Computing Useful Customer Analogies

Posted on 25-May-2013 by mathscinotes

Introduction

Communicating scientific concepts to the public is a tough problem. One of the major issues is that people have a difficult time imagining the relative scale of things -- just try to think of 1000 of something versus 10 of the same thing. You cannot really visualize 1000 of something.

I normally try to work by analogy. This means comparing an unknown thing to something that is very familiar. Astronomers do this all the time. Here is an example from an astronomy article I read today about a distant supernova called Mingus. To convey a sense of how dim this supernova is, an analogy using a firefly's light was used:

Mingus was so distant and so faint — the equivalent of looking at a firefly from 3,000 miles (5,000 kilometers) away — that its true nature remained a mystery for a while, researchers said.

People can at least try to imagine how bright a firefly is and how it might look from 3000 miles away -- even though you really cannot imagine something that like.

On a less dramatic scale, I was asked if I could compare the yearly operating cost of one of our products (an Optical Network Terminal [ONT]) to that of a common electrical device -- a 100 W incandescent light bulb. I thought it would be useful run through how I answered that request.

Background

The basic facts of the analysis are straight forward and are listed here:

Our salesman a couple of simple pieces of information about ONT power usage that customers will remember:

  • How much does it cost to power an ONT for a year?
  • How does that cost compare to the cost of powering a 100 W lightbulb for some period of time?

Analysis

Figure 1 shows my calculations to estimate the values requested by our salesmen. I decided to provide the answers in the following form:

  • Cost of running an ONT for a year in Minnesota.
  • Cost of 1 year of ONT operation versus operating time for equivalent cost of operating a 100 W light bulb.
  • Cost of 1 month of ONT operation versus operating time for equivalent cost of operating a 100 W light bulb.

Figure 1 shows how I computed the answers. Since an ONT draws 10 W from the outlet, the 100 W light bulb draws power at ten times the rate of an ONT.

Figure 1:Calculations for ONT Annual Operating Cost.

Figure 1:Calculations for ONT Annual Operating Cost.

  • Cost of running an ONT for a year in Minnesota = $9.43.
  • Cost of 1 year of ONT operation equals that of a 100 W light bulb running for 5 weeks.
  • Cost of 1 month of ONT operation equals that of a 100 W light bulb running for 3 days.

Conclusion

This was a simple calculation example, but it represents the kind of math that is routinely done to assist customers with understanding our products.

Posted in Electronics | Comments Off on Computing Useful Customer Analogies

Lightning Protection Math

Posted on 17-May-2013 by mathscinotes

Quote of the Day

In the eyes of those for whom you care, beware of valuing good things they might be but aren't, more than those good things that they are already.

- A. Orcim Namuh (1997)

Introduction

Lightning Striking a Car and Jumping Over the Tire.

Lightning Striking a Car and Jumping Over the Tire (Quora).

I get asked a lot of questions about the specific values that are used in engineering standards. At some level, you just meet the required values in these standards. You do not need to know why they were set to their specific values -- you just conform. However, it is useful to have some insight into where these numbers come from. The most common questions on standards that I receive are about the various wire gauges and voltage/current levels associated with surge protection (aka lightning protection). With respect to telephony circuits, the standard for short-length (< 500 feet) telephone circuits is GR-1089, and I refer people to that standard for specific numbers to meet. If folks are looking for the rationale behind commonly used telephony wiring practices, I generally refer them to this article from OSP magazine. In this post, I will walk through the mathematics behind the protection levels that are discussed in this article.

I like this article because it explains the origins of some magic numbers that I encounter all the time. This post is focused on US standards, so I will be using US units. While I do not like using these units, their use actually make sense when I am trying to explain the origin of US telephony standards.

Here are some specific telephone wiring numbers that I encounter frequently and I will address in this post.

  • 2000 A surge current value.

    I am going to speculate on where this number comes from, but I believe that I have a reasonable rationale for it. It is based on a chart that gives rate of occurrence of various levels of surge current.

  • Ground wire lengths of 20 feet between the service panel and the telephone interface

    This is a company-specific recommendation that I see all the time. I first encountered this specification for the maximum length of a grounding wire while working with a customer who had spent much of his career with GTE. It turns out that GTE was the source of the 20 foot ground wire distance limit. Using some common telecom assumptions, I will show how this length and the cable's insulation rating are related.

  • Communication cable with 5000 V insulation rating

    While not commonly seen today, 5 kV rated cable used to be common. It turns out that this wire rating is closely tied to the 20 foot ground wire length.

Wiring practices are frequently used for decades -- once installers are trained, companies do not like to retrain them. I am not sure that some of these practices still make sense, but people still follow them. I do not understand that behavior -- that is a topic for a blog on human behavior and is not appropriate for a math blog.

Background

Lightning Damage Example

There are some lightning strikes that are so powerful that they literally vaporize hardware. Figures 1 and 2 are from my brother's house that suffered a lightning strike last year. Figure 1 shows where the lightning damaged the outside of the house (a metal chimney is right behind this wall), and Figure 2 shows a wall outlet blown out from the same lightning strike. Every outlet and appliance on that circuit was destroyed.
Figure 1: Damage to My Brother's Chimney from Lightning. Figure 2: One of a Number of Blown Outlets at My Brother's Home.

I have seen many examples of lightning damage to electronic hardware and even homes. Some of these examples are quite dramatic -- circuit boards literally blown to pieces. On field trips, I have inspected homes that had their entire sides damaged. No electronics will survive this type of strike. In other cases, the damage suffered is more subtle. A circuit card may be rendered inoperative, but with no visible damage. When it comes to the damage of the house, mostly it's the windows and doors that are affected, which eventually leads to replacing them. You might consider opting for the services of local firms or contacting Renewal by Andersen Windows & Doors if you find yourself in such a familiar situation.

That said, we incorporate surge protection on all of our circuit boards to try to limit the amount of damage lightning does. However, there are limits as to the level of lightning-generated current and voltage surges that can be withstood.

Magnitude of a Lightning Strike Current Surge

Figure 3 shows the frequency of lightning strikes per year for a given current surge level (Source>).

Figure 3: Frequency of Lightning Strikes By Current Surge Level.

Figure 3: Frequency of Lightning Strikes By Current Surge Level.

Now for some speculation based on the following reasonable assumptions:

  • Telecom gear is generally expected to have a mean lifetime of 10 years => We are looking for a yearly occurrence rate of 0.1 strikes per year. I illustrate how I read this value off of Figure 3 in the Analysis section of this blog.
  • Most homes are in environmentally shielded regions.

Using these assumptions, we can read off of Figure 3 that we can expect to see a 2000 A (2 kA) current once every 10 years on average. I speculate that reasoning such as this was used when the 2 kA surge standard was established for lightning testing.

Home Electrical Model

Figure 4 shows the model for home wiring discussed in the OSP article.

Figure 4: Illustration of Home Wiring and the Levels of Surge Protection.

Figure 4: Illustration of Home Wiring and the Levels of Surge Protection.

I want to highlight the following characteristics of the wiring in Figure 4.

  • All wiring in the home is referenced to Earth at the service panel.
  • The phone circuits are grounded to the service panel by a 20 foot long cable.
  • A person on the phone touching a refrigerator could be exposed to the voltage difference between an appliance (metal grounded to the service panel through safety ground) and the phone ground.
  • The home ground rod provides a resistance to Earth that can be as high as 25 Ω.

    This is the value allowed by the National Electrical Code (NEC). Unfortunately, the ground resistance often ends up much higher.

  • The ground rod is connected to the service panel by a 2-foot long, #6 AWG

    This is the length assumed in this example. Most electrical inspectors recommend keeping this length as short as possible.

  • The service panel is connected to the telephone NID (Network Interface Device) by a 20 foot long, #10 AWG wire.

    I know of many telephone system installers that enforce a 20 foot limit for this cable.

While this problem setup has been a bit long, we now can perform some basic analysis.

Analysis

Figure 5 shows how I setup my analysis for duplicating the results from the OSP article. Assume for this discussion that the lightning induces a negative potential on the ground (i.e. current is drawn from the house). Lightning can generate either positive or negative potentials -- for this discussion, I find it a bit easier to visualize the surge current being drawn out of the house.

Figure 5: Surge Analysis Setup.

Figure 5: Surge Analysis Setup.

Figure 6 shows my analysis that duplicates the results of the OSP article.

Figure 6: My Derivation of Numbers from the OSP Magazine Article.

Figure 6: My Derivation of Numbers from the OSP Magazine Article.

Conclusion

This blog post is a review of an article on the cable gauge and insulation requirements for telephony grounding. I wanted to make sure that I understood where all the numbers in a figure from that article came from. I believe that I have duplicated every result. These numbers may not be as relevant in today's telecom market, but people still follow them.

Appendix A

I have included a PDF copy of the OSP article just in case the link moves.

Posted in Electronics | 3 Comments

Mothers and Sons

Posted on 17-May-2013 by mathscinotes

Quote of the Day

Your work is to keep cranking the flywheel that turns the gears that spin the belt in the engine of belief that keeps you and your desk in midair.

- Annie Dillard.

Figure 1: Mom stressed by her kids.

Figure 1: Mom stressed by her kids.

I had to laugh yesterday. We live next to a mom with two boys -- a 4-year old and a newborn. As I went out for my nightly walk, this rather haggard-looking mom told me that her 4-year boy is defiant and difficult to handle. She knows that my wife and I raised two sons, so she asked me if it gets any easier as they get older. My answer was simple. I told her that, last weekend, my mother (79 years old ) accused me of being defiant and difficult to handle. I am 56 years old. So it does not get any easier.

 

Posted in Humor | Tagged , | Comments Off on Mothers and Sons

Superman, Chicken Little, and Knowable Unknowables

Posted on 15-May-2013 by mathscinotes

Quote of the Day

Who does not grow, declines.

— Rabbi Hillel. This statement is true for almost any human activity. If you are not improving, you are declining.

Figure 1: Some very confident engineers thinks of themselves as supermen.

Figure 1: Some very confident engineers thinks of themselves as supermen or superwomen. (Source)

I was having a discussion with other managers about the difficulty of creating accurate schedules for development programs. Other than dealing with an economic decline through layoffs, I cannot think of a more difficult task for a manager than create accurate schedule for bleeding edge projects.

Typically, I work directly with the engineers involved and have them create time estimates for their portions of each development effort. I find that about half the engineers always generate optimistic schedules and the other half generate pessimistic schedules. I give these two types of engineers the following names:

  • Superman

    These folks wake up every morning thinking they have an "S" on their chest. There is nothing they cannot do, if only management will get out of the way. If they do get behind schedule, they think that all they need to do to get back on schedule is to come in and work on a weekend. The theory here is that there are so many distractions during the week that real engineering can only occur when they are alone and on the weekends. However, that miracle weekend never seems to occur.

  • Chicken Little

    These folks are just the opposite of Superman. They find it impossible to plan because the number of things that could go wrong are too numerous to count. Why even try to plan when unexpected things happen every day?

Figure 2: Chicken Little, for which the sky is always falling.

Figure 2: Chicken Little, for which the sky is always falling. (Source)

I deal with Superman and Chicken Little the same way -- I introduce the concept of "knowable unknowables." Knowable unknowables are program events that will introduce delays in a program, but I cannot state what these events are at the start of the program. They include things like unexpected circuit board layout errors or undocumented defects in new chips. I know these events will occur, but they are unknowable at the start of the program. As long as you are willing to deal with averages, it is amazing how predictable these unpredictable events are.

With Superman, you introduce doubt into their plans by warning them about recent events that have slowed progress on other programs and that these events could occur on their program. Slowly, you get them to agree that things may not go as smoothly as they think. Slowly their schedule lengthens to reflect historical norms.

With Chicken Little, you just remind them that it is rare for every possible bad thing to happen on a program. You tell them that they need to plan for a reasonable number of unexpected events. I have gone as far as telling my Chicken Littles that they should assume 1 major problem (defined as slipping the schedule by 1 month) and 3 minor problems (a minor problem is a 2 week schedule slip). Plan for normal execution times for everything else. As with the Superman, Chicken Little soon has a schedule that reflects historical norms.

This approach seems to work. At least I can go home at night comfortable in knowing that my program schedules do not assume any miracles or disasters.

Posted in Management | 2 Comments

Exoplanet Orbit Example

Posted on 14-May-2013 by mathscinotes

Quote of the Day

Politics is a way of ruling divided societies without undue violence.

— Bernard Crick

Introduction

Figure 1: Vortex Coronograph of XXX System.

Figure 1: Vortex Coronagraph of HR 8799 System. (Source)

This is an exciting time for astronomy -- we are just now beginning to obtain spectra from exoplanets. It seems as if new exoplanet discoveries are being announced every week.

I was reading an article on Space.com about some great work on obtaining the spectra from planets orbiting HR 8799 (Figure 1). While looking at the image, I thought it would be interesting to see if I can duplicate some of their orbital calculations.

Background

This analysis will be very approximate. I will apply some simple orbital mechanics. There are four planets in the article's image. To estimate their orbital radii and periods, I need to make a few assumptions.

  • The orbits are centered on the middle of the dark region.

    This is equivalent to saying that the star is much more massive the planets. A planet and its star rotate about a foci of the orbital ellipse called the barycenter. With the star being much more massive than the orbiting planets, the barycenter of the orbit is very near the star (maybe even inside the star's diameter).

  • The orbits are perfect circles.

    Another assumption that makes my analysis simple. This assumption allows me to measure the orbital radii by measuring from the middle of the dark region to the center of the planets.

  • The orbital plane is perpendicular to our line of sight.

    I really have no idea as to the plane angle relative to our line of sight. I will simply make the simplest assumption. Again, this means that we are looking at a perfect circle.

Analysis

My analysis consists of two parts: (1) determination of the orbit size, and (2) determination of the orbital period.

Orbit Size Determination

Figure 2 shows how I estimated the orbital radii of the four planets. I put the image into Visio and I just started adding some dimensions. I then used the Wikipedia radius of 68 AU for planet e as a reference value to use to estimate the radii of the other planets.

Figure 1: Orbit Measurements Taken From Wikipedia Article on HR 8799.

Figure 2: Orbit Measurements Taken From Wikipedia Article on HR 8799.

Figure 3 shows my scaling calculations.

Figure 2: Orbital Radii Calculations.

Figure 3: Orbital Radii Calculations.

My radii estimates are within 6% of the published values. Not bad considering the assumptions that I had to make.

Orbit Period Determination

Figure 4 shows how I estimated the orbital periods. Note how close my estimated values are to published values.

Figure 3: Determining the Orbital Period of the Planets of HR 8799.

Figure 4: Determining the Orbital Period of the Planets of HR 8799.

My results are within a few percent of the published results. Again, not bad considering my assumptions.

Conclusion

I feel like I understand the orbital basics of this exoplanet system with just a little bit of algebra.

Posted in Astronomy | Comments Off on Exoplanet Orbit Example

Goldilocks Problems

Posted on 9-May-2013 by mathscinotes

Quote of the Day

Take calculated risks. That is quite different than being rash.

— General George S. Patton

Figure 1: Goldilocks and the Three Bears.

Figure 1: Goldilocks and the Three Bears. (Source)

I have been working on a simple optical deployment problem that is all too common. A customer has put together an optical plant (fiber, connectors, splitters, etc) that does not have enough loss on it — the laser transmitter is so bright that it blinds the receiver. In other deployments, customers sometimes have too much loss in their optical plant and the laser light is too dim for the receiver to read the data reliably. I refer to this situation as a Goldilocks problem.

Engineers do not like Goldilocks problems — not too little, not too much,  only just right works. In meetings with customers on optical plant issues, I prefer to use baseball for my analogies. For example, when customers ask how they should set the optical video power for their customers, I tell them that ideally they want the optical power “right in the middle of the strike zone.”

In this particular case, the amount of communication required to solve this simple problem has been surprising. Our modern trouble tracking systems are impressive, but they do generate a flood of email. I count 46 emails involved in resolving this issue — back in the old days there would have been four emails:

  • report of trouble from the customer
  • request for power data
  • return of power data
  • email diagnosing the problem and proposing a solution (i.e. add an attenuator — equivalent of sunglasses for optical telecommunication systems)

I am a student of the history of engineering. I find the story of how people came to be builders of things endlessly fascinating. Engineering processes and their history are also interesting. I started my engineering career as an integrated circuit designer with a handheld calculator and a set of x-acto knives for cutting rubylith. The changes during my 34 year career have been breathtaking. I sometimes wonder what it would be like to build the pyramids using the same approach to engineering processes that we use today. Could you imagine telling someone that they have to remove and rework a 100 ton block because a dimension was slightly off? The Great Pyramid of Giza contains almost 600,000 blocks — did they actually have a bill of materials?  Did they have Engineering Change Orders? I am sure they had some system of engineering control, but I have never seen any discussion about it.

The more I think about it, the more impressed I am with what the pyramid builders did. How many emails would we need today to build a pyramid?

Posted in Management | Comments Off on Goldilocks Problems

Standards of Readability

Posted on 1-May-2013 by mathscinotes

Quote of the Day

Do not forget what is being a sailor when you become a captain.

— African proverb

Figure 1: Newton's Pincipia is my vote for the world's most obscure writing.

Figure 1: Newton's Pincipia is my vote for the world's most obscure writing. (Source)

I had a discussion with one of my engineers this morning about documentation and our company's standard of readability. When I was in school, I always tried to write so that I could be understood. It was while working as a US Navy contractor that I discovered that I need to write so that I could not be misunderstood. This lesson was drummed into me by a safety engineer -- a man to whom I am in debt. His writing is so clear that I hope that I someday get near his level. I tell the engineers in my group that we write so that we cannot be misunderstood.

I do have one documentation horror story that I want to relate. I used to work as a proposal manager on large defense contracts. I had a former physics professor (PhD from a very well known institution) who worked on some of my proposals as a technical contributor. I could not read a thing that man wrote! I even brought in a very good writing consultant to work with him and that did not help at all. Finally I sat down with him and told him that his writing was terrible and he was going to need to do something else. He demanded to know exactly what was wrong with his writing and I told him that no customer could understand what he was writing. He then told me that he viewed his writing as a form of filter -- any customer that could not understand what he wrote should not be reviewing this proposal.

I then tried to explain to this very intelligent man what the life of a government proposal reviewer was like. I decided to present this poor writer with the following proposal review scenario:

  • your proposal is the 20th one the reviewer has seen this week,
  • most of the proposals have been a struggle to get through,
  • Friday at 4:00PM is the first time he starts reading your proposal,
  • your proposal is difficult to read
  • the reviewer decides to give your work a low score and go home for the weekend,
  • all of our work has been for nothing.

After some moaning and groaning, he got the point. You write for audience and you do not create unnecessary obstacles.

Posted in Technical Writing | Comments Off on Standards of Readability

How Big is Phobos When Seen from the Surface of Mars?

Posted on 1-May-2013 by mathscinotes

Quote of the Day

Man is only born ignorant. It takes four years of college to make him stupid.

— Mark Twain

Introduction

Figure 1: Good Color Image of Phobos. (Source)a

Figure 1: Good Color Image of Phobos. (Source)

The thought of alien worlds with multiple moons has always intrigued me. I am listening to the audio book "A Princess of Mars" by Edgar Rice Burroughs. I downloaded the audio book from Libravox, which provides free downloads of readings from classic works. Normally, I do not listen to much science fiction, but I watched the movie "John Carter" and there was something I liked about the story.

In "A Princess of Mars", Burroughs describes the moons of Mars, Phobos (Figure 1) and Deimos, as being large and very bright at night.

The nights are either brilliantly illumined or very dark, for if neither of the two moons of Mars happen to be in the sky almost total darkness results, since the lack of atmosphere, or, rather, the very thin atmosphere, fails to diffuse the starlight to any great extent; on the other hand, if both of the moons are in the heavens at night the surface of the ground is brightly illuminated.

He also commented on Phobos' speed across the sky with this statement.

... the nearer moon of Barsoom raced through the western sky toward the horizon ...

I started to wonder if these characteristics were true. So I thought a few calculations would be in order ...

Background

I can believe that Phobos moves across the martian sky pretty fast, but I am not sure about the movement of Deimos. I also cannot believe that they appear to be very large in the sky. Thus, my reading has made me interested in two questions about Mars and its moons.

  • How large are Phobos and Deimos as seen from Mars compared to the Moon when seen from Earth?
  • How fast do the two moons move relative to each other when viewed from Mars?

Figure 2 is a good graphic that illustrates how Phobos and Deimos move about Mars. Their orbits are nearly circular and they both can transit the Sun.

Figure 1: Graphical Illustration of the Orbits of Phobos and Deimos.

Figure 2: Graphical Illustration of the Orbits of Phobos and Deimos.

Analysis

Angular Size of Phobos and Deimos Compared to the Our Moon

Figure 3 shows a transit of Phobos across the Sun (Source). Figure 4 shows the transit of Deimos across the Sun (Source).

Figure 2

Figure 3: Transit of Phobos Across the Sun When Viewed From Mars (Photographed by the Opportunity Rover).

Figure 3: Transit of Deimos Across The Sun When Viewed From Mars (Photographed by the Opportunity Rover).

Figure 4: Transit of Deimos Across The Sun When Viewed From Mars (Photographed by the Opportunity Rover).

Our Moon, as seen from Earth, has nearly the same angular extent as the Sun -- that is why we have such spectacular eclipses. However, Figure 1 and 2 show that Phobos and Deimos have significantly smaller angular extent than the Sun when viewed from Mars. Since the Sun as viewed from Mars is smaller than the Sun viewed from Earth, both Phobos and Deimos as viewed from Mars must have significantly smaller angular extent than our Moon when viewed from Earth. This qualitative argument is supported by the quantitative argument I make in Figure 5.

Figure 4: Calculations Showing the Angular Extent of the Sun, Phobos, and Deimos.

Figure 5: Calculations Showing the Angular Extent of the Sun, Phobos, and Deimos.

Size is not the only factor affecting the brightness of an object -- some objects reflect more light than others. This factor is called albedo. It turns out that the albedos of Phobos and Deimos are about half that of the Moon. Compared to the Earth's moon, the moons of Mars do not reflect much of the light that they receive.

Angular Speed of Phobos and Deimos as seen from Mars

Figure 6 shows a great time-lapse photo of Phobos and Deimos from Mars as seen by a Rover (Source). Note that Phobos and Deimos appear to move in opposite directions when viewed from the surface of Mars, even though they both revolve in the same direction around Mars. This is because of the rotation rate of Mars is slower than Phobos, but faster than Deimos. My measurements in Figure 7 show that Phobos appears to move ~12 faster than Deimos.

Figure 5: Relative Movement of Phobos and Deimos When Viewed from Mars.

Figure 6: Relative Movement of Phobos and Deimos When Viewed from Mars.

Figure 6: Measurements of the Relative Movements of Phobos and Deimos.

Figure 7: Measurements of the Relative Movements of Phobos and Deimos.

Figure 8 show my rough calculations that demonstrate that the relative motions measured in Figure 6 make sense when you take the rotation rate of Mars into account.

Figure 7: Calculations of Angular Movements of Phobos and Deimos.

Figure 8: Calculations of Angular Movements of Phobos and Deimos.

Conclusion

I think Burroughs was using some literary license when talking about how impressive the moons of Mars are at night. We can say that:

  • The angular extent of the Sun is smaller at Mars than Earth \Rightarrow less light is available at Mars than at the Earth.
  • When viewed from Mars, both Phobos and Deimos are much smaller than the Moon when viewed from Earth \Rightarrow less area means that light is received from the Sun, so less is available to reflect.
  • Phobos and Deimos have albedo values about half that of the Moon \Rightarrow the moons of Mars do not reflect as much of the light they receive as the Moon does.
  • These three factors (I refer to this situation as "bad cubed") means that Phobos and Deimos will reflect much less light than the Moon.

I was surprised to realize that Phobos and Deimos appear to move in opposite directions.

While the moons of Mars may not be very bright, it would still be a great view to see in person.

Posted in Astronomy | Tagged | 2 Comments

Calculator to Select Connector for Joining Wires

Posted on 26-April-2013 by mathscinotes

Quote of the Day

Nobody washes a rental car.

— Truism on the importance of ownership and maintenance

Introduction

Figure 1: Example of a Crimped Connection using Commonly Available Connector.

Figure 1: Example of a crimped connection using a commonly available connector. Many mechanical engineers love crimped connections because they can be hermetic. However, they require the correct tool to be properly executed. (Source)

I have written dozens (hundreds?) of small Mathcad function to help me in my daily work. Since I plan to teach another Mathcad class soon, I am gathering examples that might be good to use as application examples. Yesterday, I was working with a customer on selecting wires for supplying power to our products. I used an old calculator that I have decided to show my students in the class. I will discuss how I used this calculator here.

These wires need to be joined (i.e. spliced). The customer wanted to use crimp connectors for this joining process rather than soldering. Crimping wire connections is preferred by many engineers because:

  • simpler

    There are numerous hand tools that allow you to simply put the wires together and join with by simply squeezing the tools handle.

  • safe

    Soldering can involve heavy metals and nasty fluxes.

  • reliable

    When performed by the proper tool, crimp joints can be very reliable.

This particular customer wanted to use this brand of connectors. There are rules on which connectors must be selected for a given area of copper. It turns out that I have a Mathcad worksheet that helps me to quickly select the specific connector for the given wires being used.

Background

Wires are pretty straightforward, but the units of measure (in the US) are rather strange. The following Wikipedia reference will provide the proper background to understand this calculator.

Analysis

Figure 1 shows the basic setup used to define the characteristics of both the wire gauges and the connectors.

Figure 1: Mathcad Worksheet Section that Defines the Wire Types and Connectors.

Figure 1: Mathcad Worksheet Section that Defines the Wire Types and Connectors.

Figure 2 shows the user input section of the worksheet. I use some simple control ("text boxes") to accept user input. I also have a small program that searches for the connector size that matches my needs. The calculator assumes that multiple wires of two different gauges are being joined.

Figure 2: Mathcad Worksheet User Input and Computation Section.

Figure 2: Mathcad Worksheet User Input and Computation Section.

Conclusion

This blog just reviews a routine wire area and connector calculator. I use this calculator so often that I do not even think about it.

You can get a copy of the calculator here. It is in Mathcad 15.

Posted in Electronics | 1 Comment

Photo Showing Ship On the Horizon

Posted on 22-April-2013 by mathscinotes

Quote of the Day

Men are born ignorant, not stupid. They are made stupid by education.

— Bertrand Russell (1872-1970). I see lots of problems with this quote, but there is an element of truth in it. I do think that education done poorly can drain all the excitement and wonder out of a child.

I read a lot of nautical history. Many of these history references talk about how sailors have long known the Earth was round. One of the reason why sailors knew the world was round had to do with the appearance of ships and islands on the horizon. Here is a photo that nicely illustrates how the top of a ship is the last part visible as it crosses over the horizon (Source).

Figure 1: Container Ship On the Horizon.

Figure 1: Container Ship On the Horizon.

Posted in General Science, Naval History, Navigation | 2 Comments