The Gyroscope and the Aeroplane.

Progress, Volume V, Issue 5, 1 March 1910, Page 153

The Gyroscope and the Aeroplane.

(Gordon Stewart, A.M.1.E.E., in Aero.) One of the most familiar phenomena associated with a gyroscope, and at the same time the one upon which the explanation of all the others depends, is that displayed when an attempt is made to tilt the axis of

revolution of a horizontally revolving gyroscope out of the perpendicular. As was previously explained, this would be accompanied by a pronounced tendency for the gyroscope to tilt the axis of revolution m a direction at right angles to that attempted. That is to say, that if A in fig. 1 represented a horizontally revolving gyroscope wheel revolving about the axis B, perpendicular to the paper, in a clockwise direction, and an attempt was made to deflect the axis out of the perpendicular by tilting the plane of revolution about the diameter C D. the system, rather than obey this motion, would exert a pronounced tendency to turn about the diameter E F. that is a diameter at right angles. Before attempting to explain this phenomenon it will be necessary for the reader to understand and appreciate two simple mechanical facts. The first of these facts is one of Newton 's laws of mechanics, and is

briefly as follows : "If a body is moving at a certain velocity in a certain direction its velocity can only be increased by the application of a force acting in that direction"; and conversely, "its velocity can only be decreased by the application of a force acting in the opposite direction." Also, the greater the force, the greater the rate of increase or decrease of velocity as the ease may be. The second of these facts may be briefly

stated as follows: — If a wheel situated as shown in fig. 2 were to turn about the diameter A B in such a way that the portion 11 to the right-hand side of A B was moving upward through the plane of the paper, and the portion L to the left-hand side was moving downwards through the plane of the paper, it is obvious that a particle on the rim of the wheel situated at P would have a smaller velocity about the diameter than a similar particle situated at Q. This is very obvious, for it will at once be understood that the velocity of each of the partides about the diameter A B is dependent upon its distance from the axis of revolution. That is to say, the velocity of P is proportional to its radius of revolution, and that of Q is proportional to QS. Now. returning to the actual instance of a revolving gyroscope wheel and applying the above stated facts to our reasoning, we will imagine that the heavy rim of the wheel is made of a number of equally weighty particles — a, b, c, d, e,f, . . v, w, x, — shown in fig. 3 (twenty-four in all) , situated at equidistant points around the rim and revolving about the vertical axis X in the direction slioavii by the arrow. We will now determine the nature of the forces Avhich must be applied to the wheel in order to tilt the axis of rotation X in such a direction that the top of the axis above the plane of the paper moves in the direction X P. and the lower end below the plane of the paper in the direction X S Or in

other words, that the rotating wheel may be tilted aboiit the axis P Q We have previously stated that the wheel must be rotating at a high speed about its axis X. Now in a certain small interval of time the wheel will make one complete revolution. And in one twenty-fourth part of that interval the weighty particle a will have taken up the position occupied by the particle b in figure 3 (since there are twenty-four equidistant particles). It lias already been explained that where the wheel is revolved or tilted about the axis P Q the particles do not all move with the same velocity, but that they move with a velocity proportionate to their distance from PQ. Hence the particle am revolving to b has reduced its velocity about P Q from that proportionate to a X to that proportionate to & A; that is to say, its velocity has been diminished by an amount proportionate to the difference between aX and &A, namely, by an amount proportionate to dK. Similarly, the particle &in moving to c has had its velocity reduced by an amount proportionate to bh, and c in moving to d by cM. d in moving to c by dN, and so on.

We know from our previous statement that the velocity of a body cannot be decreased except by the application of a force in a direction opposite to that of its motion and vice versa. Therefore, since in moving from a to b the particle a has decreased its velocity there must have been some force acting up through the plane of the paper proportionate to the change. Since this force is acting directly up through the plane of the paper towards the reader we will represent it by a plus sign, and will draw it to a scale proportionate to the decrease aK. Similarly we will represent the force acting on b when passing to c by a plus sign proportionate to bh, and that acting on c when passing to d by a sign proportionate to cM, and so on. We will now consider the particles h, i, 3, 1-, I. and m. The particle gin moving to h has had its velocity increased by an amount proportionate to ffli, and every other one of these particles in turn has had its velocity increased by various proportionate amounts. In order to have had their velocities increased, they must have been acted upon by forces acting in the direction of their motion, and since their motion about P Q is in a direction upward through the plane of the paper, the various forces must act in the same direction. This is denoted in fig. 8 by similar plus signs proportionate in their dimensions to the value of the respective forces. Turning our attention to the forces acting upon the particles on the opposite side of the diameter R S, we shall find that the particle m in moving to n is acted upon by a force proportional to mT in an opposite direction to that of its motion about P Q ; nnd since its motion about P Q is upward through the plane of the paper the force must be in the opposite direction, that is downward through the plane of the paper, or in a direction away from the reader. Similar proportionate forces will be found to act upon the particles n, o, p, q, and r. These are represented in fig. 3 bv minus signs proportionate in their dimensions to the value of the respective forces. In a precisely similar manner it will be found that there are similar minus signs appended and representing the forces acting upon the particles t, v, v, w, and x. A glance at fig. 3 shows that all the forces acting upon that part of the gyroscope wheel above the diameter R S are of the plus sign — that is, they are acting- up through the plane of the paper. And that all the forces acting below the line R S are oC the minus sign — that is. they are acting downward through the plane of the paper It will at once be recognised that all the plus forces may be represented by v one resultant force acting somewhere on the line X P, and all the minus forces by a similar but opposite resultant force acting somewhere on the line X Q. Xow these two resultant forces are parallel to each other, but act in opposite directions. Therefore, they form a couple or turning movement tilting the revolving gyroscope wheel about the diameter R S. This explanation is simple to a degree, and the reader should not be surprised if in his attempt to deflect the axis of rotation of a revolving gyroscope he should find that it had a preference to be deflected in the opposite direction, for he will now understand why, and will realise that should he desire to deflect the axis about the diameter R S, he should proceed tfo do so about the diameter P Q and vice versa.