The primary function of a control system during powered flight is to orient and stabilize the rocket vehicle. To orient the vehicle in some desired angular direction, it is necessary to develop torque to turn the body. Control ceases and the body is stabilized when sensing instruments, usually gyroscopic devices, indicate that the proper attitude has been achieved.1
During the propulsion phase, control torque is usually developed either by aerodynamic forces acting on control surfaces or by rocket forces.
Techniques for aerodynamic control are essentially the same as those used in conventional aircraft. At very high altitudes, however, aerodynamic surfaces become ineffective because of low air density Therefore, other means of producing torques are required in the vacuum environment of upper altitudes and space.
The method employed on the V-2 and Redstone missiles is to deflect the exhaust jet of the main propulsion motors by carbon vanes (fig. 1). Both missiles actually use aerodynamic control surface as well as jet vanes. At takeoff, the missile speed is zero, and the jet vanes provide stabilization. As the missile speed increases, the aerodynamic surfaces becomes effective and aid in the control process.2
1 Miller, J. A., Designing Flight Control Systems for Ballistic Missiles, Aviation Age, November 1957, p. 92.
2 Redstone, Flight, May 23, 1958, p. 705.
A variation of the jet vane is the jetavator.3 This device is a ring placed around the circumference of the motor nozzle. Deflecting the ring deflects the exhaust, just as with vanes. However, the jetavator has the advantage of not causing propulsion losses when in the neutral position, since, unlike vanes, it does not interfere with the exhaust flow. Jetavators have been most frequently applied to control of solid-propellant rockets.
Control of liquid rockets is frequently based on swiveling the entire rocket motor, as on the Thor.4-6 Separate rocket nozzles may also be used to obtain a sideward component of thrust for control. Such small separate rockets are usually employed to control orientation about the longitudinal or roll axis of a vehicle.
Regardless of the details of mechanism, the magnitude of the control torque produced by the ejection of mass from the vehicle is equal to the sideward reaction force multiplied by the perpendicular distance from the center of gravity to the line of action of the sideward force.
3 Subsonic Snark Adds Effectiveness to SAC Forces, Aviation Week, vol. 69, No. 11, September 15, 1958, p. 50.
4 North American Aviation, Inc., Rocketdyne Division, press release No. NR-38.
5 Atlas Propulsion System Background, North American Aviation, Rocketdyne Division, press release No. RS-4, March 10, 1958.
6 Thor Propulsion System Background, North American Aviation, Rocketdyne Division, press release No. RS-5, June 1, 1958.
By deflecting the rocket exhaust or by swiveling the rocket motor the body of a vehicle may be rotated in any desired manner. Since the thrust from the main propulsion system is normally along the longitudinal axis of the craft, rotating the vehicle also rotates the direction of primary thrust in space. Adjusting the direction of the thrust in this manner may be used in turn to control the direction of flight of the vehicle.7
The magnitude of control torque required during the propulsion phase is determined by the various disturbing influences which act upon the vehicle during this period, including aerodynamic effects wind, sloshing of propellants,8 and various structural effects, such as body bending.9
Nature of the control problem
In unpowered flight in space the principal control problem is that of controlling the attitude or orientation of the vehicle with respect to a specified reference system. The techniques used in attitude control are rather widely different for different kinds of space missions.10
The attitude control problem has two major parts: (1) Applying control torques, and (2) establishing an orientation reference system.
An aircraft utilizes surfaces to deflect the airstream in order to obtain control torques. Without an external airstream to deflect, space vehicles are able to produce torques only through the use of self-contained mass. In some special cases there are exceptions to this rule which will be considered later. In general, however, either a mass must be ejected by rocket units, or masses must be rotated internally to produce the required reaction torque.
Unlike the large rocket motors used for primary propulsion, the small rockets used for control only rotate the vehicle about its center of mass and do not influence the flight path. Generally, the thrust of such units is small, a matter of a few pounds, and they may be of the monopropellant type using a gas stored under high pressure or decomposing hydrogen peroxide.
Control torques may also be produced by rotating masses within the craft. The physical principle involved is the law of conservation of angular momentum. A familiar illustration of the consequences of this law is the manner in which the rotational speed of a swivel chair or a piano stool may be controlled by extending and retracting weights. If the stool is spun with the weights extended and the weights are then retracted to a position closer to the axis of rotation, the rate of spin of the stool will increase. If the weights are extended outward from their original position, the spin rate of the stool will decrease.
7 Orr, J. A., Powered Flight, Navigation, spring 1958.
8 Wang, C. J., and R. B. Reddy, Variational Solution of Fuel Sloshing Modes, Jet Propulsion, November 1958.
9 Beharrell, J. L., and H. R. Friedrich, The Transfer Function of a Rocket-Type Guided Missile with Consideration of Its Structural Elasticity, Journal of Aeronautical Sciences; vol. 21, No. 7; July 1954.
10 Roberson R. E., Attitude Control: A Panel Discussion: Problems and Principles, Navigation; vol. 6, No. 1; spring 1958.
Now consider a wheel mounted so that its spin axle is perpendicular to the longitudinal axis of the space vehicle (fig. 2). If, initially, the wheel and the vehicle are not rotating, the angular momentum of the system comprising the vehicle and the wheel is zero. Now if the wheel is caused to rotate, it will have an angular momentum. However, the total angular momentum of the vehicle and the wheel must remain zero. Thus, the reaction of the vehicle to the motion of the wheel is to rotate in the opposite direction so that the total angular momentum of the system is zero.11
In actual application. three wheels with their spin axes mutually at right angles are usually required to control the vehicle about its roll, pitch, and yaw axes; rotating masses are used in a variety of ways.
One axis of the vehicle can be made to remain fixed in space by spinning the entire vehicle about the axis to be stabilized.12 In spin-stabilizing the payload stage of a Moon rocket, as in the Pioneer lunar probe, the vehicle is spun at propulsion cutoff in an orientation which, when the vehicle reaches the Moon's vicinity, enables it to be placed in orbit around the Moon by the firing of a reverse-thrust rocket.
11 Angle, E. E. Attitude Control: A Panel Discussion: Attitude Control Techniques Navigation; vol. 6, No. 1; spring 1958.
12 Buchheim, R. W. Lunar Instrument Carrier-Attitude Stabilization, The RAND Corp., Research Memorandum RM-1730, June 5, 1956.
The attitude control system must be able to overcome any external or internal disturbing influences. Disturbing torques that must be considered when designing a stabilization and control system may be due for example to- 13-17
The unintentional or uncompensated motion of internal masses. The relative importance of these disturbing torques depends upon the particular vehicle under consideration.
Torques due to aerodynamic effects are of primary importance to satellites. With proper aerodynamic design, such forces might actually be used to aid in the attitude stabilization of a low-altitude, short duration satellite.18 At altitudes of 1 million feet and above, the air density is so low that aerodynamic effects usually are of little importance.
Torques due to magnetic fields might arise from induced currents in the conducting parts of the vehicle. Torques of this nature are also primarily of concern to satellites. Care in design details will assure that these effects are negligible.19
The Earth's gravitational field acts more strongly on a nearer mass than on a farther one. As a consequence, a torque arises that tends to force an elongated vehicle to orient itself in such a way that its long axis points toward the Earth's center. This gravitational gradient torque can also be used as a control torque if the vehicle is properly designed.20-22
The gradients of the gravitational fields of the other members of the solar system will also apply torques to space vehicles. However, unless the craft is in the vicinity of a planet, all such torques are negligible except that exerted by the Sun.
Torques due to solar radiation pressure23 are present when there is an inequality in the effective reflecting area of the vehicle about the center of mass. Conceivably, such torques could be used for control purposes by adjusting the reflectivity of the proper part of the vehicle. At best, however, radiation pressure torques are quite small,
13 Roberson, R. E., Attitude Control of a Satellite Vehicle-An Outline of the Problems presented at the Eighth International Congress of Astronautics, Barcelona, 1957, American. Rocket Society Paper 485-57.
14 Vinti, J. P. Theory of the Spin of a Conducting Satellite in the Magnetic Fields of the Earth, Ballistics Research Laboratory, Rept. No. 1820, Aberdeen Proving Ground, July 1957.
15 Roberson, R. E., Gravitational Torque on a Satellite Vehicle, Journal of the Franklin Institute, vol. 265 No. 1, January 1958.
16 Manring and Dubin, IGY World Data Center, Satellite Rept. No. 3, May 1, 1958.
17 Roberson, R. E., Torques on a Satellite Vehicle From Internal Moving Parts, Journal of Applied Mechanics; vol. 25, No. 2, June 1958.
18 DeBra, D B. The Effect of Aerodynamic Forces on Satellite Attitude, Lockheed Aircraft Corp., Missile Systems Division, Rept. No. MSD 5140.
19 See footnote 14.
20 Baker, R. M. L., Attitude Control: A Panel Discussion; Passive Stability of a Satellite Vehicle, Navigation, vol. 6, No. 1, spring, 1958.
21 Klemperer, W. B., and R. M. Baker, Jr., Satellite Librations, Astronautica Acta, Vol III, 1957.
22 The Investigation of the Passive Stability of a Satellite Vehicle, Aeronutronic Systems Inc., publication No. U-225, July 3, 1958.
23 See footnote 12, p. 63
particularly if care is taken to balance the effective reflecting area on either side of the craft's center of mass.
The importance of torques due to meteorite impact is rather difficult to determine. It is true that the impact of even a small meteorite could cause an angular disturbance; but the probability of such an occurrence seems to be very low.24
The importance of disturbances due to the motion of internal masses depends upon the detailed design of the vehicle. Unless great care is taken, the torques caused by internal rotating machinery, such as power units, or by people, are likely to be the predominant disturbing influence that the control system must handle.25
When a properly designed aircraft is given a small angular displacement, say in pitch, it will return to a neutral position without the need of control surface deflections. However, space vehicles requiring attitude stabilization must be under continuous active control If a disturbance acts on the vehicle, only by applying a control torque can the resulting displacement be removed. Without control, even very small disturbing torques will eventually subject the craft to large orientation errors.
The very small magnitude of the forces involved in space vehicle orientation control leads to a need for equipments that may be rather difficult to test under conditions at the Earth's surface.26
Reference system instrumentation
The establishment of reference coordinates is a problem that is not unique to space vehicles. However, the great distances and long durations of time over which the reference system of a space vehicle must be maintained lead to difficulties that do not occur in the case of aircraft.
Gyroscopes, which are merely elaborate spinning wheels, will maintain a fixed direction in space if they are not subjected to disturbances. In a practical case, however, it is just a question of time before the orientation of a gyro drifts away from the desired reference direction. The disturbing effects of high accelerations during launching, coupled with the relatively long duration of space flights, make it very difficult to establish a satisfactory preset reference system using gyros alone.
Instruments such as accelerometers or pendulums are of no use here. An accelerometer will always indicate zero in the weightless environment of a space vehicle, and a pendulum will simply assume any random position.
The stars provide a natural reference system which may be used in orienting a space vehicle. Star-tracking telescopes attached to the space vehicle can detect any disturbance of the attitude of the vehicle and signal operation of an appropriate torque-producing mechanism for correction.
Another device for instrumenting the orientation control of a satellite would be an optical one to scan the Earth's horizon, and thus establish the vertical direction.
24 See footnote 16, p. 64
25 See footnote 17, p. 64
26 Space Vehicle Attitude Control Experiment, Aeronutronic Systems, Inc., Publication No. U-142, January 28,1958.
The Earth's magnetic field can also be used to sense direction in space for orientation reference, as was done in Sputnik III.27
The overall shape of the vehicle and distribution of internal equipments are of vital importance in orientation control. Two cases of particular importance are (a) spin stabilization; and (b) satellite orientation.
For successful spin stabilization it is necessary that the axis of spin be the axis about which the vehicle has either maximum or minimum inertia.28 29 The third, intermediate inertia, axis of a vehicle is not usable for stable spin. Thus a spin-stabilized vehicle should be flat (a coin-shaped body would be an example) or long (like a pencil). Uniform spherical shapes are generally undesirable for spin stabilization.
Stable orientation of a nonspinning satellite is greatly aided by use of the gravitational gradient torque, and this torque is available only if the vehicle is packaged to be relatively long and thin with its long axis pointing toward the center of the Earth. Distribution of internal equipment must be arranged to accommodate, and be usable in, this aspect.
27 Stockwell, R. E., Sputnik III's Guidance System, Missile Design and Development, vol 4, No. 9, September 1958, p. 12.
28 See footnote 12, p. 63.
29 Bracewell, R. N.. and O. K. Garriott, Rotation of Artificial Earth Satellites, Nature vol. 182, September 20, 1958, p. 760.