Gyroscopic effect

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The gyroscopic effect or gyroscopic effect (from Greek γύρος gyros , German , rotation ' and σκοπεῖν skopein , German , see' and Latin effectus , effect ' ) is that by gyroscopic moments and centrifugal forces expressing inertia of a rotating body with respect to changes in direction of the axis of rotation. In everyday life it becomes noticeable through the peculiar stubbornness of a running symmetrical top against changes in the direction of its figure axis or the self-control of rolling wheels . Other less common terms are deviation resistance , deviation moment and gyral force .

Almost all applications of the gyroscope based on the centrifugal moment in the regular precession of the symmetric top so the curve gyro , the edge runners and the gyroscopic stabilization .

Gyroscopic effect on two-wheelers

Weight force and contact force (red) form a force couple (blue) that rotates the angular momentum (green) (turquoise)

The gyroscopic effect can be clearly seen on a bicycle tire rolled over a horizontal surface. The tire rolls almost straight ahead for a surprisingly long time. A torque that would overturn the tire around its support causes its rotational movement to precession , see picture. That is, it rotates around the vertical axis. In the tilted position in the picture, the weight force and contact force (red) form a force couple with moment (blue). According to the law of twist , the moment is equal to the change in angular momentum (turquoise), which is opposed to the gyroscopic effect as inertia. Therefore the angular momentum (green) rotates in the direction of the moment. Since this rotation takes place in the same direction as the tilting direction (if the tire tilts to the right, it also rotates to the right), the tire steers itself out. This effect does not last indefinitely. If the rolling speed falls below a certain value, the tire will eventually tip over.

Contrary to popular belief, the gyroscopic effect is only to a small extent responsible for the fact that a (forward) free-running bicycle with the usual steering geometry automatically balances itself. The effect of this effect on the (self) steering behavior of the bicycle is speed-dependent and is relatively little pronounced in a speed range customary for bicycles (rotation speed of the front wheel).

The self-balancing behavior of bicycles is mainly due to the steering geometry, in which the real contact point of the front wheel is behind the theoretical intersection between the steering axis and the ground - the contact point follows the intersection; accordingly, the distance between the two points is usually called lag. When tilting the wheel z. B. to the right creates a moment around the steering axis due to the wheel contact force, which generates a steering angle to the right. The torques generated by the weights of the front wheel and the handlebars around the steering axis go in the same direction.

This "geometric self-balancing" works in the same direction as the precession movement of the rotating and sideways tilting front wheel. Both effects are superimposed, with the proportion of the gyroscopic effect in the normal speed range for bicycles i. d. Usually only the "geometric self-balancing" is stabilized.

Gyro theory

If the gyro experiences an additional rotation, the rotation of the gyro adjusts itself to the additional rotation. This is the result of the gyroscopic effect, which, according to the rule of parallelism in the same direction , tries to bring the axis of the forced rotation in direction and orientation to coincide with the axis of the self-rotation.

The gyroscopic effect is unusual because humans only have a feeling for the forces expressed in tension and pressure, but not for the axial nature of the torque, in which the inertia of the gyro is expressed. If, for example, a force is exerted on a top, then the torque generated by the force and the counteraction at the support point is perpendicular to the force, which is why a rapidly rotating top of a force sometimes unexpectedly evades its line of action. However, a body that rotates less rapidly gives way to a surge of force .

The gyroscopic effect is a d'Alembert inertial force and, as such, a moment that is opposite to an attacking moment:

Moment and gyroscopic action are in dynamic equilibrium . Thus, according to the principle of swirl , the gyroscopic effect corresponds to the negative angular momentum change and is equal to the sum of the gyroscopic effects of the Euler and centrifugal forces in the body:

see the rate of twist on the rigid body .

Web links

Single receipts

  1. ↑ a b c d Grammel (1920), p. 70.
  2. ↑ a b c d e f g Grammel (1950), p. 60 ff.
  3. ↑ a b Klein and Sommerfeld (1910), p. 763 f.
  4. ↑ Magnus (1971), p. 85
  5. ↑ Klein and Sommerfeld (1910), p. 962
  6. ↑ Grammel (1920), p. 186.
  7. ↑ A single line of code was sufficient for the balance control. on: heise.de , November 2, 2012.
  8. ↑ New free-hand bike: It's the mass that matters. In: Spiegel online. April 15, 2011.
  9. ^ JDG Kooijman, AL Schwab, JP Meijaard, JM Papadopoulos, A. Ruina: A Bicycle Can Be Self-Stable Without Gyroscopic or Caster Effects . In: Science . tape 332 , no. 6027 , 2011, pp. 339–342 , doi : 10.1126 / science.1201959 .
  10. ^ Grammel (1950), p. 75.
  11. ↑ Grammel (1920), p. 59.

literature

  • K. Magnus : Kreisel: Theory and Applications . Springer, 1971, ISBN 978-3-642-52163-8 , pp. 85 ( limited preview in Google Book Search [accessed November 23, 2019]).
  • R. Grammel : The top . Its theory and its applications. Vieweg Verlag, Braunschweig 1920, p. 70 ( archive.org - "swing" means angular momentum and "torsional balance" means rotational energy). or R. Grammel : The top . Its theory and its applications. 2. revised Edition volume

     1 . Springer, Berlin, Göttingen, Heidelberg 1950, DNB  451641280 , p. 60 ff .
  • F. Klein , A. Sommerfeld : Theory of the gyro . The technical applications of the gyro theory. Book IV. Teubner, Leipzig 1910, p. 763 ( archive.org [accessed November 23, 2019]).