Determining the Bandwidth of A Pulse

Posted on 3-December-2013 by mathscinotes

Quote of the Day

The odds are good, but the goods are odd.

— Statement made by an Alaskan woman after she told me that there were 1.6 men for every woman in her town.

Introduction

Figure 1: Power Lines are Hazardous for Low-Flying Airplanes.

Figure 1: Power Lines are Hazardous for Low-Flying Airplanes.

I was reading an article in Photonics Spectra magazine about the use of a laser radar system to assist pilots in detecting wires while flying low (Figure 1), and I saw two commonly used bandwidth estimation formulas that most engineers do not think much about. I have worked on laser radar systems in my past and the bandwidth of these systems drives their cost and performance. I thought it would be useful to review how engineers estimate the bandwidth required for the pulse detection circuits used in these systems.

I should point out that electrical circuits process signals that vary in time, but these circuits are usually designed based on the frequency content of the signals being processed. A co-worker once told me that

Electronic systems are hard to design using time-based approaches (e.g. differential equations), but are relatively easy to design using frequency-based approaches (e.g. Bode plots). Unfortunately, it is relatively hard to test electronic systems using frequency-based approaches, but these same systems are usually easy to test using time-based methods (e.g. oscilloscopes). Thus, we need to become proficient at switching between both time and frequency points of view.

I have found this bit of wisdom to often be true.

Background

Why do we care about bandwidth?

The bandwidth of a circuit tells us the range of signals that the circuit must process in order to meet the performance requirements of the system. Unfortunately, narrowband problems are easier and cheaper to solve than wideband problems.

Definitions

The words "narrow" and "wide" are relative terms. Thus, the definitions of narrowband and wideband are relative terms as well.

Narrowband
A narrowband circuit is a circuit that can process the signals through it as if were a single frequency.
Wideband
A wideband circuit is a circuit that must process a range of frequencies that cannot be treated as if they were a single frequency.

My Objective

In practice, all real signals have infinite bandwidth. Because real circuit cannot process infinite bandwidth signals, we need to approximate infinite bandwidth signals with finite bandwidth signals. In general, wider bandwidth implies a greater percentage of the signal energy or power being processed by the circuit. For the discussion that follows, I will be working with energy because a pulse has finite energy and this radar detects pulses. The same type of analysis holds for random pulse sequences or continuous waveforms, which have a finite power level. You use power for signals that exist for long times (theoretically, infinitely long) and energy for signals that exist for finite times.

There are two common bandwidth approximations used in electrical engineering.

  • \displaystyle BW=\frac{1}{2\cdot \tau }\text{ }\to {{E}_{Circuit}}=77.4\%\cdot {{E}_{Signal}}
  • \displaystyle BW=\frac{1}{\tau }\text{ }\to {{E}_{Circuit}}=90.3\%\cdot {{E}_{Signal}}

where

  • ESignal is the total energy in a pulse.
  • ECircuit is the total pulse energy processed by the circuit.
  • τ is the pulse width.
  • BW is the circuit bandwidth.

Analysis

I will approach the problem in two stages:

  • Derive the Fourier Transform of a Pulse Signal

    This is a direct application of the Fourier Transform to a normalized pulse waveform (unit width and height).

  • Derive a Formula for the Percentage of Signal Energy As a Function of Bandwidth

    Higher fidelity systems process a higher percentage of the total signal energy. I will derive an expression for the signal energy percentage as a function of circuit bandwidth and will plot it.

Derivation

Figure 2 shows my derivation of the Fourier transform of a unit pulse.

Figure 2: Definition of the Fourier Transform of a Pulse.

Figure 2: Definition of the Fourier Transform of a Pulse.

Energy Percentage Versus Bandwidth

Figure 3 shows my derivation of a formula for the percentage of signal energy as a function of bandwidth.

Figure 3: Energy Versus Bandwidth

Figure 3: Energy Versus Bandwidth

Conclusion

While reading the article mentioned in the introduction, I started to wonder what fraction of the signal energy was being processed by the circuit. I could not remember the energy fractions, so I decided to re-derive them here.

Posted in Electronics | 2 Comments

Sahara Water Math

Posted on 2-December-2013 by mathscinotes

Quote of the Day

The greatest of faults, I should say, is to be conscious of none.

— Thomas Carlyle, historian and philosopher

Introduction

Figure 1: The Sahara Desert is a the world's largest hot desert.

Figure 1: The Sahara Desert is a the world's largest hot desert. (Source)

I was watching an episode called "Sahara" of the series "How the Earth Was Made" and they had a very good discussion of the history of the Sahara Desert and how it formed. During the presentation, they discussed how ground water can be found that is very old and very hot. I thought I would look into this a bit.

Background

Here is the video I was watching. I find this material interesting and I want to see if I can dig up some additional information.

Analysis

Water Temperature

At 38:40 in the video, they begin talking about the temperature of the water coming out of deep wells in the Sahara. They said that the temperature can be as high as 66 °C and is heated geothermally (see this blog post for more details). The geologist also mentions that the wells can be as deep as 0.75 mile (~1200 meters). Let's do some rough figuring.

  • Except close to the surface, the ground temperature increases at ~25 °C for every 1000 meters (the number varies by location)
  • Let's assume that the Sahara ground temperature starts off around 30 °C (I am using the Sahara's mean temperature for the initial ground temperature).
  • Going down 1200 meters would mean that the ground temperature would increase over the surface temperature by \text{30}{{\text{ }}^{{}^\circ }}\text{C=1200 m}\cdot \frac{{\text{25}{{\text{ }}^{{}^\circ }}\text{C}}}{{\text{1000 m}}}.
  • I would expect the water temperature at 1200 meters down to be about 60 °C = 30 °C (surface temp) + 30 °C (geothermal temperature rise).

This is similar to what they said in the video.

As a boy, I used to work in fields that were irrigated. The water was cold. It came out of pumps that drew water from 60 meters underground. This also makes sense to me because the average temperature of our soil here is only about 10 °C. The Sahara does not have a cold winter and I would think their ground would never have an opportunity to get very cold.

Dating Water

The show talked about "ancient water" or "fossil water". How does one determine the age of water? Whenever I hear someone mention the age of a material, I usually start to think of some form of isotope dating. I quickly discovered that was the case here as well. I have discussed isotope dating methods before and the method is basically the same here (see the Appendix for details). The basic idea is simple.

  • Cosmic rays strike the atmosphere and hit water molecules in the air creating Krypton-81.
  • Some of this Krypton-81 dissolves in the rain that falls to the ground.
  • Once on the ground, the rain begins its descent into the water table.
  • The Krypton-81 has a half-life of 229,000 years. Scientists can sample the water from the Sahara aquifers and determine its age based on the amount of Krypton-81 it carries.

Note that while the approach is simple, measuring the tiny quantity of Krypton-81 atoms is not easy.

Conclusion

This is just a quick note to describe a science program on television that I found interesting. The idea that the Sahara has a massive amount of ancient water underneath it is amazing. I have always wondered why the pyramids were erected out in the desert. It appears that the area around the pyramids were not always a desert – even during the relatively recent time of man.

Appendix

Here is a link to a great description of using Krypton isotopes to date water. The original paper is available here. I will include a brief screenshot here (Figure 2) in case any of these references move.

Figure X: Nice Discussion on How to Date Water.

Figure 2: Nice Discussion on How to Date Water.

Save

Save

Save

Posted in General Science, Geology | Comments Off on Sahara Water Math

A Problem Solved in Excel and Mathcad

Posted on 30-November-2013 by mathscinotes

Quote of the Day

All of the animals except man know that the principal business of life is to enjoy it."

- Samuel Butler

Introduction

FIgure 1: HMS Dreadnought, the ship that changed naval gunnery.

FIgure 1: HMS Dreadnought, the ship that changed naval gunnery.

I use both Excel and Mathcad in my daily work. Most people would consider me very proficient in both. Though it has taken me a long time to become a master of Excel as there weren't as many resources around when I started learning.

In any case, I frequently get asked, "Which tool is better?" Like all other interesting questions in Engineering, the answer is "it depends". Both have their strengths and Microsoft has other uses that can connect with Excel, like Azure Virtual Desktop for cloud usage which can make it easier when moving about, but it is all a case of preference.

As an example, I decided to work a simple problem in both Excel and Mathcad. A number of the advantages and disadvantages of both tools can be seen in this example. The key problem with Excel is its cell-oriented approach. While the cell-oriented approach works for small problems, it has major issue with large problems. As you know, MS Excel is one of the best alternatives to Google products but, there are also other software manufactures that offer an Excel alternative. You could take a look at Web Safety Advice for more information.

Background

My Example

I am reading the book Dreadnought Gunnery and the Battle of Jutland and it presents an interesting fire control example from the Battle of Jutland in the form of Table 1.

Table 1: Original Table of Fire Control Information from the"Run to the South" Engagement.
Table 1: Original Table of Fire Control Information from the

I want to verify that I understand what I have read by duplicating the results shown in Table 1. This problem is most easily approached as a vector analysis problem. There is also some unit conversion involved. My interest in this problem is driven by my desire to code a naval warfare simulation and I want to make sure that I understand the fire control issues involved.

Engagement Geometry

Figure 2 is an illustration of the critical variables in this problem. This is a very common type of fire control situation from World War 1. Here are the details:

  • There are two ships: SMS Lützow and HMS Lion.

    HMS Lion was the flagship of the Grand Fleet's battlecruisers. SMS Lützow was a battlecruiser with the German Imperial Navy.

  • Both ships are on headings given in terms of the points of the compass.

    Historically, compass readings were given in terms of 32 compass points. Each of the points was evenly spread over a 360 ° circle -- each point represents an 11.25 ° increment.

  • The fire control example is from the standpoint of the HMS Lion.

    This means that the target bearing reading is given from the standpoint of HMS Lion. Note that target bearings are given with respect to the ship's heading and not the compass.

  • Two fire control examples are listed in Table 1. Figure 2 only illustrates one example. The second is similar.
Figure 1: Engagement Geometry.

Figure 2: Engagement Geometry.

Analysis

I go through some of the basic fire control equations in this blog post, so I will not review them here.

Excel Version of My Analysis

Here is my approach to duplicating Table 1 in Excel:

  • Table 1 is row-oriented. I decided that for a column-orientation would be a bit easier to work with in Excel.
  • Inputs to the problem are tan-colored. Over time, I intend to add additional cases to the table and I want to highlight which cells need to filled with information.
  • I show the Excel formulas I used in the comments column. One of the issues with Excel is that the formulas get complex and difficult to read. There are things you can do to minimize that, but you will often see formulas in Excel that are difficult to figure out.
  • You need to explicitly handle unit conversion in Excel. This is one of my biggest gripes with Excel.

I wrote up the Excel solution and I did not get the results of Table 1. Unfortunately, I made a unit error. However, I eventually did get it right.

Table 1: Screenshot of My Excel Version of the Jutland "Run to the South" Rate Table.

Here is how I see the advantages and disadvantages of Excel.

  • (Advantage) Repeating simple formulas over and over is very simple in Excel.

    This is why Excel is so popular with accountants. They do not tend to have complex formulas, just lots of them.

  • (Disadvantage) Complex formulas are a pain in Excel.

    I cannot tell you how many hours I have spent trying to figure out some complex array formula in Excel. That same formula in Mathcad would be simple.

  • (Disadvantage) You must handle unit conversions yourself.

    This is painful -- especially in the US where I need to convert between unit systems all the time.

  • (Advantage) Power tabular data display capabilities.

    Excel is really good at displaying and analyzing tabular data.

  • (Advantage) Everyone has access to Excel.

    Most folks can get access to Excel one way or another (e.g. use it online with Microsoft Live). I frequently solve problems in Excel that really would be more appropriately done in Mathcad simply because my customers do not all have Mathcad. In these cases, I use Mathcad to help me verify my Excel solution.

Mathcad Version of My Analysis

Figure 3 shows my version of this analysis using Mathcad, which was correct the first time I went through it. The key to this success was that Mathcad handles the units automatically. To be completely honest, when I had the unit problem in Excel, I decided to write up the problem in Mathcad. Seeing the correct unit conversions in Mathcad allowed me to easily see the error in my Excel. Note that I only solved one engagement scenario in this example. I could easily take this work and put it into a Mathcad program that would allow me run as many scenarios as I wish. Here are the advantages and disadvantages of Mathcad:

  • (Advantage) Math-like notation.

    If you are familiar with mathematical notation, you can pick up the Mathcad syntax pretty quickly.

  • (Advantage) Automatic unit handling.

    I use this capability all the time. It does take a bit of getting used to -- especially for temperatures and decibels. However, it is a powerful feature.

  • (Advantage/Disadvantage) Requires using a Mathcad program to repeat the analysis steps with different parameters.

    I actually like putting things into Mathcad programs. I usually solve one case and get it right, then I put the equations into a program. That is what I would do here. However, it is an extra step. Excel makes it easy to repeat your calculations in adjacent rows/columns.

  • (Disadvantage) Does not display tabular data as cleanly as Excel.

    Getting a nice tabular display really requires inserting an Excel component into the Mathcad worksheet. This is not difficult, but native Mathcad does not do it well.

Figure 3: Mathcad Version of My Analysis.

Figure 3: Mathcad Version of My Analysis.

Conclusion

I have decided not to choose between Mathcad and Excel -- I use them both and frequently on the same problem. Each has their strengths and I want to use these strengths to solve my problems. In this case, I thought I would blog about a common situation for me.

  • I wanted to use Excel to make a clean looking table and to allow others to work with the data.
  • I had some trouble getting my Excel formulas correct.
  • I solve one case in Mathcad and use that solution as a guide in getting my Excel to work.
Posted in Ballistics, History of Science and Technology, Military History, Naval History | 2 Comments

Snake Venom Math

Posted on 26-November-2013 by mathscinotes

Quote of the Day

It is easier to exclude harmful passions than to rule them, and to deny them admittance than to control them after they have been admitted."

— Seneca

Introduction

Figure 1: View from My Hotel.

Figure 1: View from My Hotel.

I was a recently in Barbados doing some field work. Before going anywhere in the field, I like to check to see if there is anything in the area I will be visiting that could hurt me. I have become more careful since a trip to Florida a few years ago where I was warned that an installer had seen a coral snake in one of our enclosures the week before. There are no poisonous snakes in Barbados -- I had nothing to worry about. While doing the research, however, I encountered an interesting table going through the lethality of the most dangerous snake venoms. I thought this table would be interesting to discuss here.

Before I dive into the topic of snake venom, I do want to share a photo from Barbados (Figure 1). It was fun working there and the people could not have been friendlier. If I get to go again, I will bring my wife.

Background

I stumbled upon Table 1 in the Wikipedia on this page. To discuss this table, I first need to define the column headings.

  • "Species" is actually the common name of the snake.
  • LD50 SC is the subcutaneous dose that will kill 50% of the subjects tested.
  • "Dose" is the amount of venom delivered in a strike.
  • "Mice" is the number of mice that could be killed per dose, based on number of mice that would be killed by this dose if it was 100% lethal and equally divided between the mice.
  • "Humans" is the number of humans that could be killed per dose, based on the number of humans that would be killed by this dose, assuming that the dose was
    • equally divided between the humans.
    • the human have the same venom sensitivity as the mice.
    • the dose is 100% lethal.

I find this table interesting for a number of reasons:

  • You can see that there is a wide variation in the lethality of the different types of snake venom.
  • The amount of venom injected varies widely between species.
  • A little bit of calculator work showed that the "Mice killed Per Dose" and "Humans Killed Per Dose" were scaled versions of the LD50 value. The mouse was assumed to have a mass of 20 grams and the human a mass of 75 kg. We can determine the number of animals killed per dose (N) with the equation N=\frac{\frac{Dose}{L{{D}_{50}}}}{m}, where m is the mass of the animal in question.

There were a number of assumptions involved in making this table. I thought it might be interesting to investigate those assumptions.

Table 1: Wikipedia Table on Snake Lethality.

Species

LD50 SC (mg/kg)

Dose (mg)

Mice

Humans

Inland taipan

0.010

110.0

1,085,000

289

Black mamba

0.050

400.0

400,000

107

Forest cobra

0.225

1102.0

244,889

65

Eastern brown snake

0.030

155.0

212,329

59

Coastal taipan

0.106

400.0

208,019

56

Mainland tiger snake

0.190

336.0

138,000

31

Caspian cobra

0.210

590.0

135,556

27

Russell's viper

0.162

268.0

88,211

22

King cobra

1.090

1000.0

45,830

11

Cape cobra

0.400

250.0

31,250

9

Gaboon viper

5.000

2400.0

24,000

6

Saw-scaled viper

0.151

72.0

23,841

6

Fer-de-lance

3.100

1530.0

24,380

6

Jameson's mamba

0.420

120.0

12,709

4

Many-banded krait

0.090

18.4

10,222

3

Analysis

Variations in the Amount of Venom Injected

I assume that the amount of snake venom injected in a strike can vary widely. In fact, some other snake lethality charts actually list the variations. On one web page, they actually show a chart with how the amount of venom injected varies with subsequent strikes. The amount of venom and its potency also varies with the age and size of the snake.

Figure 2: Venom Injection Variation.

Figure 2: Venom Injection Variation.

 

Differences in Mouse and Human Lethality Levels

I have always wondered how well any test results translate from mice to humans. In the case of Table 1, assuming that the mouse and human lethality concentrations are the same is the simplest approach. However, I have no basis on which to believe this assumption is accurate. As a counter-example, consider the case of the Sydney funnel-web spider. It has a venom that is deadly to humans (and other primates), but does not affect other mammals. So I guess I do not really believe the column on human lethality is accurate -- the venom could be more or less lethal than indicated.

Calculation of the Number of Mice and Humans Killed

The lethality of the venom is referred to as LD50, the dose that is lethal to 50% of the subjects exposed. Yet the calculations seem to assume that 100% of those exposed to an equal division of the venom would die. That does not seem correct.

Conclusion

Everyday I see examples of data presented that seem to create more questions than they answer, which is just what Table 1 did for me.

Posted in General Science | Comments Off on Snake Venom Math

Fire Control Formulas from World War 1

Posted on 23-November-2013 by mathscinotes

Quote of the Day

When fascism comes to America, it will be wrapped in the flag carrying the Cross.

— Sinclair Lewis

Introduction

Figure 1: HMS Dreadnought, the ship that changed the direction of naval gunnery.

Figure 1: HMS Dreadnought, the ship that changed the direction of naval gunnery. (Source)

I am reading the book "Dreadnought Gunnery and the Battle of Jutland: The Question of Fire Control". This very informative book provides the details on how fire control developed during its very early days. This period of time is interesting to me because, in my opinion, it was the start of modern computing. The big naval revolution driving the development of fire control was the introduction of long-range torpedoes (see Whitehead Torpedo). Prior to the arrival of torpedoes, ships simply engaged at ranges that allowed them to directly point their guns at one another, a process referred to as direct fire. The threat from torpedoes drove ships to engage at longer ranges that required the development of indirect fire. Indirect fire means aiming and firing a projectile without relying on a direct line of sight between the gun and its target. Effective indirect fire meant developing a number of new technologies: range finding, precision hydraulics, control systems, and calculation systems.

A Google Preview of "Dreadnought Gunnery" is available here if you are curious about the book. I have read some criticism of the book on Amazon because it is a slightly reworked PhD thesis. That doesn't bother me in the least, but some folks may not like the academic writing style. The book's Appendix contains a one-page summary of the fire control formulas that were solved by the analog computers used on the Dreadnoughts (Figure 1). The equations seemed a bit odd to me until I derived them myself. It turns out I have seen them before, but in a different form. I thought I would show the equivalences here. I will be using these fire control formulas in some simulations I plan to prepare. Ultimately, I want to do some analysis of the error sensitivity of these formulas.

All the mathematics is in this post is done in Mathcad. I use Mathcad's unit handling ability to perform the various conversions required.

Background

Figure 2 is a scan of the fire control formulas shown in the Appendix of "Dreadnought Gunnery". I have added some markups in tan to indicate my names for the various equations.

Figure 1: Fire Control Equations from "Dreadnought Gunnery".

Figure 2: Fire Control Equations from "Dreadnought Gunnery".

I will derive these formulas and show how they are similar to formulas you have seen in other contexts.

Analysis

Mathematical Objectives

Battleship gunnery used mechanical integrators to convert measured range and bearing rates into projected target positions in the future. These projections are important because projectiles require time to arrive at their target location -- a concept referred to as deflection or lead (rhymes with "need"). The Appendix in "Dreadnought Gunnery" derives three rate expressions.

  • \frac{dR}{dt}: Range Rate of Change
  • \frac{d\beta }{dt}: Target Bearing Rate of Change
  • \frac{{{d}^{2}}R}{d{{t}^{2}}}: Rate of Change of the Range Rate

These are the formulas that I will focus on. They are presented in the Appendix using units of knots, yards, degrees, and minutes. This will introduce some conversion constants.

Own Ship and Enemy Fire Control Geometry

One of the things that confuses me about the formulas in Figure 1 is their notation. For example, x is used to represent the relative velocity of the enemy ship in a direction perpendicular to the range vector. I prefer to call this velocity component vp. The variable a is used to represent the relative velocity of the enemy ship in the direction of the range vector. I prefer to call this velocity component vr. I REALLY like variable names that mean something to me (e.g. v for velocity). I also changed designation of the target angle relative to the range vector from an iota (ι) to a theta (θ) because it is easier to see a theta. So I renamed all the variables in Figure 2 to what you see in Figure 3.

Figure 2: Updated Fire Control Geometry.

Figure 3: Updated Fire Control Geometry.

Range Rate Formula

The range rate equation is simply the relative radial velocity between the own ship and the enemy ship. This calculation involves a little bit of vector math and then some unit conversions, which are shown in Figure 4.

Figure 3: Derivation of Range Rate Equation.

Figure 4: Derivation of Range Rate Equation.

Note that in Figure 4 I show the variables ves and vos divided by knot. This approach is used in Mathcad to perform unit conversion.

Bearing Rate Formula

Figure 5 shows my derivation of the bearing rate formula. Note that the Appendix refers to a magnetic bearing and in Figure 2 I show a line-of-sight bearing (i.e. bearing relative to a ship's course). If the ship is not changing course, the rate of change in magnetic bearing and the rate of change in line-of-sight bearing are equal. I make this assumption in Figure 5.

Figure 4: Derivation of Bearing Rate Formula.

Figure 5: Derivation of Bearing Rate Formula.

This equation is really a restatement of the angular velocity equation from elementary physics.

Rate of Change of the Range Rate

Figure 6 shows my derivation of the rate of change of the range rate.

Figure 5: Rate of Change of Range Rate Derivation.

Figure 6: Rate of Change of Range Rate Derivation.

The rate of change of the range rate is really just a restatement of the centripetal acceleration equation from elementary physics.

Conclusion

I was able to derive all the expressions from the Appendix of "Dreadnought Gunner". I was also able to show the expressions in the Appendix are actually commonly seen equations from physics, just hidden a tad by notation.

Posted in Ballistics, History of Science and Technology, Military History | 11 Comments

WW2 Sub Skippers Were Very Young

Posted on 15-November-2013 by mathscinotes

Quote of the Day

I am not a product of my circumstances. I am a product of my decisions.

— Stephen Covey

I was watching this Youtube video about two famous WW2 submarine skippers, Morton and O'Kane, and I started to wonder just how old these skippers were during WW2.

Hollywood movies usually show WW2 sub skippers as men in their late 40s or 50s (e.g. Operation Pacific or Run Silent Run Deep). I found a list of the top scoring US submarine skippers of WW2 and was able to figure out their birthdays. Given their birthdays, I determined that they had an average age of 32 years on December 7th, 1941.  The following table summarizes their ages and their post-war "ships sunk" scoring. When you think about the responsibility they had, these men were very young.

Ships Sunk Rank Captain Birthday Age at time of Pearl Harbor Attack Ships Sunk Tonnage
1 Richard H. O'Kane 02-Feb-1911 30 Years, 10 Months and 5 Days 24.0 93,824
2 Slade D. Cutter 01-Nov-1911 30 Years, 1 Months and 6 Days 19.0 71,729
3 Dudley W. Morton 17-Jul-1907 34 Years, 4 Months and 20 Days 19.0 54,683
4 Eugene B. Fluckey 05-Oct-1913 28 Years, 2 Months and 2 Days 16.3 95,360
5 Samuel D. Dealey 13-Sep-1906 35 Years, 2 Months and 24 Days 16.0 54,002
6 Reuben T. Whitaker 23-Sep-1911 30 Years, 2 Months and 14 Days 14.5 60,846
7 Gordon W. Underwood 03-Jun-1910 31 Years, 6 Months and 4 Days 14.0 75,386
8 Royce L. Gross 29-Sep-1906 35 Years, 2 Months and 8 Days 14.0 65,736
9 Charles O. Triebel 17-Nov-1907 34 Years, 0 Months and 20 Days 14.0 58,837
10 John S. Coye Jr. 24-Apr-1911 30 Years, 7 Months and 13 Days 14.0 38,659
11 William B. Sieglaff 06-Jul-1908 33 Years, 5 Months and 1 Days 13.0 32,886
12 Thomas S. Baskett 04-Sep-1913 28 Years, 3 Months and 3 Days 12.0 27,273
13 Henry C. Bruton 15-Feb-1905 36 Years, 9 Months and 22 Days 11.0 54,564
14 Bafford E. Lewellen 22-Sep-1909 32 Years, 2 Months and 15 Days 11.0 23,685
15 Charles H. Andrews 14-May-1908 33 Years, 6 Months and 23 Days 10.0 57,243
16 Robert E. Dornin 30-Dec-1912 28 Years, 11 Months and 7 Days 10.0 54,595
17 Eric L. Barr Jr. 02-May-1912 29 Years, 7 Months and 5 Days 10.0 46,212
18 Ralph M. Metcalf 22-Jun-1913 28 Years, 5 Months and 15 Days 10.0 40,040
19 Raymond H. Bass 15-Jan-1910 31 Years, 10 Months and 22 Days 10.0 37,977
20 Malcolm E. Garrison 29-Mar-1910 31 Years, 8 Months and 8 Days 10.0 37,368
21 Thomas B. Klakring 19-Dec-1904 36 Years, 11 Months and 18 Days 10.0 33,122
22 John A. Moore 12-Jan-1910 31 Years, 10 Months and 25 Days 9.5 45,757
23 Glynn R. Donaho 25-Mar-1905 36 Years, 8 Months and 12 Days 9.5 29,870
24 Eli T. Reich 20-Mar-1913 28 Years, 8 Months and 17 Days 9.0 59,839
25 Walter T. Griffith 03-Jun-1911 30 Years, 6 Months and 4 Days 9.0 45,874
  Average Age   32 Years, 0 Months and 0 Days   1,295,367

Note that in 1940 (pre-WW2), the average age of an Army major (comparable to Navy Lt. Commander) was 48. The demands of war thrust young people into command roles much more quickly than in peacetime.

Posted in History Through Spreadsheets, Military History | 3 Comments

Inserting Images into Excel Comments Using VBA

Posted on 14-November-2013 by mathscinotes

I use Excel for basic statistical analysis of manufacturing and field return data as part of daily routine. I also use Excel for department budgeting. During these tasks, I frequently need to add information to my spreadsheets about my information sources (see Wikipedia entry on data provenance). Since much of my information comes to me in the form of email or web pages, a quick and easy way to document this information is to take a screenshot of the information and insert the information into an Excel comment.

For years I have included images in Excel comments using the manual procedure described here. This approach works well but is slow. I finally decided that there has to be a better way and I wrote a Visual Basic for Applications (VBA) macro that handles all the ugly details. Here is a link to this spreadsheet. The spreadsheet does use a VBA macro. If you are concerned about security, just look in the macro and see what it does.

To see a sample image (Saturn), just mouse over the cell with the little red triangle in the upper right corner.

A little discussion on how to use the macro is in order:

  • Put an image into your clipboard (I use PicPick)
  • Select the cell where you want to put the image
  • Click the button labeled "Press"
  • Your selected cell will now have little red triangle in the upper right corner. You will see your image when you mouse over this cell.
  • I used a button for this example, but in my work I assign both a Quick Access toolbar icon and a keyboard shortcut to this macro.

Many thanks to the folks at these two web sites for posting code and clues that helped me put this macro together.

Posted in Management, software | 27 Comments

A Tale of Getting Older

Posted on 11-November-2013 by mathscinotes

I was with a couple I have known for years this weekend. They have two daughters separated in age by five years. The younger daughter is just finishing high school and still lives at home. The older daughter is no longer living at home, but was visiting her parents this weekend. The tale begins with the daughters in the kitchen hearing their parents having the following dysfunctional discussion.

Father from the kitchen:  ”I can’t find my glasses – do you know where my glasses are?”

Mother from upstairs: ”Molasses? It’s in the cupboard.”

Father from kitchen: ”Not molasses, glasses ..”

The mother and father went back and forth like this for a while. It was a classic case of two people not quite hearing things correctly. The two young women listened quietly to this miss-communication. After the mom and dad got things straightened out, the younger daughter turned to her older sister and said, “At least you had them during their good years.”

Her response was priceless.

Posted in Personal | Tagged | Comments Off on A Tale of Getting Older

Another Glamour Shot from the World of Engineering

Posted on 25-October-2013 by mathscinotes

Things are starting to get cold now in Minnesota and all nature's creatures are looking for a nice warm place to stay for the winter -- including me. Today's photo shows a frog who found one of my optical network terminals a nice, warm place to hang out. Unfortunately, he decided to place himself right on top our our phone ringer circuit. This circuit generates over 100 V when ringing a phone. Apparently, someone called this customer after the frog had positioned himself on top of the ringer circuit. Frogs do not do well with 105 V placed across their little bodies.
frog

Posted in Electronics | Comments Off on Another Glamour Shot from the World of Engineering

More Bugs in My Optics

Posted on 19-October-2013 by mathscinotes

I had another optical failure related to bug intrusion. I do not yet understand how the bugs do it, but somehow they increase my optical loss enormously. This particular optical node was not properly sealed and box elder bugs got in. They are looking for a warm place to winter. Figure 1 shows what it looked like in the field. My wife does not like these bugs at all -- I will not show her this photo.

Figure 1: Box Elder Bugs Inside an Optical Network Unit.

Figure 1: Box Elder Bugs Inside an Optical Network Unit.


While people may think an engineer's work is always high tech, I want to remind them that we spend a lot of time on little things -- like making sure bugs and water cannot ruin our day. Still, it would be nice if we could find a way to get rid of these horrible things once and for all from locations like this. Having the node sealed is one way to keep them out, but some bugs (like termites) can chew through the casing and worm inside regardless, which can be an absolute nightmare. I know some services exist to help keep these issues down, like the terminix pest control options on the market, so perhaps next time I will give those a go.

It really is something else to open a case expecting to deal with a burnt-out wire or some technical difficulty only to have to scrape so many bugs away instead. Hardly a sanitary thing to experience, truth be told.

Posted in Fiber Optics | Comments Off on More Bugs in My Optics