EP0396473B1 - Method of/and device for displaying tidal movement - Google Patents

Description

The invention relates to a method and an apparatus for representing the movement of a tide.

An apparatus is known for representing the movement of a tide constituted by a needle rotating at a constant speed of 1 revolution per 12 h 25 min approximately in front of a circular scale graduated in tide hours. See prior art US-A-4623259, GB-A-2050656.

The present invention aims to provide a better representation of this movement.

This is achieved, according to the invention, by basically representing this movement by the rotation of an ellipse, this rotation being carried out so that the time interval which elapses between the successive passages of the major axis of the ellipse and of the minor axis of the ellipse by the same position corresponds to the time interval which elapses between a successive high tide and a low tide.

• on utilise le contour de l'ellipse pour commander la lecture d'une échelle graduée en heures de marée,
• on représente les heures de la marée par des graduations sur une échelle fixe, l'échelle représentant l'intervalle de temps moyen entre une marée haute et une marée basse successive, on fait tourner l'ellipse autour d'un axe perpendiculaire au plan de l'ellipse et son centre, l'ellipse étant choisie en sorte que la différence des longueurs du grand axe et du petit axe de l'ellipse soit égale à l'écart entre les deux graduations qui correspondent respectivement à ladite marée basse et ladite marée haute successives, et on utilise le bord de l'ellipse pour commander la lecture des graduations sur l'échelle,
• on utilise le bord de l'ellipse comme curseur sur l'échelle,
• on utilise le bord de l'ellipse comme came pour commander le déplacement d'un index sur l'échelle,
• on utilise une échelle rectiligne,
• on fait tourner l'ellipse à une vitesse variable suivant une courbe liée à l'âge de la lune en sorte que la rotation de l'ellipse soit au moins approximativement en phase avec le cycle lunaire, la durée d'une rotation complète de l'ellipse variant entre un tour par 24 h 38 mn et un tour par 24 h 74 mn, avec une moyenne d'un tour par 24 h 52 mn,
• on commande le mouvement de l'ellipse au moyen d'un quartz et d'un microprocesseur,
• pendant la rotation de l'ellipse, on déplace son centre au moyen d'une autre ellipse attaquant comme une came une piste circulaire concentrique à ladite ellipse et solidaire de ladite ellipse, en animant ladite autre ellipse d'une rotation à vitesse uniforme d'un tour par 24 heures, et le rapport de la différence des longueurs du grand axe et du petit axe de ladite ellipse à la différence des longueurs du grand axe et du petit axe de ladite autre ellipse est compris entre 2 et 3, de préférence entre 2,3 et 2,7, et encore mieux égal à 2,5 ou voisin de 2,5.

The method of the invention can, according to different embodiments, in particular present one or more of the following additional characteristics:

• we use the outline of the ellipse to control the reading of a scale graduated in tide hours,
• the hours of the tide are represented by graduations on a fixed scale, the scale representing the mean time interval between a high tide and a successive low tide, the ellipse is rotated around an axis perpendicular to the plane of the ellipse and its center, the ellipse being chosen so that the difference in the lengths of the major axis and the minor axis of the ellipse is equal to the difference between the two graduations which correspond respectively to said low tide and said tide high successive, and we use the edge of the ellipse to control the reading of the graduations on the scale,
• we use the edge of the ellipse as cursor on the scale,
• we use the edge of the ellipse as a cam to control the movement of an index on the scale,
• we use a straight scale,
• the ellipse is rotated at a variable speed along a curve related to the age of the moon so that the rotation of the ellipse is at least approximately in phase with the lunar cycle, the duration of a complete rotation of l '' ellipse varying between one revolution per 24 h 38 min and one revolution per 24 h 74 min, with an average of one revolution per 24 h 52 min,
• the movement of the ellipse is controlled by means of a quartz and a microprocessor,
• during the rotation of the ellipse, its center is displaced by means of another ellipse attacking like a cam a circular track concentric with said ellipse and integral with said ellipse, by animating said other ellipse with a rotation at a uniform speed of one revolution per 24 hours, and the ratio of the difference in the lengths of the major axis and the minor axis of said ellipse to the difference in the lengths of the major axis and of the minor axis of said other ellipse is between 2 and 3, preferably between 2.3 and 2.7, and even better equal to 2.5 or close to 2.5.

The invention also relates to an apparatus for indicating the hours of a tide, characterized in that it comprises an ellipse and means for rotating the ellipse around an axis perpendicular to the ellipse at its center in that the interval of time between the successive passages of the major axis of the ellipse and the minor axis of the ellipse by the same position corresponds to the interval of time that passes between a high tide and a low tide successive.

• il comprend une échelle graduée en heures de marée et l'ellipse est choisie en sorte que la différence des longueurs du grand axe et du petit axe de l'ellipse soit égale à l'écart entre les deux graduations qui correspondent respectivement à ladite marée basse et ladite marée haute successives, et on utilise le bord de l'ellipse pour commander la lecture des graduations sur l'échelle,
• il comprend une échelle graduée en heures de marée et le bord de l'ellipse constitue une came qui actionne le déplacement d'un curseur sur ladite échelle,
• ladite échelle est rectiligne,
• il comprend des moyens pour faire tourner l'ellipse en sorte que la rotation de l'ellipse soit, au moins de façon approximative, en phase avec le cycle lunaire,
• il comprend une autre ellipse qui attaque comme une came une piste circulaire concentrique à ladite ellipse et solidaire de ladite ellipse, le rapport de la différence des longueurs du grand axe et du petit axe de ladite ellipse à la différence des longueurs du grand axe et du petit axe de ladite autre ellipse est compris entre 3 et 3, de préférence entre 2,3 et 2,7, et encore mieux égal à 2,5 ou voisin de 2,5, et des moyens pour faire tourner cette autre ellipse à une vitesse uniforme de 1 tour par 24 heures.

Depending on the embodiments, this device may also have one or more of the following other characteristics:

• it includes a scale graduated in hours of tide and the ellipse is chosen so that the difference in the lengths of the major axis and the minor axis of the ellipse is equal to the difference between the two graduations which correspond respectively to said low tide and said successive high tide, and the edge of the ellipse is used to control the reading of the graduations on the scale,
• it includes a scale graduated in hours of tide and the edge of the ellipse constitutes a cam which actuates the movement of a cursor on said scale,
• said scale is rectilinear,
• it includes means for rotating the ellipse so that the rotation of the ellipse is, at least approximately, in phase with the lunar cycle,
• it includes another ellipse which attacks like a cam a circular track concentric with said ellipse and integral with said ellipse, the ratio of the difference in the lengths of the major axis and the minor axis of said ellipse to the difference in lengths of the major axis and the minor axis of said other ellipse is between 3 and 3, preferably between 2.3 and 2.7, and even better equal to 2.5 or close to 2.5, and means for rotating this other ellipse at a uniform speed of 1 revolution per 24 hours.

• la figure 1 est un schéma d'un premier mode de réalisation de l'appareil ;
• la figure 2 est une courbe représentant les écartes entre 4 pleines (ou basses) mers selon l'âge de la lune ;
• la figure 3 est un schéma d'un deuxième mode de réalisation de l'appareil ;
• la figure 4 est un schéma des deux ellipses utilisées dans l'appareil de la figure 3 ;
• la figure 5 est une vue de détail de la fenêtre de l'appareil de la figure 3 ;
• la figure 6 est un schéma de certaines des positions des ellipses de l'appareil de la figure 3 au cours d'une rotation ;
• la figure 7 est un schéma de certaines des positions des ellipses en relation avec l'âge de la lune ;
• la figure 8 est un schéma d'une vue de face d'une réalisation selon la figure 3 comportant une échelle supplémentaire pour l'indication des coefficients de marée, et
• la figure 9 est une coupe de l'appareil de la figure 8 selon les plans 4-4 de la figure 8.

Two embodiments of the apparatus will be described below with reference to the figures in the accompanying drawing in which:

• Figure 1 is a diagram of a first embodiment of the apparatus;
• FIG. 2 is a curve representing the distances between 4 full (or low) seas according to the age of the moon;
• Figure 3 is a diagram of a second embodiment of the apparatus;
• Figure 4 is a diagram of the two ellipses used in the apparatus of Figure 3;
• Figure 5 is a detail view of the window of the apparatus of Figure 3;
• Figure 6 is a diagram of some of the positions of the ellipses of the apparatus of Figure 3 during rotation;
• Figure 7 is a diagram of some of the positions of the ellipses in relation to the age of the moon;
• FIG. 8 is a diagram of a front view of an embodiment according to FIG. 3 comprising an additional scale for the indication of the tidal coefficients, and
• FIG. 9 is a section of the apparatus of FIG. 8 according to planes 4-4 of FIG. 8.

The apparatus shown in Figure 1 is a simplified version of a semi-diurnal tide pendulum, where the result of the attractions of the moon and the sun is represented by an elliptical disc E.

The average lunar cycle is 29 days 12 hours 44 minutes and 3 seconds or 42,524 minutes and 3 seconds. 57 high tides and 57 low tides occur during this time. The average interval between two full (or low) seas is therefore 746 minutes (12 hours 26 min) + 2.10 seconds or 24 h 52 min between four full seas.

Specialists in the phenomenon of tides have long shown that this average deviation of 52 minutes from a solar day varies throughout a lunation between 38 and 74 minutes, that the duration of the tide is very close to 24 h 52 minutes during the periods of the first and last quarter of the moon (dead waters) and it is minimum (shorter tides) at the time of full moons and new moons (white waters).

The variation of these gaps being very regular from one lunation to another compared to the age of the moon (number of days elapsed since the previous new moon) -see figure 2-, we can therefore animate the elliptical disc ( figure 1) of an irregular circular movement, but in phase with the tide.

The figure of 42,522 minutes is retained as the period of lunar revolution (i.e. an error of 2 minutes and 3 seconds per cycle), so that the average interval between two full seas is 746 minutes (57 full seas = 42,522 minutes) .

• soit par une chaîne d'engrenages et de cames entraînés par un mouvement d'horlogerie ayant un axe tournant à la vitesse régulière d'un tour en 746 minutes (ou ses multiples ou sous-multiples),
• soit par un mouvement piloté à quartz et équipé d'un microprocesseur approprié.

Daily variations in the speed of rotation of the elliptical disc during a lunar revolution are obtained for example:

• either by a chain of gears and cams driven by a clockwork movement having an axis rotating at the regular speed of one revolution in 746 minutes (or its multiples or submultiples),
• either by a quartz-driven movement equipped with an appropriate microprocessor.

In FIG. 1, the means which rotate the ellipse counterclockwise around a axis perpendicular to the ellipse at its center (J) have been shown diagrammatically at M. It is not necessary to describe them in more detail, their realization being within the reach of those skilled in the art, since the functions of these means have been explained above. The rectilinear scale R, here vertical, graduated in hours of tide, is also shown, in front of which the ellipse rotates so that the edge of the ellipse sweeps across this scale, successively designating the hours.

The apparatus shown also includes an ordinary pendulum P.

We know that each point of a coast has its own tide in advance or behind a certain number of minutes compared to the passage of the moon to the local meridian.

This figure, called port establishment or initial time, is more or less constant for each location throughout the year.

• 1) Régler le variateur de vitesse sur le chiffre correspondant à l'âge de la lune, le jour de sa mise en route,
• 2) Régler le disque elliptique sur l'état présent de la marée à l'endroit considéré.

To use the tidal pendulum, you must therefore make two prior adjustments:

• 1) Set the variable speed drive to the number corresponding to the age of the moon, the day it starts up,
• 2) Adjust the elliptical disc to the present state of the tide at the location considered.

To know the state of the tide in another place, it will be enough to add or subtract the differences of the "establishments" between the two places.

However, it should be noted that since the proposed system does not take into account all the factors of variation, the time of any tide will only be indicated to the nearest hour, but on the other hand the cumulative annual error does not exceed not 1/2 hour.

• la représentation du mouvement des marées par une ellipse rappelle la réalité mécanique du phénomène dû à l'attraction universelle,
• l'ellipse permet de représenter graduellement le mouvement de marée montante et descendante ainsi qui les deux discontinuités (marée haute et marée base) au cours desquelles le mouvement change de sens,
• si l'ellipse tourne dans le sens anti-horaire, la pente de la tangente à l'ellipse au point d'intersection de l'ellipse avec l'axe vertical de l'échelle graduée ou à travers une fenêtre F (voir figure 5) indique instantanément le sens du mouvement (marée montante / ou descendante \),
• par un choix approprié des dimensions de l'ellipse, on peut illustrer la règle des douzièmes (voir ci-après).

This simplified device has the following advantages in particular:

• the representation of the movement of the tides by an ellipse recalls the mechanical reality of the phenomenon due to universal attraction,
• the ellipse allows to gradually represent the movement of rising and falling tide as well as the two discontinuities (high tide and base tide) during which the movement changes direction,
• if the ellipse turns anti-clockwise, the slope of the tangent to the ellipse at the point of intersection of the ellipse with the vertical axis of the graduated scale or through a window F (see figure 5 ) instantly indicates the direction of movement (rising / falling tide \),
• by an appropriate choice of the dimensions of the ellipse, one can illustrate the rule of twelfths (see below).

An improved version of the device is shown in Figure 3.

This device includes an ellipse L and another ellipse S representing the respective effects of the moon (ellipse L) and the sun (ellipse S) if the ratio (ba) / (dc) of the difference in length between the major axis and the minor axis of the large ellipse (L) at the difference in length between the major axis and the minor axis of the small ellipse (S) is between 2 and 3, preferably between 2.3 and 2.7, and even better equal to 2.5 or close to 2.5.

For example, for a small tidal pendulum, you can choose b - a = 2.5 cm and d - c = 1 cm. For a large wall clock, choose for example b - a = 2.5 m and d - c = 1 m. These examples are of course not limiting.

The ellipse S is placed inside the ellipse L, in a central circular opening N.

Appropriate means diagrammed in Z animate the ellipse S of a uniform circular movement of one revolution per 24 h around its fixed center I, corresponding to the solar rhythm, and the ellipse L of a circular movement corresponding to the average rhythm from the passage of the moon to the meridian, a revolution in 24 h 52 min around its center J, which is vertically mobile under the action of the rotation of S which acts like a cam in the circular cavity of L.

The device has a vertical scale (shown schematically by window F) graduated in hours of the tide. If we take the examples above, the graduations cover 2.5 cm (small pendulum) or 2.5 m (wall pendulum).

When the two major axes of the ellipses are parallel, the two actions of the sun and the moon combine; these are the high (figure 6A) and low (figure 6B) high water tides (at the time of syzygia = full moon and new moon).

When the two major axes of the ellipses make an angle of 90 °, the actions of L and S contradict each other; these are the high (figure 6C) and low (figure 6D) tides of dead water (at the times of squaring = first quarter and last quarter).

This device gives several categories of indications for the coasts subjected to the regime of semi-diurnal tides.

• lorsque l'ellipse L a son axe vertical, c'est l'heure de marée haute,
• on voit constamment le sens du phénomène ascendant ou descendant dans une fenêtre appropriée (détail figure 3) selon la convention générale des signes
     / = croissant   \ = décroissant,
• au moyen d'un tracé d'ellipse approprié, on peut juger de la vitesse de la montée ou de la descente de la marée proportionellement à l'angle α ou β vu dans la fenêtre (figure 3) et restituer ainsi visuellement la règle des douzièmes (le niveau monte, ou baisse, de 1/12e la première heure, de 2/12 la deuxième heure, de 3/12 les troisième et quatrième heure, de 2/12e la cinquième heure et de 1/12 la sixième heure),
• la hauteur du sommet de l'ellipse L vue dans la fenêtre donne une indication sur l'amplitude de la marée (marées de morte eau et de vive eau), on peut réaliser une double échelle graduée car la hauteur des marées est liée à l'âge de la lune selon une courbe de même nature que celle de la figure 2 (les coefficients de marées sont maximum aux syzygies et minimum aux quadratures). Dans la pratique, pour séparer ces deux échelles de lecture, on peut lier l'échelle des heures de marées à l'axe J de sorte qu'elle monte et baisse verticalement en même temps que l'ellipse L, et on obtient alors la même lecture que sur l'instrument simplifié de la figure 1.

If you rotate the ellipse L anti-clockwise and the ellipse S in the direct direction:

• when the ellipse L has its vertical axis, it is high tide time,
• we constantly see the direction of the ascending or descending phenomenon in an appropriate window (detail in figure 3) according to the general convention of signs
  / = increasing \ = decreasing,
• by means of an appropriate ellipse plot, we can judge the speed of the rise or fall of the tide in proportion to the angle α or β seen in the window (Figure 3) and thus visually restore the rule of twelfths (the level goes up or down by 1 / 12th the first hour, 2/12 the second hour, 3/12 the third and fourth hour, 2 / 12th the fifth hour and 1/12 the sixth hour ),
• the height of the top of the ellipse L seen in the window gives an indication of the amplitude of the tide (dead and fresh water tides), we can make a double graduated scale because the height of the tides is linked to the age of the moon according to a curve of the same nature as that of figure 2 (the tidal coefficients are maximum at syzygies and minimum at quadratures). In practice, to separate these two reading scales, we can link the tide hours scale to the J axis so that it rises and falls vertically at the same time as the ellipse L, and we then obtain the same reading as on the simplified instrument of figure 1.

It is also possible to provide (FIG. 8) an index linked to the vertical displacement of the axis J in front of a second fixed graduation F ′ secured to the base of the device.

The height of the tides (or coefficient) varies in the same direction as the distance of the axes I and J (figure 6) measured at the time of the high sea. One can imagine a mask so that F ′ is only readable when the large ellipse L has its vertical axis.

If the two ellipses S and L rotate in the same direction, the angle γ made by their two main axes varying from 0 ° to 360 ° during a lunar cycle (Figure 7), we can read the age of the moon on a circular disc D integral with S and with the same center I (Figure 8), graduated in 29.5 lunar days. The reading of the lunar days on the disk D will be made with respect to a reference P drawn on a half major axis of the ellipse L.

This disk D can be located in front of the ellipse L as in the case of figure 8 or behind the ellipse L and, in this case, the reading will be done in a window practiced in L. This disk D can be adjustable in rotation around the center I, in relation to the ellipse S so as to adjust the lunar calendar independently of the local tide times.

We know that the speed of rotation of the ellipse L is not constant, so we will have differences in reading the age of the moon as a result of the variation from 24h38 to 24h74 mentioned previously. However, the average being exactly 24 hours and 52 minutes, the precision of this lunar calendar will be sufficient.

To restore the phenomenon of tides more completely, we can link the speed of rotation of the ellipse L to phenomena of longer period such as for example the Saros of about 18 years.

• 1) pour lire l'âge de la lune (variations de γ), les deux ellipses doivent tourner dans le même sens ;
• 2) pour percevoir du premier coup d'oeil le sens de la marée, (montante ou descendante) selon la convention habituelle des signes (croissant / ou décroissant \), l'ellipse L doit tourner en sens inverse des aiguilles d'une montre.
• 3) si l'on veut lire directement l'heure, avec 24 graduations par tour au lieu de 12 comme sur un cadran de pendule classique, l'ellipse S doit tourner dans le sens des aiguilles d'une montre.

The direction of rotation of the two ellipses does not affect the result of the tide times and heights. However:

• 1) to read the age of the moon (variations of γ), the two ellipses must rotate in the same direction;
• 2) to perceive at first glance the direction of the tide, (rising or falling) according to the usual convention of signs (increasing / or decreasing \), the ellipse L must turn in an anticlockwise direction .
• 3) if you want to read the time directly, with 24 graduations per revolution instead of 12 as on a classic pendulum dial, the ellipse S must rotate clockwise.

Claims (16)

1. A process representing the movement of the tide in which an elliptical disc is rotated in such a way as the interval of time between two successive runs of the disc's long axis and its short axis through the same point are equivalent to the time interval between high and low tide, one after the other, by making the disc rotate at a variable speed according to a curve linked to the moon's age in such a way as the disc's rotation will be at least roughly in phase with the moon's cycle, the duration of a complete rotation of the disc varying between 24hr 38min and 24hr 74min, the average rotation being 24hr 52min.
2. A processs according to claim 1 characterized by the use of the disc's contour for the control of the read-out of a graduated scale showing tidal hours.
3. A process according to claim 2, in which tidal hours are represented by graduations on a fixed scale, this scale representing the average time interval between a successive high and low tide, the disc being rotated about a perpendicular axis in the centre of the disc's plane, the elliptical disc being designed in such a way as the difference in length between the long axis and the short axis is equal to the difference between the two graduations which correspond respectively to a successive low and high tide, and the edge of the disc is used to obtain the read-out of graduations on the scale.
4. A process according to claim 3 characterized by the use of the elliptical disc's edge as a cursor on the scale.
5. A process according to claim 2 characterized by the use of the elliptical disc's edge as a cam to control the movement of an indicator on the scale.
6. A process according to one of claims 2 to 5 characterized by the use of a rectilinear scale.
7. A process according to one of the preceding claims characterized by the use of a quartz crystal and a microprocessor to control the disc's movement.
8. A process according to one of claims 1 to 7 characterized, during the disc's rotation, by the capability of displacement of the centre of the disc by means of another disc coming into contact with, like a cam, a circular track concentric to the said disc and interdependent with the said disc, by stimulating the other said disc into a rotation at a uniform speed of one rotation per 24 hrs, the ratio of the difference in lengths between the long axis and the short axis of the said elliptical disc to the difference in lengths between the long axis and the short axis of the other said disc being between 2 and 3, preferably between 2.3 and 2.7, and best of all being 2.5 or very near to it.
9. An instrument for giving the "tidal time" or indicating "tidal hours", characterized by the use of an elliptical disc (E;L) and the means (M;Z) of making the disc turn about an axis perpendicular to the disc at its centre (J) in such a way as the time interval between the successive runs of the disc's long axis and its short axis through the same position corresponds with the time interval between a succesive high and low tide, the means (M) for producing rotation of the elliptical disc (E) being such that the disc's rotation is, at least approximately, in phase with the lunar cycle.
10. An instrument according to claim 9, characterized by the use of a scale (R) graduated in tidal hours and by the fact that the difference (a-b) between the lengths of the long and short axes of the disc (E;L) is equal to the difference between the two graduations corresponding respectively to the said successive low and high tides, and by the use of the edge of the elliptical disc for obtaining the read-out of graduations on the scale (R).
11. An instrument according to claim 10, characterized by the positioning of the disc (E;L) in such a way as the edge of the disc sweeps over the said scale. (R).
12. An instrument according to claim 10, characterized by the constitution by the edge of the disc (E;L) of a cam, this cam setting into motion a cursor on the said scale (R).
13. A process according to one of claims 10 to 12 characterized by the fact that the said scale is rectilinear.
14. An instrument according to one of claims 9 to 13 characterized by the capability of displacement of the centre (3) of the said disc (L) in a straight line, actionned by another disc (S) whose centre (I) is in a fixed position and which turns about a perpendicular axis at its centre (I), this other disc (S) coming into contact with a circular track concentric to the said disc (L) like a cam, and interdependent with the said disc (L), the ratio of the difference (a-b) of the lengths between the long and short axes of the said disc (L) to the difference (c-d) between the lengths of the long and short axes of the other disc (S) being between 2 and 3, with preference between 2.3 and 2.7, and better still 2.5 or thereabouts, and the means being provided for to make this other disc rotate at a uniform speed of one rotation per 24 hours.
15. An instrument according to 14, characterized by the inclusion of a scale (F₁) with tide coefficient graduations marked and on which moves an indicator whose displacement is linked to the movement of the said disc's centre.
16. An instrument according to claim 15 characterized by the use of a circular disc (D) interdependent with the other elliptical disc (S) and with the same centre (I), this disc (D) marked with lunar day graduations, and the means defining a mark linked to the said elliptical disc (L) in order to determine the read-out of lunar days on the said circular disc (D).

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