive heating and/or uniform illumination of the solar cells placed around the spacecraft. For instance, the Apollo CSM had a roll rotation of about one rpm for uniform heating during its flight to the Moon and back, the Pioneer 6, 7, 8, 9 probes had solar cells around their cylindrical body that needed uniform illumination.
Active stabilization methods are quite diverse, they are based on active steering and are often used not only to keep the attitude of the rocket, but to change it. Most of the launch vehicles follow their paths thanks to continuous attitude control. Let us take a closer look to these methods.
One of the oldest methods are movable air vanes. Changing positions of these vanes, it is possible to control aerodynamic forces influencing the rocket. As well as air fins, this method is applicable only on first stages of launch vehicles and only on smaller ones. The V-2 was steered by air vanes, and also the Juno I, the first US launch vehicle. Air vanes lead to permanent increase of the structure mass and additional permanent drag losses.
Jet vanes is another method which appeared quite early. The idea is that an inclined refractory vane is placed into the jet and redirects the thrust vector creating torque. The major problems of this method are as follows. First, it is difficult to find a material which could withstand high thermal and pressure loads inside the jet for a long time (several minutes); the shape of a vane changes due to partial burning. Second, a jet vane decelerates the flow thus diminishing the specific impulse and the thrust. The loss of efficiency is permanent since jet vanes obstruct gas flow even when no control interventions are performed. So, jet vanes are mostly used on devices where the engine works for a short time, these are some winged and ballistic missiles, and this method is not widespread now. However, the Juno I, as like as the Redstone and their predecessor V-2, had jet vanes. They were also used on the Soviet launch vehicle Kosmos (based on the ICBM R-12).
Another steering method is gas or liquid lateral injection into the nozzle. This flow plays role of vanes, thus no refractory materials are needed. The gas may be redirected from the thrust chamber or be taken from a separate supply. Fluid is injected through two pairs of opposite slits, one pair for the pitch and another for the yaw. A pressure jump appears near the injection zone. This jump is not uniform, but integrally it gives rise to a force in the direction of the slit from which the fluid was injected. The physical reason is deceleration of the gas flow. This method leads to some decrease of the specific impulse and of the thrust as well, however this occurs only during control interventions. Such system based on freon injection
into the nozzle was used on the first and the second solid stages of the Japanese Mu-3 and M-V series of launch vehicles (except for the last M-V-II, where moving nozzles were used).
Gimbaled engines is one of the most wide-spread methods nowadays. The idea of this method is that the engine is mounted on a Cardan joint that enables to tilt the engine in two perpendicular directions up to certain limiting angle (several degrees in most cases; for the first stage of the Saturn V it was 70). The engine tilt creates a moment arm, so torque appears. Varying the tilt, it is possible to vector the thrust and so to steer the rocket. Gimbal actuators are usually driven with hydraulics (or by electricity) If there is only one gimbaled nozzle on the rocket axis, only the pitch and the yaw may be controlled, the rolling should be steered in other manner (for instance, with a special small engine as it would be done on the first stage of the future Ares I launch vehicle, which has single engine solid stage with a gimbaled nozzle). However, if there are more than one nozzle, the roll may be controlled as wekk. For that, twin nozzles are tilted in opposite direction, and a roll torque appears. In the case of a liquid propellant engine, usually the whole engine is gimbaled. It is not possible in the case of a large solid rocket motor, thus such motors are provided with movable nozzles tilted with actuators. However, the RD-170/171 engine is not gimbaled as a whole, but four its thrust chambers may be gimbaled separately using bellows. So the Zenit launch vehicle, which flies with a RD-171 on the first stage, is controlled in the roll channel as well. Often only a group of engines are gimbaled while others a fixed, as it was on the Saturn V, where the central engine was fixed on both the first and the second stages, and four outboard engines were gimbaled. On the Saturn I/IB, four central engines were fixed and four outboard engines were gimbaled. Sometimes a group of engines is gimbaled only in the pitch channel and another in the yaw channel, as it was done on the Energia launch vehicle. Gimballing engines do not lead to decrease of the specific impulse nor the thrust, however, the effective thrust
(along the axis of the rocket) diminishes due to appearance of a non-axial component.
Gimbal is effective only if the engine is far from the center of mass and so can create a significant moment arm. This condition is satisfied for most launch vehicles, but on spacecraft it should not necessarily be so. For example, in the Ascent Stage of the Apollo Lunar Module the engine was very close to the center, thus gimbal would have been useless; this stage was steered only by small attitude control motors. The engines were gimbaled on all other stages of the Apollo spacecraft.
Stabilization and steering with special vernier engines (or steering nozzles) is also one of the most wide-spread methods. Small engines (or, more generally, nozzles) the thrust vector of which do not pass through the center of mass create controlling torques and rotate the rocket about its axes. To vary controlling interventions, the nozzles may be gimbaled or, alternatively, their thrust may vary. Verniers may be organized in different ways. These may be small separate engines consuming the same components as the main engine and even organized with it in a common assembly, as it is done on the RD-107/108 engines of the Soyuz rocket, where steereing nozzles were installed (2 and 4 respectively). Another reason for using verniers on the R-7, the predecessor of the Soyuz, was to diminish the effects of the impulse of aftereffect: the main engines had been cut off shourtly before the required velocity count was intergrated, and the steering engines continued to work until the required velocity was achieved. Verniers may be a stand-alone assembly, as the vernier engine for steering in the roll channel of the future Ares I aunch vehicle. Sometimes verniers are organized in special assemblies, as it was on the Apollo spacecraft (both CSM and the Lunar Module; the verniers of the LM had separate tanks but also took some propellant from the main tanks of the Ascent Stage). In some cases no there are no special vernier engines provided, and gas from the turbine of the turbopump is used for steering, it is directed to special gimbaling
vernier nozzles. Such design was used, for example, on the Luna-16/17 and other E-8 lunar probes. If separate engines are used as verniers, their mass and the mass of their propellant increase the mass of the structure.
One of the rarely used methods of steering (possible only on multi-engine rockets) is thrust differentiation, when control torques are provided by varying thrusts of the opposite engines. This method was applied on the Soviet lunar rocket N1 (probably it was the only launch vehicle where it was used; however, later vernier engines were also added for better roll control). Nearly no losses are related to this method. Its greatest problem is that there should be enough engines on the rocket and their distance from the rocket axis should not be small, so that the moment arm were sufficient. It is also useless with solid rocket motors.
Other attitude control methods used on spacecraft will be discussed in the further lectures.
To keep the rocket on its predefined trajectory during launch (or performing other maneuvers in space), the rocket should be actively steered. First of all, its attitude should be stabilized and controlled to keep the rocket on the required path. In the previous section we have got an overview of the steering methods, now let us look systems and instruments used for guidance and navigation.
There are three essential conceptions related to the issue: navigation, guidance and control. Navigation is a group of methods to define the position and the attitude of the rocket, guidance uses navigation data and other information (following the target, for instance) to keep the rocket on its path, control is realization of commands issued by the guidance system to reactions of the actuators.
All launch vehicles and most of spacecraft are provided with autonomous navigation. That means that on-board devices are able to determine the attitude of the rocket, its velocity and accelerations. However, frequently additional outer sources of data are used. These may be commands form the Earth, stellar navigation (on many interplanetary probes, but also on satellites, manned spacecraft and also ICBMs), GPS data, horizon finding system, radar or other location of the surface (at landing on a celestial body), etc.
Nowadays the autonomous navigation is mostly based on the properties of gyroscopes to keep the initial preset direction for long periods of time. The attitude of the rocket may be measured with gyros by determination of angles between the preset position of the gyro and the position of its suspension fixed relative to the rocket. It is also possible to measure angular velocities with the aid of gyros. Accelerometers make it possible to find accelerations of the rocket, their working principle is measuring spring deformation by a mass, or some equivalent method. Since the working principle of gyros and accelerometers is directly related to inertia, navigation systems based on such devices are called inertial navigation systems (INS), or inertial guidance systems. These systems are based on the so-called inertial measurement units (IMUs), which contain the corresponding set of gyros and accelerometers. Together with the computer (digital or analog) which process the data and sends signals to the guidance system they form the inertial reference platform.
Gyros provide information on angular velocities of the rocket, while accelerometers give linear accelerations. Integration of the angular velocities gives the attitude of the rocket relative to the fixed axes, integration of the accelerations gives the linear velocities and double integration of the accelerations gives coordinates. So the position and the attitude of the rocket relative to the external reference frame may be determined independently.
However, data from the inertial reference platform contain errors which appear due to
limited precision of the instruments and tend to accumulate. It is also important to point out that inertial navigation does not account for gravitational accelerations, since mechanical phenomena onboard the rocket are independent (with high degree of precision) of gravity fields. Thus, all phenomena onboard the rocket falling in the gravity field of a planet are the same as they would be if the rocket were in deep space. By these reasons other data are often used for navigation together with INS data, specially in long flights. Space probes take information about their attitude from the solar sensors and stellar sensors. Ground link telemetry was used to correct trajectory of the first ICBMs. Positions of satellites are defined using GPS signals. Action sequences of probes performing planetary landings are based on data gathered by optical observations of the surface, radar location data, sometimes laser location, gamma-ray sensors etc. Crews of manned spacecraft are often also present in the control loop. For instance, precision of the inertial guidance platform of the Apollo spacecraft was such that it needed human interventions from time to time: the crew oriented the spacecraft manually using stellar observations.
Besides the navigation tasks, the stabilization problem should be solved as well (since, as we have already seen, rockets are generally unstable). If the rocket is not passively stabilized, stabilization data is issued by similar (or same) instruments and sensors as navigation data. Often the stabilization and the navigation system are actually a single system, both tasks are performed by the same devices.
Gyros, accelerometers, sensors are the measuring instruments of a rocket. Their signals should be processed and corresponding control commands should be issued and sent to actuators of the devices described above. The guidance system is responsible for this task. This system is based on a computer, which is an analog or digital device. The first such computers were, of course, analog and they appeared in the beginning of the 20th century on
torpedoes. They became much more sophisticated, but remained analog till mid 1960th, when digital computers became compact enough to be placed onboard ICBMs and launch vehicles. However, even nowadays some simplest systems are still analog.
The most simple guidance system had, obviously, the first Japanese Labda-4S rocket, where the first three stages were unguided: the first stage was aerodynamically stabilized and the next two stages were spin-stabilized. Only the fourth stage was oriented relative to the attitude of the only gyro, the stage was spun for stabilization and the instrumental unit was separated before the engine of the fouths stage was fired. The guidance system of the Juno I was also simple, only the first stage was guided. Some rockets are not controlled in all three channels. For instance, the Luna E-8 probes were not controlled in the roll channel. For the sake of simplicity and reliability, simplified guidance methods may be realized. The Soyuz launch vehicle up to the latest modernizations is put on the correct azimuth by rotation of the launch pad, since its guidance system is not designed to control azimuth autonomously. The Luna E-6 probes (Luna-9/13) had simplified landing sequence: thanks to the properties of their trajectories, it was possible not to determine the attitude of the probe relative to the Moon and so not to measure and cancel separately the vertical and the horizontal velocities. Instead, at a certain moment the probe oriented itself along the local vertical line and later could begin the decelerating burn (by a signal of the radio altimeter) without any change of its attitude. Thus, there was no need to continuously control the attitude and the position along the trajectory, it was enough to keep the attitude. A similar method was used on the return rockets of the Luna E-8-5 sample probes (Luna-16/20/24). Before launch from the Moon, the local vertical direction was determined by a pendulum system in the instrument unit of the descent stage, the gyro on the ascent stage memorized this direction and during the ascent the guidance system only had to keep the rocket on this straight path. The engine was cut off by a
signal of integrator that integrated the acceleration until the predefined speed was reached. Such simplified solutions may be needed when the weight available for the navigation system is limited; but they restrict additionally the trajectory and on the mission as a whole (for instance, the Luna E-8-5 could deliver samples only from the Eastern side of the lunar disk). However, the computer era and complex digital devices, having introduced high flexibility and having increased the performance, brought new problems as well. While analog devices are generally very reliable, digital devices may suffer from failures caused by radiation, their programming is potentially related to possible errors and needs complex testing works. One of the most expensive failures of a launch vehicle occurred in Jun 1996, when the first Ariane V exploded, since a program error resulted in wrong commands sent to the nozzle actuators. They forced the rocket to rotate to angles at which it could not withstand aerodynamic forces and desintegrated. The Space Shuttle has three computers onboard which check continuously each other and each one runs independent realization of the control algorithms.
There is a number of methods how control and guidance may be performed basing on the data provided by the navigation system. The Control theory is the discipline addressing these issues. Let us recall the principle concepts related to the problem.
An open-loop control means that the system does not analyze the results of control interventions and issues commands following a pre-programmed pattern. Such simplistic way of guidance may be met, for instance, in a spin-stabilized stage which accelerates during a preset time or until propellant depletion; in a timer-controlled operations onboard a spacecraft; etc. Close-loop control is used very often: if applied, control interventions depend on the results of the previous ones. The most simple example is engine cut-off by a signal of the integrator of accelerations. Active stabilization is impossible without closed-loop control, since the magnitude of each control intervention should depend on the current attitude of the
rocket. Thus, the output is fed back into the input through the rocket attitude, and the control loop is closed through the body of the rocket.
A different concept is open-loop navigation. While control points the rocket to the desired direction, navigation determines the path where to point. Open-loop navigation is the simplest approach. It means that if some deviation from the preset path occurs, the system tries to return the rocket to that path. For instance, if the attitude of the rocket changes, the system simply commands to restore the attitude, not taking care if the new trajectory (shifted from the initial, since the rocket has flown with a wrong attitude for a while) is optimal or not. The close-loop navigation is a more sophisticated strategy. If applied, the system will not necessarily re-establish the initial attitude. It will compute in the real time a new optimal path and will send the rocket to this path. Implementation of this strategy needs more complex algorithms and quicker computers. The example is the Saturn V, where this strategy was implemented on the second and the third stages. However, an open-loop navigation was implemented on the first stage. This is because the first stage works when the rocket passes through dense air layers and is subject to intensive aerodynamic loads. Thus, the main task for the rocket at that time is to fly directly “into the wind”, not allowing any tilt relative to its velocity vector; otherwise the rocket may break. So it flies with a preprogrammed tilt angle to safely leave the dense atmosphere. The path of the rocket may deviate from the correct one due to winds and errors, but these trajectory imperfections are corrected by the second stage. On the very last seconds of the orbital injection the Saturn V also switched to an open-loop navigation and flied at a preprogrammed tilt angle. This is because residual errors at this point are so small that their elimination would cost more than the imperfections themselves.
The navigation and guidance systems of a launch vehicle are usually confined in one unit that is placed on the upper stage. Besides instruments and electronics, this unit include power
supply batteries, antennas for ground link, etc. Electric wiring connects this system with the actuators on all stages, vents, pyrotechnic devices etc., and also with sensors inside the tanks (they signal propellant levels), interstages and nose fairings (they signal the stages and the fairing separation) and others. The radio transmitter send telemetry to the ground link. If the upper stage of a launch vehicle is different in different flights (or may be absent in other flights), the upper stage may be provided with a separate instrument unit, the example is the Proton. Satellites and spacecraft have their own control systems independent of that of their launch vehicles.
Stick is unstable, any deviation from equilibrium should be met by a corresponding shift of the hand so that the stick could stand (By source)
Suspended body is stable, any deviation from equilibrium gives rise to a force that returns it to the equilibrium position (By source)
The first stage of Japanese Lambda-4S was aerodynamically stabilized (By source)
SBS-3 satellite with a PAM module released from the Shuttle cargo bay (By source)
Pioneer 6 Sun orbiter (By source)
Apollo 16 CSM on orbit around the Moon (By source)
Fins with movable rudders of the Redstone launch vehicle (By source)
Launch of a Redstone (By source)
Scheme of the launch vehicle Kosmos, view from side and from tail.
1) Jet vane supprot
3) Jet vane
Gas pass-by from the chamber to the nozzle (By V.I.Feodosjev, osnovy tehniki raketnogo poleta.)
Scheme of the Aestus, the upper stage engine of the Arian V. Gimbal unit is seen (By source)
Soyuz launch vehicle, the 1st and the 2nd stages. Small vernier engines are seen (By source)
INS of Minuteman III ICBM (By source)
IMU of the Peacekeeper ICBM (By source)
Gyrostabilized platform of Minuteman III ICBM (By source)
Due to simplified guidance system of the ascent rocket, all landing sites of E-8-5 are near the Eastern side of the lunar disk (By source)
Luna-16 on the surface of the Moon (By source)