Imagine flying a 100,000-pound aircraft almost straight into the center of a Category 5 hurricane.

You get tossed around so violently that you physically cannot speak. The roar of 150- mile-per-hour winds drowns out the noise of the engines. And one of your most trusted turbulence trackers is a small stuffed Muppet dangling wildly inside the cockpit.

During the hurricane season, which begins in June and runs through the end of November, NOAA sends flying weather labs aloft.

The agency has two Lockheed WP-3D Orion turboprop airplanes — nicknamed Kermit and Miss Piggy — for those missions, each staffed by three pilots, two flight engineers, an in-flight meteorologist, several navigators, a network administrator, avionics technicians and scientists.

The planes, based in Lakeland, Fla., logged their first flights 50 years ago. They fly into some of the world’s worst weather to collect data that helps researchers better understand storms, improve forecast models, and protect lives and property.

The official call signs of the two planes are “NOAA42, Kermit” and “NOAA43, Miss Piggy.”

Kermit and Miss Piggy are believed to have flown more hours and been in service longer than any other P-3 Orions in history, NOAA officials said.

For their first 15 years of flight, the two turboprop planes were designated by their tail numbers.

But the flight crews on one of the planes developed a reputation for being untidy, earning their aircraft a nickname.

“It was referred to as ‘The Pig’,” said Capt. Nathan Kahn, the commanding officer of the aircraft operations center at the National Oceanic and Atmospheric Administration.

One of the crew members leaned in to the reputation and doodled sketches of Miss Piggy with the airplane, causing shenanigans, as Muppets tend to do. The doodles were likely put up inside the plane, Captain Kahn said, and the plane’s new moniker, Miss Piggy, stuck.

The creator of the Muppets, Jim Henson, or a member of his staff, were made aware of the nickname and the doodles, Captain Kahn said, and decided that the doodles were not good enough for planes serving such vital missions. Mr. Henson died in 1990, and was uninvolved in the decision making, according to the Jim Henson Legacy.

Michael K. Frith, the creative director of the Jim Henson Company in the early 1990s, is a native of Bermuda, and growing up on an island in the Atlantic Ocean gave him a deeply personal connection to the catastrophic power of hurricanes.

Mr. Frith, who could not be reached for comment, drew Kermit as a sky hopper, wearing a vintage leather aviation hat and goggles.

Miss Piggy graces the other plane, with a scarf blowing in the wind and with her autograph, dotted with two hearts for the i’s in her name. In one hand, she is ready to release a paper airplane.

The planes’ World War II-style Muppet insignia were added in 1992.

In 1996, NOAA added a higher-altitude Gulfstream-IV, with an elongated nose, to its fleet. That one, naturally, is named after the Muppet with a prominent nose, Gonzo, who is depicted flying like Superman from the middle of a hurricane.

Ed Eyth, who was a successor of Mr. Frith’s as creative director, did the Gonzo artwork.

Though the planes track weather year-round, they’re best known as hurricane hunters. There is a purpose to the marriage of whimsical pop culture with serious government scientific operations.

“We hope to stimulate children’s interest in science and weather studies,” NOAA said in its announcement in 1992. “We also hope to promote hurricane preparedness and general awareness of dangerous weather in all age groups.”

Hurricane specialists at NOAA take the planes on tour annually, stopping in hurricane-prone cities along the Gulf Coast to train local officials and the public in severe weather preparedness.

“For the most part, the aircraft have their own souls, like they’re as much a part of the crew as any member of the crew is,” said Captain Kahn, who has flown both Kermit and Miss Piggy on grinding eight-to-10 hour missions.

It’s a lot like riding “a roller coaster through a carwash,” he said.

“The windshield is totally full of water,” he said. “You can’t see anything in front of you. You’re going up. You’re going down. You’re going sideways.”

The missions are recognized on the sides of the aircraft, which are covered in dozens of red storm stickers, resembling the kill marks of a fighter pilot.

Each sticker represents a named storm that the crew has successfully mapped.

“When we’re getting bounced around in the turbulence, you can definitely start to see Kermit and Miss Piggy dance,” Captain Kahn said of the plush toys wildly dancing, spinning and smacking against the windshield when the planes enter the worst part of a storm.

The planes — which have been overhauled and given meticulous daily care — are slated to fly research missions through 2030.

Afterward, officials hope to put them on permanent display in the Smithsonian or another aviation museum.

There are plans to add a fourth Muppet to the fleet.

NOAA officials would not say which one, but it’s easy to envision Animal, whose penchant for smashing drum sets is a metaphor for a hurricane’s destructive power, or the Swedish Chef, whose chaotic kitchen could resemble the volatility of a storm.