10, GUIDANCE

A. THE GUIDANCE OF SPACE VEHICLES

The guidance process

The guidance process consists of measurement of vehicle position and velocity, computation of control actions necessary to properly adjust position and velocity, and delivery of suitable adjustment commands to the vehicle's control system.

Guidance phases

Guidance operations may occur in the initial, midcourse, or terminal phases of flight.

Ballistic missiles are commonly guided only during the initial flight phase, while rocket engines are burning.

A cruise type of missile, such as the Snark or Matador, uses midcourse guidance, operating continuously during cruising flight. Air-to-air missiles such as Sidewinder employ terminal guidance systems that lead the missile directly to the target on the basis of measurements on the target itself.

Any or all of these three kinds of guidance will be necessary for space flight, depending on the type of vehicle and mission involved.

Initial guidance

Space-flight missions in the immediate future will use ballistic rockets, and the guidance of such vehicles will be extensions of current ballistic missile guidance techniques. For ballistic missiles, guidance (sometime referred to as ascent guidance) is used only during powered flight, and guidance accuracy depends upon accurate establishment of flight conditions at the point of transition from powered to free flight. The necessary initial free-flight conditions are the position and velocity.

There is no single set of initial conditions required to arrive at a specified target, but rather there are an infinite number of possible free-flight paths originating at points in space in the vicinity of some nominal starting point which terminate at the desired destination. For each such point there is a corresponding proper velocity. It is the task of the guidance system to cause the rocket to take up any one of these free-flight paths. The path selected for a given flight is determined ad hoc by the system as a running decision process during powered flight, on the basis of a complex of criteria involving structural loading, propellant economy, accuracy, etc. This approach is used because of the extreme difficulty of guiding a rocket along a single fixed powered trajectory in the face of detailed uncertainties in engine performance, aerodynamic and wind effects, component weights, etc. While the number of acceptable trajectories is infinite, practical limits on rocket behavior actually restrict the usable range to a zone fairly close to a nominal "optimum" trajectory.

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68 ASTRONAUTICS AND ITS APPLICATIONS

When a suitable combination of position and velocity is reached, the guidance system must immediately signal cutoff of the propulsion system-in fact, it must signal cutoff a little ahead of time on the basis of a prediction process to compensate for time lags in the operation of engine controls.

Whether the rocket is an ICBM, a satellite launcher, or a launcher for a ballistic space vehicle, the powered flight guidance process is similar in all cases. The only material difference lies in the level of velocity required.

Midcourse guidance

Using modern components and techniques, initial guidance will be accurate enough in most instances for establishing Earth satellites, placing payloads on the Moon's surface, establishing satellite orbits around the Moon, and the like. However, for travel to the other planets of the solar system, or very precise lunar missions, midcourse and terminal guidance systems will probably be required. Midcourse guidance will certainly be required for vehicles using electrical propulsion systems for long periods in space.1

Some measurements and computations for midcourse guidance can be made at Earth stations when a vehicle is not too far away; however, the limited range capabilities of optical and radar observations severely circumscribe such operations. For flights to regions substantially farther than, say, the Moon, except perhaps for probing flights, a guidance capability in the vehicle itself is indicated.

The guidance process then involves: measurements on board the space craft by a navigator or automatic equipment, based on star or planet sightings; computations of suitable control actions; and signaling operation of control rockets.2 If suitable instrumentation is available the guidance process might be continuous or nearly continuous with periodic small steering corrections. If a human navigator is involved, observations would probably be made periodically rather than continuously.

The form of the computation process will depend somewhat upon the kind of instruments used for observations; however, it will probably be some variation of the techniques used by astronomers to determine the orbits of celestial bodies. One large difference, of course, is the time available for determining a precise orbit. For space navigation this determination must be made promptly and reliably, while the astronomer may proceed in a leisurely manner with careful checking.

Terminal guidance

Terminal guidance systems by their nature require some form of information from the target, such as infrared radiation, a radar echo, etc. This intelligence is then used to steer the vehicle to its destination,3 whether it be a planet, satellite, or military target.


1 Spitzer, L., Interplanetary Travel Between Satellite Orbits, Journal of the British Interplanetary society vol. 10, No 6, November 1951.

2 Press, S. J., An Application of Solar Radiation to Space Navigation, Douglas Aircraft Co., Inc., engineering Paper No. 655

3 Gates, C. R., Terminal Guidance of a Lunar Probe, Jet Propulsion Laboratory, External Publication No. 506, California Institute of Technology, May 14, 1958.


ASTRONAUTICS AND ITS APPLICATIONS 69

Inertial guidance systems

Basically, an inertial guidance system consists of three accelerometers mounted on a gyro-stabilized platform, and some form of computer.4-7

Accelerometers are small mechanical devices that respond to accelerations of the vehicle. Each accelerometer measures acceleration in a single direction; therefore the three accelerometers are used to take measurements of the complete motion of the vehicle in space.These instruments are usable only during powered flight-in the "weightless" environment of free space flight they indicate nothing, regardless of the vehicle's trajectory.

The stabilized platform isolates the accelerometers from rotational motions of the vehicle and maintains the proper orientation of accelerometer axes.

The computer operates mathematically on the accelerometer indications to determine the true position and velocity of the vehicle and steering commands for the control system.

The critical components are the stabilization gyros and the accelerometers.8 Disturbances due to imperfections in the gyros cause the platform to "drift" or rotate slowly. This drift rotation causes misalignment of the accelerometers-the "up and down" measuring accelerometer begins to measure "left and right '' motion, so to speak, with resulting errors in navigation.

Imperfections in the accelerometers also result in incorrect determinations of position and velocity. At present accelerometer inaccuracy is the largest single source of error in ballistic missile inertial guidance systems.

Inertial guidance systems are based entirely on measurements of acceleration, and involve no contact with the world outside the vehicle after launching. Thus, there is no known way of interfering with their operation-a point of some importance in military applications.

Radar guidance systems for ballistic rockets

Radars, and other similar radio devices, are also commonly used to determine vehicle position and velocity.9-11

Radar guidance systems are principally distinguished by the configuration of antennas used and the method of determining velocity information.


4 Wrigley, W., R. B. Woodbury, and J. Horvorka, Inertial Guidance, Institute of Aeronautical Sciences, Preprint No. 698, 1957.

5 Newman, T., Inertial Navigation, Arma Engineering, vol. 2, No, 2, October-November 1958. p. 8.

6 Bishop, L. E., and B. W Tooker, Inertial Platforms: The Key to Modern Guidance Arma Engineering, vol. 2, No. 1, July-August 1958, p. 4

7 Frye, W. B., Fundamentals of Inertial Guidance and Navigation, Lockheed Aircraft Corp., Missile Systems Division, Rept. No. LMSD-2204, August 5, 1957.

8 Draper, C. S., W. Wrigley, and L. R. Grohe, The Floating Integrating Gyro and Its Application to Geometrical Stabilization Problems on Moving Bases, S. M. F. Fund Paper No. FF-13, Institute of Aeronautical Sciences,1955,

9 Campbell, J. P., Interim Engineering Report A18-1 on Doppler Velocity for Space Navigation, Wright Air Development Center Contract AF-33(616)-5487, General Precision Laboratories, April 1958.

10 Campbell, J. P., Interim Engineering Report A18-2 on Doppler Velocity for Space Navigation, Wright Air Development Center Contract AF-33(616)-5487, General Precision Laboratories, June 1958.

11 Campbell, J. P., Interim Engineering Report A18-3 on Doppler Velocity for Space Navigation, Wright Air Development Center Contract AF-33(316)-5487, General Precision Laboratories, August 1958.


70 ASTRONAUTICS AND ITS APPLICATIONS

All radar systems for guidance employ one or more radar beacons (repeater transmitters) in the rocket, a ground computer, and a radio command link to the vehicle. The achievable accuracy is largely affected by the baseline length or distance between individual antennas on the ground, the path of the vehicle during propulsion, the unpredictable features of the propagation path between the radar system antenna and the vehicle, and, of course, equipment errors.

These guidance systems, like any radio device, are susceptible to jamming and other interfering measures. However, modern electronic design practice includes rather effective means for counteracting external interference.

Combined radar-inertial systems

It is possible, in principle, to combine the measurements of vehicle velocity made by a radar and by an accelerometer to obtain a better overall measure of velocity than can be obtained by either measurement technique alone.12 The reason for the possibility of improvement by such a dual system is the fact that radar systems are better for measuring slowly changing velocities, while accelerometers are better for rapidly changing velocities, and both occur in rocket flight. This process, of course, complicates the guidance system, adding either ground and airborne radar components to an inertial system or an airborne inertial system to a radar guidance system.

Illustrative accuracy data

An ICBM at a range of 5,500 nautical miles will have an impact miss distance in the direction of flight of approximately 1 nautical mile for an error of 1 foot per second in the magnitude of its cutoff velocity. The following table is presented to indicate comparative miss distances for various space-flight missions. The tabulation gives representative miss distances (in nautical miles) calculated for 1-foot- per-second error in the magnitude of velocity at thrust cutoff.13

TABLE 1.-Miss distances

Point on Earth (5,500 nautical mile ICBM)

Destination: Nautical miles
Moon
1
Mercury
20-100 
Venus
40,000
Mars
25,000
Jupiter
20,000
Saturn
65,000
Uranus
200,000

 

For establishing a satellite at an altitude of 1,500 miles, for example an error of 1 foot per second in orbital velocity will cause the orbit to depart from circularity by about 1 mile.

Navigation in space

Each "fix" on the orbit of an unpowered vehicle in free space (under the gravitational attraction of a single body, the Sun) requires six independent measurements of vehicle position or velocity.

A number of combinations of quantities might conceivably be measured


12 Mundo, C. J, Aided Inertial Systems, Arma Engineering, vol. 2, No. 2, October-November 1958, p. 15.

13 Ehricke, K. A., Instrumented Comets: Astronautics of Solar and Planetary Probes, Convair Rept. AZP-019, July 24, 1957.


ASTRONAUTICS AND ITS APPLICATIONS 71

by optical or radar instruments to obtain the six independent measurements. Some possible examples are:

These measurements must be related to a known reference system, and this reference system must be maintained by some form of instrumentation on board the rocket. The best known way of implementing such a reference system is by a gyrostabilized platform. Three mutually perpendicular directions or axes precisely defined on the platform can be oriented so that these three directions are parallel to the directions defined by the axes of the reference system to be used in navigation. The gyros will act to keep the reference system from rotating in space no matter how the vehicle moves. Over a long time, however, imperfections in the gyros will cause the platform and the reference to drift out of alinement. To remove these errors it is necessary periodically to correct the platform alinement by sightings on the fixed stars.

If some rocket thrust is used (an ion rocket, for instance), the trajectory followed by the spacecraft will not be so simply determined as that of an unpowered vehicle, and more frequent measurements will be required for use in more elaborate guidance computations by automatic equipment.15

B. PHYSICAL CONSTANTS

Precision in guidance depends not only upon the performance of instruments, but also upon the accuracy of the fundamental standards used, directly or indirectly, in the guidance measurements.16-20

One of the most basic and obvious of these fundamental constants is the specification of distance between the starting point and intended target point of a desired trajectory. The precision of this distance is dependent mainly upon the precision of knowledge of the Earth's radius. The current figure for the mean radius of the Earth is probably correct to within an error of a few hundred feet. If the error is, say, 300 feet, the strike error at the end of a 5,500-nautical-mile ballistic trajectory will be a little less than 1,000 feet-there is a magnification factor of about 3 between radius error and impact error at such


14 Porter, J. G., Navigation Without Gravity, Journal of the British Interplanetary Society, voI. 13. No. 2. March 1954.

15 Roberson, R. E., Remarks on the Guidance of Ion-Propelled Vehicles, North American Aviation, Autonetics Division, June 21, 1958.

16 Herrick, Samuel, Formulae, Constants, Definitions, Notations for Geocentric Orbits, Systems Laboratories Corp., Rept. SN-1. May 28. 1957.

17 Herrick. Samuel, R. M. L. Baker, and C. G. Hetton, Gravitational and Related Constants for Accurate Space Navigation, American Rocket Society, Preprint No. 497-57.

18 Buchheim, R. W., Motion of a Small Body In Earth-Moon Space. The RAND Corp Research Memorandum RM-1726, June 4, 1956.

19 Study of High-Precision Geocentric Orbits, Aeronutronics Systems, Inc., Doc. U-094, August 12, 1957.

20 High-Precision Orbit Determination, Aeronutronics Systems, Inc., publication No. U-220, June 27,1958.


72 ASTRONAUTICS AND ITS APPLICATIONS

a range. The magnification factor increases sharply with increasing range.

Another basic constant is the mean value of gravity at sea level. The current estimate of "g" is probably correct to within an error of less than 0.001 percent. This mean value of g, together with the mean radius of the Earth, effectively defines a quantity proportional to the total mass of the Earth. The total mass of the Earth figures in all trajectory calculations. For example, the period of a satellite is dependent upon this parameter; and, in fact, measurement of satellite periods is a good way to determine the total mass of a parent body. As a result, we have good data on the masses of those planets that have satellites (moons), and less accurate data on the masses of planets without moons.

Since the Earth is not a perfect uniform sphere, it is not enough to specify its mean radius and gravity. It is also necessary to specify the degree of departure from the ideal sphere. The principal one of these additional specifications is the flattening," the measure of difference between the radius of the Earth at the poles and at the Equator. The Earth is about 30 miles thicker across the Equator than from pole to pole.

The net assembly of these geophysical constants is known with a precision that is adequate for most space-flight purposes except for flights to actually contact other planets without midcourse or terminal guidance. Present knowledge is also probably inadequate for circumlunar flights intended to return to a small preset recovery area on the Earth; but the errors here can also be made good by midcourse or terminal guidance.

The mass of the Moon is also a parameter of importance for lunar and interplanetary flights. The Moon's mass is roughly one-eightieth of the Earth's; and current estimates are probably correct to within about 0.3 percent. This precision is adequate for all but very refined lunar flights-particularly for the circumlunar case just mentioned.

The constant of greatest importance in interplanetary flights is the astronomical unit-the mean distance from Earth to Sun. All of the dimensions used by the astronomer in the solar system are known to very great precision in terms of the astronomical unit as a reference base; for example, the distance from Earth to Mars at a given instant can be obtained very accurately, from available data, in astronomical units. However, the length of the astronomical unit in terrestrial dimension standards, like meters or statute miles is rather poorly known; and, therefore, such a measure as the distance from Earth to Mars is rather poorly known in terms of standards like meters or miles. No vehicle using initial guidance alone is likely to make a hit on any of the planets (except by accident) until the length of the astronomical unit is better known in terms of Earth


ASTRONAUTICS AND ITS APPLICATIONS 73

standards usable in guidance systems. The expected miss in shots to Venus and Mars, from this source of error, is likely to be many tens of thousands of miles.

These physical constants of primary relevance to astronautics are part of the general family of astronomical constants, and any improvements in their precision will be reflected in improvements in others.21

Another related area that needs wholesale improvement is detailed specifications of the high upper atmosphere, which are vital to accurate determination or prediction of satellite orbits.

In the future, it will be necessary to have the same kind of refined knowledge about the other planets as is now needed for the Earth.


21 Clemence, G. M., On the System of Astronomical Constants, The Astronomical Journal vol, 53, No. 6, May 1948.


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