EIGHT AMAZING ENGINEERING STORIES EBOOK
Eight Amazing Engineering Stories reveals the stories behind how How Not to Be Wrong - The Power of Mathematical Thinking ebook by Jordan Ellenberg. This book reveals some of the stories behind how engineers use specific elements to create the material world around us. In eight chapters, the EngineerGuy team exposes the magnificence of the eBook | ISBN ebook, pages. Published April 20th by Articulate Stories, please sign up. Be the first to ask a question about Eight Amazing Engineering Stories.
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Editorial Reviews. About the Author. Make magazine's blog called the EngineerGuy video team eBook features: Highlight, take notes, and .. August 8, cittadelmonte.info: Eight Amazing Engineering Stories: Using the Elements to Create Extraordinary Technologies (): Bill Hammack, Patrick Ryan. Eight Amazing Engineering Stories reveals the stories behind how engineers use specific elements to create the material world around us. In eight chapters, the.
Hammack, Patrick M. Ziech All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means including photocopying, recording, or information storage and retrieval without permission in writing from the publisher. Articulate Noise Books. First Edition:
As executive director for the division of Bell Labs that worked on silicon -- the dominant medium for computer memory at the time -- he worried that these new bubbles might divert funding and support from silicon research. Boyle invited his friend and colleague George Smith to help him come up with a competitor to this new technology. On a chalkboard, they devised a way to use silicon, silicon dioxide, and metal electrodes to store charge in specific areas on the surface of the silicon.
The conversation took about an hour as they jotted down in their notebooks that the device could be used as an imaging device and a display device in addition to being used for computer memory.
After reflecting on their chalkboard talk for a few weeks, they decided to build a prototype CCD. Within a week, they had a working device that proved the concept of their idea. A great engineer, Tompsett carefully turned the brainstorm of a charge-coupled device into a reality. His name alone appears on the first patent for the CCD as an imaging device; the patent was titled, appropriately enough, Charge transfer image devices. While one might feel Tompsett was overlooked for the Nobel Prize, the prize is generally given for the invention or discovery of fundamental concepts in physics.
Boyle and Smith indeed laid down the idea of a CCD, but controversy arises because the only practical application of a CCD is as an imaging device. For instance, if you drop this book, gravity will accelerate it toward the center of the earth until it comes to rest on the ground.
But how does a smartphone know which way the phone is rotated, so the screen is always right-side up? To ensure that the screen on your smartphone always is pointed in the correct direction, engineers place tiny accelerometers inside the phone to orient it with respect to the earth. An accelerometer is a device that measures gravitational pull. But how can these tiny accelerometers tell which way is up? Basics of an Accelerometer You can see the essential principles of an accelerometer in the simple device shown in the next figure.
When that device is upright, gravity stretches the spring downward, as indicated by the mark labeled 1g, meaning one unit of gravitational acceleration. One g is what you feel with little or no other acceleration on earth; for reference, when a roller coaster car takes off you feel about 2. On the device 0g occurs when the tube lays flat so the spring feels no gravitational pull, and the spring has no extension.
This distance from 0g to 1g sets the scale for marking 2g, 3g, etc. We can use this accelerometer to measure the upward vertical acceleration experienced by the tube. If we were to quickly jolt the tube upwards, we would see the weight drop inside the tube, possibly to 2 or 3gs.
Three of these basic accelerometers can be used tell us the orientation of an object. A simple accelerometer: A glass tube with cork stoppers at each end makes up the housing. The seismic mass is a lead ball tethered to the housing by a spring. In an oblong box, align one accelerometer each along the x, y and z axes. By measuring changes in the lengths of the springs, we can detect which edge points up relative to gravity.
In the first position, the xaxis accelerometer records 1g, while in the y and z direction the weights lie against the side of the tubes and the springs are not extended. Rotate the box so it sits on its long edge, and the y-axis accelerometer will register 1g, while the x and z accelerometers will read 0g.
Although the accelerometer inside a smartphone is a bit more complex, it works using these same principles. Three of these simple accelerometers can determine the orientation of a box. Note the change in the x and z accelerometers. When the box lies on its z-axis, the ball in the accelerometer along that axis lies flat while the spring in the accelerometer on the x-axis is extended.
When the box is rotated, the ball in the x-axis accelerometer lies flat, while the ball stretches the spring in the accelerometer along the z-axis. As with all technologies, though, power comes with peril -- even with such a seemingly innocuous object as a smartphone accelerometer.
Researchers at the Georgia Institute of Technology showed that such an accelerometer could track the keystrokes of a computer user. They placed a phone on the table beside a computer keyboard. Since the accelerometer samples a phones vibration about times per second, it would jiggle slightly with each press of the neighboring keyboard.
The keyboard moved the table slightly, and the ultra-sensitive accelerometer detected these small vibrations of the table. For example, in typing canoe the user would create four keystroke pairs: The accelerometer would determine for those pairs if the two letters were related in one of four ways: They compared this to a preloaded dictionary of likely words to determine the most probable word made for these pairs of keystrokes.
Small wonder, then, that Melvin Kranzberg, a historian, once observed technology is neither good nor bad; nor is it neutral.
The Accelerometer Inside a Smartphone The figure below shows a typical smartphone accelerometer. Its very small, only about microns long on each side. The housing, which is stationary, is the large block at the base, to which are attached several stationary polysilicon fingers. The seismic mass is the roughly H-shaped object with the tongues extending from it; its tethered at the ends so it can jiggle left and right between the stationary fingers.
Recall that in our simple accelerometer with the weight and spring arrangement, we measured the acceleration of the box by how much the weight moved relative to the tube. This device measures acceleration by the degree to which one of the tongues hanging off the H-shaped section moves relative to the two stationary fingers.
We did this by eye for the weight and tube accelerometer, but here we use the electronic properties of silicon. The tongue and two stationary fingers form a differential capacitor, a device that stores charge. As the accelerometer moves, the charge stored within the differential capacitor changes, causing a flow of current. Through careful calibration, engineers can link the magnitude of the current flow with the pull that the accelerometer feels from gravity.
Using a Capacitor to Make an Accelerometer We can make the simplest capacitor from two metal plates with an air gap between them, as shown in the next figure. If we hook these capacitors to a battery, current will flow as charge builds up on the plates: Once enough charge builds up, the current stops because the.
For most well-made capacitors, this situation will persist until we change something in the circuit. For example, if we move the plates a little closer, then current will flow again as the charge is redistributed. You can picture how a capacitor would be useful in an accelerometer: Imagine one plate as the housing and the other as the seismic mass.
When we hold that accelerometer stationary, no current flows. But move the seismic mass, or the top plate, and a current now starts to flow. Just as we did with the weight and tube accelerometer, we can calibrate this: Subject the two-plate capacitor accelerometer to known accelerations and measure the currents that flow. The leftmost image shows a two-plate capacitor before the circuit is closed.
There are no charges on the two metal plates. When the circuit is closed center image a charge builds up on the plates and current stops flowing. If the plates are moved closer together, as in the image on the left, current flows until the charge is redistributed on the plates. A smartphone accelerator doesnt quite work like this, but were getting close. The problem is that our two-plate capacitor has a serious defect.
In the simple two-plate capacitor, the relationship between plate position and current is non-linear. This makes the accelerometer difficult to calibrate. Engineers prefer a linear response; that is, if we reduce the distance by one-quarter and then by another quarter, wed like to see the same drop in capacitance each time.
This would allow for a more uniform sensitivity across the useful range. So if we set up a slightly different capacitor where the top and bottom plates are stationary and the middle one moves, the current generated by changes in this differential capacitor will be linear. In this differential capacitor, we measure the difference in the charges that form in the bottom capacitor the bottom and middle plate and the top capacitor the middle and top plate.
On the left, the capacitor is uncharged. If we use the same size batteries and keep the middle plate exactly between the top and bottom plate, then positive charge as shown in the middle image will build up equally on both plates.
If we move the middle plate closer to the bottom plate, the capacitance of the bottom. The difference in capacitance is linear with respect to the motion of the middle plate. Look at what happens if we charge the differential capacitor using two batteries with opposite polarities: Current flows until the middle plate becomes negative and the top and bottom plates are positive. Now, if we move the middle plate, current will flow to redistribute the charge.
If we measure that flow only between the middle and bottom plate, it will be linear with the middle plates motion. At the end of the chapter, there is an explanation of the mathematics of capacitors. This is exactly how the accelerometer works: The tongue from the H-shaped piece corresponds to the middle plate, and the two stationary fingers are the fixed plates of the differential capacitor.
At rest, no current flows. But if we move the accelerometer, the tongue will jiggle, creating a current proportional to the acceleration. Now we have the perfect device to put in our phone and tell us which way is up, but that is only half the battle.
The next problem lies in making something so small but so complex. How to Make an Accelerometer It would seem nearly impossible to make such an intricate device as the tiny smartphone accelerometer; at only microns across, no tiny mechanical tools could craft such a thing.
Instead, engineers use some unique chemical properties of silicon to etch the accelerometers fingers and Hshaped section. The method is known as MEMS, or micro electro-mechanical systems.
To get an idea of how they do this, let me show you how to make a single cantilevered beam out of a solid chunk of silicon. A cantilevered beam is one that is anchored at one end and sticking out over a hole; for instance, a diving board is a cantilevered beam. The moving section of the smartphone accelerometer is just a complex cantilevered beam. Lets start by etching a hole in a piece of silicon. Empirically, engineers noticed that if they poured potassium hydroxide KOH on a particular surface of crystalline silicon, it would eat away at the silicon until it formed a pyramid-shaped hole.
To make a pyramidal hole in silicon, engineers first cover all but a small square of the plane -thats what we meant by a particular surface -- with a mask of silicon nitride Si 3N4.
The mask is impervious to the KOH, so the KOH etchant will now only etch within the square shape cordoned off by the mask until its washed away.
This directional etching occurs because of the unique crystal structure of silicon. The three main steps from left to right to make a pyramidal hole in a piece of crystalline silicon. Each step is shown from three angles top to bottom: In a chunk of silicon, each silicon atom has four closest silicon neighbors surrounding it.
The four neighbors create a tetrahedral region around the silicon at the center. Millions of these units make up a slab of silicon. Theyre packed together in an open structure that is not the same in every direction. For example, the number of atoms along the three directions shown above -- labeled , , and  - differ in the number of atoms in the planes perpendicular to each direction.
The atoms are packed more tightly along the  direction than in the  direction. This means that the KOH dissolves both the surface and the surface, but it chews through the latter much faster.
This is why it makes a pyramidal hole. Crystal structure of silicon. Every atom in a silicon crystal is identical. Each is bonded to four other silicon atoms. The darkened atoms in this figure show most clearly that each atom has four nearest neighbors. Note that there are more atoms in the plane perpendicular to the  direction than there are in planes perpendicular to the  direction. To make a cantilevered beam, engineers mask all the surface except for a U-shaped section. At first the.
KOH will cut two inverse pyramids side by side. As the etching continues, the KOH begins to dissolve the silicon between these holes. If we wash KOH away at just the right point before it dissolves the silicon underneath the mask, it will leave a small cantilever beam hanging over a hole with a square bottom. The three main steps left to right to make a cantilevered beam in a piece of crystalline silicon.
Although engineers use these principles to produce smartphone accelerometers, they use much more complicated masks and multiple steps. As you can picture, first a machine would apply a mask, then etch the silicon, change the mask, and etch some more; the process is repeated until they create an intricate structure. While complex, a key point is that the whole process can be automated.
Engineers now make all sorts of amazing things at this tiny scale: In Depth: The Mathematics of Capacitors Simple algebra reveals why the capacitance of a two-plate capacitor changes non-linearly with a change in the plate separation and why a differential capacitor changes linearly. The capacitance between two plates, which is just the amount of charge that it can hold, depends on three factors: The dielectric constant is the ratio between the amount of electrical energy stored in a material by an applied voltage to the energy stored if the space between the plates were filled with a vacuum.
We define capacitance as. Where is the dielectric constant, A is the area of the plates, and d is the distance between the plates. If we move the plates closer together by a small amount, say , then the new capacitance is.
The Taylor Series is a useful way to simplify some mathematical formulas under certain conditions. For example,. You can test for yourself how much smaller y must be than x for this to be true. Here, we are assuming that the change in the distance between the two plates will be much smaller than the original distance, so we approximate with a Taylor Series. That squared term causes a non-linear response, which is most easily seen in the plot below.
This plot shows the response of both a two-plate and a differential capacitor. The y-axis is the fractional change in the separation of the plates -- here they are getting closer together -- and the x-axis shows the change in capacitance. Note how the two-plate capacitor deviates from a linear response, while the differential capacitor has a linear response in the same range.
To overcome the non-linear problem, engineers use a differential capacitor. As described in the chapter on the accelerometer, this capacitor has three plates: The capacitance of each plate is then:.
Of course if the plate is perfectly centered, the difference between these two capacitances would be zero, but it will change if we move the middle plate down by. That is, as the center plate gets further from the top plate by and closer to the bottom plate by. This difference becomes:. In , Robert Bunsen was on a search for a new element. Having already invented his famous burner, Bunsen was working with co-discoverer Gustav Kirchhoff famous today for his eponymous laws of electricity to extract a new element from mineral water.
Boiling down 30, liters of water, they extracted from it everything they already knew about -- lithium, sodium, potassium, magnesium, and strontium. What remained was a thick liquor of some unknown substance, which Bunsen placed in the flame of his burner. Two brilliant blue lines appeared in the flame when viewed through a prism, indicating a new element.
He named it cesium, from the Latin caesius, meaning blue-gray. The defining characteristic of this soft, silvery metal is its low melting point of 29 oC. Place some in your hand and itll melt, but it is so reactive that it will also burn your palm: The moisture in your skin will decomposed into hydrogen and oxygen.
Cesium has two traits important in making the first atomic clock, as described in this chapter. First, its low melting point makes it easy to create a gas. Second, the element has only one stable isotope Cs , so all cesium atoms are identical, allowing it to be used as a standard in timekeeping.
There, an international team of clock watchers combine the results of almost clocks to create Coordinated Universal Time UTC , the world standard for civil timekeeping.
Our high-tech world depends on accurate time in nearly every respect, but perhaps the most striking example is the global positioning system GPS , which requires time be measured to an accuracy of at least one nanosecond to operate correctly. To achieve that accuracy, every GPS satellite orbiting the earth contains an atomic clock that marks time with incredible accuracy. To make a clock extraordinarily accurate requires a standard that will remain the same over long periods of time.
For the atomic clock, it is easy to specify that standard: The energy difference between the ground states of a cesium atom -- a difference of 3. This energy difference is the same for every atom of cesium kept at the same conditions of pressure and temperature.
The hard part is engineering a device that uses this standard to make a reliable, useful clock. To understand the engineering principles used in designing an atomic clock, we need first to understand how to keep time by resonance. Basics of Modern Timekeeping In the past, time was measured using physical actions, such as the flow of water in elaborate sixth century BC Chinese clocks, or the hourglasss flowing sand. In our modern age, we measure time by resonant control.
See figure for a definition of resonance. The most familiar example of using resonance for timekeeping is the pendulum of a grandfather clock: It swings back and forth with a regular period, typically two seconds for the pendulum to complete one arc. The period is the time it takes for the pendulum to swing completely in one direction and then back again to its original starting point. Based on this period, the manufacturer designs the gears in the clock to translate this periodic motion, or resonance, into a movement of the hands that marks time in minutes.
If there were no friction or drag, the pendulum would swing forever, keeping perfect time; but, of course, the arc slowly decays, that is, it gradually stops swinging. On each swing, the pendulum loses a little energy to friction and does not return to as high a point as it did before. If you wanted a grandfather clock to keep better time, you could tap it every time the pendulums arc decreased just a little bit to put it back on track.
Resonance is the tendency of a system to oscillate with larger amplitudes at some frequencies than at others; these points are called a systems resonant frequencies. All resonators, if moved from rest, transform their stored energy back and forth from potential to kinetic at a rate depending on the mass and stiffness of the spring or pendulum, or equivalent electrical properties.
At each oscillation, that is, the change from potential to kinetic energy, the resonators lose a small portion of their energy to internal friction and so eventually decay. There are many ways to create resonance, all of which can be used to tell time. Shown in this figure are a an electric circuit with an inductor and capacitor; b a pendulum driven by gravity; c a quartz resonator; d a tuning fork made of steel or quartz; and e a hairspring with a balance as used in early twentieth century watches.
In essence, this is precisely how an atomic clock works. It also has a resonator keeping fairly good, although not perfect, time. Taking the place of the pendulum inside the clock is a piece of quartz, and the tap comes from an electronic signal guided by a device that uses cesium atoms to detect when the resonators period has decayed a tiny bit.
Picture the atomic part like cruise control. In a car, you use cruise control to set a constant speed, and if the car speeds up or slows down on a hill, the control system responds automatically to keep the cars speed at its set point.
Eight Amazing Engineering Stories
In an atomic clock, the speed is the period of the resonator. If it slows down, a circuit tells it to speed up a bit and vice versa. In engineering parlance, this is a type of feedback control. As you might guess, creating the cruise control from a cesium atom is pretty complex. Lets break it down by looking at the resonator that lies at the heart of an atomic clock. Quartz Resonators A pendulum is only one of many ways to create resonance for measuring time.
A pendulum system would be far too inaccurate for an atomic clock, so engineers use a piece of quartz, typically just a solid, rectangular slab a few millimeters in length and width and fractions of a millimeter in thickness. It doesnt seem obvious that it would work as an oscillator, at least not as obvious as a pendulum, yet the principles are the same.
For a moment, instead of thinking about a slab of quartz, think of a rectangular. If you tap it, it vibrates back and forth. It doesnt last for long, but it does have a periodic motion or resonance, and just like the pendulum, its motion stops eventually. A piece of quartz will resonate in the same way.
A piece of quartz can oscillate vibrate in many different ways, each of which has a different frequency depending on the thickness and dimensions of the crystal. Shown above are some of its main modes of vibration. Most important for the atomic clock is the thickness shear vibration mode bottom right in the figure. The most precise crystals vibrate in the fifth overtone of this mode at frequencies of 5 MHz or 2.
Tap it in the right way see next figure , and it will oscillate at five million times per second, or 5 MHz. Unlike Jell-O, we dont tap the quartz to have it oscillate. To start the oscillation of the quartz to measure its period, engineers use the piezoelectric properties of quartz.
The word piezoelectricity comes from the Greek verb piezein, which means to squeeze or press. To start the quartz crystal oscillating, we tap it with a jolt of electricity a small voltage across the quartz and then measure the vibration from the current it produces.
That tap will keep the quartz resonator going for a long time; for example, its oscillations will last roughly 1, times longer than the swing of a pendulum of a grandfather clock. A piezoelectric material can convert mechanical motion into electricity and vice versa. For example, if we were to attach two foil electrodes to a piece of quartz and then strike it with a hammer, the crystal would generate a current.
And if, in turn, we apply a voltage across those electrodes, the crystal will deform. It might seem the quartz oscillator solves the problem of creating precise time. Quartz is ideal for clocks because of its outstanding physical hardness as well as its mechanical and chemical stability.
A quartz resonator provides precision only to about 1 second in years for a short period of time although the best resonator can achieve 1 second in 3, years , but if we combine it with feedback from an atomic standard, we can make a clock with astounding accuracy.
Cesium-based Atomic Clocks Recall that our idea was to take an oscillator and, just as the period of its motion begins to decay, give it a tap to restore its oscillations. The atomic part of an atomic clock uses cesium to create a way to determine when the oscillations of a quartz crystal have decayed too much and the crystal needs to be tapped. We do this by measuring a particular property of cesium. The atoms in pure cesium exist mostly in two slightly different forms: A low energy form and one of just slightly higher energy.
For an atomic clock, these two variations, usually called states, have two properties critical in making a clock: They can be separated by a magnet because they differ in their magnetic properties. The lower energy atoms can be converted to the higher energy ones if we bombard cesium with radiation of exactly the right value as characterized by the energys wavelength.
In that word exactly lies the heart of the atomic clocks great accuracy. Engineers tie the frequency of the quartz resonator to the wavelength of the radiation bombarding the cesium. That is, if the resonators frequency changes, then the radiation changes wavelength and no longer converts the lower energy to the higher energy atoms. This means that if we can detect whether higher energy cesium ions are being converted from the lower energy ones then we have a feedback mechanism for keeping the quartz resonators frequency accurate.
Heres how its done. In an oven, we heat cesium chloride to create a gaseous stream of cesium ions. The stream contains. The higher-energy ions are discarded, and the lower-energy ions are allowed to pass into a chamber. Inside that chamber, we bombard the ions with energy equal to the energy difference between the two lowest ground states of cesium, which converts the lower- to the higher-energy ions. As these gaseous ions leave the chamber, they pass through another magnet that directs high-energy ions toward a detector, discarding any lower energy ones.
The detector converts the arriving ions into a current. The key to understanding how this creates an extraordinarily accurate clock is seeing what happens if the energy isnt tuned to just the right wavelength to make the atoms change. A schematic of the first atomic clock made in An oven creates a gaseous stream of cesium. This gas contains a mixture of cesium in its lowest and next-to-lowest energy states. The stream flows through a set of magnets that remove the high-energy atoms.
The lower-energy atoms flow into a chamber where they are bombarded by microwave radiation whose frequency is tied to the frequency of the quartz oscillator.
If that radiation is of the right frequency or, equivalently, wavelength , all of the cesium atoms in the lower energy state are converted to higher energy. As they exit the chamber, a second set of magnets directs these higher-energy atoms to a detector. The signal from this detector provides feedback to the quartz oscillator: Should the frequency of the oscillator drift, the signal from the detector decreases, indicating the quartz oscillator needs to readjust its frequency see the next figure for the signal from the detector.
In this way, the quartz oscillator can keep time such that it loses only a second or so in a million years. The trick here is to tie the current from the detector to the quartz oscillator.
When the oscillations. A detector at the end of the chamber measures the number of high-energy cesium ions produced.
It converts the number into a current. If we plot that current versus the oscillator frequency, we can see a clear current spike at the optimal frequency. When the electronics of the atomic clock detect this current decreasing, they send a voltage to the quartz resonator and, via the piezoelectric effect, restore its oscillation frequency.
The decrease in current tells the electronics to tap the oscillator and correct the period of oscillation. The electronics create this tap, of course, by applying the proper voltage that, via the piezoelectric effect, deforms the quartz and restores its oscillation frequency.
Uses of Accurate Time Its very nice to have clocks that keep such extraordinary time, but of what use are they to engineers? Well, an incredibly important use of atomic clocks is our global positioning system, used in almost every facet of life today. The obvious uses of GPS include guiding commercial planes, helping us find a location, and keeping track of a fleet of cargo trucks.
However, GPS reaches even deeper into our world, striking at the core of our society: Farmers use GPS extensively for precision or site-specific farming. This technology allows farmers to apply pesticides, herbicides, and fertilizers precisely, which reduces expenses and increases yield. Before GPS, a 4,acre farm needed eight or nine tractors; today the same farm needs just three or four.
A GPS navigation unit makes life easier, whether its a trip for pleasure or tracking a trucking fleet so its operations can be optimized. But in the great, even astonishing, precision of GPS lies the potential to guide a weapon exactly to its target.
In the United States, the Department of Commerce requires all exportable GPS devices to shut down when they travel faster than 1, knots or when their altitude is above 18, meters.
This restriction prevents GPS devices. How the GPS System Works The global positioning system consists of twenty-four active satellites orbiting the earth, with more added every year Some satellites are in reserve in case of outages.
Maintained by the United States Air Force, they circulate around the earth in about 12 hours at whats called medium earth orbit; that is, 20, km above the earth.
In comparison, geostationary satellites like Meteosat meterology satellites orbit at about twice the distance of the GPS satellites. In some ways, it would be easier to operate the system if the GPS satellites were geostationary, but they would then be too far away to transmit a strong enough signal. A typical GPS satellite contains four atomic clocks: Ground stations called the Control Segment of the GPS system in Hawaii, Ascension Island, Diego Garcia, Kwajalein, and Colorado Springs monitor the satellites operational health and also transmit to the satellites their exact position in space.
For example, the ground station sends corrections to a satellites position information and also transmits clock offsets to correct any changes in the satellites atomic clocks.
The satellites are synchronized with each other and to a master clock -- called GPS time -but only to within about a millisecond. The signals are traveling at the speed of light, so this millisecond means an error of about a million feet or kilometers.
The ground stations could update the clocks, but practice has shown it is better to leave the clocks alone and send to the satellite how much its time is offset. These offsets are then sent in the signal from the satellite to the receiver.
Each satellite sends out a signal every millisecond. This signal contains the exact position of the satellite and the time including correction that the signal left the satellite.
The position information is the satellites ephemeris, from the Greek word ephemeris meaning diary or journal. On the ground, a GPS receiver detects these signals, recording the time they arrive.
Using the difference between the arrival time and the departure time embedded in the signal, the receiver calculates its distance from a satellite: The time difference multiplied by the speed of light the radio signals travel this fast, attenuated a bit by the ionosphere and troposphere, which well ignore here gives the distance between the receiver and the satellite.
In principle, if the receiver knows its distance from three precisely located satellites, it can determine its own position, but as well see, it really takes four satellites.
Three satellites would suffice for location, except that the clock on the receiver isnt accurate. We could put an atomic clock in the receiver, but then it would be very expensive and likely quite large. So, to correct the receivers clock, we use a fourth satellite.
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The Mathematics of GPS When a receiver locates its position based on its distance from satellites of known location, it is solving four equations simultaneously.
To calculate the distance from the receiver to a satellite we use this formula from solid geometry:. Where d1, d2 and d3 are the distances between the receiver and each satellite, which are obtained using the speed of light as described above; and xi, yi, and zi are the coordinates of the satellites, which are embedded in their signals.
Because all three satellites have synchronous time from their atomic clocks, we only have three unknowns: Note that if the satellites werent synchronized wed have three more variables, an insolvable problem! These three equations. Every one of the distances is wrong because the clock in the receiver is not accurate. In principle, the receiver can use simultaneous signals from three satellites to determine its position, but as noted in the text it needs a fourth satellite to correct the receivers clock.
Using information from the first satellites signal -- the time it was sent and its position -- the receiver can determine that it lies on the surface of a sphere of radius d 1. From the second satellite, it creates another sphere of radius d 2 -- the distance the receiver is from the satellite.
The receiver must be where those two spheres intersect, as shown by the circle represented by the shaded area. The location must lie on that circle.
The distance from the third satellite creates another sphere, whose interaction with the first two spheres narrows the receiver location to two points: One can be rejected immediately because it is far from the earths surface, the other is the correct location of the receiver.
Weve assumed above that the receiver is synchronized with the satellites, which it would be if it had an atomic clock built into it, but, as noted above, to keep the receiver cheap and compact it has only a low accuracy clock. So, we need to correct the distances by the error in the receivers clock. If the receiver differed from satellites by t then the distance error is ct where c is the speed of light.
Our three equations then become:. We now have three equations and four variables: We need a fourth equation, which we get from a fourth satellite. Just as with the first three satellites, the receiver calculates its position from this fourth satellite:.
We now have four unknowns and four equations. These four equations are highly non-linear and cannot be easily solved in the usual way by substituting. Instead, engineers use a procedure called NewtonRaphson iteration. To implement this iteration, they expand each equation into an infinitely long polynomial based on the trial set of values for the position.
These four linearized equations can be solved simultaneously to determine whether this guess was right; if not, we substitute the values generated and repeat. If the receiver starts with a good guess of where it is -- usually its last location -- then this can often converge in one iteration. If you instead used the GPS receiver, turned it off, and then flew half way around the world, it would take a bit of time for the receiver to locate itself.
All atoms consist of a nucleus composed of protons and neutrons surrounded by a cloud of negatively charged electrons. The protons are positively charged, while the neutrons have no charge, but they are each 2, times the size of an electron.
Thus, the mass of an atom is pretty much just the size of its nucleus. Several forms of many atoms occur naturally, and we call these different forms isotopes.
Isotopes differ from one another in the number of neutrons each isotope contains; for instance, while the most common naturally-occurring form of the element carbon has 6 neutrons, the isotope of carbon that has 6 protons and 8 neutrons in its nucleus used for carbon dating is written as 14C, where the superscript lists the number of protons and neutrons together.
The nucleus is filled with positively-charged protons, which repel each other. The force that keeps the nucleus from flying apart is known as the strong nuclear force. This is one of four fundamental forces of nature the other three being the weak nuclear force, electromagnetism, and gravity and is also the strongest. It is incredibly powerful at short distances, but at distances more than a few angstroms 1 x m long, the force drops to zero.
The balance between these two opposing forces -- protons repelling each other and the strong nuclear force keeping them together -- helps to explain why some elements can undergo fission.
This graph shows the amount of binding energy per nucleon. A nucleon is either a proton or a neutron. The x-axis shows the total number of nucleons, which equals the atomic mass. Thus, the elements appear from lightest to heaviest from left to right on the x-axis. The greater the binding energy, the more stable the nucleus.
Elements to the left of iron have a tendency to combine fusion to become more stable. For example, in the sun, hydrogen, the lightest element, undergoes fusion to become helium, the second lightest element. Elements to the right of iron can become more stable by splitting apart fission.
Fission In undergoing fission, a nucleus splits apart, releasing the energy binding it together. Elements with atomic numbers larger than iron are less stable than those with fewer protons. As the atomic number increases, the number of protons being packed together increases, yet geometry indicates that they must become further apart as their number increases.
This means that the strong interaction is diminished, yet every pair of protons in the nucleus stills feels an electrical repulsion. Thus, the force that holds the nucleus together weakens, and the force driving it apart increases. This makes atoms of high atomic. Nuclei are typically stable, so fission requires adding energy to the nucleus.
Typically, we break up a nucleus by bombarding it with neutrons. That sounds exotic, but its good enough to think of the bundle of neutrons and protons at the nucleuss core as a rack of billiard balls and the bombarding neutrons as a cue ball.
Just as with cue balls, the degree to which the rack breaks up depends on the speed of the cue ball; the analog in nuclear physics is slow and fast neutrons. Bombarding U with slow neutrons causes its nucleus to begin to vibrate violently because the kinetic energy of the moving neutron is transferred to the particles in the nucleus.
The uranium atom then breaks apart: Not all nuclei will easily undergo fission. Most elements are stable so that when bombarded with neutrons they simply absorb the neutron and decay later, or they require very high energy fast neutrons.
To extend the analogy with billiard balls a bit, imagine the rack of balls being sticky so they require a faster higher kinetic energy cue ball to break them apart. To extract nuclear energy in a practical way requires elements that are reasonably stable so they can be stored without appreciable decay but are capable of undergoing fission with neutrons of all energies.
Only four elements meet these criteria: You can visualize fission by picturing the uranium atom as a spherical liquid drop before the neutron hits; after impact, it vibrates, becoming elliptical and stretching until it looks like a Q-tip. Eventually the thin section breaks and the nucleus splits -fissions -- into smaller parts, with splinters flying off.
For U those splinters are typically two or three neutrons. For the chaotic explosion of a bomb the reaction releases more and more energy; where as in a nuclear power plant the reaction releases enough energy to just sustain the reaction.
Here U has the two essential properties to sustain a chain reaction. First, it can undergo fission from slow neutrons and, second, that fission generates more than one neutron. To see why both of these are needed, lets look at trying to generate a chain reaction in natural uranium. Natural uranium is made up of mostly U with a tiny bit of U.
Fast neutrons will cause both U and U to fission. The neutrons created when either of these isotopes fission, however, will be slow neutrons. Slow neutrons will cause U to fission, but not U. Instead, a U atom absorbs slow neutrons and then decays later without releasing any neutrons that would continue the chain reaction. Effectively the U quenches the chain reaction. The case is even worse if we start with slow neutrons: Only 1 in U atoms will fission, and U never will.
To make U undergo a chain reaction, we need to remove some of the U. This process of creating uranium with a U concentration greater than found in nature is called enriching.
Named for the planet Uranus, this elements defining characteristic lies in its nearly unique ability to start a nuclear chain reaction that releases tremendous amounts of energy.
One kilogram of uranium has the energy of over 1, tons of TNT. Splitting the uranium atom offers the promise of bountiful energy via nuclear power, but also the ability to destroy the world with atomic bombs. Uranium, a silvery, ductile metal, powered the first nuclear bomb. On August 6, , at 8: Uranium brought massive changes to our society, allowing it to compete with silicon to define the twentieth century.
Future historians will call the century the dawn of electronics, or the opening of a century of death, depending on what plays out in the twenty-first century. Oddly, for an element with such life-changing promise or peril, it isnt rare; its more common in the earths crust than tin. What prevents nuclear weapons from proliferating around the globe is the difficulty with purifying uranium so it can power a bomb.
Allied forces had captured Heisenberg, winner of the Nobel Prize in Physics for his uncertainty principle, as part of an operation begun on February 24, They kept them secreted away at a large, isolated house fifteen miles from Cambridge, where the British secret service clandestinely recorded their conversations.
Shortly before dinner on August 6, , Otto Hahn told the others of a BBC announcement that an atomic bomb had been dropped on Japan. Immediately Hahn added, They can have only done that if they have uranium isotope separation. Heisenberg, doubtful of the report, chimed in that the United States Manhattan Project must have spent the whole of their ,, in separating isotopes. Hahn felt separating isotopes was still twenty years away; another scientist added that he didnt think the bomb had anything to do with uranium.
The scientists continued discussing the difficulty and outlined methods of separating isotopes. Its telling that of all the steps to make a nuclear bomb, these experts focused on one aspect: Operation Alsos: As part of Operation Alsos -- a largely BritishUnited States effort to find out just how close the Nazis were to a nuclear bomb -- the soldiers were to seize any German nuclear resources. The team pushed through the Eastern edge of the Black Forest to find their target: Under interrogation, the scientists revealed that Germanys most secret nuclear information was sealed in a metal drum sunk in a cesspool behind the house of physicist Carl von Weizsacker -- a man famed in the early s for explaining the nuclear process inside stars.
With this information, the allied forces soon captured the remaining chief scientists, including Heisenberg. The Allies faced a problem: If they formally arrested and charged these scientists with war crimes, they would call attention to the two US nuclear bombs being readied for testing in America.
One general suggested that the simplest solution would be to shoot all the scientists. Unpalatable and barbaric to the Allied Command, they eventually decided to keep them detained incommunicado at an isolated house fifteen miles from Cambridge. Owned by the British secret service, the house, called Farm Hill, had microphones installed, a standard practice with senior prisoners of war, although the detained scientists themselves were unaware of the microphones.
One scientist asked Heisenberg, I wonder whether there are microphones installed here? Heisenberg replied, Microphones installed? Laughter Oh, no, theyre not as cute as all that. I dont think they know the real Gestapo methods; theyre a bit old-fashioned in that respect. Making highly enriched uranium, the essential ingredient of a nuclear bomb, a high-ranking US.
A bomb maker or power plant operator needs a rare variant of the element uranium, the isotope U, that easily releases its nuclear binding energy. While the principles behind a nuclear bomb can be understood by anyone with basic scientific knowledge, the engineering to enrich uranium is tremendously difficult since nature doesnt make it easy. The key engineering problem lies in separating two nearly identical uranium isotopes.
To extract nuclear energy in a practical way requires elements that are reasonably stable so they can be stored without appreciably decaying, but that are capable of undergoing fission with neutrons of all energies.
Of these, U is even rarer than U, and plutonium is made in a nuclear reactor from U, so in some sense is harder to produce than U. Pure U can easily sustain a chain reaction that releases tremendous energy. Each time a U atom undergoes fission, it releases a tiny amount of energy, roughly three million times the energy released when a single octane molecule in gasoline combusts.
The key, of course, is that this happens very many times and, because of the chain reaction, it occurs at nearly the same time. This chain reaction cannot happen in naturally occurring uranium, which consists mostly of U; only 1 atom in is U. The U will quench completely the chain reaction. So, to get such destructive power, a bomb maker needs to remove the U in natural uranium so it becomes enriched in U. Luckily this is a difficult engineering problem to solve. The Power of the First Nuclear Bomb The first nuclear bomb, which destroyed Hiroshima, contained about 60 kilograms about pounds of uranium U, of which only g 1.
This was enough, though, to create an explosion equal to 13 to 18 kilotons of TNT. For example, to sort silverware we note the different shapes of spoons, forks, and knives. Industrially, the same principle applies: To separate iron from plastic in a recycling center, we use a magnet; copper is leeched from its ore by sulfuric acid; and to desalinate ocean water, engineers boil the water, producing steam consisting of pure water.
However, the two uranium isotopes U and U have nearly identical physical, magnetic, and chemical properties. This means that no magnets will tug on one more than the other, no solvent will wash away only one isotope, and neither will boil before the other. So, to separate them, engineers exploit the one slight difference between them: That tiny weight difference means the two isotopes will move at slightly different speeds when exposed to a force.
With less than a two percent difference, its just enough to make separation possible, but not easy. Consider this: If these two uranium isotopes were to race the 2, miles from New York to Los Angeles, the lighter isotope would arrive 25 feet ahead of the heavier one.
How Uranium Was Enriched for the First Atomic Bomb To enrich uranium for the first atomic bomb, engineers built immense gaseous diffusion plants that capitalized on the fact that U would move slower. In essence, these plants allow a gas of uranium to flow through miles of piping in a kind of race, where at the end the lighter U wins out. Such plants are immense: For the Manhattan Project, which built the first atomic bomb, the building housing the diffusion plant covered over 40 acres and was a half-mile long in the shape of a U, containing a twisted maze of miles of piping.
To start this race, engineers would combine uranium with fluorine to create uranium hexafluoride -- UF6 and UF6. Although solid at room temperature, UF 6 turns into a gas, commonly called hex, at Next, they sent this gas through a tube encased in a chamber. Lower pressure in the chamber compared to the tube results in more of the UF6 than UF6 passing through perforations in the tubes wall. The chamber traps any gas that escapes the tube. As you might guess, the amount of separation, or enrichment, is slight: So, to increase the separation, this slightly enriched stream is passed through another tube and chamber, called a stage, which enriches it a bit more, and then through another stage and another.
In the single stage shown on the left, a pressure difference forces hex gas containing both U and U isotopes to flow through a porous pipe. The light U travels faster and further and thus is more likely to pass through the barrier.
The isotope separation in a single stage is very small. To achieve great separation, many such stages are linked together. The drawing on the right shows three linked stages.
Note that the enriched stream passes into the next stage. Thus this stream becomes more and more enriched as it passes through the stages. Gaseous Diffusion A gaseous diffusion plant, like the one used in the Manhattan Project, works by molecular effusion, meaning that one of the two isotopes to be separated is more likely to pass through the perforations in the tube.
This tube is, more precisely, called a barrier, but these perforations are not microscopic. They are sized based on results from the kinetic theory of gases that show molecules travel at different speeds because of differences in their masses. Because the velocity is inversely proportional to the square root of the mass, a lighter particle will travel faster than a heavier one. This means that in a gas mixture of two particles of different weights, the lighter one will have a higher probability of hitting a hole in the barrier.
It has a higher probability because it travels further on average than does a heavier molecule; this typical distance traveled, called the mean free path, sets the size of the holes in the barrier. At atmospheric pressure, the mean free path of a molecule is about one ten-thousandth of a millimeter or one-tenth of a micron. This is just another way of representing the distance that, on average, a molecule travels before colliding with another molecule that changes its direction or energy.
Thus, to ensure the necessary separation for an atomic bomb, the diameter of the billions of holes in the barrier must be less than one-tenth the mean free path, otherwise both effusing isotopes would pass through the barrier. The exact composition and preparation of the barriers used today in separating uranium are secret, but for earlier barriers, engineers rolled Teflon powder onto nickel gauze to create pores of 0.
Modern Method: Centrifuge Gaseous diffusion plants are very large and thus expensive to build and operate. Part of this cost is that they take great amounts of energy to run. For example, all of the compressors and heaters generating pressure and heating the hex the uranium fluoride gas throughout the miles of tubing require vast amounts of energy to operate. Early plants used so much energy that many people wondered whether it would take more energy to enrich the uranium than the energy produced by that uranium in a nuclear reactor!
At roughly the same time as the first gaseous diffusion plants were developed, a few scientists and engineers. He also shares how a single CCD is used with a color filter array to create colored images. Bill shows the world's smallest atomic clock and then describes how the first one made in the s worked. He describes in detail the use of cesium vapor to create a feedback or control loop to control a quartz oscillator.
He highlights the importance of atomic team by describing briefly how a GPS receiver uses four satellites to find its position. Bill takes apart a smartphone and explains how its accelerometer works. He also shares the essential idea underlying the MEMS production of these devices. Bill explains that the hardest step is making the proper type of uranium.
Weapons and power plants require uranium that contains a greater amount of the isotope uranium than found in natural uranium, which is mostly uranium He outlines the key difficulty in separating the two isotope: They have nearly identical properties. He explains the two key methods for separation: Gas diffusion and centrifuges. Bill explains the essential principles of a lead-acid battery. He shows the inside of motorcycle lead-acid battery, removes the lead and lead-oxide plates and shows how they generate a 2 volt potential difference when placed in sulfuric acid.
He explains how the build up of lead sulfate between the plates will make the battery unusable if it discharged completely, which leads him to a description of how to make a deep cycle battery used for collecting solar energy. Bill describes how metals like aluminum and titanium are made resistant to corrosion by growing an oxide layer into the metals. These is the same process used on many Apple products. Bill details how a microwave oven heats food. He describes how the microwave vacuum tube, called a magnetron, generates radio frequencies that cause the water in food to rotate back and forth.
He shows the standing wave inside the oven, and notes how you can measure the wavelength with melted cheese. He concludes by describing how a magnetron generates radio waves.
Bill shows how the three key characteristics of laser light - single wavelength, narrow beam, and high intensity - are made. He explains the operation of a ruby laser - the first laser ever made - showing how electronic transitions create stimulated emission to give coherent light, and then how the ends of the ruby cavity create a narrow wavelength highly collimated beam.
Eight Amazing Engineering Stories: Description Eight Amazing Engineering Stories reveals the stories behind how engineers use specific elements to create the material world around us. In eight chapters, the EngineerGuy team exposes the magnificence of the innovation and engineering of digital camera imagers, tiny accelerometers, atomic clocks, enriched uranium, batteries, microwave ovens, lasers, and anodized metals.
In addition, short primers cover the scientific principles underlying the engineering, including waves, nuclear structure, and electronic transitions. Eight Amazing Engineering Stories forms the basis of the fourth series of EngineerGuy videos found on-line.
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