Math Encounters Blog

John Wayne Math

Posted on 25-September-2012 by mathscinotes

My oldest son and I have been watching some old cowboy movies -- John Wayne has figured prominently in these movies. While watching "Stagecoach", the question came up as to how many movies John Wayne has made. I grabbed the movie lists from a number of sites on the web (here, here, here, and here). The lists were all different. I simply threw the lists into Excel, cleaned up the names so they all agreed, and removed duplicates. Here is the list. I filtered out all of his television work, but left in some movie narration. The Duke performed in 168 movies over a 50 year period. Unfortunately, not all of the movies survive. This is quite a list.

"The Searchers" is still my favorite cowboy movie.

Table 1: John Wayne Movies
168	The Shootist	1976
167	Brannigan	1975
166	Rooster Cogburn	1975
165	McQ	1974
164	Cahill U.S. Marshal	1973
163	The Train Robbers	1973
162	The Cowboys	1972
161	Big Jake	1971
160	Chisum	1970
159	Rio Lobo	1970
158	The Undefeated	1969
157	True Grit	1969
156	Hellfighters	1968
155	The Green Berets	1968
154	The War Wagon	1967
153	Cast a Giant Shadow	1966
152	El Dorado	1966
151	In Harm's Way	1965
150	The Greatest Story Ever Told	1965
149	The Sons of Katie Elder	1965
148	Circus World	1964
147	Donovan's Reef	1963
146	McLintock!	1963
145	Hatari!	1962
144	How the West Was Won	1962
143	The Longest Day	1962
142	The Man Who Shot Liberty Valance	1962
141	The Comancheros	1961
140	North to Alaska	1960
139	The Alamo	1960
138	Rio Bravo	1959
137	The Horse Soldiers	1959
136	I Married a Woman	1958
135	The Barbarian and the Geisha	1958
134	Jet Pilot	1957
133	Legend of the Lost	1957
132	The Wings of Eagles	1957
131	The Conqueror	1956
130	The Searchers	1956
129	Blood Alley	1955
128	The Sea Chase	1955
127	The High and the Mighty	1954
126	Hondo	1953
125	Island in the Sky	1953
124	Trouble Along the Way	1953
123	Big Jim McLain	1952
122	Miracle in Motion	1952
121	The Quiet Man	1952
120	Flying Leathernecks	1951
119	Operation Pacific	1951
118	Rio Grande	1950
117	Sands of Iwo Jima	1949
116	She Wore a Yellow Ribbon	1949
115	The Fighting Kentuckian	1949
114	Fort Apache	1948
113	Red River	1948
112	Three Godfathers	1948
111	Wake of the Red Witch	1948
110	Angel and the Badman	1947
109	Tycoon	1947
108	Without Reservations	1946
107	Back to Bataan	1945
106	Dakota	1945
105	Flame of Barbary Coast	1945
104	They Were Expendable	1945
103	Tall in the Saddle	1944
102	The Fighting Seabees	1944
101	A Lady Takes a Chance	1943
100	In Old Oklahoma	1943
99	Flying Tigers	1942
98	In Old California	1942
97	Lady for a Night	1942
96	Pittsburgh	1942
95	Reap the Wild Wind	1942
94	Reunion in France	1942
93	The Spoilers	1942
92	A Man Betrayed	1941
91	Lady from Louisiana	1941
90	The Shepherd of the Hills	1941
89	Dark Command	1940
88	Seven Sinners	1940
87	The Long Voyage Home	1940
86	Three Faces West	1940
85	Allegheny Uprising	1939
84	New Frontier	1939
83	Stagecoach	1939
82	The Night Riders	1939
81	Three Texas Steers	1939
80	Wyoming Outlaw	1939
79	Overland Stage Raiders	1938
78	Pals of the Saddle	1938
77	Red River Range	1938
76	Santa Fe Stampede	1938
75	Adventure's End	1937
74	Born to the West	1937
73	California Straight Ahead!	1937
72	I Cover the War	1937
71	Idol of the Crowds	1937
70	Conflict	1936
69	King of the Pecos	1936
68	Sea Spoilers	1936
67	The Lawless Nineties	1936
66	The Lonely Trail	1936
65	The Oregon Trail	1936
64	Winds of the Wasteland	1936
63	Lawless Range	1935
62	Paradise Canyon	1935
61	Rainbow Valley	1935
60	Texas Terror	1935
59	The Dawn Rider	1935
58	The Desert Trail	1935
57	The New Frontier	1935
56	Westward Ho	1935
55	Blue Steel	1934
54	'Neath the Arizona Skies	1934
53	Randy Rides Alone	1934
52	The Lawless Frontier	1934
51	The Lucky Texan	1934
50	The Man from Utah	1934
49	The Star Packer	1934
48	The Trail Beyond	1934
47	West of the Divide	1934
46	Baby Face	1933
45	Central Airport	1933
44	College Coach	1933
43	His Private Secretary	1933
42	Riders of Destiny	1933
41	Sagebrush Trail	1933
40	Somewhere in Sonora	1933
39	The Life of Jimmy Dolan	1933
38	The Man from Monterey	1933
37	The Telegraph Trail	1933
36	The Three Musketeers	1933
35	Haunted Gold	1932
34	Lady and Gent	1932
33	Ride Him, Cowboy	1932
32	Running Hollywood	1932
31	Texas Cyclone	1932
30	That's My Boy	1932
29	The Big Stampede	1932
28	The Hurricane Express	1932
27	The Shadow of the Eagle	1932
26	Two-Fisted Law	1932
25	Arizona	1931
24	Girls Demand Excitement	1931
23	Maker of Men	1931
22	The Deceiver	1931
21	The Range Feud	1931
20	Three Girls Lost	1931
19	Born Reckless	1930
18	Cheer Up and Smile	1930
17	Men Without Women	1930
16	Rough Romance	1930
15	The Big Trail	1930
14	Salute	1929
13	Speakeasy	1929
12	The Black Watch	1929
11	The Forward Pass	1929
10	Words and Music	1929
9	Four Sons	1928
8	Hangman's House	1928
7	Mother Machree	1928
6	Noah's Ark	1928
5	Annie Laurie	1927
4	The Drop Kick	1927
3	The Great K & A Train Robbery	1927
2	Bardelys the Magnificent	1926
1	Brown of Harvard	1926

Posted in Personal | Comments Off

Another Young Couple Starting Their Life Together ...

Posted on 13-September-2012 by mathscinotes

I am going to be sentimental for a while. Thirty-three years ago I married the love of my life. We have two sons. One son is getting married this week to a wonderful girl he met while going to university in Montana. I am now sure that I will never get him back. I guess that is the way things are supposed to work. I think back to all the time spent helping him with homework, teaching him to ride a bicycle, coaching his soccer practice, and taking him to hockey practice. All the things that dads do. It has all been about bringing him to this point. He is now on his own -- an accountant at a hospital who is marrying a nurse. My son is doing very well as an accountant, but he dreams of owning his own firm at some point in the future. This could easily become a reality if he keeps working hard.

I was never sure about having children. I was worried that I did not know much about being a dad. My dad died when I was fourteen -- I was the oldest of five children. My mother was a secretary who did not drive. We lived in a small agricultural town and the townsfolk wanted to help. All we had to do was work. They also offered me and one of my brothers a job -- that is how small towns are. I worked at that job until I completed my engineering degree. While my mother did her best, my brothers and sister have always felt that something was missing without our father being there.

We were not alone in these feelings. Once, while I was delivering newspapers, the wealthiest man in town stopped me and told me that we must call him if we ever needed anything. With tears in his eyes, he told me that his dad had died in a hunting accident when he was a boy and that he knew what we were going through. That image has stuck with me my whole life. He knew. I couldn't begin to imagine what the grieving process would have been like for him as a young child.

My worries about being a dad evaporated when the boys came -- I soon realized that being a dad just required love. I could not have had two better sons. They are now both fine young men. My father would be very proud of how they turned out. I appreciate that every day I get to do things that he never was able to do -- things like attending his son's wedding.

I can only hope my son and his bride will be as happy as my wife and I. Things were not always easy. Early in my career, I was a contractor for the US Navy, and I was away from home for long periods of time. My wife had to handle two rambunctious boys on her own. While away from home, I would often think of those two boys with their smiling, toothless grins. They were not small long enough. All parents need to remember that children are only children for a very short period of time. They are gone before you know it.

My son and his bride will have their own adventures. That is the way of the world. Somehow it all leaves me both happy and sad. I guess that is what being a dad is about. For me, I will now have a daughter to love. This will be another new experience for me and I will try to cherish every moment.

Posted in Personal | 1 Comment

A Good Analog Computation Example

Posted on 31-August-2012 by mathscinotes

Introduction

I am always looking for real-world examples of analog computation and this blog post will discuss one of the best examples of analog computation that I found. I found this little gem in EDN magazines' Design Ideas section, which is a great place to look for clever analog solutions for real problems.

The circuit that I am going to review here is shown in Figure 1. During my analysis, I will break the circuit down into sub-circuits and then analyze the sub-circuits.

Figure 1: EDN Circuit For Measuring Available Wind Power.

This circuit generates a voltage that is proportional to the wind power currently available. It does this using two sensors:

anemometer/wind turbine
I usually think of four rotating cups whose motion generates a signal with a frequency proportional to wind speed, which is how this circuit represents wind speed.
base-emitter junction of a transistor
The base emitter junction's voltage variation with temperature provides an analog for the temperature variation of the air's density.

This review needs to cover a lot of technical territory so let's dig in ...

Background

For background on windmills and how they work, see this web site. The key equation for computing the maximum normalized power from a windmill is given by Equation 1. The normalized power is defined as the available watts per unit area of wind turbine.

Eq. 1

$\displaystyle P=\frac{1}{2}\cdot A\cdot {{\rho }_{Air}}\cdot v_{_{Air}}^{3}\Rightarrow {P}'=\frac{P}{A}=\frac{1}{2}\cdot {{\rho }_{Air}}\cdot v_{_{Air}}^{3}$

where

ρ_Air is the density of air, which is a function of temperature and pressure.
v_Air is the air velocity.
A is the area of the wind turbine.
P′ is the watts per unit area of the wind turbine.

Our objective in this post is to analyze the circuit shown in Figure 1 and demonstrate how that circuit implements Equation 1.

Before we do any electronics design, we need to beat Equation 1 into a form that can be implemented using electrical components. Figure 2 goes through this derivation.

Figure 2: Rework of Equation 1 into am Electronics-Friendly Form.

Analysis

Requirements

The circuit designer (Woodward) appears to have worked to the following requirements:

The circuit is generate 1 V of output for every 1 kW/m²of available wind power per unit area.
The circuit can produce a wide range of values. A value needs to be chosen in order to determine concrete part values.
The circuit is to use a single power supply voltage.
This circuit provides a nice illustration of designing an analog circuit for single supply operation. A one-supply design is normally preferred over a multi-supply design because it is cheaper. The designer used parts based on the 4000 series of CMOS devices. This is a very old family, nonetheless, many designers have a fondness for this family of digital parts for analog applications. See Appendix B for details on using these parts in analog applications.
The anemometer measuring the wind speed generates a signal with a frequency variation of 10 Hz per 1 m/s of wind velocity.
The circuit can be adapted to various types of anemometers. We need to pick a specific conversion factor in order to pick specific components. Appendix C gives examples of anemometers that would work for this circuit.
The circuit will compensate for air density variations with temperature.
It turns out that this compensation is relatively simple. Appendix A contains a derivation of the calibration equation presented in the designer's original article.

For this analysis, I will break the circuit up into three sub-circuits:

Forward-Biased Diode
The forward diode voltage drop will be shown to have a temperature variation very similar to that of air.
Frequency-to-Voltage Conversion
This circuit will be used to multiply the forward diode voltage drop times the frequency of the signal from an anemometer.
Level Shift and Amplify Stage
This circuit removes a DC bias and properly scales the output signal level.

Forward-Biased Diode Voltage and the Density of Air

Figure 3 shows how the density variation for air on a percentage basis is similar to the percentage forward voltage variation across a diode or base-emitter junction.

Figure 3: Variation of Air Density with Temperature Compared to a Diode's Variation.

Note that the molecular weight of air is 28.97 gm/mol, which is computed at this web site.

Voltage-to-Frequency Converter Section Operation

Figure 4 summarizes how the frequency-to-voltage converter works.

Figure 4: Voltage to Frequency Converter Subsection Operation.

As shown in Figure 4, the frequency-to-voltage converter circuit generates an output with ripple on it. This ripple will be filtered out by the low-pass filter incorporated into the Level Shift and Amplify sub-circuit.

Figure 5 shows how I will represent the frequency-to-voltage converter as a circuit element.

Figure 5: Symbolic Representation of the Frequency-to-Voltage Converter.

The Ref pin shown in Figure 5 deserves some comment. It connects to the positive input pin of the operational amplifier. In a system with bipolar supplies, the Ref pin would be connected to ground. Because this is a single-power supply application, the Ref pin will be connected midway between ground and the supply voltage value. The single-supply setup will product a V_OUT with a DC bias. This bias is removed by the Level Shift and Amplify stage.

Level Shift and Amplify

Figure 6 shows the final stage of the circuit, which takes the output of the frequency-to-voltage converters and provides some amplification and removes the 2.5 V bias.

Figure 6: Output Circuit for Level Shift and Amplify Stage.

The component values can be selected as shown in Figure 7.

Figure 7: Component Selection for Output Circuit Stage.

Entire Circuit

Figure 8 shows the whole circuit from my point of view.

Figure 8: Whole Circuit from a Block Diagram Viewpoint.

We can determine the components required as shown in Figure 9.

Figure 9: Check of Final Component Values.

Conclusion

I went through this circuit in excruciating detail because I thought it does a nice job of illustrating the kind of interplay between physics and electronics that often occurs in analog sensor applications. Also, I have a circuit application that I am working on that will use a circuit related to this one and I wanted to review this work before I pressed on with my circuit.

Appendix A: Derivation of Calibration Equation

The original article contains an equation that is useful for calibration. I derive his expression in Figure 10.

Figure 10: Derivation of Circuit Calibration Equation.

Appendix B: Designing Linear Circuits with 4000 Series CMOS Parts

There are quite a few designers who still use 4000 series parts (in this case, 74HC4000 series). See this document for details on applying these digital parts in an analog application.

Appendix C: Example of an Anemometer with 10 Hz per m/sec Output

I thought it was worthwhile showing some anemometers with 10 Hz per m/sec output. Both examples are powered.

Posted in Electronics | Comments Off

Book Review:"Iron Men and Tin Fish"

Posted on 29-August-2012 by mathscinotes

I just finished reading the book "Iron Men and Tin Fish" by Anthony Newpower (ISBN 978-1-59114-623-0). It is a short book that does a really nice job of covering the use of torpedoes during World War 2. The author looks at torpedoes from the Japanese, American, German, and British perspectives. I particularly like how he sectioned off each story with the use of chapters, as it allows the reader to decipher a difference between each set of torpedoes. Book Layout is very important for books like this, and especially when it concerns history. It provides more of an experience for the readers. As a result, you can truly immerse yourself into what the author has found. His observations can be distilled to these few points:

The Japanese had the best torpedoes during the war.
They developed a superior set of vehicles and the tactics to apply them. It is amazing how the Allies underestimated the importance of the torpedo to Japanese naval strategy.
The British, American, and German navies all tried to sense the presence of a ship using magnetic field-sensing exploders. All failed.
The magnetic field of the Earth proved to be too variable to count on.
The British figured out that their magnetic field-sensing exploder system did not work before the war and ended up producing effective and reliable torpedoes.
They had an excellent test program and acted on the results. Their primary torpedo of WWII was the MK VIII, which was used to sink the Argentine light cruiser Belgrano during the Falkland's War.
The Germans saw the exact same problem (and some additional ones) at the start of the war and fixed it after a number of months of internal bureaucratic squabbling.
Eventually, the Germans captured a British torpedo and ended up copying the British contact exploder.
The Americans had almost exactly the same problems as the Germans, but they tried to blame the crews rather than fix the problems.
This was an excellent view into a management structure that was overly bureaucratic and unwilling to admit error. Eventually, an admiral did take responsibility, but only after years of time and many men dying. During the effort at fixing their torpedoes, the Americans ended up copying a German electric torpedo that was discovered on a beach. This helped alleviate the problem.

There have been a number of movies made on this topic. One pretty good one is "Operation Pacific." There have also been a number of magazine articles on the topic. For example, this magazine article discusses how Einstein worked on the problem and quickly came to the correct conclusion. No one listened to him -- very unfortunate.

As an engineer who is now in management, I always find these case studies of dysfunctional organizations interesting. I also find it interesting how most of the management lessons that I have learned are "negative" -- things that I will make sure that I do not do in my group.

Posted in History of Science and Technology, Underwater | Comments Off

Heating a Room with People

Posted on 28-August-2012 by mathscinotes

I am currently sitting in a really boring meeting that is being held in a very small room. The room is packed full of people and it is hot in here. Of course, there is a part of me that is glad that the room is hot because I would hate for it to be too cold. I hate being cold, and if it goes on to affect my concentration, then I definitely won't be a happy bunny. My friend found himself in the same situation not so long ago. His boiler had decided to break on him and he was subsequently left with no heating and no hot water, which as you can imagine, was a complete nightmare for him. It wasn't until he was pointed in the direction of somewhere like this gas boiler service Durham company that he was able to get warm again. Thank goodness because I'm not sure how he would've coped otherwise.

So, after all of that, you could definitely say that the heater in the room that we were in was definitely working. Maybe it was too warm... All the same, I'm just glad that we weren't freezing cold. After thinking about it though, this situation reminds me of a conversation I had with a Universal HVAC services engineer many years ago about the heat load that people present to a cooling system. During that discussion, the HVAC engineer casually mentioned that he models every person as a 100 W load. I should be able to estimate that number based on the average daily calorie consumption of a person. Consider the calculation I show in Equation 1.

Eq. 1

$\displaystyle P=\frac{E}{T}=\frac{2000\text{ kcalorie}}{24\text{ hours}}\cdot \frac{1\text{ hour}}{3600\text{ seconds}}\cdot \frac{4187\text{ Joules}}{\text{kcalorie}}=96.9 \text{ W}$

where

E is the average daily energy consumption of a human being. I am using the FDA recommended value of 2000 calories.
T is length of a day.

The use of 100 W per person seems like a reasonable average number.

Posted in Construction | 3 Comments

Laser Slope Efficiency and Curve Fitting

Posted on 23-August-2012 by mathscinotes

Introduction

I have spent much of my summer dealing with issues related to the high temperature characteristics of lasers. These issues have stirred within me an interest in laser slope efficiency . Slope efficiency, also known as SE, is simply the slope of the laser's output power versus drive current curve. It varies from part-to-part and with temperature.

I am interested in how SE changes at temperatures above room temperature, which I will define here as 25 °C. I have drive current versus optical power and temperature data, and I need slope efficiency versus optical power at various temperature levels. This means more hammering of data into the form that I need for presentation.

This post will assume some knowledge of the electrical characteristics of a laser, which I covered in this post.

Background

If I had my choice, I would make SE a constant. Unfortunately, nature has not been that kind. As with most things electronic, things degrade rapidly with increasing temperature. In order to plot SE versus optical power at various temperatures, we need to precisely define what SE is. Equation 1 presents the formal definition.

Eq. 1

$\displaystyle SE=\frac{d{{P}_{Output}}\left( {{I}_{Drive}},T \right)}{d{{I}_{Drive}}}$

where

P_Output is the laser output power, which is a function of drive current and temperature
T is the ambient temperature that is varying over a range from 30 °C to 80 °C
I_Drive, the drive current into the laser.

Note that Equation 1 shows SE as a function of I_Drive and temperature. However, I need to relate SE (the derivative of P_Output) to P_Output. All I need to do is to plot SE versus P_Output by using I_Drive as a parameter.

Analysis

My Data

Figure 1 shows a plot of the data I have. The data always comes to me in the form of an Excel worksheet, and it shows P_Output versus I_Drive at various temperatures. What I need is SE versus P_Output at various temperatures.

Figure 1: Drive Current Versus Optical Power and Temperature

Approach

Here is my approach for analyzing this data:

I insert an Excel component into Mathcad, and I then insert the data into the Excel component.
I perform a two-dimensional curve-fit using cubic splines to generate P_Output(I_Drive,T).
I compute SE by taking a derivative of P_Output with respect to I_Drive.
Compute P_Output versus the same I_Drive values that I used to compute SE.
I now plot my SE versus P_Output for the same values of I_Drive at various temperatures.

Interpolation

Figure 2 shows a screenshot from Mathcad of my data and interpolation approach. I used a Mathcad program to actually process the data. I find the programs simple to develop and easy to use.

Figure 2: Test Data Component and Interpolation Programs.

Slope Efficiency Versus Optical Power at Various Temperatures

Figure 3 shows the final result of my work. Note how SE degrades with temperature.

Figure 3: Slope Efficiency Versus Optical Power at Various Temperatures.

: Figure 3: Laser Tracking Error Versus Temperature.

Conclusion

I thought this was a good, practical example illustrating two-dimensional interpolation applied in an actual application. I often need to present data in a way that differs from how the data was originally gathered. Interpolation allows me to obtain the data I need with minimal effort.

Posted in Electronics, Fiber Optics | Tagged measurement approach | 4 Comments

Laser Tracking Error and Curve Fitting

Posted on 23-August-2012 by mathscinotes

Introduction

I had a request for an example of how the output power of a laser varies with temperature. We call this parameter tracking error. Tracking error varies from part to part and the manufacturers simply put a bound on this variation (e.g. ±1.5 dB). The variation is a function of temperature, but the variation is not consistent between parts.

The specific request I received was to provide an example of a part's tracking error for temperatures above room temperature. I have monitor current versus optical power and temperature data, and I need optical power versus temperature at fixed monitor currents. I ended up using Mathcad to beat my data into a form that makes generating plots easy.

This post will assume some knowledge of the electrical characteristics of a laser, which I covered in this post.

Background

Optical communication systems assume that the light power coupled onto a fiber from laser's front facet and the light emitted from the laser's rear facet (and measured by the monitor photodiode) are linearly related. Tracking error is a measure of the maximum deviation of this relationship from linearity. These deviations are primarily due to mismatches in the thermal coefficient of expansion for the materials that make up the optical modules. In order to plot tracking error versus temperature, we need to precisely define what tracking error is. Equation 1 presents the formal definition.

Eq. 1

$\displaystyle \text{Tracking Error }={{\left. \max \left( 10\cdot \log \left( \frac{{{P}_{Output}}\left( T \right)}{{{P}_{Output}}\left( 25{}^\circ C \right)} \right) \right) \right|}_{{{I}_{Monitor}}\text{ constant}}}$

where

P_Output is the laser output power
T is the ambient temperature that is varying over a range from -40 °C to 85 °C
I_Monitor, the current from the monitor photodiode, is held at a constant value.

Tracking error is the largest source of variation that we see in a laser's output power. It is also not predictable in any way that I have seen -- you cannot compensate for it like other temperature-dependent parameters.