The city of East Lansing is trying to attract more summer tourists. They've decided to replace much of the abandoned buildings on Grand River with an amusement park. They've hired the Tyrell Corporation to build it. You and your team recently graduated from MSU engineering program and have started working for Tyrell under their chief engineering officer Dr. Eldon Tyrell. Dr. Tyrell wants your team to design the amusement park's main attraction, the Nexus-6 roller coaster. The design of the Nexus-6 is such that a single occupant is strapped into a body suit that has a single connecter near the middle of the back of the suit, which connects to a metal alloy cable. This cable is attached to a well-oiled apparatus that slides along the track of the roller coaster.

The design calls for an initial hill that rises well above much of the EL skyline and easily the tallest coaster in the world while the rider is suspended underneath the track. The rider then drops down into the first of several loop-the-loops achieving a speed at the bottom of the first loop (pictured above) of 150 mph (the world's fastest coaster surpassing Dubai's Formula Rossa). All the while the rider is suspended on the outside of the loops. People are calling Dr. Tyrell a crazy man for conceiving of such an idea. Your team has been tasked with developing the detailed plans that demonstrate the ride will be safe, particularly with respect to the single metal alloy cable suspension system. Below is experimental data collected on the metal alloy. Don't let Eldon down.

In a last ditch effort to attract tourists and avoid yet another scandal, the East Lansing city council has hired Blue Sun to build a large swing carousel, which is meant to be taller than the SkyScreamer at Fiesta Texas in San Antonio. The lead designer, Malcolm Reynolds, has dubbed the ride “Serenity” due to its expected calming effect on riders. Reynolds's design hinges on a dubious science article that suggests a calming experience when people feel a “net” acceleration between 1.5g's and 2g's. Reynolds's design calls for riders to be transported up to a height of 70 meters and swung in a horizontal circle.

You and your team have been hired by Blue Sun to design and demonstrate the safety of the ride. At present, Reynolds has not decided on how many riders Serenity can carry at a time, that's up to you and your team to decide. Furthermore, Reynolds has asked your team to design the cabling system for the chairs as well. Data on the steel that is to be used in the cabling system is in the figure below. Reynolds is more of an “idea man.”