Question About Old Square Rigged Ships

On those old sailing ships, you had three masts. When the ship is sailing with the wind behind it, are the sails that are “shadowed” by the rearmost sails providing any thrust?
It seems (to me) that any sail not directly touched by the wind would not really contribute to pushing the ship forward-an I correct? Also, in the 1600’s ships would usually have a small sail mounted on the bowsprit-this seems to have been abandoned by the 1800’s-were these sails pretty ineffective?

First, the best point of sailing on a square rigged ship is with the wind off the quarter, that is with a following wind that is not coming from straight astern but rather from an angle. As you suggest when the wind is from directly astern the forward sails are in the wind shadow of the sails farther to the rear.

Second, the square sails on the bowsprit were not as effective as a series of jib sails rigged from the foremast to the bowsprit.

First, most of the time, you wouldn’t be sailing dead downwind.

For when you are sailing dead downwind:

The aft mast (mizzen) is generally the smallest and carries the least sail, so it makes sense to set all possible sail on it even though it’s sails shadow the mains, to help distribute the load.

The sails on the foremast would be shadowed to a significant extent, but you’d still hoist sails on it. First, the foremast and mainmast aren’t the same height, so the gaps between the cources and topsails (and between upper and lower courses and upper and lower topsails, if so rigged) on the mainmast wouldn’t match the same gaps from the foremast. They might more closely match those on the mizzen, but they’d be far enough away, and the air would be turbulent enough after rushing by the after sails, that there’s still a point in hoisting them.

The proof for this is that even when sailing dead downwind, the foremast’s sails usually won’t hang limp. But even if they did hang limp, you’d hoist them, in case you needed to adjust course.

I’m assuming you intend to make all possible speed, and be prepared for all possible events, which is definitely the case for a warship, and generally the case for a merchant in wartime. However, a merchant ship carries a far smaller crew, so might not always do everything possible at every moment to optimize every factor.

There would never be an occasion that a ship would carry all its canvas. There would simply be no point as some will always be masked by others. The skill of a sailing master is to decide the best spread to achieve his objective.

I don’t think this is right.

There is no reason that when on a reach (wind roughly perpendicular to course) all sails should not be bent & drawing. The expression “all plain sail to the royals” covers this case.

Here’s a (not very impressive) photo of the Cutty Sark with all sail set.

Or even, as suggested, when running with the wind of the quarter, or on a broad reach (wind on your five/seven, and wind on your four/eight respectively).

There’d have to be some good reason to sail dead downwind. As Spavined Gelding said, the ship is faster with the wind coming over the quarter. If you wanted to get someplace that was 100 miles dead downwind, you’d set course a few degrees to the right (the wind would come from the starboard quarter and fill all the sails), travel 50 miles (plus a bit), turn left, brace the sails, and travel the remaining distance with the wind from the port quarter. It’s a longer route, but you make it in less time.

Those may not be all the sails, though. I don’t see any studding sails (mounted on extensions attached to the yards). Only used in very light winds, as I understand it.