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12^th graders learn trigonometry and physics by building, launching and gathering data on model rockets

We are deeply saddened by the loss of the brave crew of the Space Shuttle Columbia. We honor their memory by continuing to educate children about the significance and wonder of science and space exploration.

By Emily Weinstein

A rocket on the launch pad in Cunningham Park.

February 2003 - Under a dense cloud cover and whipped by biting winds, facing unexpected aeronautical competition from the re-routed planes leaving Kennedy Airport for Thanksgiving celebrations, the 12th graders in Jim Napolitano’s math applications class braved the elements in the name of science.

The class was testing how the shape of a model rocket’s nosecone affects the altitude it achieves. Under the watchful eyes of several New York City Parks Department officials, they conducted their launches in Cunningham Park, the day before Thanksgiving.

The launch was part of a project undertaken by the class in collaboration with the Salvadori Center’s Architect-Educator Janny Gédéon. (Jim, their teacher, had attended this year’s Summer Institute and has been implementing Salvadori projects in his classrooms.) Nonplussed by the cold, he was an energetic launch director.

A trail of smoke accompanies the hiss of the launch.

The mission outline called for the class to measure the altitude of rockets at the apex of their flight, comparing the effect of different nosecones for the same rocket and engine. Having spent the past few weeks designing and building model rockets and the host of instruments needed to gather data on their flights, the students were anxious to launch their creations. When the countdown for the first launch began, the shivering crowd crackled with excitement. The student holding the launch button, pressed it, and…nothing. An audible groan rose from the class, which was quickly interrupted by the hiss and “shoop” of the rocket zipping into the air. The crowd cheered, arms above their heads, before retreating, turtle-like, into their jackets.

Danielle Bero, Claudia Rios and Mauricio Villegas proudly showed off their red rocket, which won the class design competition. The students amassed an impressive amount of knowledge about aeronautics, ably using terms such as “resistance” and “turbulence.” Danielle Bero learned that when building rockets, ”It’s the little things that matter so much. A tiny dent in the nose cone can make it go off course.”

The recovery system successfully deploys and the rocket descends to Earth.

Anthony Rush explained how the recovery system of the rockets had to be adapted to extreme weather conditions. “If we used a parachute, the wind would carry it too far away, so we used a streamer instead, which slows down the rocket without taking it too far.” He learned a lot from the project, including, “all the different kinds of resistance that go against flight--wind resistance, gravity resistance, air resistance.”

Diana Panora watched a rocket disappear into the clouds, “I didn’t think it would go so far.”

With wind picking up, the launches continued. A rocket drifted toward the outfield of the neighboring baseball diamond. “We’ll probably lose it,” said teacher Jim Napolitano. “But that’s rocketry.”

Several data-gathering teams ringed the field, located at predetermined distances from the launch pad. Each team used its own homemade theodolite, a mapping instrument, to measure the angle of the rocket’s flight relative to the ground. Using the distance from the launch site and the tangent function, they could then calculate the rocket’s height.

>> Click here for an in-depth look at how a theodolite works.

Ruth (left) and Joseph Faillace check that their measuring device starts out level.	Loading the engine.	Teacher Jim Napolitano helps Caitlin Mangan connect the rocket to the launch button.

Because one of the students using the machine was left-handed, and his classmate at the other end of the field is right-handed, “we even built different lefty and righty versions,” said Joseph Faillace.

“I’m going to the bathroom,” announced the team’s data recorder. She was clutching her clipboard under her arm in order to keep her hands inside her sleeves.
“ Are you kidding? It’s tile and concrete. It’ll be even colder in there,” hypothesized Joseph.
“ But maybe they have a hand dryer in there.”
The ingenuity that built the theodolite on the camera tripod was thus applied to survival.

Low-flying planes now began playing hide and seek with the clouds. No more launches, announced Jim. There was a chance, however remote, that a rocket could end up in a passenger jet’s engine. “Once they get lost in the clouds, you can’t tell what’s happening,” he said. “Safety first.”

With this activity, Jim’s students were learning to collect data from concrete experiences. “Then they move from the concrete--the data from these launches--to the abstract--trigonometry.” Unlike traditional teaching methods that emphasize abstract concepts without demonstrating their practical uses, said Jim, the rocket launching introduced trigonometric and physics concepts through their real-world applications, making the ideas immediately relevant and more understandable.

Danielle Moore measures the distance from the launch site to her data-recording post.

Trudging across the muddy field, I encountered another data-collection team. Danielle Moore and her friend Rachel Gordon explained how they used trigonometry, figuring out how the angles corresponded to various heights. Using a fixed distance from the launch site as one leg of an imaginary triangle, they used the tangent function to calculate what the height of the rocket would be for various angles relative to the ground. Did they build their rocket together? “We do everything together,” laughed Danielle. “I’m her twin,” said Rachel. “I’m the good Danielle.” “And I’m the bad Rachel,” grinned Danielle. They gathered their data sheets, linked arms and headed for the warmth of the school bus.

So concluded another great American experiment in flight.

Questions? Comments? Email emily@salvadori.org