EP0396473A1 - Method of/and device for displaying tidal movement - Google Patents

Abstract

The invention relates to the displaying of tidal movement. <??>Elipse (E) is rotated so that the time interval which elapses between successive crossings of the major axis of the elipse and of the minor axis of the elipse through a same position corresponds to the time interval which elapses between a successive high tide and low tide. <??>The invention applies to the construction of devices of any size to display tidal movement. <IMAGE>

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.

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.

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 successive high tide, 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,
- the edge of the ellipse is used as a cam to control the movement of an index on the scale,
- a straight ladder is used,
- 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 the 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 moved 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 uniform speed d '' one revolution per 24 hours, and the ratio of the difference of the lengths of the major axis and the minor axis of said ellipse to the difference of 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.

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 tide low and said high tide successive, 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 straight,
- 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 of 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;
• - Figure 2 is a curve representing the gaps 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 a 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
• - Figure 9 is a section through the apparatus of Figure 8 along planes 4-4 of Figure 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) .

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. There is also shown the rectilinear scale R, here vertical, graduated in hours of tide, in front of which the ellipse rotates so that the edge of the ellipse sweeps this scale by 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 of the variation factors, 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.

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 represent gradually 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, we 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.

If you rotate the ellipse L anti-clockwise and the ellipse S in the direct direction:
- when 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 twelfths (the level rises, or falls, 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 summit 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 conventional pendulum dial, the ellipse S must rotate clockwise.

Claims (16)

1. Method for representing the movement of a tide in which an ellipse is rotated so that the time interval which elapses 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 time interval between a successive high tide and a low tide, by rotating the ellipse at a variable speed following 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 the ellipse varying between one revolution per 24h 38mn and one revolution per 24h 74mn, with an average of one revolution per 24h 52mn . 2. Method according to claim 1, characterized in that the contour of the ellipse is used to control the reading of a scale graduated in hours of tide. 3. Method according to claim 2, in which the hours of the tide are represented by graduations on a fixed scale, the scale representing the average time interval between a high tide and a successive low tide, the ellipse around an axis perpendicular to the plane of the ellipse in its center, the ellipse being chosen so that the difference in length between the major axis and the minor axis of the ellipse is equal to the difference between the two graduations which correspond respectively to said successive low tide and said high tide, and the edge of the ellipse is used to control the reading of the graduations on the scale. 4. Method according to claim 3, characterized in that the edge of the ellipse is used as cursor on the scale. 5. Method according to claim 2, characterized in that the edge of the ellipse is used as a cam to control the movement of an index on the scale. 6. Method according to one of claims 2 to 5, characterized in that a straight ladder is used. 7. Method according to one of the preceding claims, characterized in that the movement of the ellipse is controlled by means of a quartz and a microprocessor. 8. Method according to one of claims 1 to 7, characterized in that during the rotation of the ellipse, the center is moved by means of another ellipse attacking like a cam a circular track concentric with said ellipse and integral with the said ellipse, by animating the said other ellipse with a rotation at a uniform speed of one revolution per 24 hours, the ratio of the differences in the lengths of the major axis and the minor axis of the said ellipse to the difference in the lengths of the major axis and the minor axis of said other ellipse being between 2 and 3, preferably between 2.3 and 2.7, and even better equal to 2.5 or close to 2.5. 9. Apparatus for indicating the hours of a tide, characterized in that it comprises an ellipse (E; L) and means (M; Z) for faure to rotate the ellipse around an axis perpendicular to the ellipse in its center (J) so that the time interval which elapses 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 time interval which s 'flows between a successive high tide and a low tide, the means (M) for rotating the ellipse (E) being such that the rotation of the ellipse is, at least approximately, in phase with the lunar cycle. 10. Apparatus according to claim 9, characterized in that it comprises a scale (R) graduated in hours of tide and in that the difference (ab) of the lengths of the major axis and the minor axis of the ellipse (E; L) is equal to the difference between the two graduations which correspond respectively to said successive low tide and said high tide, and the edge of the ellipse is used to control the reading of the graduations on the scale (R). 11. Apparatus according to claim 10, characterized in that the ellipse (E; L) is arranged so that the edge of the ellipse sweeps across said scale (R). 12. Apparatus according to claim 10, characterized in that the edge of the ellipse (E; L) constitutes a cam which actuates the movement of a cursor on said scale (R). 13. Apparatus according to one of claims 10 to 12, characterized in that said scale (R) is rectilinear. 14. Apparatus according to one of claims 9 to 13, characterized in that the center (J) of said ellipse (L) is movable along a straight line, under the action of another ellipse (S) whose center ( I) is fixed and which rotates around an axis perpendicular to its center (I), this other ellipse (S) attacking like a cam a circular track (N) concentric with said ellipse (L), and integral with said ellipse ( L), in that the ratio of the difference (ab) of the lengths of the major axis and the minor axis of said ellipse (L) to the difference (cd) of the lengths of the major axis and of the minor axis of said other ellipse (S ) being between 2 and 3, preferably between 2.3 and 2.7, and even better equal to 2.5 or close to 2.5, and means (Z) being provided for rotating this other ellipse at a uniform speed of 1 revolution per 24 hours. 15. Apparatus according to claim 14, characterized in that it comprises a scale (F ′) graduated in tidal coefficients and on which a movable index moves whose displacement is linked to that of the center of said ellipse. 16. Apparatus according to claim 15, characterized in that it comprises a circular disc (D) integral with said other ellipse (S) and with the same center (I), this disc being graduated in lunar days, and means defining a coordinate system linked to said ellipse (L) to determine the reading of lunar days on said disk (D).

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