(Super Cool) Math for Nerds

Thanks to the “help” of the Davidson Academy STEM problem-solving class (they did all the work), we have solved the problem of gravity. Wait, that was last week . . . we have solved the problem of when to launch our balloon!

Luke used his advanced bribing skills to encourage his classmates to compete with their advanced math skills. They were given the technical specifications of the balloon (check our blog post “Stats for Nerds”) and offered a \$10 League of Legends gift card to whoever returned the correct answer first.

Our goal is to launch the balloon so that when it reaches its peak of 120,000 feet, the sun is setting (or rising) at that height – giving us amazing video footage of a sunset 23 miles above the surface.

This is trickier than it seems. Being 23 miles above the surface, the sunset/sunrise times are pretty different than the sunset/sunrise time on the ground. The time it takes for the balloon to ascend must also be factored.

The first few people to answer were Paolo, Justin, and Siddu. Their answers told us to launch at approximately 3:15 am or 5:30 pm. A huge thank you to everyone who helped solve this problem! It was quite a fun hour.

Yes, rocket science can be done with triangles and circles. We simplified the problem to a diagram that looked a little like this:

After some reflection, the marvelous James Marshall (one of Davidson’s math instructors) revised this answer. He took into account the position of Reno on the northern hemisphere, and the tilt of the Earth’s axis. Thanks to more circles and triangles, he provided a much more accurate answer – showing that our previous answer was off by a whole hour.

If that didn’t make sense to you, it simply means that Mr. Marshall is a very smart man:

Thanks to the power of Davidson mathletes, we know that to take an amazing once-in-a-lifetime sunset/sunrise photo, we must launch the balloon from Reno at 4:20 am or 5:24 pm.