At the end of the Second World War in August 1945 large numbers of U.S. bombers were scrapped. This included not only the B-17 and the B-24, but also the, at that time still modern, B-29. This piston engine bomber was further developed into the B-50, fitted with more powerful piston engines. However, by that time it was evident that the jet bomber would soon replace the older generation of piston engine bombers. The first jet bomber to go into production after the war was the North American B-45 Tornado. With its straight wings and conventional construction it was not an excellent performer. It was evident that much more was needed.

This would come from captured German aerodynamic research data on swept wings. With aircraft nearing the critical speed of sound swept wings had many advantages and soon the German ideas were put into practice. The first swept wing fighter would be the North American F-86 Sabre. Soon the swept wing bomber would also be reality. Built by Boeing, designated as B-47 and named the Stratojet it was a quantum leap in aircraft development. Boeing initially entered the unknown when they started this project but soon it would be evident that Strategic Air Command would have its multi-engine jet bomber with a speed performance similar to the latest jet fighters….

Early design and development:

In 1944 the U.S. government released the specifications for a jet-powered bomber to replace the existing B-29. Three companies, Boeing, Convair and Martin finally received a development contract and all three companies built prototypes for testing. The final bomber prototypes from Convair and Martin were the XB-46 and XB-48. They both had straight wings. Convair’s B-46 was fitted with 4 jet engines housed in two underwing engine nacelles. Martin’s B-48 even had six jet engines, grouped in sets of 3 under each wings. The XB-46 and XB-48 made their first flight in the early summer of 1947 when the Boeing design Model 450, known as XB-47, was still under construction. The XB-46 and XB-48 both did not meet the specifications for speed. Boeing’s design was originally also envisioned with a straight wing but with captured German research data available on swept wings the design team made a radical re-design of the original project.

By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems.

Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing.

Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory.

The photoelectric effect and photons

In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.

We spend most of our life in a world of macroscopic objects moving and interacting, yet many – perhaps most – people can't describe correctly the trajectory of an object thrown from a moving car. We are aware there are rules that govern motion and interactions, but what they are, when they apply, and how they can be applied to predict the motion of a pool cue ball after it collides with an object ball, for example, are a mystery to most people, judging by how often casual pool players “scratch” by pocketing the cue ball. Even engineers, who have all had at least a year-long course in physics, are often uneasy when they are asked what exactly Newton's Laws mean instead of just reciting the words. As a matter of fact, the vast majority of people are still Aristotelian thinkers in their understanding of the laws that govern motion. In this chapter we will revisit these fundamental concepts with the goal of increasing the level of comfort with the concepts of forces and motion. Newton's Laws

The traditional formulation of Newton's Laws is something like these below:

These statements are a combination of definitions and empirical (“determined by observation”) laws. For example, a force (F) is often described as a “push or pull that, if acting alone on a body, causes a constant acceleration.” This is a circular definition that makes the Second Law a meaningless statement. The First Law also has conditions on it: you can't be in an accelerating or rotating system.

This book is based on notes prepared for a graduate course “Scientific Foundations of Engineering” in the Gordon Engineering Leadership Program at Northeastern University. The elevator speech on why such a course is needed goes as follows: (1) most engineering students take all of their basic science courses during freshman year, (2) they don't like those freshman courses very much, and (3) they forget the material as quickly as they can and concentrate on the specifics of electrical engineering, or mechanical engineering, or other engineering discipline where their interests and enthusiasm lies.

This summary may be unfair to some engineering students, but most engineering students (and their professors) at least grudgingly admit that it isn't terribly far off. And, in general, this approach serves the students well through their undergraduate education process and in their industrial careers – as long as they remain specialized in their specific engineering discipline. However, consider the case where an electrical engineer is leading a multidisciplinary project. One day a mechanical engineer who reports to her walks into her office and says, “Boss, this isn't going to work – we can't get the heat out!” A conventionally trained electrical engineer isn't likely to be able to frame a single substantive question about the problem. She hasn't studied heat transport or thermodynamics since the freshman year (if at all!), and likely has forgotten anything she ever knew about the subject. The ability to frame questions which put fundamental boundaries on the problem, “What is the power load? How hot will the device get? How much blackbody emission is there at that temperature? What is the thermal conductivity of the substrate?”, will not only enable an engineering leader to quickly frame the gravity of the problem, but will undoubtedly earn her a reputation as someone with whom you want to have done your homework carefully before making rash statements about engineering limits!

Science curricula often employ a “spiral curriculum” model. In physics for example, mechanics, thermal physics, and electromagnetics are surveyed in freshman year, revisited in specialized courses in sophomore or junior year, and often studied again from a quantum statistical viewpoint in a senior class. Engineering education more often selects a “breadth” coverage of the vast range of engineering applications, rather than the depth of understanding that the spiral curriculum seeks to impart.

Once fundamental scientific laws are understood, engineering technology depends on advances in materials – materials science – more than any other factor. Historically, ages have been named for the most advanced materials technology available: Stone Age, Bronze Age, Iron Age. If you look around the room you are in, you will recognize that our current age is the age of manufactured materials: plastics, ceramics, acrylics, polyester fibers, etc. Underlying the “Information Age” are the advances in electronic materials that have made possible the computers, displays, and communications equipment that enable information transfer and processing. Selecting materials with desirable properties and then processing to enhance these properties is now standard practice. The next generation of materials will include nanoscale manipulation and fabrication of materials unlike anything found in nature. These new nanomaterials can be predicted to have properties exceeding any currently available materials.

Materials are characterized by response functions that describe the materials’ response to applied forces or fields. For example, the electromagnetic properties of materials can be characterized by the electric permittivity (electric polarization of materials in response to an applied electric field), electrical conductivity (electrical current in response to an applied electric field), and magnetic permeability (magnetic polarization in response to an applied magnetic field). One of the fundamental mechanical properties is the elasticity, which describes the deformation of the material in response to applied forces. The elasticity, as with other response functions, depends on the physics and chemistry at the atomic scale and on the structure of the material at a micro- and mesoscale, which is larger than the atoms but smaller than the macroscopic sample. For example, crystal structure, grain boundaries, and dislocations are key determining factors for elastic, plastic, and fracture properties. There are three elastic regimes: tensile/compressive elasticity, shear elasticity, and bulk elasticity. These are all special cases of a generalized elastic tensor, but we will consider them separately to begin.