Graphite on Canson paper.
20 x 30 cms.
Monday, December 28, 2009
Saturday, December 26, 2009
Gold Desert Eagle For Sale Uk
POLAR POLAR STAR AND THE SKY GUIANA. RETRIEVE A SCRATCH CD
Ciudad Guayana, the only city arising from urban planning in general has a poor sky in stars, the sky is almost always covered by a thin layer of clouds that dimmed the glow of the stars, the fog gets thicker as far as our eyes down to horizon.
Eventually, in the months of December and January the Guianan we witnessed an extraordinary change in the appearance of the sky, the atmosphere is lighter, the eternal haze appears decreasing clouds disappear and allowing us to enjoy a clear sky, clear blue by day and quite starry night, is in these few moments, if we look to the North not far above the horizon will see a pale and solitary star.
THE NORTH STAR AND THE SKY OF GUIANA.
Ciudad Guayana, the only city arising from urban planning in general has a poor sky in stars, the sky is almost always covered by a thin layer of clouds that dimmed the glow of the stars, the fog gets thicker as far as our eyes down to horizon.
At night it is normal to see around street lamps a subtle halo around them, no matter what time of night, there is always that strange mist whose origin is difficult to know its origin may be the result Air Pollution basic business product found on the perimeter of the city or a weather phenomenon on our unique position geographically, with the plains to the north, south and jungle in the east the Atlantic Ocean instead of the windward of the prevailing winds. Personally I believe more in the climate option but can not rule out industrial pollution.
is for this fog with the glow of city lights the sky in Guyana is particularly poor in stars allowing only those with the highest intensity observed hiding the bulk of the stellar population. Here usually we can only observe stars up to magnitude +3. On the horizon the lack of stars is particularly marked by mist and / or the clouds that are frequently observed.
I've always loved astronomy and yet never had the opportunity to observe the North Star, because in my youth watching the skies of Caracas and the Avila along with the imposing Pico Oriental Naiguatá and prevented me from your vision. The times I spend the night at these summits, the sea mist ever prevented the observation of this star so special.
sky Guiana This consent allows me to enjoy the Polar Star, the axis of the sky.
Eventually, in the months of December and January the Guianan we witnessed an extraordinary change in the appearance of the sky, the atmosphere is lighter, the eternal haze appears decreasing clouds disappear and allowing us to enjoy a clear sky, clear blue by day and quite starry night, is in these few moments, if we look to the North not far above the horizon will see a pale and solitary star.
This star is the north star, Polaris, or as identified on the planispheres, α Ursae Minori to be the main star of the constellation Ursa Minor. " Astro
unique glow modest (magnitude of +2) that we wonder why she does not bother by the movement of her companions, planets or the Sun itself, as all seem to revolve around it ... ... ..
December 2009
Tuesday, December 22, 2009
Cydia Pokemon Roms Source
Tanned Sorcerer That Ninoska
My love with summer color.
Oil on MDF.
39 x 29 cms.
Thursday, December 17, 2009
Monday, December 14, 2009
Cm 5 Days Before Period
Art Nouveau Collection. Graphite on Canson special role. 2009. Approx. 20 x 30 cms. In Sale!
Friday, December 11, 2009
Most Reliable Notebook 2010
Moon Half Moon Water Group Exhibition ESAN
Art Nouveau Series. Graphite on Canson paper.
SALE!
Tuesday, December 1, 2009
Kates Playground 2010 Stream
RETRIEVE A scratched CD.
A method easy home run.
In more than one occasion we had to throw the odd CD with information of interest or a little game for the computer because of scratches on the surface of the polycarbonate, ie face away from the plating where the labels are written .
When trying to read a CD with a line that can be deep or shallow with many stripes, just the CD in our PC can not read it and eventually we reported a problem in reading. The source of the trouble is that the laser beam is deflected by the line as a prism or diffusing the light beam by preventing the reflection of it in the plating return to photo diode receiver.
A less drastic solution to throw our CD is trying to erase the lines or polishing the CD using either toothpaste or a polishing compound silver ornaments.
's worth a try as we lose nothing by doing so and if we can win instead of just throw our valuable CD.
The intention of this post is to explain my experience with it, since I have used this procedure on two occasions (the third to make the post) with satisfactory results. Getting a CD player could read them allowing me to backup information.
For the purposes of this procedure manual is to be a little patient, because the speed with which they can eliminate the stripes is slow to negligible values, depending on the employee polishing the optical surface can be a bit dull due to " grain "of the compound that we are using to polish, if very fine, polished face of the CD will be perfect.
This procedure is simple, we only need silver polish, or abrasive paste or liquid with fine-grained, soft, clean cloth, and scrub hard surface damaged. Never apply this procedure on the side of the platinum or labels. If the line is on this side and "started" the silver of the face, we lost the CD.
A method easy home run.
In more than one occasion we had to throw the odd CD with information of interest or a little game for the computer because of scratches on the surface of the polycarbonate, ie face away from the plating where the labels are written .
When trying to read a CD with a line that can be deep or shallow with many stripes, just the CD in our PC can not read it and eventually we reported a problem in reading. The source of the trouble is that the laser beam is deflected by the line as a prism or diffusing the light beam by preventing the reflection of it in the plating return to photo diode receiver.
A less drastic solution to throw our CD is trying to erase the lines or polishing the CD using either toothpaste or a polishing compound silver ornaments.
's worth a try as we lose nothing by doing so and if we can win instead of just throw our valuable CD.
The intention of this post is to explain my experience with it, since I have used this procedure on two occasions (the third to make the post) with satisfactory results. Getting a CD player could read them allowing me to backup information.
For the purposes of this procedure manual is to be a little patient, because the speed with which they can eliminate the stripes is slow to negligible values, depending on the employee polishing the optical surface can be a bit dull due to " grain "of the compound that we are using to polish, if very fine, polished face of the CD will be perfect.
This procedure is simple, we only need silver polish, or abrasive paste or liquid with fine-grained, soft, clean cloth, and scrub hard surface damaged. Never apply this procedure on the side of the platinum or labels. If the line is on this side and "started" the silver of the face, we lost the CD.
Also be careful and treat it possible that the platinum layer is not affected during this procedure, I mean, come off at the edges of the CD or the central area near the hole spin because the cleaner- polish we use.
By reducing the lines to the point that they are only a shadow of what they were, the laser light is diffused CD or refracted slightly, allowing the player to read the CD. Achieved, it is best to perform a backup.
For this test, use a CD in good condition that we painted intentionally.
The following images show step by step method of recovery:
By reducing the lines to the point that they are only a shadow of what they were, the laser light is diffused CD or refracted slightly, allowing the player to read the CD. Achieved, it is best to perform a backup.
For this test, use a CD in good condition that we painted intentionally.
The following images show step by step method of recovery:
image of the CD browser.
original CD surface.
scratched surface of the CD, in this case was intentional to show the procedure.
Note that the transparent surface was very scratched and some deep scratches.
To minimize the risk of damaging or scratching the silvery side of the CD, put it on a soft, clean, dust free and supported on a flat surface.
We added the silver polish.
precedes polishing, scrubbing and replacing the surface polish if necessary.
We do making circles around the surface to be polished to avoid leaving a pattern of polishing.
Shortly after starting the polishing process can see the improvement in scratch.
Each time you want to check the progress of polishing, retired with a soft cotton cloth, clean and dry the traces of silver polish.
polishing final appearance.
With the polished surface, the CD / DVD shows the contents of the CD that had not recovered could be shown.
The method works because the grinding grubbed a thin layer of transparent optical plastic eta CD is removed from the line, to be polished or at least very shallow scratches, the CD / DVD will have no problem reading it again. You can take the opportunity to make a backup CD.
As shown, the procedure is simple and economical and best of all is that we could save the information contained on the CD.
polished quality will be determined primarily our own standards of work and even with good patience or using a machine to help us with the polished surface quality stay the same or better than the original.
Obviously depending on the damage to the CD in the clearcoat, you may not achieve enough to polish the CD is read by the reader's computer, however, as I mentioned, it is worth trying.
Monday, November 2, 2009
Pinnacle Tv Center 150e/55e
I'm participating in the exhibition "Traces, colors and textures" in the university gallery ESAN (CENDOC / library).
The opening is Friday November 6, time 7:00 pm.
encopntrarme hope with all my friends there and please warn all those who wish to acquire great works of art.
Sunday, November 1, 2009
Boscovs Free Shipping 2010
SOLAR TIME, TIME LEGAL. - II -
The time difference between the meridian of Puerto Ordaz and the Rio Chico is 3 °: 33 '(-62 °: 27'-[-66 °]), corresponding in time: 14 minutes 12 seconds ahead.
taken as the time zone to regulate the legal time in Venezuela is the -4:30 'UTC, the meridian that corresponds to the Time Zone is -67 °: 30' (15 ° x -4:30 ') the Chico River Meridian disagrees in 1 °: 30 '(-66 ° - [-67 ° 30']) which led in time is 6 minutes fast (1 °: 30 'x 4 minutes), which implies that time difference between the Meridian of Time Zone and Puerto Ordaz is 20 '12 "ahead.
For September 2, Equation of Time is to +3 seconds, which added to the time between meridian gives the total of 20 ': 15. "
However, due to poor resolution in the graduation of our quadrant azimuthal orientation error sundial with respect to the meridian of Puerto Ordaz and omitting the second, we can clearly see that the discrepancies in the photograph is 20 minutes ahead of the sundial with respect to the mechanical clock (synchronized by the Cajigal Observatory) is for all practical purposes identical to the 20 minutes calculated.
By 20 September, the equation of time is +6 minutes rounding, which according to the above, the advancement of the clock Sun should be 26 minutes, 20 minutes corresponding to the time difference between meridians and 6 minutes of the Equation of Time. The next picture shows time and time Solar Legal.
can clearly see that the shadow of the gnomon is very close to 3 pm while the cellular clock indicates 2:34 PM, so that the time difference is (3h: 0m- 2h: 34m) for 26 minutes, as expected value.
The photograph below shows the time Solar and Legal for October 1, 2009.
The difference in date is approximately one month compared with the first record, yet We can easily see that the discrepancy between the sundial and the bracelet is 30 minutes and we can see that the difference of 20 'we had in the first record of the previous month but not maintained the sundial and the mechanic are exactly in the same place.
What has changed between a date and the other is the true position of the Sun to the Sun means and the time difference between the two suns is 10 minutes 4 seconds according to the tables that determine the equation of time for the first October. Again, if the time difference product of the separation between the meridian (20 ') we add the value of the Equation of Time for the day in question we obtain that the time difference between the sundial and the mechanical clock is 30 minutes which is noted in the photograph.
With these examples, it is clear that the time difference normally seen between the sundial and the mechanic has two sources, first to the angular distance between the meridian of the place where is located the sundial and the Meridian Country reference to establish the Legal Time and second, by the separation that currently exists for the measurement of time between the hour circle of the sun mean sun and the true, the so-called equation of time.
In our case at this latitude and location, the best time for both clocks den "same time" would be for the February 15, when the equation of time is -14:09 minutes so that the difference between the clocks would be 5 minutes.
Obviously the time difference of the clocks directly read is not accurate to the calculations due to various errors in the sundial (manufacturing details, orientation, resolution, width of the gnomon, etc), besides the digital clock employee only shows the minutes. Considering that only employ minutes and round values, our "uncertainty" between the measured with digital clock and the calculated cell should be around 2 minutes in the best. However, within minutes the results are excellent.
I tried to be worn in a very tangled subject, with the hope that this report has not confused over what they were and that allows the reader to understand better what the measurement of time, that when one is facing these strange and beautiful instruments Solares know the reason why they differ from the hours between his watch and clock Sun ... ... In my opinion, I think the graphics displayed cases accurate enough to leave no doubt about the origin of the discrepancy between the sundial and clock time gives us Legal.
SOLAR TIME, TIME LEGAL. - II -
Sundial vs Mechanical Watch
Trying to understand time.
The intention of the previous post is to show a more explicit, rational or justified, by the sundial hours usually vary with time in the watch and not just say simply that the difference is observed is due to the mechanical watch is the movement of an imaginary sun gear and the sun regularly makes true variable-speed ahead at times and falling behind in others. How curious is the engine of our intelligence wanted to go for the more anxious a possible route that took us to unravel the mystery of the mean sun, from where he and his close relationship with the real sun.
Also, we know that this imaginary Sun called "Sun Media" is conveniently placed Ecuador on the other blue and that his commuting from west to east is performed at a constant rate throughout the year. As your speed is the average value of true solar day length throughout the year, while the real sun, which directly controls our lives moves over the sky at variable speed and makes bending over Ecuador blue, for this two cases, at some time during the real Sun is ahead of the mean sun, otherwise you fall behind and in another match. Because these oscillations Sun's true that is placed on one side or the other of the mean sun, our watch does not indicate the time recorded by the sundial but was compensated for the time difference between the meridian of reference to establish the Legal Time and longitude on which is the sun clock
Something else we learned in the last post is that the time difference between the sundial and the wrist is due to two causes conjugate of geographic origin and other astronomical. The cause is geographically the angular difference between the reference meridian and the Time Zone adopted by the country and the meridian where the sundial taken hours. The cause is due to astronomical annual movement Sun in the sky.
Again, comparing the mean solar day about Sidereal day, this is late with respect to the sidereal time in 3 minutes 56.5554 seconds each day. Hence if we consider the sidereal day of 24 hours, the mean solar day has 24 hours 3 minutes 56.5 seconds and if the basis is a 24-hour solar day, sidereal day have 23 hours 56 minutes 3.4 seconds long.
The reason that the mean solar day is delayed with respect to the sidereal day is due to the displacement of the earth around the sun
Being the center "O" land "T1" line and a star turn with the center of the sun and those with the meridian of the place (OS line in Figure 6), in the course of a sidereal day the Earth changes from "T1" to "T2" to travel on its orbit, leaving the star "E "again aligned with the meridian (O'-E), but due to displacement, the sun," S "is not completed yet and need additional time to elapse so that the angle" SO'-E "is fulfilled and the sun reaches the meridian.
Sundial vs Mechanical Watch
Trying to understand time.
The intention of the previous post is to show a more explicit, rational or justified, by the sundial hours usually vary with time in the watch and not just say simply that the difference is observed is due to the mechanical watch is the movement of an imaginary sun gear and the sun regularly makes true variable-speed ahead at times and falling behind in others. How curious is the engine of our intelligence wanted to go for the more anxious a possible route that took us to unravel the mystery of the mean sun, from where he and his close relationship with the real sun.
Also, we know that this imaginary Sun called "Sun Media" is conveniently placed Ecuador on the other blue and that his commuting from west to east is performed at a constant rate throughout the year. As your speed is the average value of true solar day length throughout the year, while the real sun, which directly controls our lives moves over the sky at variable speed and makes bending over Ecuador blue, for this two cases, at some time during the real Sun is ahead of the mean sun, otherwise you fall behind and in another match. Because these oscillations Sun's true that is placed on one side or the other of the mean sun, our watch does not indicate the time recorded by the sundial but was compensated for the time difference between the meridian of reference to establish the Legal Time and longitude on which is the sun clock
Something else we learned in the last post is that the time difference between the sundial and the wrist is due to two causes conjugate of geographic origin and other astronomical. The cause is geographically the angular difference between the reference meridian and the Time Zone adopted by the country and the meridian where the sundial taken hours. The cause is due to astronomical annual movement Sun in the sky.
Again, comparing the mean solar day about Sidereal day, this is late with respect to the sidereal time in 3 minutes 56.5554 seconds each day. Hence if we consider the sidereal day of 24 hours, the mean solar day has 24 hours 3 minutes 56.5 seconds and if the basis is a 24-hour solar day, sidereal day have 23 hours 56 minutes 3.4 seconds long.
The reason that the mean solar day is delayed with respect to the sidereal day is due to the displacement of the earth around the sun
Being the center "O" land "T1" line and a star turn with the center of the sun and those with the meridian of the place (OS line in Figure 6), in the course of a sidereal day the Earth changes from "T1" to "T2" to travel on its orbit, leaving the star "E "again aligned with the meridian (O'-E), but due to displacement, the sun," S "is not completed yet and need additional time to elapse so that the angle" SO'-E "is fulfilled and the sun reaches the meridian.
The phenomenon occurs because the stars are extremely far from Earth and translational movement of the world practically does not alter the position of the star in the sky, while the Sun is very close and their position in the sky is strongly affected by the translation.
The reason is not used Sidereal time despite constant for the adjustment of mechanical watches is due to the delay of the mean sun (and thus the true sun is always close to the average Sun) day by day so that after 6 months, the watch indicate almost noon when the sun is as true midnight would have moved across the world as a tour along the ecliptic.
The sidereal time is used in astronomy to indicate hours of celestial phenomena and ease of monitoring of the stars with telescopes.
After this torturous journey from where you know the average time is regulating the progress of our watches.
· · · 0 · · ·
from 09 December in the year 2007 the National Executive declares a time zone change, from UTC -4:00 to UTC -4:30, implying Watch our nationwide were delayed 30 minutes. Although information about what meridian is taking the official time is confusing, some say it is the meridian passing through Rio Chico (-66 °) and others that passes near Villa de Cura (-67 °: 30 '). Regardless of the meridian in question, time is fixed to the spindle -4:30, which means that in one case an additional adjustment is necessary to obtain the value of -4:30 and the other does not.
For demonstration purposes, we will take as a reference meridian passing through Chico River which corresponds to -66 ° and the longitude of Puerto Ordaz where the sundial corresponds to -62 °: 27 ' . Measurements were taken on 2 September 2009 as shown in the picture below.
The time difference between the meridian of Puerto Ordaz and the Rio Chico is 3 °: 33 '(-62 °: 27'-[-66 °]), corresponding in time: 14 minutes 12 seconds ahead.
taken as the time zone to regulate the legal time in Venezuela is the -4:30 'UTC, the meridian that corresponds to the Time Zone is -67 °: 30' (15 ° x -4:30 ') the Chico River Meridian disagrees in 1 °: 30 '(-66 ° - [-67 ° 30']) which led in time is 6 minutes fast (1 °: 30 'x 4 minutes), which implies that time difference between the Meridian of Time Zone and Puerto Ordaz is 20 '12 "ahead.
For September 2, Equation of Time is to +3 seconds, which added to the time between meridian gives the total of 20 ': 15. "
However, due to poor resolution in the graduation of our quadrant azimuthal orientation error sundial with respect to the meridian of Puerto Ordaz and omitting the second, we can clearly see that the discrepancies in the photograph is 20 minutes ahead of the sundial with respect to the mechanical clock (synchronized by the Cajigal Observatory) is for all practical purposes identical to the 20 minutes calculated.
By 20 September, the equation of time is +6 minutes rounding, which according to the above, the advancement of the clock Sun should be 26 minutes, 20 minutes corresponding to the time difference between meridians and 6 minutes of the Equation of Time. The next picture shows time and time Solar Legal.
can clearly see that the shadow of the gnomon is very close to 3 pm while the cellular clock indicates 2:34 PM, so that the time difference is (3h: 0m- 2h: 34m) for 26 minutes, as expected value.
The photograph below shows the time Solar and Legal for October 1, 2009.
The difference in date is approximately one month compared with the first record, yet We can easily see that the discrepancy between the sundial and the bracelet is 30 minutes and we can see that the difference of 20 'we had in the first record of the previous month but not maintained the sundial and the mechanic are exactly in the same place.
What has changed between a date and the other is the true position of the Sun to the Sun means and the time difference between the two suns is 10 minutes 4 seconds according to the tables that determine the equation of time for the first October. Again, if the time difference product of the separation between the meridian (20 ') we add the value of the Equation of Time for the day in question we obtain that the time difference between the sundial and the mechanical clock is 30 minutes which is noted in the photograph.
With these examples, it is clear that the time difference normally seen between the sundial and the mechanic has two sources, first to the angular distance between the meridian of the place where is located the sundial and the Meridian Country reference to establish the Legal Time and second, by the separation that currently exists for the measurement of time between the hour circle of the sun mean sun and the true, the so-called equation of time.
In our case at this latitude and location, the best time for both clocks den "same time" would be for the February 15, when the equation of time is -14:09 minutes so that the difference between the clocks would be 5 minutes.
Obviously the time difference of the clocks directly read is not accurate to the calculations due to various errors in the sundial (manufacturing details, orientation, resolution, width of the gnomon, etc), besides the digital clock employee only shows the minutes. Considering that only employ minutes and round values, our "uncertainty" between the measured with digital clock and the calculated cell should be around 2 minutes in the best. However, within minutes the results are excellent.
I tried to be worn in a very tangled subject, with the hope that this report has not confused over what they were and that allows the reader to understand better what the measurement of time, that when one is facing these strange and beautiful instruments Solares know the reason why they differ from the hours between his watch and clock Sun ... ... In my opinion, I think the graphics displayed cases accurate enough to leave no doubt about the origin of the discrepancy between the sundial and clock time gives us Legal.
Thursday, October 15, 2009
Wording For Deceased On Wedding Program
"V" Pink Fabric
September 2009. 
New Series Art Nouveau.
September 2009.
"V"
special Graphite on Canson paper. Approx. 20 x 30 cms.
SALE!
Saturday, October 3, 2009
Hypoglycemia And Thrush'
SOLAR TIME, TIME LEGAL. - I -
Trying to understand time.
in the previous release for the sundial azimuthal quadrant had highlighted the phenomenon of the time displayed by the clock "mechanical" and that shown by the sundial for the time differed from the picture in about 20 minutes and This lack of agreement was interpreted by people as a defect in construction or design of the sundial, forgetting the fact that our watch is who in any case we would be lying on the hour. No matter
the way on how you look, but the Sun that governs our lives since the beginning of time. It is the Sun which tells us when to leave and when to return. It's the Sun that inspires and feeds, not all cultures in vain they worship Him, either endian or just bronze ... and the Sun with whom you try to set the hours and day length.
try to be brief and explicit in a very confusing topic and wide, trying to clear our concern for the cause of the discrepancy between solar time and clock time "mechanic." Although today most of our watches are electronic, we will define as "mechanical" all man-made clocks and whose hours regularly pass every day.
The establishment of "time", has proven to be an astronomical task quite difficult and this is evidenced by the existence in the "times" following
Sidereal Time.
Time.
True Solar Time, or Time.
mean solar time.
Civil Time.
Astronomical Clock.
Standard Time (Official Time).
Universal Time (UTC), among others. Before proceeding
remember a little regard to geographical and celestial coordinates.
relying on the figure below, in the geographic coordinate system we have the north pole "N" and the south pole "S" through which passes the axis of rotation of the Earth and the plane perpendicular to this axis that cuts into two equal parts the globe is the Earth Ecuador. Any plane parallel to Ecuador determines a geographical parallel to Ecuador as a distance on a meridian plane determines North and South latitude parallel.
Prolonging the world axis passing through the pole "N" and "S" in the sky determines the North and South Celestial Poles or Boreal and Austral (P and P ') and is the imaginary axis on which the stars rotate with the apparent movement from east to west. The projection of the Earth Ecuador in Ecuador determines the blue sky.
The extension of the flat southern or meridian lines in the sky determines the hour circle.
the same way that the Earth is measured the latitude of a place on a meridian, the sky is measured in the "decline" (d) to a celestial body on its Circle Time and is the angular distance separating it from Ecuador Celeste. The decline is positive (+), Northern Lights or and minus (-), South Austral otherwise.
Corresponding to the longitude, the sky is called Right Ascension (RA) to the angle formed by the Circle Time the star with the hour circle of vernal point or point Aries, which is taken into the sky as the origin of right ascensions. The right ascensions (RA) is measured from west to east as the sun moves throughout the year, ie, contrary to the apparent motion of stars in the sky and is given in time. The point of origin, or Aries vernal point is the point of intersection between Ecuador and the Ecliptic Celeste. This point indicates the Spring Equinox falls 21 March. At this intersection, the Sun moves across the sky in their annual travel passes from the southern hemisphere to northern hemisphere. In conclusion, on the celestial sphere Circle Time that passes through the Vernal Point is equivalent the prime meridian or Greenwich geographic.
On the other hand, if an observer "A" on Earth is the sun, culminating in its meridian, to the observer "B" at the very moment the sun is not on the meridian, but shifted to the east. There should be a time "H" for the sun to fill the new position "S" (Circle Time) on the meridian of the observer "B", see figure below.
Returning to the measurement of time, cases of interest are the Legal Time and True Solar Time, with the True Solar Time True Local Time, which is unique to where you are measuring. This time is defined by the position of the sun in the sky with respect to the meridian of the place and mark the noon just as the sun is on the meridian. True Solar Time is precisely the time indicated by sundials.
legal time is the time taken by the government of a country to set the time in all its national territory and refers to a particular meridian as a reference point for setting the clocks on its territory, in turn, this reference meridian is referred to an international time zones, which in the case of Venezuela the government adopted corresponding to -4:30 UTC (Coordinated Universal Time). Which means that the Legal Time in Venezuela is behind in 4 hours 30 minutes with respect to Universal Time taken on the meridian "LOST" or Greenwich. In short, the legal time is the time indicated by clocks "mechanism", as our clock bracelet.
If the reference meridian have a sundial at noon the watch should be given the same time that the clock of the Sun To the extent that the sundial is relocated to the east or west of this meridian reference , the hours reported by both clocks start to differ, fast or slow the sundial with respect to the wristwatch, the discrepancy being equal to the angular difference between the meridian on the location of the sundial and the meridian of reference taken to "hours", ie its hour angle. Remember that you can give the location of the Sun or any celestial body in hours with respect to a meridian is taken as reference.
To clarify: if the reference meridian for a country is -60 ° (longitude W 60) and the sundial is on the meridian -70 °, the time difference between them is the angular difference between the meridian sundial and the reference meridian, hence -70 ° - (-60 °) = -10 °. We know by definition that 15 ° is 1 hour and therefore 1 ° are 4 minutes from half time, the time difference between both clocks is -10 ° x 4 minutes = -40 minutes, (the hour angle between the sundial and the reference meridian is -40 minutes). That is, the sundial would be 40 minutes late with respect to the wristwatch, so that when the clock mechanical indicates 12 pm, the sundial on the meridian -70 ° accuse 11:20 AM.
up lines I wrote that "should give equal time if the sundial was on the reference meridian", what happens is that they usually do not agree on a certain number of minutes and this is where the complication begins.
The problem started when astronomers try to set the duration of 24 hours a day on accurate with reference to the Sun By measuring the time when a star passes the meridian twice in the place of observation and do the same with Sol, put in comments clear that "solar day" is different from "day Sidereal ", that the difference between the two days is not constant throughout the year, declining in a few months and increasing in others.
Viewed from Earth, the Sun has two simultaneous movements in the sky, the most obvious is that provided for the nights and days and goes from east to west, the other movement is slower and goes from east to west similar to that done during the moon phase changes. This last movement of the Sun is what allows us to see new stars and constellations each month, is that we change the starry nights of spring by winter and is also responsible for all four seasons.
The Sun's path in sky is called ecliptic, and through the constellations of the zodiac, provided the Sun a year to complete a cycle on this path.
The movement of the sun that determines the days and nights due to the rotation of the Earth on its axis, viewed from space above the north pole is done in a counterclockwise direction, as reflected in the sky as Sun's apparent motion that allows us to see the sunrise and sunset to the west.
On the other hand, the movement of the sun determines the seasons, going from west to east along the year is due to the shifting of the Earth around the Sun, seen from space above the north pole is it anti-clockwise, but since the Earth is reflected in the sky as a translation from east to west. As the rotation axis is tilted with respect to the orbital plane, the Sun's apparent annual movement across the sky is not made on the celestial Ecuador, but in a path inclined with respect to the equator, known as the ecliptic.
Earth's orbit is an ellipse where the Sun occupies one focus, resulting from this is that the distance between two bodies varies as the Earth orbits the Sun With the change of distance, force gravitational changes as well and to maintain the dynamic equilibrium and the earth does not end up clashing with the Sun, the travel speed is variable, so that being near the Sun the Earth moves faster than when you are away. Johannes Kepler from the observations of the motion of the planets, particularly Mars had noticed that the planets move with greater speed during the approach to the Sun that during his departure, less of this behavior his second law, which postulates that areas swept by a planet in equal times are equal.
SOLAR TIME, TIME LEGAL. - I -
Sundial Clock Mechanical vs
Sundial Clock Mechanical vs
Trying to understand time.
in the previous release for the sundial azimuthal quadrant had highlighted the phenomenon of the time displayed by the clock "mechanical" and that shown by the sundial for the time differed from the picture in about 20 minutes and This lack of agreement was interpreted by people as a defect in construction or design of the sundial, forgetting the fact that our watch is who in any case we would be lying on the hour. No matter
the way on how you look, but the Sun that governs our lives since the beginning of time. It is the Sun which tells us when to leave and when to return. It's the Sun that inspires and feeds, not all cultures in vain they worship Him, either endian or just bronze ... and the Sun with whom you try to set the hours and day length.
try to be brief and explicit in a very confusing topic and wide, trying to clear our concern for the cause of the discrepancy between solar time and clock time "mechanic." Although today most of our watches are electronic, we will define as "mechanical" all man-made clocks and whose hours regularly pass every day.
The establishment of "time", has proven to be an astronomical task quite difficult and this is evidenced by the existence in the "times" following
Sidereal Time.
Time.
True Solar Time, or Time.
mean solar time.
Civil Time.
Astronomical Clock.
Standard Time (Official Time).
Universal Time (UTC), among others. Before proceeding
remember a little regard to geographical and celestial coordinates.
relying on the figure below, in the geographic coordinate system we have the north pole "N" and the south pole "S" through which passes the axis of rotation of the Earth and the plane perpendicular to this axis that cuts into two equal parts the globe is the Earth Ecuador. Any plane parallel to Ecuador determines a geographical parallel to Ecuador as a distance on a meridian plane determines North and South latitude parallel.
The line crossing the surface of the sphere representing the Earth and connects the poles "N" and "S" is the southern or meridian line and the distance between two lines measures in the southern Ecuador gives the difference in length between the two meridians. The length of a geographical point is determined by the angular distance between the level of Ecuador reference meridian of Greenwich or Prime Meridian and the Meridian passing through the location of the point. The length is East (E) or west (W) at this Meridian, if not referenced "E" or "W" to the plans are positive west south and east are counted negative.
Prolonging the world axis passing through the pole "N" and "S" in the sky determines the North and South Celestial Poles or Boreal and Austral (P and P ') and is the imaginary axis on which the stars rotate with the apparent movement from east to west. The projection of the Earth Ecuador in Ecuador determines the blue sky.
The extension of the flat southern or meridian lines in the sky determines the hour circle.
the same way that the Earth is measured the latitude of a place on a meridian, the sky is measured in the "decline" (d) to a celestial body on its Circle Time and is the angular distance separating it from Ecuador Celeste. The decline is positive (+), Northern Lights or and minus (-), South Austral otherwise.
Corresponding to the longitude, the sky is called Right Ascension (RA) to the angle formed by the Circle Time the star with the hour circle of vernal point or point Aries, which is taken into the sky as the origin of right ascensions. The right ascensions (RA) is measured from west to east as the sun moves throughout the year, ie, contrary to the apparent motion of stars in the sky and is given in time. The point of origin, or Aries vernal point is the point of intersection between Ecuador and the Ecliptic Celeste. This point indicates the Spring Equinox falls 21 March. At this intersection, the Sun moves across the sky in their annual travel passes from the southern hemisphere to northern hemisphere. In conclusion, on the celestial sphere Circle Time that passes through the Vernal Point is equivalent the prime meridian or Greenwich geographic.
On the other hand, if an observer "A" on Earth is the sun, culminating in its meridian, to the observer "B" at the very moment the sun is not on the meridian, but shifted to the east. There should be a time "H" for the sun to fill the new position "S" (Circle Time) on the meridian of the observer "B", see figure below.
In this way we can set the time difference between observer A and observer "B", ie has to distance in time (hours, minutes and / or seconds) is the observer "A" observer "B". The Earth takes 24 hours to complete a full 360 degrees so that each hour represents an angular displacement of 15 degrees. In fact, by convention, the globe has been divided into 24 time zones from Greenwich, are counted towards this positive and negative if taken in a westerly direction. In the case of Venezuela, the reference time zone to set the time in the country is in the UTC -4:30, indicating that we are 4 hours and 30 minutes late with respect to the time taken in Greenwich or seeing another Thus, while the sun at noon on the Greenwich meridian must spend 4 hours and 30 minutes for the sun is just above our reference meridian and indicating that it is noon. This UTC -4:30 time zone corresponds to the length -67.50 °, which is the same as the meridian +292.5 °.
Returning to the measurement of time, cases of interest are the Legal Time and True Solar Time, with the True Solar Time True Local Time, which is unique to where you are measuring. This time is defined by the position of the sun in the sky with respect to the meridian of the place and mark the noon just as the sun is on the meridian. True Solar Time is precisely the time indicated by sundials.
legal time is the time taken by the government of a country to set the time in all its national territory and refers to a particular meridian as a reference point for setting the clocks on its territory, in turn, this reference meridian is referred to an international time zones, which in the case of Venezuela the government adopted corresponding to -4:30 UTC (Coordinated Universal Time). Which means that the Legal Time in Venezuela is behind in 4 hours 30 minutes with respect to Universal Time taken on the meridian "LOST" or Greenwich. In short, the legal time is the time indicated by clocks "mechanism", as our clock bracelet.
If the reference meridian have a sundial at noon the watch should be given the same time that the clock of the Sun To the extent that the sundial is relocated to the east or west of this meridian reference , the hours reported by both clocks start to differ, fast or slow the sundial with respect to the wristwatch, the discrepancy being equal to the angular difference between the meridian on the location of the sundial and the meridian of reference taken to "hours", ie its hour angle. Remember that you can give the location of the Sun or any celestial body in hours with respect to a meridian is taken as reference.
To clarify: if the reference meridian for a country is -60 ° (longitude W 60) and the sundial is on the meridian -70 °, the time difference between them is the angular difference between the meridian sundial and the reference meridian, hence -70 ° - (-60 °) = -10 °. We know by definition that 15 ° is 1 hour and therefore 1 ° are 4 minutes from half time, the time difference between both clocks is -10 ° x 4 minutes = -40 minutes, (the hour angle between the sundial and the reference meridian is -40 minutes). That is, the sundial would be 40 minutes late with respect to the wristwatch, so that when the clock mechanical indicates 12 pm, the sundial on the meridian -70 ° accuse 11:20 AM.
up lines I wrote that "should give equal time if the sundial was on the reference meridian", what happens is that they usually do not agree on a certain number of minutes and this is where the complication begins.
The problem started when astronomers try to set the duration of 24 hours a day on accurate with reference to the Sun By measuring the time when a star passes the meridian twice in the place of observation and do the same with Sol, put in comments clear that "solar day" is different from "day Sidereal ", that the difference between the two days is not constant throughout the year, declining in a few months and increasing in others.
Viewed from Earth, the Sun has two simultaneous movements in the sky, the most obvious is that provided for the nights and days and goes from east to west, the other movement is slower and goes from east to west similar to that done during the moon phase changes. This last movement of the Sun is what allows us to see new stars and constellations each month, is that we change the starry nights of spring by winter and is also responsible for all four seasons.
The Sun's path in sky is called ecliptic, and through the constellations of the zodiac, provided the Sun a year to complete a cycle on this path.
The movement of the sun that determines the days and nights due to the rotation of the Earth on its axis, viewed from space above the north pole is done in a counterclockwise direction, as reflected in the sky as Sun's apparent motion that allows us to see the sunrise and sunset to the west.
On the other hand, the movement of the sun determines the seasons, going from west to east along the year is due to the shifting of the Earth around the Sun, seen from space above the north pole is it anti-clockwise, but since the Earth is reflected in the sky as a translation from east to west. As the rotation axis is tilted with respect to the orbital plane, the Sun's apparent annual movement across the sky is not made on the celestial Ecuador, but in a path inclined with respect to the equator, known as the ecliptic.
Earth's orbit is an ellipse where the Sun occupies one focus, resulting from this is that the distance between two bodies varies as the Earth orbits the Sun With the change of distance, force gravitational changes as well and to maintain the dynamic equilibrium and the earth does not end up clashing with the Sun, the travel speed is variable, so that being near the Sun the Earth moves faster than when you are away. Johannes Kepler from the observations of the motion of the planets, particularly Mars had noticed that the planets move with greater speed during the approach to the Sun that during his departure, less of this behavior his second law, which postulates that areas swept by a planet in equal times are equal.
FIGURE 1
The drawing above (figure 1) allows us to visualize the second law of Kepler. Earth when it is near perihelion moves quickly and after a while "T" is changed from P1 to P2 sweeping the area A1 of the graph. When close to apohelio (aphelion) moves slowly from P3 to P4 and sweeping the area A2 for the same time "T". For areas A1 and A2 are equal to require the speed of the Earth at aphelion is lower than at perihelion.
Taking the earth as our frame of reference and considering fixed, describing the Earth orbits around the Sun is projected on the sky so that it is the Sun who apparently moves around the Earth in an elliptical orbit.
The Sun's position can be referred to the axis connecting the peak with the perigee, line "B" B1 "in Figure 2, or referred to the line" Aries-Libra "(A-Li) corresponding to the line of intersection between the plane of the ecliptic Ecuador and blue.
FIGURE 2 is called "anomaly" of the Sun the angle between the axis of the apses and the sun as shown in Figure 2.
The "length" of the Sun is the angle formed by it with respect to the line of the equinoxes "A-Li", if we take the point position of the Sun "S2" in Figure 2, the Sun's longitude is defined by the angle "AT-S2" measured or ever taken in the direction of motion of the Sun is preferred to use the "length" of the sun instead of the "anomaly" for measurements and take the origin of celestial coordinates is the vernal point.
The "length" of the Sun is not commensurate with the time due to irregular motion and is referred to as the orbital speed change daily traffic is reflected in the Sun for the reason sky where the Sun is not true serves as an indicator of the time because it is an element of variable speed clocks reproducible.
To avoid this drawback, measurements do a lot of true solar day length and its average value is obtained (compared with the sidereal time), so we have a fictitious Sun moving at constant speed on the ecliptic and it takes just as Sun to cover it completely true, with the same fictitious with the real sun at perigee and apogee. Based on the perigee
simultaneously, the true Sun is ahead of the fictitious due to the higher initial velocity with which the sun starts true, so that in the way of "B" to "A" to "S2" (Figure 2) real Sun will advance to the sun fictional, tying two suns at the peak, but as the real sun is slower at the apogee, the fictional Sun anticipates this, so that during the journey "B1" to "S3" true Sun is late with respect to the dummy.
The difference between the length of the Sun real and fictional Sun's longitude is called "Equation of the Centre."
FIGURE 3
Without the tilt of the ecliptic with respect to Ecuador Celeste, the fictional Sun would move at constant speed on Ecuador would serve well to establish the "Mean Time" (because the length "L" covered by the fictitious sun would equal right ascension "AR"), but taking into account the slope (Figure 3) the length "L" of the Sun dummy that is measured in the plane of the ecliptic only match with ascension "AR" which is measured at the Equator on the equinoxes (about Aries "A" Libra "Li") and the Solstice (Cancer "Ca" and Capricorn "Cp"), ie at 90 °, the 180 º to 270 º and 360 º (0 º). Considering that our sun moves fictitious constant speed along the ecliptic, means without a rigorous mathematical proof that the Right Ascension and therefore the Sun's hour angle remains unchanged fictional time proportion basis, so that in the interval "Aries-Cancer, the fictional Sun is ahead of his ascension, behind Ascension in the area "Cancer-Libra, on the way ahead" Libra-Capricorn "and again behind his ascension on the tour" Capricorn-Aries. " Under these conditions, the fictional Sun does not serve us to measure the time since his ascension has variable speed. Recall that the ascension of a celestial body is the equivalent of and longitude is the vernal equinox origin. The hour circle time or measured by the Ascension.
FIGURE 4
return to this point again to try to clarify it, because it is crucial for the solution of the problem, but from a more analytical and less intuitive. Figure 4 shows the spherical triangle "A-SF-BA" which is the vernal point or origin of the coordinates, point "A" point "Sf" dummy representing the sun and the "B" is the projection of "Sf" perpendicular to Ecuador (Circle Time PB), so that the dihedral angle "AOB" formed by the planes "AOPA" and "BOPB" is the right ascension (RA) from the Sun dummy, the angle "AO-Sf" is the length (L) of the fictional Sun and the dihedral angle formed by the planes "AOBA" and "AO-SF-A" is the inclination of the ecliptic (E). A fundamental relationship for spherical triangles is that states:
Tg (AR) = Tg (L) xCos (E)
From this formula we can easily deduce that if the angle (E) formed by the planes of the ecliptic and the plane equator is zero, the angle swept by "Sf" equals the right ascension (RA), but if the tilt angle "E" is different from zero, the angle "L" swept "Sf" is different from right ascension "AR", but we can deduce from this fundamental relationship, which for angles 0 º, 90 º, 180 º and 270 º angles "L" and "AR" are equal. This demonstrates the trigonometry that if "L" is constantly changing, the angle "AR" does not, falling behind or ahead of the angle "L". For
jump this drawback turns the plane of the ecliptic around the axis formed by the Aries point "A" and point of Libra "Li" as indicated by the arrow in Figure 5 to match the equatorial plane, so the fictional Sun Ecuador is killed on the spot taking the place of "B" so that the angle "AR" is equal to angle "L".
FIGURE 5
fictional Sun shot on Ecuador is called "mean sun" and forms a spherical isosceles triangle with the Sun Aries fictitious point "A", so that the length " L "swept Sun dummy is equal to the angle swept in Ecuador by the mean sun and is equal to the right ascension "AR" of the mean sun, so you get an imaginary sun crosses the Ecuador at a constant speed at which the angle the mean sun time grows proportionally to time (Figure 6) and now have a Sun that allows us to adjust mechanical watches. The average Sun and Sun agree fictional Aries point A and point pound "Li."
FIGURE 6 days is called "Solar Middle double pass to the reference meridian and fixed the mean sun mean noon is the source of half time.
FIGURE 7
already been mentioned that the difference between the length of fictional and Sol Sol true length is called "Equation of Center" and the angular difference between the two Suns is due to the difference velocity of each other.
To facilitate the following analysis, killed the real sun on Ecuador (see Figure 7) and recalling that the mean sun is the sun fictional Ecuador.La killed in the Equation of Center (EC) we can write it like this:
EC = "AO" mean sun "-" AO "Sol real shot
Reduction to be known as Ecuador (RE), the length difference between the real sun and the true ascension of the Sun (point "C" in Figure 7) and we can formulate as follows:
RE = "AO" Sol real shot "-" AOC "
This angular difference between the length of Sol Ascension real and stems from the inclination of the ecliptic with respect to Ecuador.
Both deviations are added to form what is known as the Equation of Time (ET), so that:
ET = EC + ET
RE = ("AO" mean sun "-" A- true sun down ") + (AO-Sol real shot "-" AOC ")
ET =" AO "mean sun" - "AOC"
Recall that the angle measured in Ecuador "AO" mean sun "is the ascension of the mean sun and the trajectory "AOC" is the true ascension of the sun. We must also remember that the hour angles of celestial bodies are measured under the same right ascension.
As we have already seen, the real sun is early or late with respect to the mean sun and the difference between the mean sun Ascension and Ascension of the Sun truly is the "Equation of Time." In short, the equation of time is the correction to add to the true solar time (HSV) to the mean solar time (HSM).
ET = HSM - HSV
As the instruments of observation and measurement have improved over time, is to become clear that the vernal point is not fixed with respect to the stars (precession) nor what is the semi-major axis (line of apses) of Earth's orbit, so that tables are published each year with the equation of time every day of every month and these are available online.
However, because it functions both deviations of cyclical the sum of them vanishes certain angle covered, so that by that time the hour angle (Ascension) the real Sun and the Sun half agree with what the sundial and the mechanical clock show the same time. This is repeated four times throughout the year in the months April, June, September and December.
In the next release will conclude the study by comparing the time shown by the sundial Azimuthal and the mechanical clock in three different days. The calculations necessary to enable us to verify this difference observed according to the Equation of Time and the difference between the meridians, plus you will notice that the time difference is not constant throughout days.
Saturday, September 5, 2009
Disposable Serving Platters
CLOCK SUN AZIMUTH. The dog
To obtain the required values \u200b\u200balong the solar day to make our path, we can facilitate our calculations relying on a spreadsheet. Completed
calculations, we have the position of the Sun in our sky hour by hour and month by month, which will establish the length and direction of the shadow.
The azimuth determined by this formula does not tell us if it is negative or positive (if another formula determined by the hour angle), ie if the azimuth angle is before or after Meridian. What if we determine this formula is when the sun is north or south is. This point is very important to know where it is headed in the shadow of the gnomon our determined with full accuracy for the case of zero angle "0 °", which corresponds to noon. To this point of time, the azimuth can take the value zero "0 °" or 180 degrees. If the calculated value is 0 º, our sun is to the south and if the calculation indicates 180 °, the Sun will be the North. The azimuth angle is taken from the meridian of the place counted from the South Pole.
This point is important in order to correct the path so and properly target our clock with respect to geographic north, in the same way we had to target other sundials outlined in previous articles.
To determine the length of the shadow according to the height of the sun in the sky enough to solve a simple trigonometric equation.
In the figure above we can deduce the length of the shadow produced by the gnomon.
Tangent (a) = HEIGHT GNOMON / LONG SHADOW
From equation
know the angle of the Sun's altitude (a) and height of the gnomon, with these data we can calculate the length of the shadow. With the calculated azimuth angle we can draw on our quadrant azimuth lines that indicate the time and month.
For the drawing of lines on our quadrant azimuth, we can do "old" with a ruler and square, or, like me taking advantage of technology and printing on paper with the dial 1:1 scale previously developed a program design.
Our reference is the place where is the projection of the tip of our gnomon on a horizontal plane from the place where it will be built. For each hour will place a point whose location is defined by the azimuth and length of the shadow in the direction that corresponds (North or South) as the azimuth either 0 º or 180 º. These points will unite with a continuous line being drawn is a parable that is the journey that makes the tip of the shadow on the floor as they pass the hours. Parables drawn for the months, we join the points for hours, so are drawn on the dial a series of straight lines tend to converge.
The gnomon for my watch is 100 mm high with a pyramid shape and the template to construct shown in Fig.
The following photos show the azimuthal quadrant template, trim excess paper to put on quadrant carton of 2 mm thick substrate would be the same.
time when we are placing the template on the cardboard printed azimuthal quadrant.
Quadrant stuck to the cardboard base.
trim excess cardboard.
ready
azimuthal quadrant.
gnomon templates glued to cardboard 2 mm thick.
Cutting the gnomon.
Armando gnomon.
placing the gnomon on the dial.
Local Solar Time 9:00 AM.
Note that solar time is defined by the tip of the triangular shadow.
Azimuth dial clock dial to Landscape.
As I mentioned at the beginning of the post, this watch azimuth has the advantage of letting us know the month of the year and even the date and time if the azimuth plane size is large enough to allow this resolution.
The basic problem is that the trajectory of the Sun from January to July, is retraced by the same route, which prevents good to first determine the month of the year. One way to save the point is to divide the quadrant into two equal parts by the sagittal axis, so that put a half months ranging from January to June and the other half of the layout of the remaining months as shown in the picture below.
to interpret, at least we know where half of the year we are making reference to the station in question or knowing that he has passed one of the solstices.
If we were quadrant with the layout of the previous figure for the corresponding months of January through July, we would see reflected in the evenings and the rest of the year during the morning.
The following image shows the tip of the shadow falling on a parabolic lines of the azimuth quadrant, in this case (not identified in this prototype) corresponds to 1 September and True Solar Time 9:00 AM .
I should clarify that the sundial gives the True Local Time, which does not correspond to the legal or official time.
In the case shown, the sundial indicates approximately 9:00 am while mechanical clock that gives us 8:40 am. We quickly realize that there is a difference of about 20 minutes between the two "hours" for the day when the photos were taken. This difference is more pronounced in this clock with respect to the first that have been developed in this Blog by time change decreed by the Government of Venezuela.
In the next release (published in Technical Note) will expose more explicit this phenomenon to clarify any doubts that this difference of hours awake in the observers, as a rule people unconsciously compare their mechanical watch against the Solar, blaming the lack of "accuracy" between times read as a problem of design or manufacture of the sun clock
I hope this brief summary has been clear enough for those who wish to make your own sundial dial Azimuthal can build it without major problems and enjoy the fascination that these small monuments to the sun awaken our consciences. 
CLOCK SUN AZIMUTH.
The sundial worked before was to Declining Quadrant in this installment we look at the Azimuth sundial.
sundial in the Azimuthal Azimuthal or the gnomon is parallel to the axis of the world such as watches that are based on the equatorial quadrant, but is positioned vertically, perpendicular to the ground and the hours are defined by the projection of the shade of the same according to the height of the sun in the sky and the angle measured on the horizon and azimuth angle, ultimately by the sun's position in the sky with reference the horizontal plane.
In principle, it seems that we can make a sundial by simply placing a vertical rod and drawing on the ground grade the hours spread evenly around the vertical rod. Nothing could be further from reality, as when performing this simple design we will quickly realize that the clock does not indicate the correct time, and what is worse, the shadow on the ground is not equal in length or angle though we measure at the same time from month to month.
Unlike Equatorial sundial in azimuth time is not determined by the angle of the shadow over the southern boundary, but is determined by two variables: the length of the shadow and the angle is with respect to the meridional plane.
To understand a little what happens to the shadow, we observe the behavior of the Sun, in their movement across the sky throughout the day and year.
Although we can divide the day into 24 hours and that the Sun apparently moves to meet that schedule, we note that in the different seasons of the year the sun's position is not fixed with respect to reference objects that we have on our horizon that will slowly changing. The cause of this phenomenon is due to two reasons:
First, the axis of rotation of the earth is inclined to its orbital plane and the second by the observer's location on the globe, ie the latitude.
Being tilted the axis of rotation of the earth on its orbit, the Sun elevation changes throughout the year in northern latitudes and reaches its maximum height above the horizon at the summer solstice, and the height minimum in the winter solstice, which is our case here in Venezuela. During the equinoxes the Sun moves across the sky Ecuador.
The sundial worked before was to Declining Quadrant in this installment we look at the Azimuth sundial.
sundial in the Azimuthal Azimuthal or the gnomon is parallel to the axis of the world such as watches that are based on the equatorial quadrant, but is positioned vertically, perpendicular to the ground and the hours are defined by the projection of the shade of the same according to the height of the sun in the sky and the angle measured on the horizon and azimuth angle, ultimately by the sun's position in the sky with reference the horizontal plane.
In principle, it seems that we can make a sundial by simply placing a vertical rod and drawing on the ground grade the hours spread evenly around the vertical rod. Nothing could be further from reality, as when performing this simple design we will quickly realize that the clock does not indicate the correct time, and what is worse, the shadow on the ground is not equal in length or angle though we measure at the same time from month to month.
Unlike Equatorial sundial in azimuth time is not determined by the angle of the shadow over the southern boundary, but is determined by two variables: the length of the shadow and the angle is with respect to the meridional plane.
To understand a little what happens to the shadow, we observe the behavior of the Sun, in their movement across the sky throughout the day and year.
Although we can divide the day into 24 hours and that the Sun apparently moves to meet that schedule, we note that in the different seasons of the year the sun's position is not fixed with respect to reference objects that we have on our horizon that will slowly changing. The cause of this phenomenon is due to two reasons:
First, the axis of rotation of the earth is inclined to its orbital plane and the second by the observer's location on the globe, ie the latitude.
Being tilted the axis of rotation of the earth on its orbit, the Sun elevation changes throughout the year in northern latitudes and reaches its maximum height above the horizon at the summer solstice, and the height minimum in the winter solstice, which is our case here in Venezuela. During the equinoxes the Sun moves across the sky Ecuador.
The above figure represents the sky for two different observers, one located in Ecuador and the other above the equator. Each observer will see the sky slightly different due to its geographical position.
To the observer who is in Ecuador, the Sun reaches the zenith at noon on the equinoxes and its shadow would be right at your feet, while in the midday sun solstices is inclined with respect to the vertical an angle equal to the inclination of the earth on its orbit, which is about 23.5 degrees. In this case, the shadow of the observer will have a length and the same would be projected in the direction of one pole as the winter solstice or the summer.
For the observer located at another latitude, during the equinoxes the sun is not in the zenith distance if not the same at an angle equal to your latitude which depends on where the observer is.
If you pay attention to the trajectories of the Sun shown in the figure above, we conclude that for the latitudes they are over Ecuador and particularly in those places that are beyond the tropics (Cancer and Capricorn) the arc described by the sun during the summer solstice is higher than that reported during the winter solstice is the reason why in summer the days are longer in winter while the equinoxes, the days and nights are equal. The same is true for observers who are below the equator, only here, the longest day occurs during the winter solstice.
The system used by convention to give the position of a star in the firmament is the "celestial coordinates" whose reference points are the right ascension and declination.
The right ascension is equivalent to the meridian system used geographically with respect to a reference point for the case of the celestial coordinate system is the vernal equinox (start of the spring equinox.)
The decline is the equivalent latitude, taking as reference the celestial Ecuador Ecuador is the projection of Earth in the sky.
For the development of our watch we are only interested azimuth of the sun's decline over the months. His ascension did not take into account, but the hour angle measured from the meridian that passes through the zenith of the observer.
our clock to calculate azimuth, we have to base on the horizontal coordinate system in which the position of a celestial body is defined by its azimuth (azimuth angle is measured on the horizon taking as "zero" reference meridian of the place normally see South Pole) and the same height above the horizon. With these data we can set the length of shadow of our gnomon with its projection angle in the horizontal plane and thus trace our azimuthal quadrant.
If we have the position of a star "A" in the sky (see figure above), and draw lines linking the star "A" to the zenith "Z" of the observer and the elevated pole " P "we obtain the spherical triangle" AZPA "which secures the side" PZ "located on the meridian of the place, while the side" PA "stands on the hour circle of the sun and rotates around the pole "P", causing the height and azimuth of the sun varies over time.
This triangle "AZPA" is called "triangle of position and by means of spherical trigonometry can be deduced given other elements, thus solving all problems arising in celestial navigation and projection problems for our clock azimuth.
From the figure we can raise the hand "PZ" is the zenith distance of the pole and is the complement of latitude "l": PZ = 90 - l.
The fixed side of convenience "PA" is the polar distance of the star and is the complement of its declination "d": PA = 90 º - d.
side "ZA" is the zenith distance of the star, snap up "a": ZA = 90 ° - a.
The hour angle of the sun is equal to the time since passing the meridian of the place and that it is local solar time you start counting from that time. The times are negative numbered degrees of longitude east and west longitude positive. However, before we can determine that for equidistant hours before noon and after noon, the sun's altitude will be the same.
short, the height "a" of the sun we can determine the following findings:
Sen = sin sin d + cos lx cos lx cos dx H.
Where "H" is the hour angle measured from the meridian, this angle is 15 ° for each hour and 7 ° for half hour. Determined
height "a" of the Sun in terms of hour angle we can calculate the azimuth (Z), which is the other information we need to chart our azimuthal quadrant.
Cos Z = (lx Sen Sen - Sen d) ÷ (lx Cos Cos a).
To solve these equations need to know the declination "d" of the Sun during the months of the year. This information is readily available on the Web. However the table used development of this watch is as follows.
To obtain the required values \u200b\u200balong the solar day to make our path, we can facilitate our calculations relying on a spreadsheet. Completed
calculations, we have the position of the Sun in our sky hour by hour and month by month, which will establish the length and direction of the shadow.
The azimuth determined by this formula does not tell us if it is negative or positive (if another formula determined by the hour angle), ie if the azimuth angle is before or after Meridian. What if we determine this formula is when the sun is north or south is. This point is very important to know where it is headed in the shadow of the gnomon our determined with full accuracy for the case of zero angle "0 °", which corresponds to noon. To this point of time, the azimuth can take the value zero "0 °" or 180 degrees. If the calculated value is 0 º, our sun is to the south and if the calculation indicates 180 °, the Sun will be the North. The azimuth angle is taken from the meridian of the place counted from the South Pole.
This point is important in order to correct the path so and properly target our clock with respect to geographic north, in the same way we had to target other sundials outlined in previous articles.
To determine the length of the shadow according to the height of the sun in the sky enough to solve a simple trigonometric equation.
In the figure above we can deduce the length of the shadow produced by the gnomon.
Tangent (a) = HEIGHT GNOMON / LONG SHADOW
From equation
know the angle of the Sun's altitude (a) and height of the gnomon, with these data we can calculate the length of the shadow. With the calculated azimuth angle we can draw on our quadrant azimuth lines that indicate the time and month.
For the drawing of lines on our quadrant azimuth, we can do "old" with a ruler and square, or, like me taking advantage of technology and printing on paper with the dial 1:1 scale previously developed a program design.
Our reference is the place where is the projection of the tip of our gnomon on a horizontal plane from the place where it will be built. For each hour will place a point whose location is defined by the azimuth and length of the shadow in the direction that corresponds (North or South) as the azimuth either 0 º or 180 º. These points will unite with a continuous line being drawn is a parable that is the journey that makes the tip of the shadow on the floor as they pass the hours. Parables drawn for the months, we join the points for hours, so are drawn on the dial a series of straight lines tend to converge.
The gnomon for my watch is 100 mm high with a pyramid shape and the template to construct shown in Fig.
The following photos show the azimuthal quadrant template, trim excess paper to put on quadrant carton of 2 mm thick substrate would be the same.
time when we are placing the template on the cardboard printed azimuthal quadrant.
Quadrant stuck to the cardboard base.
trim excess cardboard.
ready azimuthal quadrant.
gnomon templates glued to cardboard 2 mm thick.
Cutting the gnomon.
Armando gnomon.
placing the gnomon on the dial.
Local Solar Time 9:00 AM.
Note that solar time is defined by the tip of the triangular shadow.
Azimuth dial clock dial to Landscape.
As I mentioned at the beginning of the post, this watch azimuth has the advantage of letting us know the month of the year and even the date and time if the azimuth plane size is large enough to allow this resolution.
The basic problem is that the trajectory of the Sun from January to July, is retraced by the same route, which prevents good to first determine the month of the year. One way to save the point is to divide the quadrant into two equal parts by the sagittal axis, so that put a half months ranging from January to June and the other half of the layout of the remaining months as shown in the picture below.
to interpret, at least we know where half of the year we are making reference to the station in question or knowing that he has passed one of the solstices.
If we were quadrant with the layout of the previous figure for the corresponding months of January through July, we would see reflected in the evenings and the rest of the year during the morning.
The following image shows the tip of the shadow falling on a parabolic lines of the azimuth quadrant, in this case (not identified in this prototype) corresponds to 1 September and True Solar Time 9:00 AM .
I should clarify that the sundial gives the True Local Time, which does not correspond to the legal or official time.
In the case shown, the sundial indicates approximately 9:00 am while mechanical clock that gives us 8:40 am. We quickly realize that there is a difference of about 20 minutes between the two "hours" for the day when the photos were taken. This difference is more pronounced in this clock with respect to the first that have been developed in this Blog by time change decreed by the Government of Venezuela.
In the next release (published in Technical Note) will expose more explicit this phenomenon to clarify any doubts that this difference of hours awake in the observers, as a rule people unconsciously compare their mechanical watch against the Solar, blaming the lack of "accuracy" between times read as a problem of design or manufacture of the sun clock
I hope this brief summary has been clear enough for those who wish to make your own sundial dial Azimuthal can build it without major problems and enjoy the fascination that these small monuments to the sun awaken our consciences.
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