## Sailor's aid or sailor's nightmare - the tides explained

by Grant Headifen on 18 Sep 2010

*As sailors, we all know that tides come twice a day, vary according to the moon, and, depending on where you are sailing are either unimportant, reasonably important, or critically important to a successful completion of your voyage. But why the moon? and if the moon only circles the earth once a day, why are there two tides? Here, Grant Headifen of Nauticed, explains:*It's not surprising if you don't exactly understand how tides work - Tides took a lot of figuring out by some very smart people over the ages - including Galileo - but here's the story:

**Gravitational pull:**

But now that the principle causes of tides are understood and quite well mathematically modeled, they are pretty easy to understand by the average Joe when explained properly.

Tides exist solely because of the celestial bodies the moon and the sun. The moon is relatively close but comparatively small. The sun is far away but a giant when it comes to mass. Gravitational pull increases linearly with mass but decreases inversely with the square of the distance. So when you balance these out and do the calculations, the sun’s effect is 46% that of the moon.

So the moon has the dominant and most noticeable effect on the earth’s tides. However the Sun still has a significant effect.

There are a couple of tricks to understanding the tides that took the physicists quite a while to figure out in the old days. The moon circles the earth about every 24 hours and 50.4 minutes. But for most of us it seems that the tide takes about 6 and a bit hours to go out and 6 and a bit hours to come back in. That’s a frequency of 12 and a half hours not 24:50 hours. What’s up with that?

Tide is actually a gravitational concept rather than specifically related to the movement of our oceans. All celestial objects are susceptible to tidal effects from other 'relatively close' bodies. Consequently a planet with in gravitational range of another body will experience pull leading to stresses acting to deform the shape of the planet.

That means that as the moon circles the earth, the earth is deformed by the moon. Similarly, the moon also experiences deformation by the earth and thus is suffers a tide effect. The effect is called tidal force. Fortunately for life on earth, the deformation is small but it does lead to the rising water that we experience. Therefore, with out the moon, life on earth would be vastly different.

As non celestial body and gravitational experts we’ll probably struggle to understand the resultant effect because it happens in a way that we might not initially expect.

**Double Bulge Phenomenom:**

It is suffice for this description of tides to state that the planet doesn’t just bulge towards the distant body but actually bulges on both sides in a line between the center of the two bodies because of the volumetric stress imparted upon the planet. Various arguments still exist on why, some are flat out wrong and some are right. As sailors we really don’t care too much other than knowing the resultant.

To gain a visual appreciation for this, although not in anyway accurate in science, take a calamari ring and hold in two points opposite each other. Now hold one side still and pull the other side. You’ll see the ring bulge on both sides in a line of the direction of pull.

That is a similar resultant action to what the earth is experiencing. The bulge occurs on both sides of the planet diametrically opposite each other and in the plane of a line between the moon and the earth. So following this, we have a high tide on the same side of the planet as the moon and simultaneously on the opposite side. Thus leading to a theoretical tidal period twice for every rotation of the moon about the earth.

The double bulge concept has nothing to do with the spin and inertia of water on the earth, although you will find some arguments and textbooks reporting this as a contributing factor to the opposite bulge. Not so! In any case, again as sailors we don’t necessarily care too much. We just need to know and realize that the double bulge occurs to explain two tides in a day rather than matching the periodicity of one moon rotation per day.

The exact same concept is valid for the sun. A solar high tide exists on the same side of earth as the sun and simultaneously on the opposite side of the sun.

**Theoretical Tide Heights:**

Now let’s look at a few theoretical mathematical numbers for comparison. If the earth’s oceans were uniform in depth and no landmasses existed and just considering the moon and if the moon was rotating around the earth every 24 hours, plus a few other ands and ifs, then the theoretical rise of the water at high tide would be 54 cm (21 inches). Now consider the suns effect in the same way. This would lead to a theoretical tide rise of 25 cm (9.8 inches). If the moon and the sun aligned or were directly opposite (from the bulge theory above) then we could add these heights together and get 79 cm (31 inches). If the moon and sun were acting against each other by being 90 degrees apart, then we would subtract the numbers and be left with a tidal height of 29 cm (11 inches).

The phenomenon then of a spring tide has thus been explained. Spring tide is when the sun and moon align or are diametrically opposite. The word spring does not come from a relationship to the season but from the concept of 'force'. Meaning there is more force during this period of alignment, which occurs about every 14 days – full moon and new moon.

Consequently, a neap tide is the minimal tide effect from the action of the sun and moon opposing each other. When they are at 90 degrees from each other – not diametrically opposite each other due to the double bulge effect. Again, this occurs at a period of every 14 days.

In addition to the above, the sun and moon operate in elliptical orbits relative to the earth. You can then imagine as the sun and moon become at their closest points to the earth that a greater effect would take place. The effect is increased 18% for the moon and 5% for the sun. Since the earth rotates about the sun once per year, at a certain times of the year then you would expect all these phenomena to exist simultaneously and create a theoretical tidal height of 93 cm (37 inches).

You can also imagine a common high high tide condition existing when the moon is closest to the earth with the moon and sun aligned (or diametrically opposite). This is called a perigee spring tide and occurs every 7.5 moon cycles.

This can be further expanded to include the sun being at its closest point along with the moon and in a spring tide situation. This occurs every 18.6 years. For this reason tidal high high and low low measurements are recorded and reported over periods of 19 years by statistical governmental recording agencies.

There is one last effect to discuss and that is that the sun and moons orbits are not directly aligned with the pole of the earth. Both the sun and moon’s orbits are not in unison and change day by day. For this reason the height of each high tide will vary day by day.

And just in case you’re wondering, Venus provides the next greatest tidal effect on the earth. But it is less than 0.001% of the magnitude of the Sun’s effect.

Here is a rudimentary animation of the Moon’s and the Sun’s tidal forces on the Earth: