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Engineers need to acquire “Back-of-the-Envelope” survival skills to obtain rough quantitative answers to real-world problems, particularly when working on projects with enormous complexity and very limited resources. In the case studies treated in this book, we show step-by-step examples of the physical arguments and the resulting calculations obtained using the quick-fire method. We also demonstrate the estimation improvements that can be obtained through the use of more detailed physics-based Back-of-the-Envelope engineering models. These different methods are used to obtain the solutions to a number of design and performance estimation problems arising from two of the most complex real-world engineering projects: the Space Shuttle and the Hubble Space Telescope satellite.



1. Introduction

I was first made aware of the value of Back-of-the-Envelope (BotE) estimation techniques when I was an aeronautics graduate student at Caltech in the early 1960s. My thesis advisor and mentor, Professor Lester Lees, taught us, by example, his approach to building basic engineering models for complicated real-world problems. He showed us how simple models could be used to estimate the solutions to problems that not only served the needs of our particular graduate research projects, but often had broader import in a number of related aerospace engineering endeavors. We didn’t learn these techniques in the classroom, but in the informal setting at the coffee table in the Caltech student cafeteria.

Irwin E. Alber

2. Design of a high school science-fair electro-mechanical robot

A student’s project for the high school science fair is to design, build, and operate a moving electro-mechanical robot that will be an active ‘‘player’’ in a local robot soccer tournament. His primary goal is to design the device so that it can trap a close-by soccer ball, and then rapidly kick it past a defending goalie into the net of the defending team. His physics teacher suggests that as a first step he should consider mathematically modeling the performance of a light-weight kicking device powered by a rapidly-acting linear solenoid actuator.

Irwin E. Alber

3. Estimating Shuttle launch, orbit, and payload magnitudes

The design, construction, and operation of the Space Shuttle ranks as one of the most significant engineering achievements of the twentieth century. Officially the Space Transportation System, referred to as the Shuttle, is a complex multipurpose reusable spacecraft system capable of transporting humans into low earth orbit and returning them safely to the earth. The return is characterized by reentry into the earth’s atmosphere followed by an airplane-like return of the Orbiter to the ground. In addition, the Shuttle system is designed to place heavy cargo into earth orbit for a variety of multi-national projects ranging from the deployment and maintenance of unmanned satellites, such as the Hubble Space Telescope, to the construction and servicing of the International Space Station.

Irwin E. Alber

4. Columbia Shuttle accident analysis with Back-of-the-Envelope methods

On February 1, 2003, the Columbia Shuttle Orbiter and its brave seven member crew perished during reentry into the earth’s atmosphere at the conclusion of its 28th flight, STS-107, a multi-disciplinary science mission.

Irwin E. Alber

5. Estimating the Orbiter reentry trajectory and the associated peak heating rates

The Space Shuttle was specifically designed to provide a multi-mission reusable orbital payload delivery capability. Overall, the system was required to have the capability to launch into orbit a number of large payloads and carry out a variety of complex orbital operations. After completing the Space portion of its mission, the Orbiter was designed to be able to reenter the earth’s atmosphere at a very high speed, slow down significantly, and land intact. The Orbiter was then to be quickly re-integrated with various Shuttle launch components in order to fly a subsequent mission.

Irwin E. Alber

6. Estimating the dimensions and performance of the Hubble Space Telescope

The Hubble Space Telescope (HST) has revolutionized modern astronomy since it was first launched into orbit by the Space Shuttle Discovery on April 24, 1990. Not since the invention of the telescope in the 17th century, have the mysteries of the universe been uncovered at such a rapid pace. The most detailed looks at the farthest galaxies in the universe have been obtained using images taken by the HST. It has made some extraordinary discoveries, the most notable being the confirmation of dark matter, observations supporting the accelerating universe theory, and studies of newly discovered planets outside our solar system [1].

Irwin E. Alber


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