: The beam of my boat is 29 inches. The loom of this paddle is about 24 inches.
: Should the loom be the same size or larger than the beam? Or are they not
: really related?

Today "Greenland paddle" is used to describe almost any narrow paddle, but a West Greenland paddle is actually a fairly specific design, designed for use with a very low-volume kayak not much wider than your hips.

Although the measurements vary, a "large" West Greenland kayak (used for hunting) often has the beam of only your hips plus a fist on each side. Smaller Greenland kayaks (sport and rolling) are often your hips plus the flat of your hand on each side. The Greenland kayak and Greenland paddle are therefore a tuned pair, in that the loom size (approx shoulder width to body width) assumes that your kayak is not much wider than your hips. With wider kayaks or high-volume designs, you are outside of the range of a traditional Greenland kayak, and need to work out a hybrid paddle design that works for you. Generally I tell folks that the loom must be at least the width of the beam to keep from bashing your knuckles, but at some point even this advice will be folly. Some paddlers have told me that they enjoy using long shafted "Greenland" paddle hybrids, but I don't have much experience using them.

As other posters have mentioned, Greenland and Aleut paddles are only two designs out of many used in the arctic. If you are interested in traditional paddles with beamy boats, you may want to look at the East Canadian paddles, which were often much longer than the Greenland paddles and used with much beamier and longer kayaks. The current Sea Kayaker has an article on building an Eastern Arctic kayak. Harvey Golden also has some pictures and information at his site (look under his Canadian kayak link).

Greg Stamer