The moons are lovely...

[uzirath]

Would we even have tides without a moon?

The sun’s gravity creates a slight tidal bulge (thus “spring” and “neap” tides), so a world with no moons would have measurable but trivial tides.

And having multiple moons would make the tides unpredictable (or at least, less predictable) which would probably have some negative effects on maritime travel...

The great thing about multiple moons is that you can basically do whatever you want with tides. If all of the moons were full or new, you might have enormous tides, but the lack of a pair of distinct tidal bulges moving around the planet could mitigate this (or exacerbate it!). Add this to the complex effects of coastal geography and your planet is doing all the hand waving for you. You can justify just about anything. (Which sounds like good gaming fodder to me!)

 

[Umbran]

If all of the moons were full or new, you might have enormous tides, but the lack of a pair of distinct tidal bulges moving around the planet could mitigate this (or exacerbate it!).

This... seems a nonsensical statement. The tidal bulges are created by the moons!

Some satellites are small (like, say, Phobos or Deimos around Mars). They create negligible tidal forces.

But, let us consider the case of having several large moons...

In general, each large moon creates its own tidal effect on the planet below - each creates its own tidal bulge in the ocean that follows the moon in the sky (dragging along behind it by a bit - high tide comes somewhat after when the moon is highest in the sky).

These will interfere with each other just like sound waves or radio waves interfere with each other - when their peaks match, they add up, making a higher overall tide. You'll see maximum tides when the moons are in alignment (so, you'd see them very close to each other, possilbly evening eclipsing or transiting) in the sky. Second highest would be when they are in anti-alignment (the moons are on opposite sides of the planet), and minimal tides happen when the moons are 90 degrees apart in the sky.

Each moon has its own orbital speed. So, their tidal bulges move around the planet at different speeds - sometimes they'll add up high, sometimes they'll detract.

Now, there are two very basic scenarios:

1) The arrangement of moons is new. Their orbits are uncorrelated. The resulting tides will be chaotic - in the actual chaos-theory sense of the term. Even if you know the math, and try to calculate the tides, very small errors in your knowledge of their position at a given time will lead to large errors in you predictions of tides at a later date. Making an almanac predicting tides for seafaring communities would be very difficult.

2) The arrangement is old. In real-world physics, the moons interact with each other as well as with the planet below. They will tug and pull on each other until they reach someting like a self-reinforcing state - this can generally be characterized by a beat frequency, or a ratio: Moon One will make 3 orbits while Moon 2 makes two orbits, and they're said to have a 3:2 resonance. This will yield tides with a similar "beat" - they'll become highly predictable.

 

[Umbran]

Geez - what arc would Zarantyr subtend? Wouldn't it take up a large fraction of the sky?!

I haven't run the numbers myself, and as I noted above, there's an error in the calculations someone else did. But, they came up with Zarantyr appearing 9 times larger in the sky than our moon does.

 

[uzirath]

This... seems a nonsensical statement. The tidal bulges are created by the moons!

I was thinking that all these different bulges surging around the planet combined with the many other variables (interference, bouncing off continents, submarine geography, weather, etc.) would create a system that might produce a lot of different possibilities. But, yeah, lower tides during multiple full or new moons wouldn't make sense.

Decades ago, I worked with a few astrophysics students and their professor on this for a couple of example worlds. My memories of those conversations are hazy. My main take away was: with multiple moons, it's vanishingly unlikely that any of your players will have enough expertise (or the necessary data) to call foul on your tides.

 

[Bohandas]

Yeah, but it is several thousand miles inside the limit. 14,000 miles is really close. It is less than the circumference of the Earth! You have three basic optiosn for composition - ice, rock, or rock and iron.

Since it's one of Eberron's moons, it could also be made out of dragonshards or some other similarly mythical material.

And/or green cheese.

 

[Eltab]

Multiple large moons and their tides offers a way for savvy PCs to figure out why "When the orbs align / The goddesses of sea and fire shall be unleashed" but the early prophecies are coming true despite the moons moving away from each other in the sky.

If you want to do just simple math to justify this, a 360-day year with moons in easy factor orbits (12 x 30, 120 x 3, &c) plus one moon in a 19 x 19 orbit (actually = 361; that is deliberate) will have everything align once every 361 years - eventually all the moons and the world will be in a straight line but the moons need not all be over the same face of the world.

The prophecy is coming true due to tidal stress setting off volcanoes, and an all-five-parts-additive tide will rise on the critical day.

 

[Umbran]

Since it's one of Eberron's moons, it could also be made out of dragonshards or some other similarly mythical material.

And/or green cheese.

Which has roughly the same density was water.

Note that this isn't an issue of material strength. What material it is doesn't enter into the equation (literally) other than in its density. Bodies the size we are talking about aren't held together by the strength of the material - just by gravity. The Roche limit is the place where the tidal forces on the object will exceed the force of gravity holding the body together.