Problem Set
Whirling Wonder: A 'Pi in the Sky' Math Challenge
Overview
The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the eighth set, students use the mathematical constant pi to determine how quickly the Ingenuity helicopter's blades must rotate in order for it to fly.
Materials
Background
In this illustration, NASA's Ingenuity Mars Helicopter stands on the Red Planet's surface as NASA's Perseverance rover (partially visible on the left) rolls away. Image credit: NASA/JPL-Caltech | › Full image and caption
Joining the Perseverance rover on Mars is the first helicopter designed to fly on another planet. Named Ingenuity, the helicopter is a technology demonstration, meaning it's a test to see if a similar device could be used for a future Mars mission. To achieve the first powered flight on another planet, Ingenuity must spin its blades at a rapid rate to generate lift in Mars’ thin atmosphere. In Whirling Wonder, students use pi to compare the spin rate of Ingenuity’s blades to those of a typical helicopter on Earth.
Procedures
Joining the Perseverance rover on Mars is a small helicopter named Ingenuity. With twin counter-rotating blades spanning 1.2 meters, Ingenuity is a test of new technology and is designed to achieve the first powered flight on another world.
Despite Mars having less gravity than Earth, the atmosphere on the Red Planet is much thinner than it is here on our home planet. This makes it challenging to lift off the ground on Mars. To generate enough lift for Ingenuity, engineers determined that the helicopter's blades need to rotate at approximately 250 radians per second on Mars.
How fast – in rotations per minute – do Ingenuity’s blades spin?
How does that compare to a typical helicopter on Earth with blades that spin at 500 rotations per minute?
› Learn more about the Ingenuity helicopter
Image credit: NASA/JPL-Caltech | › Download PDF
Assessment
Image credit: NASA/JPL-Caltech | + Expand image
Extensions
Pi Day Resources
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Pi in the Sky Lessons
Here's everything you need to bring the NASA Pi Day Challenge into the classroom.
Grades 4-12
Time Varies
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NASA Pi Day Challenge
The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.
Grades 4-12
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How Many Decimals of Pi Do We Really Need?
While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.
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18 Ways NASA Uses Pi
Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.
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10 Ways to Celebrate Pi Day With NASA on March 14
Find out what makes pi so special, how it’s used to explore space, and how you can join the celebration with resources from NASA.
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Infographic: Planet Pi
This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.
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Mobile & Web Backgrounds
Can't get enough pi? Download this year's NASA Pi Day Challenge graphics as mobile phone and web meeting backgrounds:
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Pi Day: What's Going 'Round
Tell us what you're up to this Pi Day and share your stories and photos on our showcase page.
Plus, join the conversation using the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.
Related Lessons for Educators
Related Activities for Students
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Code a Mars Helicopter Video Game
Create a video game that lets players explore the Red Planet with a helicopter like the one going to Mars with NASA's Perseverance rover!
Type Project
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Make a Paper Mars Helicopter
Build a paper helicopter, then see if you can improve the design like NASA engineers did when making the first helicopter for Mars.
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Subject Engineering