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Aviation History
1953
1953 - 0922.PDF
7« THE GYROSCOPE An Explanation of Principles and 1 By A. H A SPINNING body has several remarkable properties which can be made to affect the control and stability of machines with rotating parts. The aeroplane, whether driven by a piston-engine or turbine, is in this class of machine, and so is the helicopter. A study of these properties will reveal how large the effects are and what steps are necessary to overcome them and may suggest ways in which the behaviour of the spinning body can be turned to advantage in the stabilization of the aircraft. Basic Principles.—It was Foucault in 1852 who gave the name "gyro-scope" to such a body. He was concerned to demon strate the rotation of the earth and used (in addition to the pendulum which bears his name) a rotating flywheel which successfully showed the earth's rotation—hence "gyro-scope." The property which Foucault used is known as the First Law of Gyrodynamics and states that a freely supported gyro (for example, in frictionless gimbals) will maintain its axis pointing in a given direction in space. This is, of course, the property now used to provide a pilot with an artificial horizon and direction datum, as in the gyro horizon and the directional gyro. The Second Law of Gyrodynamics concerns the effect on the gyro axrs of an attempt to change its direction. To explain this we must define some axes and, for convenience, let us imagine the gyro axis to be vertically downward (OZ in Fig. 1) and the inner gimbal ring in the vertical plane OYZ. The third axis is OX which, together with OY, is in the plane of rotation of the gyro.* If we apply a torque to the outer gimbal ring about the axis OX the gyro axis rotates, not about OX, but about OY. This rotation is called "precession" and its rate is given by the equation: L = IO.q (I) where L is the (rolling) moment we have applied about OX (lb ft) I is the gyro moment of inertia (slug-ft2) Q is the gyro angular velocity (radians per second) f and q is the resulting angular velocity about OY (pitching). Similarly, an attempt to rotate the inner gimbal ring about OY by a pitching moment M would result in an angular velocity p about OX where: M = - IQ.p (2) A rotation about the gyro axis OZ would, of course, not be resisted and would cause no tilting of the axis. The sign convention is that CI, p and q are positive in the cyclic directions X to Y, Y to Z and Z to X respectively. The direction of the precession is governed by the law that the spin axis tends to become parallel to the torque axis with the direction of the spin in the direction of the torque. If, however, the gimbals are frictionless, motion of the frame attached to the aeroplane causes no precession (or "wander") and the spin axis remains fixed in space. The Spring-restrained Gyro.—Fig. 2 shows a gyro attached to the frame (aeroplane) by a single gimbal ring which is controlled in its movement by a centering spring. Pitching and yawing of the aeroplane have no effect on the gyro axis but a rolling of the aeroplane (p about OX) applies a rolling moment L to the gimbal which, from equation 1, causes the gimbal to rotate (q about OY). This precession is resisted by the centering springs which now apply a moment to the gimbal ( —M about OY) which causes a precession p about OX. Equilibrium is reached in a steady roll when the gimbal is rolling at the same rate as the aeroplane has had a deflection, depending on the spring rate, which is indicated by the pointer. This spring-restrained gyro thus forms an indicator of rate of roll. By exchanging the axes so that the spin axis is horizontal a rate-of-turn or rate-of-pitch indicator is produced. Gyro Flying Instruments.—The gyro horizon consists of a free gyro, electrically, or air-driven, with axis vertical and the position of the gimbal rings is usually presented to the pilot as * These are the axes used in discussing aeroplane stability; OZ is vertically down, OY to starboard and OX forward. t A slug is a unit of mass, equal in pounds to the acceleration in feet per second2 experienced by a freely falling body at the place of measurement. Thus, normally, a slug may be said to be a mass of 32.2 lb. A radian is the angle formed at the centre of a circle by an arc equal in length to the radius. Thus, one radian jsec represents — or roughly 1/60/ a revolution jsec. FLIGHT in AERONAUTICS of Effects—Useful and Otherwise YATES THE first section of this article serves as an introduction to the subject of gyroscopes in general. It is followed by a summary of particular applications of the gyro principle, which will be of interest not only to readers of the first part of the article, but also to those already familiar with the basic principles involved. The applications mentioned include automatic pilots, unwanted gyroscopic effects, helicopter problems and "flying saucers." The author, a frequent contributor to "Flight," is a senior lecturer in aerodynamics at the College of Aeronautics, Cranfield. the position of a "horizon bar" relative to his airframe—rep resented by a small model. Since unavoidable friction in the gimbals will cause precession, the spin axis must either be set vertical by eye every ten minutes or so or supplied with a small correcting torque when the deviation becomes appreciable; this is easily arranged. The equations above show that the rate of precession is a minimum for a rotor of high moment of inertia rotating at high speed. The directional gyro is also a free gyro but has its axis horizontal and only the compass heading of the spin axis is required by the pilot. The single scale reading is supplied to the pilot by a ribbon moving in a window or by a dial presentation of an aeroplane in plan moving relative to a compass card. Again precession is caused by friction and the reading of the directional gyro must be corrected to agree with that of the compass every ten minutes or so. This, too, can be arranged automatically by signals from a magnetic compass (as in the Gyrosyn compass). The rate-of-turn indicator is centred by its spring and needs no correction for precession. There is not, therefore, the same need for very high rotational speed and a direct current electric motor consuming only a few watts is adequate. Automatic Pilots.—With the aid of the above signals of the aircraft attitude and rate of turn (rates of pitch and roll are not normally measured by spring-restrained gyros but must be judged by the pilot from attitude changes) the pilot finds no difficulty in controlling the aeroplane. He acts as an interpreter of the gyro signals and makes suitable control movements. The automatic pilot is merely a device for performing the same actions; it is fed, electrically or mechanically, with signals from the various gyros and applies control movements proportional to the attitude changes, rates of change and even of accelerations. The gyroscope is the detector which supplies the information that action is needed. Unwanted Gyroscopic Effects.—The aircraft engine con tains rotating parts which are free only to rotate. When the aircraft rotates about an axis other than one parallel to the engine axis gyroscopic couples will be imposed on the aircraft through the bearings. These are unwanted and not only must the bearings be designed to take the extra gyroscopic load but the flying controls of the aeroplane must be adequate to deal with the gyroscopic couple applied. Consider, for example, an engine rotating clockwise when viewed from astern. When the aeroplane yaws to starboard the Second Law states that there will be a (nose-down) pitching moment given by: M = — I Q.r where r is the rate of yaw and I is the moment of inertia of the rotating parts of the engine. This pitching moment must be trimmed out by the pilot by the use of the elevators and, since a turn normally involves the use of all three controls, this is not a serious handicap. Never theless, yawing to port will give a nose-wp pitching moment and the difference in behaviour when the aeroplane turns to port and to starboard may confuse a pilot. Similarly, a pitching of the aeroplane results in a yawing moment. APPROXIMATE MOMENTS OF INERTIA AND ROTATIONAL SPEEDS OF ENGINES AND AIRSCREWS Large Airscrew (4-blade, 11ft diam.) Rotary piston-engine Centrifugal turbojet (Thrusc 5,000 lb) Axial turbojet (Thrust 8,000 lb) Helicopter rotor (40ft diam.) 1, slugs-ft.2 50 •40 10 15 1,500 r.p.m. 1,200 1,200 10,000 10,000 250 Product 60,000 48,000 100,000 150,000 375,000
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