Marine Management Philosophy Versus Engineering Management Philosophy

Posted on 3-January-2017 by mathscinotes

Quote of the Day

Left unsung, the noblest deed will die.

— General Mattis, quoting the Greek poet Pindar. He was explaining how embedded journalists could help the US Marines tell their story.

Figure 1: General Mattis. (Source).

Figure 1: General Mattis. (Source).

I have been reading an article about our new Secretary of Defense James Mattis, a US Marine general who is well known for his thoughtful insights on the world situation. He is also viewed as a superb manager, which means I want to learn as much from his experience as possible. In the article, Mattis has listed some of his management credos. I thought I would look at coming up with corresponding credos for managing a civilian engineering team (Table 1).

 

Table 1: US Marine Versus Engineering Credos
General Mattis' View of a Marine My View of an Engineer
All of us are MAGTF (Marine Air Ground Task Force) leaders. All engineers are leaders.
Attitude is a weapon. Attitude is often your most powerful tool.
Everyone fills sandbags in this outfit. No one is above any job.
If a Marine or a unit is screwing up, hug them a little more. If someone is screwing up, for gosh sake help – unless it’s a competitor, where we just get out of their way.
There are only two types of people on the battlefield: hunters and the hunted. There are only two types of engineers: those that make things happen, and those who have things happen to them.
He encouraged simplicity in planning, and speed, surprise, and security in execution. He encouraged simplicity in planning, and speed, surprise, and security in execution.
The two qualities I look for most in my Marines are initiative and aggressiveness. The two qualities I look for most in my engineers are initiative and a can-do attitude.
Remember, Orville Wright flew an airplane without a pilot’s license. Remember, Orville Wright flew an airplane without a pilot’s license.
No better friend, no worse enemy. No better partner, no more fierce competitor.
Treat every day as if it were your last day of peace. Treat everyday as an opportunity to improve our competitive position.
This is not some JV, bush-league outfit. We’re the Marines. This is not some JV, bush-league outfit. We are industry-leaders and we need to act like it.
I have been accused of making my subordinates my equals, and I happily stand guilty. I have been accused of making my subordinates my equals, and I happily stand guilty.
I don’t want us to put someone in front of the the media that is going to have their second childhood. I only want tough Marines in front of the camera. Customer relations are for Sales and Marketing folks – customers might overdose on reality if they dealt directly with development engineers.
Engage your brain before you engage your trigger. Engage your brain before you engage your mouth – if I were King of the World, I would make this happen.
The number-one authority you have as a leader is your moral authority and your number one power is expectation. The number-one authority you have as a leader is your moral authority and your number one power is expectation.
Posted in Management | Comments Off on Marine Management Philosophy Versus Engineering Management Philosophy

Tribble Math

Posted on 2-January-2017 by mathscinotes

Quote of the Day

Politics is ethics done in public.

— Bernard Crick

Introduction

Figure 1: Captain Kirk with Tribbles. (Source)

Figure 1: Captain Kirk with Tribbles. (Source)

Over the 2016 New Year's holiday, a number of television stations were showing the remastered original Star Trek episodes. While you generally do not hear much math in a Star Trek episode, the "Trouble with Tribbles" actually had two statements to which a bit math can be applied. You can search around the Internet and find solutions for one of the statements, but I wanted to work through the math myself. It is interesting that a script writer must have actually worked through the details during time before calculators.

My Mathcad worksheet and a PDF are included here.

Background

Math Statement #1

Here is a quote from the episode (Source) that sets up the math problem.

KIRK: Here. Let me try it.
(But he can't open it either, so he tried one of the overhead doors instead. That does open, and a whole load of tribbles fall out, burying the gallant Captain up to his shoulders. Spock examines one.)
SPOCK: They seem to be gorged.
BARIS: Gorged? On my grain? Kirk, I am going to hold you responsible. There must be thousands of them.
KIRK: Hundreds of thousands.
SPOCK: One million seven hundred seventy one thousand five hundred sixty one. That's assuming one tribble, multiplying with an average litter of ten, producing a new generation every twelve hours over a period of three days.
KIRK: That's assuming they got here three days ago.
SPOCK: And allowing for the amount of grain consumed and the volume of the storage compartment.

My plan here is to duplicate the Spock's math here.

Math Statement #2

The other math statement, which left much information out, was how long it would take Cyrano Jones to cleanup all the dead tribbles – 17.9 years.

KIRK: There is one thing you can do.
JONES: Yes?
KIRK: Pick up every tribble on the space station. If you do that, I'll speak to Mister Lurry about returning your spaceship.
JONES: It would take years.
SPOCK: Seventeen point nine, to be exact.
JONES: Seventeen point nine years.
KIRK: Consider it Job security.
JONES: Captain, you're a hard man. All right! All right!

I am going to treat this statement as a Fermi problem and estimate the average tribble cleanup rate that Cyrano Jones will need to maintain to clean up all the tribbles from Math Problem #1 within 17.9 years.

Solution of a First-Order Difference Equation

Math problem #1 can be expressed as a first-order difference equation, which has the solution shown in Figure 2.

Figure 2: Solution of a First-Order Differential Equation.

Figure 2: Solution of a First-Order Differential Equation. (Source)

Analysis

Math Statement #1 Solution

Figure 3 shows my solution for the number of tribbles after 3 days.

Figure 3: Math Problem #1 Solutio

Figure 3: Math Problem #1 Solution.

Math Statement #2 Solution

I will estimate the tribble cleanup rate that Cyrano Jones will need to maintain of 17.9 years in order to clean up all the tribbles from problem #1. Based on the assumptions laid out in Figure 4, Cyrano Jones will need to average picking up 35 tribble per hour over the 17.9 years in order to clean all the tribbles up.

Figure 4: Math Problem #2 Solution.

Figure 4: Math Problem #2 Solution.

Conclusion

This was good problem that left me pleased knowing the episode author, David Gerrold, must know a bit of math.

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Posted in Science Fiction | 4 Comments

Old-School Selling of the Exploration of Mars

Posted on 28-December-2016 by mathscinotes

Quote of the Day

Late to bed, early to rise, work like hell, and advertise.

— Saying on Wernher Von Braun's desk. He was not going to repeat the mistakes of other rocket pioneers who shunned publicity.

Figure 1: Wernher von Braun in 1960. (Source)

Figure 1: Wernher von Braun in 1960. (Source)

My youngest son has been fascinated with Elon Musk's plans for colonizing Mars. He is not that different from his old man because in my youth Wernher von Braun (Figure 1) had me captivated with his plans for human-crewed missions to Mars. As I described von Braun's plans for exploring Mars to my son, I realized the both Musk and von Braun applied similar state-of-the-art marketing approaches.

You might think that Musk's use of animation and visionary storytelling were unprecedented for selling a technical program – not so. I would argue that Musk is following the von Braun playbook almost exactly.

Von Braun also applied a media full-court press for exploring both the Moon and Mars:

  • Wrote a science fiction novel, The Mars Project, with an amazing appendix containing the math and physics behind the mission plan. True, many engineers argued with von Braun about the details but he saw those arguments as unimportant – the details looked convincing. I re-read this book a couple of years ago. While the science fiction story is marginal, the vision just exudes credibility.
  • Wrote a popular science book with Willy Ley called The Conquest of the Moon that described how the Moon would be be explored. The Moon was always portrayed as a stepping stone on the way to the real goal, Mars.  As a boy, I loved this book and read it several times.
  • Teamed with famous space artist Chesley Bonestell on some beautiful space-related art that appeared in various magazines (e.g Collier's) back in the 1950s. Here is one of my favorites.

    Figure 2: Bonestell Visualization of Mars Exploration Effort.

    Figure 2: Bonestell Visualization of Mars Exploration Effort. (Source)

  • Gave presentations on space travel to any group that was willing to listen. I still remember the science teachers in my high school talking about when von Braun helicoptered in to give them a seminar on the space program. He must have given a motivational talk that rivaled anything that Vince Lombardi ever gave a football team.
  • Teamed with Disney on making some marvelous animated films on how the Mars mission would be be implemented. Fortunately, all of this animation appears to be available on Youtube.
    Figure 3: Disney-Produced Program on Exploring Space.

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Posted in Astronomy, History of Science and Technology, Management | 2 Comments

Tapered Side Angle Measurement

Posted on 23-December-2016 by mathscinotes

Quote of the Day

The secret to living well and longer is: eat half, walk double, laugh triple, and love without measure.

— Tibetan Proverb

Introduction

Figure 1:Side Angle Measurement of Slot.

Figure 1: Side Angle Measurement of Slot. (Source)

I thought I was done with my metrology review when I encountered an excellent set of discussions at the Hobby-Machinist web site. They advertise themselves as "The Friendly Machinist Forum," and all signs indicate that is true. In addition to excellent tutorials, there are some first-rate metrology discussions on that site, and I want to document a few of the examples that are shown there.

Figure 1 shows a slot with angled sides with the angle being measuring using gage balls or roller gages.

Analysis

Derivation

Figure 2: Reference Drawing Showing Critical Variables.

Figure 2: Reference Drawing Showing Critical Variables for Measuring One Angle.

The math behind this example is almost identical to that presented in this post, where I present Equation 1 as the angle solution for the measurement scenario of Figure 2.

The differences are created by my distance measurements, L1 and L2, are doubled in Figure 1 because I am measuring two angles at once. This means that I can easily adapted Equation 1 to the configuration of Figure 1 with a simple substitution.

Eq. 1 \displaystyle \theta \left( {{{L}_{1}},{{L}_{2}},{{D}_{1}},{{D}_{2}}} \right)=2\cdot \text{arctan}\left( {\frac{1}{2}\cdot \frac{{{{D}_{1}}-{{D}_{2}}}}{{{{L}_{1}}-\frac{{{{D}_{1}}}}{2}-\left( {{{L}_{2}}-\frac{{{{D}_{2}}}}{2}} \right)}}} \right)

where

  • L1 is the distance from reference to outside edge of roller gage.
  • L2 is the distance from reference to outside edge of roller gage.
  • D1 diameter of the first roller gage.
  • D2 diameter of the second roller gage.
  • θ is the angle of the drill hole relative to the surface that is drilled.

I can redefine my symbols as shown in Figure 3 and generate a new formula, Equation 2, that applies to Figure 1.

Figure 3: Variable Definitions for Figure 1.

Figure 3: Variable Definitions for Figure 1.

To obtain Equation 1 from Equation 2, you apply the substitutions {{{L}'}_{1}}\leftarrow \frac{{{{L}_{1}}}}{2} and {{{L}'}_{2}}\leftarrow \frac{{{{L}_{2}}}}{2}.

Eq. 2 \displaystyle \theta \left( {{{{{L}'}}_{1}},{{{{L}'}}_{2}},{{D}_{1}},{{D}_{2}}} \right)=2\cdot \text{arctan}\left( {\frac{{{{D}_{1}}-{{D}_{2}}}}{{{{{{L}'}}_{1}}-{{{{L}'}}_{2}}-\left( {{{D}_{1}}-{{D}_{2}}} \right)}}} \right)

where

  • L'1 is the distance between the small diameter gages.
  • L'2 is the distance between the large diameter gages.
  • D1 diameter of the first roller gage.
  • D2 diameter of the second roller gage.
  • θ is the side angle relative to the slot base.

Figure 1 Example

Figure 4 shows how to work the example of Figure 1. My formula results agree with those obtained from the scale drawing.

Figure 4: Example of Figure 1 Worked Using Equation 2.

Figure 4: Example of Figure 1 Worked Using Equation 2.

Conclusion

My plan is to continue to build up my metrology examples so that I have as complete a set as I can put together.

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Posted in Metrology | 2 Comments

Christmas Lights in Minnesota

Posted on 21-December-2016 by mathscinotes

Quote of the Day

I would have sent him further if I could.

— Andrew Jackson on his appointment of James Buchanan as Ambassador to Russia. Buchanan later became our 15th president and is generally considered by historians as the worst US president in history.

Many people in Minnesota spend much time and money on decorating their homes in lights for Christmas. Some people think it has all gotten out of hand. Here is a home in my area where one neighbor just gave up because of the incredible effort on the home next to him.

Figure 1: One Neighbor Does Not Wish to Compete. (Source)

Figure 1: One Neighbor Does Not Wish to Compete. (Source)

Figure 2 shows a sign in San Diego that accuses his neighbor of being a showoff.

Figure 2: One Neighbor is Viewed as a Showoff.

Figure 2: One Neighbor is Viewed as a Showoff. (Source)

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Posted in Humor | Comments Off on Christmas Lights in Minnesota

Quick Backup Current Limit Calculation

Posted on 20-December-2016 by mathscinotes

Quote of the Day

You know everybody is ignorant, only on different subjects.

— Will Rogers (1879 - 1935)

Introduction

Figure 1: E95 D-Cell Energy Versus Load Current. (Source)

Figure 1: E95 D-Cell Energy Versus Load Current. (Source)

I was in a meeting this morning when I was told a battery pack had insufficient capacity to meet a 24 hour backup time requirement. While in the meeting, I grabbed a specification for the battery the test engineer was using, did a quick calculation of the backup time results that the test engineer should have expected, and what needed to change in order to pass the backup time requirement. While I have discussed different kinds of battery calculations in numerous blog posts, I thought this one was more typical than most and reflects the kind of work done daily by battery engineers.

For those who like to follow along, here is my Mathcad source and a PDF.

Analysis

Observation

You can see from Figure 1 that the amount of energy that you can extract from a D-cell alkaline battery is a strong function of the load current (aka drain current). The reason that the test failed is because the test engineer failed to use the correct load current, but I did not know that when I was informed that we failed the test – you never get the full story right away.

Calculations

Capture Figure 1

Figure 2 shows how I captured the information in Figure 1 using Dagra, a program that allows you to digitize curves. I also created a function, E(x) where x is the load current, for interpolating Dagra's discrete data capture.

Figure 2: Digitize Figure 1 For Analysis.

Figure 2: Digitize Figure 1 For Analysis.

Predict the Run Time Under the Test Conditions

The test engineer used a load current of 1.6 A, which is much higher than the backup current required for our products. I first wanted to verify that the backup time he measured was reasonable consider he used this load current. I can compute E(1.6 A), which is the available energy capacity of the battery in Amp-hours. You can estimate the run time by dividing the available energy capacity by the load current, which says we should be seeing ~1.5 hours. Since the test engineer is measuring 1.5 hours, everything is working as it should be – the test engineer's expectations were incorrect.

Figure 3: My Run-Time Prediciton Versus Measured Result.

Figure 3: My Run-Time Prediction Versus Measured Result.

What happened here? The 1.6 A load current reflects normal product operation. When operating from battery, our products limit their power usage by turning off non-critical services, like wireless, that use much power.

Maximum Constant Current Load for 24 Hour Operation

The test engineer needed to know the correct load current to apply for meeting a 24 hour backup time requirement. Figure 4 shows I estimated the load current limit (422 mA) given a 24 hour backup time. Again, I used my digitized version of Figure 1. This load current level seems much more reasonable than what was tested initially.

Figure 5: Maximum Current Load for 24 Hour Operation.

Figure 5: Maximum Current Load for 24 Hour Operation.

I am confident that the unit will pass the 24 hour backup time requirement with a load current of ~400 mA.

Conclusion

All this happened during a 30 minute call in which backup time and many other subject were covered. All you need is a portable computer, an internet connection, and the right tools to work many problems quickly.

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Posted in Batteries | Comments Off on Quick Backup Current Limit Calculation

Using Excel's Solver and VBA For Repetitive Table Calculation

Posted on 16-December-2016 by mathscinotes

Quote of the Day

A belief is not merely an idea the mind possesses; it is an idea that possesses the mind.

— Robert Oxton Bolt, screenwriter and playwright

Introduction

Figure 1: Footing Diameter and Thickness Versus Deck Area. (Source)

Figure 1: Footing Diameter and Thickness Versus Deck Area. (Source)

I will be providing some employee training on Excel in January, and I need an example of how to automate the use of Excel's Solver add-in – a powerful optimization tool that few engineers use effectively. When I give a training seminar, I make a serious effort to show how I use Excel on real problems. While I generally use Mathcad for most optimization applications, Mathcad does not support integer programming – an optimization method where some or all variables are restricted to be integers. Here is where Solver shines – it supports integer programming.

While reading about how to size footings for decks, I used the table in Figure 1 to determine my footing sizes. To ensure that I understood the physics behind the table, I decided to use Excel and Solver to generate it on my own. In this post, I will be using Excel's VBA with Solver to generate the table of footing sizes for given deck tributary areas shown in Figure 1.

I am going to apologize right from the start for using US customary units – the table is in square feet and inches. Adding metric conversion would have complicated a relatively simple problem.

Here is my source for those who are interested.

Note: I am not a structural engineer. I am only using some basic math to generate a table of values. If you have a structural question, hire a structural engineer. If you have an electrical engineering question, you can give me a try.

Background

Caveats

  • There are many valid ways to fill in this table.
  • I do not know what optimization criteria was used by the standards body that created the table.
  • My objective is to minimize the amount of concrete required while meeting the code requirements (described below).
  • My results are very close to those in Figure 1, but not exactly the same.

Assumptions

There are some basic assumptions that one needs to keep in mind when computing footing sizes.

  • The table says that decks must support a live load of 40 lbf per square foot (psf) and a dead load of 10 psf, for a total deck load of 50 psf. This agrees with the building codes in my area.
  • Each footing is assumed to have a certain area of deck it is assigned to supporting that is called the tributary area.
  • The soil must support the weight of the deck tributary area and the weight of the concrete footing. The weight of the concrete footing is proportional to its volume. For this exercise, I am only interested in round footings. The table in Figure 1 includes values for square footings. I don't use square footings, so I am not interested in these values.
  • I assume a concrete density of 150 lbf per cubic foot (pcf).
  • Different soils can support different amounts of weight per square foot. In the table of Figure 1, the assumed soil loading values are 1500 psf, 2000 psf, 2500 psf, and 3000 psf.
  • I am assuming that the footing thickness is restricted to integer values of 6 or greater inches.
  • The concrete footing thickness (τ inches) is related to the diameter of the pad (D inches) by formula \tau\ge \frac{{D-5.5}}{2} , where τ and D are expressed in inches.
  • I then use Solver to compute the minimum required footing diameter.

While my focus in this post is on the use of Solver, you can solve this problem using Mathcad – just no integer programming. See Appendix A for the details.

Analysis

Formula Derivation

Equation 1 is the key formula for this post.

Eq. 1 \displaystyle {{A}_{{Footing}}}=\frac{{{{A}_{{Deck}}}\cdot {{\sigma }_{{Deck}}}}}{{{{\sigma }_{{Soil}}}-\tau \cdot {{\rho }_{{Concrete}}}}}

where

  • AFooting is the area of the footing.
  • ADeck is the tributary area of the deck being served by the footing.
  • σDeck is deck loading factor required by the applicable building code.
  • σSoil is soil loading factor required by the applicable building code.
  • ρConcrete is density of the concrete.
  • τ is the thickness of the footing. The footing thickness must conform to the constraint \tau\ge \frac{{D-5.5}}{2}, where τ and D are expressed in inches. The thickness of a footing can never be less than 6 inches.

I derive this formula in Figure 2 (see the yellow highlight).

Figure M: Derivation of Equation 1.

Figure 2: Derivation of Equation 1.

Excel VBA

The following VBA code snippet shows my VBA routine. I generated this routine by using the macro recorder to provide me clues on how to invoke the Solver routine.

Sub Deck_Table_Optimizer()

 Dim deckArea As Range
 Set deckArea = Range("_biff")

 Dim rngObjectCell As Range
 For Each rngObjectCell In deckArea
 SolverReset 'Clear out all Solver settings
 Range("_A").Value = rngObjectCell.Value 'This is the footing thickness we will be varying
 SolverOk SetCell:="_V", MaxMinVal:=2, ValueOf:=0, ByChange:="_t", Engine:=1, EngineDesc:="GRG Nonlinear"
 SolverAdd CellRef:="_t", Relation:=4, FormulaText:="integer" 'I want integer footing thickness
 SolverAdd CellRef:="_A", Relation:=2, FormulaText:=CStr(rngObjectCell.Value) 'Allowed soil pressure
 SolverAdd CellRef:="_t", Relation:=3, FormulaText:="6" 'The footing thickness greater than 6 inches.
 SolverAdd CellRef:="_t", Relation:=3, FormulaText:="_constraint"
 SolverSolve True
 rngObjectCell.Offset(0, 1).Value = Round(Range("_D").Value + 0.45, 0)
 rngObjectCell.Offset(0, 2).Value = Range("_t").Value
 Next

End Sub

Figure 3 shows the equivalent Solver dialog for this routine. Here is my key for the variables:

  • _V is the concrete volume, which we will minimize.
  • _t is the footing thickness
  • _A is the deck area
  • _D is the diameter of the footing
Figure M: Solver Dialog.

Figure 3: Solver Dialog.

Results

Figure 4 shows my Solver results. The number in red indicate where my results differ from the corresponding results in Figure 1. Both Figure 1 and Figure 4 are "correct" in that they meet the requirements – I assume the optimization criteria was different for Figure 1. In fact, Figure 1 may have been generated without an optimization criteria at all.

Figure M: Solver Generated Version of Figure 1.

Figure 4: Solver Generated Version of Figure 1.

Conclusion

In my seminar next month, I will be presenting this exercise as an example of how to use Solver and VBA to solve a repetitive nonlinear optimization problem. It surprised me how easy it was to use Solver for this type of application.

Appendix A: Mathcad Solution.

While Mathcad does not provide an integer programming feature, you can solve this problem using Mathcad. Let it solve the problem using non-integers and then round up. It may not be optimal, but it will be close. Figure 5 show my Mathcad algorithm.

Figure M: Mathcad Version of Optimization Algorithm.

Figure 5: Mathcad Version of Optimization Algorithm.

Figure 6 show the final result with Figure 1 right beside.

Figure M: Mathcad Result with Figure 1 Adjacent.

Figure 6: Mathcad Result with Figure 1 Adjacent.

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Posted in Construction, Excel | 9 Comments

Another Angle Measurement Using Roller Gages Plus Error Analysis Example

Posted on 8-December-2016 by mathscinotes

Quote of the Day

Einstein himself, of course, arrived at the same Lagrangian but without the help of a developed field theory, and I must admit that I have no idea how he guessed the final result. We have had troubles enough arriving at the theory - but I feel as though he had done it while swimming underwater, blindfolded, and with his hands tied behind his back!

— Feynman Lectures on Gravitation (1995) p.87. Feynman was showing how to derive the theory of general relativity. Even Feynman struggled to understand how Einstein obtained his theory of general relativity given the state of knowledge at the time.

Introduction

Figure 1: Example of Measuring a Small Angle.

Figure 1: Example of Measuring a Small Angle.

While I covered angle measurement in a previous post, that approach can be difficult to apply for acute angles. The approach presented in this post works well for acute angles, but will not work for obtuse angles.

As part of this post, I will also demonstrate how to perform a tolerance analysis on this approach. The tolerance analysis is important in understanding the level of accuracy required in your linear measurements to achieve the desired angle accuracy.

This example was motivated by material presented on this web page.

Background

All the background required is covered in my previous metrology posts:

Analysis

Definition and Derivation

Figure 2 show the configuration of the two roller gages of diameter D with the angle. A slip gage is used to measure the distance L between the outer gage and the upper leg of the angle. I have included a red-legged reference triangle in Figure 2. The formula for θ is found by applying the definition of the sin of angle (opposite/hypotenuse). This means that \sin \left( \theta \right)=\frac{L}{D}.

Figure 2: Symbol Definitions.

Figure 2: Symbol Definitions.

Example

Figure 3 show the calculations associated with the example of Figure 1. My results are in reasonable agreement with the angle measurement taken from the Figure 1, which is a scale drawing.

Figure 3: Calculations For Example of Figure 1.

Figure 3: Calculations For Example of Figure 1.

Tolerance Analysis

Figure 4 shows how I performed my tolerance analysis. In this analysis, I wanted to estimate the impact of tolerance errors in the roller (±0.0001 in) and slip gages (±0.001 in). These errors produce an error in the angle measurement of 2.5 arcminutes.

The error analysis makes use of the concept of differentials.

Figure 4: Error Analysis.

Figure 4: Error Analysis.

Conclusion

This post ends my series on using roller gages and gage balls. This effort has been part of my attempts to gather information and tutorials on making accurate measurement of tough parameters.

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Posted in Metrology | 1 Comment

Demise of the Pearl Harbor Strike Force

Posted on 7-December-2016 by mathscinotes

Quote of the Day

The success of the British aerial torpedo attack [at Taranto, Italy] ... suggests precautionary measures be taken immediately to protect Pearl Harbor ... the greatest danger will come from the aerial torpedo.

— Frank Knox, US Secretary of the Navy (1940), issuing a warning before the Pearl Harbor attack on Pearl's vulnerability to torpedoes. The warning fell on deaf ears. The main resistance he faced was the general belief that Pearl Harbor was so shallow that dropped aerial torpedoes would impale themselves on the muddy bottom. Since American aerial torpedoes could not be dropped into Pearl Harbor, it was assumed that no one else's could either – a combination of hubris and lack of imagination. People are at their most dangerous when their certainty exceeds their actual knowledge.

Introduction

Figure 1: Course of the IJN Pearl Harbor Strike Force.

Figure 1: Course of the IJN Pearl Harbor Strike Force. (Source)

I just watched a wonderful BookTV presentation by three authors on the WW2 attack on Pearl Harbor, which occurred 75 years ago today. While I am generally familiar with what happened during that attack, I had not looked at the details of the attack. In particular, this show motivated me to look at the Imperial Japanese Navy (IJN) attack force composition and what happened to these ships over the course of the war. The fate of these ships reflects what happened to the rest of the IJN during the Pacific War.

For those who are interested in reviewing my work, here is my spreadsheet.

Background

The following background material describes how the US became so vulnerable to an aerial torpedo attack. To some extent, it was a lack of imagination.

The Importance of the Torpedo in WW2

People often think of WW2 naval battles in terms of surface actions involving battleships and heavy cruisers. However, relatively few ships in WW2 were sunk by gunfire – when you needed to sink a ship, you used a torpedo. A case in point is the British destruction of the battleship Bismarck. While the ship was struck with hundreds of shells, it was actually rendered unmaneuverable and eventually sunk by torpedoes. It took the US Navy a long time to appreciate the importance and danger presented by Japanese torpedoes, which may have been the world's best.

The following quote from Capt. Wayne Hughes' book Fleet Tactics explained that the US Navy performed so poorly in sea battles during the early part of World War II because:

(1) The United States failed to grasp that the killing weapon was the torpedo; (2) The United States had no tactics suitable for night battle at close quarters; (3) The United States was slow to learn. Because of the rapid turnover of tactical leaders, the pace of the battles overwhelmed the Americans; (4) Above all, the United States did not exploit its potentially decisive radar advantage.

Warnings About Pearl Harbor's Vulnerabilities Went Unheeded

The vulnerability of ships in harbor to aerial attack had been foretold a number of time prior to Pearl Harbor:

  • Bradley Fiske (1911), who patented the concept of the aerial torpedo, developed an attack method for use in shallow water. The first actual aerial torpedo attack occurred in 1915.
  • Billy Mitchell (1924) warned that war with Japan would begin with a surprise attack on Pearl Harbor.
  • In the Battle of Taranto (1940), the British used obsolete Swordfish torpedo planes to deliver a devastating attack on the Italian Navy while in port – the Japanese studied this battle closely. Following the same shallow water attack method recommended by Fiske, the British used torpedo bombers (Figure 2) flying at low speed dropping torpedoes modified with special fins that reduced how deeply the torpedo would dive after launch. This prevented the torpedo from burying itself in the mud at the bottom of the harbor.
  • Frank Knox (1940), US Secretary of the Navy, warned that precautions needed to be taken to protect ships in Pearl Harbor from torpedo attack. Clearly, no effective actions were taken in response to his warning.
Figure M: Swordfish Torpedo Bomber.

Figure 2: Swordfish Torpedo Bomber. The slow speed of this bomber contributed to the success of this aircraft at the Battle of Taranto.  In an odd twist of fate, the slow speed of this aircraft also helped make it effective in torpedoing the battleship Bismarck – its speed was below the minimum value supported by the Bismarck's analog fire control computers. This meant the Bismarck's anti-aircraft guns could not be aimed accurately at the attacking Swordfish.  (Source)

IJN Type 91 Torpedo

The IJN had just one aerial torpedo – the Type 91. It was produced in five different models and was considered a workhorse weapon. Figure 3 shows an old Type 91 on display in a park (Source). It strikes me odd how old torpedoes end up in parks – there is a Torpedo Mark 14  on display at a zoo near my home.

Figure M: Type 91 on Display in a Park.

Figure 3: Type 91 on Display in a Park.

Figure 4 shows one of the Type 91 after having been pulled from the bottom of Pearl Harbor.

Figure M: Torpedo Salvaged from Pearl Harbor Bottom.

Figure 4: Torpedo Salvaged from Pearl Harbor Bottom.

Torpedo Shallow Water Modifications

An aerial torpedo will follows an in-water trajectory that may take it as deep as 200 feet (source: personal experience) before it pulls up to its running depth of ~ 15 feet. Because Pearl Harbor has a depth of ~45 feet, the Japanese modified the Type 91 torpedo with tail fins that would enable the torpedo to quickly pull out of its post-launch dive (Figure 5). This modification was similar to that done by the British on their torpedoes for the Battle of Taranto. The details of this modification are well described on this web page, and I refer you there for more details.

Figure M: Type 91 Modification for Shallow Water Operation.

Figure 5: Type 91 Modification for Shallow Water Operation (Source).

I should mention that using wooden attachments on torpedoes was common during WW2. Appendix A shows how the US used wooden attachments with aerial torpedoes.

Fate of The Pearl Harbor Attackers

Most discussions of the Pearl Harbor strike force focus on the surface ships, and I will focus on those units here. However, there was a significant submarine component that I will address in another post.

Pearl Harbor Strike Force's Eventual Destruction

Historians debate the exact number of ships involved in the Pearl Harbor task force. My work here is based on the Wikipedia's list. The numbers debate usually centers on the facts that (1) two destroyers were split off to attack Midway, and (2) difficulty in counting the large submarine force in the region – some with a direct role and others in a support role.

Figure 6 is my version of the Wikipedia's list of surface combatants, augmented with their date of destruction and the means of their demise. The Wikipedia lists 30 surface warships (including Midway attackers) and 32 submarines. All but one of the surface ships assigned to the IJN's Pearl Harbor strike force were sunk during the war. One ship, the destroyer Ushio, survived the war and was scrapped a few years after the war's end.

Figure M: Strike Force Ships and Their Day of Destruction.

Figure 6: Pearl Harbor Strike Force Surface Ships and Their Day of Destruction.

Figure 7 shows a timeline that indicates the rate of destruction of these ships. Clearly, 1944 was a pivotal year – the rate of destruction peaked at 14 ships during that year, which means that nearly half of the strike force was destroyed in that one year.

Figure M: Timeline of Destruction Dates.

Figure 7: Timeline of Destruction Dates.

Means of Destruction

Figure 8 shows that most of the ships were destroyed by aircraft or submarines. Only one ship, the battleship Kirishima, was destroyed by gunfire. It was sunk by the USS Washington in the Second Naval Battle of Guadalcanal – a classic nighttime action between battleships. These surface actions were rare. Most battleships spent the war doing shore bombardment or convoy protection.

Figure 8: Means of Destruction for the IJN Strike Force.

Figure 8: Means of Destruction for the IJN Strike Force.

Conclusion

While the Pearl Harbor attack was a spectacular tactical success, the strategic situation unraveled at the Battle of Midway – a mere 6 months later.

Appendix A: Wooden Attachments on US Torpedoes.

Figure 9 shows a Torpedo Mark 13 with a wooden nose cape and rectangular tail assembly.

Figure M: Wooden Drop Hardware on US Torpedo.

Figure 9: Wooden Drop Hardware on US Torpedo. (Source)

Appendix B: First Aerial Torpedo Attack.

Figure 10 shows a report of the first aerial torpedo attack conducted by the British against the Turks in WW1.

Figure M: Account of First Aerial Torpedo Attack.

Figure 10: Account of First Aerial Torpedo Attack. (Source)

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Posted in History Through Spreadsheets, Military History | 4 Comments

Measuring Round-Over Radius Using a Roller Gage

Posted on 6-December-2016 by mathscinotes

Quote of the Day

Of course her kids come before you! Hell, her kids come before her.

— I saw this on Pinterest, but I once heard a manager say something similar to an employee. I always work to keep my priorities properly set – family is first.

Introduction

Figure 1: Bullnose Radius Measurement Example.

Figure 1:Round-Over Radius Measurement Example.

This blog post shows how to measure the radius on a rounded corner (a.k.a. bullnose) using a roller gage. I saw this method being used on this web page, and I wanted to document it here for future reference.

You might wonder why an electrical engineer is so interested in mechanical metrology. Unfortunately, I regularly deal with issues involving precision mechanical measurement. For example, I just left a meeting where we discussed flatness issues with connectors that have been reworked onto printed circuit boards. We have discovered that a mounting problem introduced an angle on a connector that results in failures at a specific temperature. This type of precision work justifies the granite slab and metrology gear that I keep in our workshop.

In this post, I will work through the basic geometry associated with this measurement and will work an example.

Analysis

Definitions

Figure 2 shows the key variables in the problem.  The blue circle represents the radius of the round-over that we wish to measure. We can derive an expression for the radius R in terms of h1, H, and D1 by applying the Pythagorean theorem to the red-legged right triangle.

Figure 2: Definitions of Terms.

Figure 2: Definitions of Terms.

Derivation

Figure 3 derives an expression for the radius of the round-over.

Figure 3: Derivation of Bullnose Radius Formula.

Figure 3: Derivation of Round-Over Radius Formula.

Example

Figure 4 shows how I computed the round-over radius for the example of Figure 1. The formula and the scale drawing agree.

Figure 4: Worked Figure 1 Example.

Figure 4: Worked Figure 1 Example.

Conclusion

I plan on using this measurement method on a project very soon. I have one more metrology example to work through and it will include determining the level of accuracy (i.e. tolerance) of these measurements.

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Posted in Metrology | 1 Comment