OUR DAILY ROUTINE IS DETERMINDED by weather. When it's stormy or windy, we hunker down in port. When it's calm, we go out, day or night, always hunting close to shore. Once we hit promising waters, three crew members take a position: Karlsen steers from the flying bridge while two more men sit in the crow's nest atop the 30-foot mast.

With the windchill regularly dipping into the single digits, each man swaddles himself in fluffy coveralls, insulated boots, mittens, and thick hats with earflaps. Like members of any expedition, they develop their own lingo. Before I flew out from Sweden, Sommerseth asked me to bring a few tins of dipping tobacco, which is three times cheaper there than in Norway. When I rib him about this expensive and nasty habit, he shrugs and says, "It costs a lot to be a man." That becomes the trip's version of "Put up or shut up," and the guys start mumbling it before heading out into the frigid air.

On a typical day, we troll in a grid about a half-mile from shore, with Karlsen moving Sofie slowly to avoid speeding past any feeding minkes. "What should I look for?'' I ask the first time I stand beside him on the flying bridge.

"Whale," he says. Touché.

Minkes surface for only about three seconds every five to ten minutes to grab a quick breath. If the seas are calm, spotting a dorsal fin isn't difficult. But crews usually have to hunt in choppier waters, where seeing the prey requires a trained eye.

Forty feet above the water, the crow's nest swings wildly through the air, but the perspective is superior. Typically, the guys up top are the first to shout "Whale!" When that happens, they trip an alarm, a weird clanking noise that resonates throughout the boat.

Anytime a whale is sighted, the harpooner mans the cannon, while the captain steers to where he expects the creature to resurface. Constantly feeding, minkes like to weave around and double back. But as I'll see, Karlsen always seems to guess correctly about where they'll emerge, and when he does, it's game over. Of the six minkes we would pursue while I was on board, only one would safely slip back into the ocean.

The green-painted cannon gives Sofie a menacing look. Its base, a wide tripod of steel tubing, supports a four-foot-long cast-iron barrel that swivels freely in all directions. The firing mechanism is shaped like a big pistol handle, and a spotting scope runs the length of the tapered barrel. The grenades are specially designed explosives that cost $600 each. The boat carries 18 of them—about $11,000 worth.

The grenade's tip features a strange-looking feature that is meant to help the harpoon stay its course while moving through water. It's round, with a concave nose and sharp, toothy edges. This scooped-tip shape chews into the whale's skin on impact and makes the harpoon plunge in deeper. At the grenade's base, where it attaches to the harpoon, it's mounted with a hook that sets in the blubber as it enters the whale. A cord from the hook pulls tight and detonates the grenade's penthrite explosive once it gets two feet in, obliterating up to 70 pounds of flesh or vital organs.

Shooting these rounds at moving targets involves a lot of pressure to aim true, so the boat's owners almost always shoulder the responsibility. "When I hit a whale, we all hit it," Skarheim tells me solemnly. "When I miss, it's only me that missed."