Is a sailboat with its engine running a power-driven vessel?

Yes. Under the COLREGs a sailing vessel is one under sail with any engine not being used, so as soon as the engine is driving the boat she counts as a power-driven vessel, even with the sails up.

Rule 3 of the collision regulations defines a sailing vessel as any vessel under sail, provided that propelling machinery, if fitted, is not being used. A power-driven vessel is any vessel propelled by machinery. So a yacht that is motor-sailing, with the engine in gear and the sails up, is a power-driven vessel for the purposes of the rules.

This changes several things:

• Who gives way: you follow the rules for power-driven vessels. You keep clear of boats under sail, and in a crossing situation with another power-driven vessel you give way if she is on your starboard side. Meeting head-on, both turn to starboard.
• Lights at night: you must show a white masthead light shining forward, as well as your sidelights and stern light. A masthead tricolour light is only for use under sail, so switch it off when the engine goes on.
• Day shape: by day, a vessel under sail and also being propelled by machinery should show a black cone, point downwards, forward where it can best be seen (Rule 25). Many small yachts forget this, but it is the rule.
• Sound signals: the manoeuvring signals (one short blast for turning to starboard, and so on) are for power-driven vessels, so they now apply to you.

A common mistake is to motor-sail with the sails up and assume other boats will treat you as a sailing boat. They cannot tell from a distance whether your engine is running, which is exactly why the cone and the masthead light exist. If you are relying on the engine, behave as a motor boat and give way accordingly.

More in the book: Chapter 13, The rules of the road