Our world relies on the sea more than ever: 80% of goods traded worldwide move by ship. Today’s mariners take it for granted that they can get an accurate chart of the tides for any location on Earth. This would not have been possible without the work of countless scientists through history. The first workable solution, Lord Kelvin’s tide-predicting machines, came in the 1870s. They were complex masses of gears and pulleys that were the most advanced mechanical computers of their day:

Why this complexity? Ancient Greek philosophers had already deduced that the Moon caused the tides. Isaac Newton determined the Moon’s gravity was responsible in the 1680s, and Pierre-Simon Laplace produced a more refined theory in the 1770s incorporating the Earth’s rotation and landmasses. But Laplace’s equations were very challenging to actually solve for any given location – hence the machines. Let’s go through the different layers that make tides so complicated.

Layer 1: Tides come from the Moon’s gravity

You might remember that the Moon’s gravity causes tides from science class. Those Greek philosophers realized this because high tide gets later by about 50 minutes each day, just as the Moon rises 50 minutes later each day. The connection makes sense, but how does it work?

Think of two satellites orbiting the Earth. The closer satellite feels more gravity than the farther satellite, so it orbits faster. This is why Mercury, the closest planet to the Sun, is also the fastest.

The satellites start lined up… …but they don’t stay that way

If we tied the satellites together with a very strong cable, we could force them to orbit together. This would stretch the cable out taut. This stretching is the “tidal force”.

Tying the satellites together puts tension on the cable. This is the tidal force.

The Moon’s gravity has the same effect on the Earth as they both orbit their common center of mass. Instead of the cable stretching taut, the Earth stretches out. Water stretches more easily than land does, so it bulges up on the sides of the Earth closest to and farthest from the Moon.

Then as the Earth turns and the Moon orbits, you get high and low tide every half day (plus 50 minutes). That said, the actual moment of high tide isn’t always when the Moon is straight overhead or straight down, because the Earth drags the oceans along as it spins.

Layer 2: Tides come from the Sun’s gravity, too

The Moon isn’t the only large object whose gravity affects the Earth’s oceans. The Sun does, too. So when the Sun, Earth, and Moon are lined up (Full and New Moon), high tides are higher and low tides are lower. This is a “Spring Tide”. When they’re least lined up (First and Last Quarter Moon), tides are more smoothed out. This is a “Neap Tide”.

This is where my science class explanation ended. But it’s not enough to actually predict the tides.

Layer 3: The Earth is tilted

Check out this tide chart from Gulfport, Mississippi. Notice that it only has one high and one low tide per day. What’s going on?

The Moon’s orbit is tilted about 28 degrees from the Equator. So the tidal bulges (blue) are tilted to the Earth’s axis (solid red). As a spot partway up the Earth’s surface turns through this tilted bulge, its path (dashed line) takes it through one high tide and one low tide each day. Somewhere closer to the Equator will have a mix of 12-hour and 24-hour tides.

So to recap: The biggest astronomical components of the tides are:

• ~12 hour Lunar tide

• 12 hour Solar tide

• ~24-hour Lunar tide

• 24-hour Solar tide

These are the biggest pulleys on the tide-predicting machine. There are other, smaller astronomical components too. But even if you knew all of them, that’s still not enough to predict the tides.

Layer 4: The Earth has land

Unfortunately for our perfect astronomical model, the oceans have these annoying chunks of land stuck in the middle.

The Earth: not 100% ocean

The astronomical components are the forces that drive the tides, but the actual tides at any location are the result of those forces creating waves that slosh around in between the land. You end up with situations like tides circling New Zealand and Madagascar every 12 hours, or several “amphidromic” points in the ocean which experience no ~12-hour lunar tides at all:

Map of the strength of the 12-hr lunar tide

So to predict the tide in any given harbor, you need to know:

• The strength of each astronomical component in that harbor

• The phase of each component (how early or late its peak is compared to the theory)

• Extra components from the shape and depth of the harbor

• The phases of those extra components

How machines changed the game

If you’re a scientist in 1800, you’re stuck calculating all these numbers by hand, then laboriously calculating their effects forward in time to make a full tidal table.

Kelvin’s machine automates the second half of that task. As the pulleys spin, they pull on a common chain by the correct amount for each of the calculated components. A year’s worth of tidal tables can be put together in half an hour, if you know the components. Even better, you can “guess and check” the components by comparing your machine’s output to past records, and adjusting the pulleys until you get something that works correctly.

Tide predicting machines were used up until the 1970s, when computers finally got good enough to replace them.

There is yet more weirdness

The picture of tides in this post is still incomplete. We haven’t even explained tidal bores!

Tidal bore in Moncton, NB, Canada

Every time I think I understand how tides work, there’s some additional wrinkle that I can’t explain. (Tides are not the only such subject.) So we won’t try to finish the whole story in this one post. Just remember next time you’re at the beach: tides are weirder than you think.

Coming Soon: Vikings. Vikings Everywhere.