# hw2 - Homework 2 Due 31 January, 2011 at Midnight 1....

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Homework 2 Due 31 January, 2011 at Midnight 1. Consider a pilot in a human centrifuge. How fast does the arm of the centrifuge have to rotate in order to generate a 5G, 6G, and 7G acceleration (assume that it is moving at constant angular velocity)? A human centrifuge. You may assume the distance from the axis of rotation to the center of the gondola holding the pilot is 25 ft. Reference: Balldin, U.I. Acceleration Effects on Fighter Pilots. Chapter 33, Medical Aspects of Harsh Environments.

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2. Derive equation 8 in the roller coaster handout. 3. If you have not read Angels and Demons, please consider this a spoiler alert. At the end of Angels and Demons (by Dan Brown), Robert Langdon uses a window cover from a helicopter to slow his descent. This ending is potentially troubling. I would like you to use the tools we have developed thus far to determine whether or not this ending is feasible. Please state your case as succinctly as possible. 4. Design an escape vehicle for a rocket on the launch pad. The design criteria are: Start height: ~367ft End height: 0ft (ground level) Horizontal distance: 1200’ Time requirement: 2 minutes for the crew to travel from the crew vehicle hatch to the ground. This 2 minutes includes 30 seconds for the crew to walk/run from the spacecraft hatch to the escape vehicle. So that would make it more like 1:30 from start to finish. Also, here are some useful body sizes taken from our “standard anthropometric database”, the 1988 ANSUR US Army Anthropometric Database (which can be ordered from the Army, many if not most anthropometric studies in literature reference it: NATICK TR-89/044) which may help in looking at ranges of sizes of potential riders. Stature (standing height, floor to top of head):
5% female: 152cm / 60.15” 50% male: 175cm / 69.09” 95% male: 186.65cm / 73.48” Sitting height (seatpan – top of head) 5% female: 79.53cm / 31.31” 50% male: 91.42cm / 35.99” 95% male: 97.19cm / 38.26” Some things to consider: Because one or more of the astronauts may be incapacitated (it’s safe to assume that, if they are using the escape vehicle, they are having a “bad day”), it’d be safe to assume that you shouldn’t have any negative normal Gs, i.e. the normal force vector should always be pointing toward the floor. This way they can’t fly out. Passive start system. You can’t have an electromagnetic / compressed air / hydraulic launch system, as there may be significant damage at the pad when this system is used. Although you technically have 1:30, the faster the better. Remember, there’s a 380’ tall rocket not too far away from you which is getting ready to explode. ASTM F2291-09 sets a hard vertical G limit ( e n ) of 6G. But that is for seated passengers. They don’t specify anything for standing. The braking ( e t / e b ) accelerations / decelerations can be as important as the normal ( e n ) accelerations, as the vehicle has to stop safely at the end. For reference, airport trams appear to have accelerations / decelerations of about 0.14G. It is believed that if the accelerations are anticipated you can withstand higher without falling, but we couldn’t find a value for that.

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hw2 - Homework 2 Due 31 January, 2011 at Midnight 1....

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