Estimating the RMS Ring Voltage at a Telephone

Posted on 11-November-2014 by mathscinotes

Introduction

Figure 1: Old Bell 2500 Series Phone.

Figure 1: Old Bell 2500 Series Phone.

I just saw a customer report of phone ringing issues with an old 2500 series phone (Figure 1). While these are good phones, they can be difficult for Fiber-to-the-Home (FTTH) deployments because they have 1 Ringer Equivalence Number (REN) ringers. By specification, homes are permitted to have as many as five of these phones (5 REN total load) on a single line and they will still ring with proper volume. To support this requirement, modern Subscriber Line Interface Circuits (SLICs) used to ring phones in FTTH products are designed to drive a 5 REN load. However, some of these old phones appear to have not aged well and they are becoming difficult to ring – they behave as if their equivalent load on the line is now more than 1 REN. In fact, I just saw one with a 1.1 REN rating when it was new.

The specifications for ringing a phone require that the ring voltage be 40 VRMS with a 5 REN load. I had a conversation with an old POTS engineer today about how to compute the RMS ring voltage on at a phone and I thought I would document this discussion here. This is a routine question, but we have a new engineer who wants to see how the calculation is performed. I decided the best way help would be to provide a worked example.

Background

Definitions

A few definitions are useful to review.

Ringer Equivalence Number (REN)
The electrical load placed on a phone line by the single electric bell of a Model 2500 phone, which we call a REN. In the US, the number of these old phones allowed on a line is limited to 5, which is called a “5 REN load”. In impedance terms, one REN is equivalent to a 6930 Ω resistor in series with an 8 µF capacitor – a 5 REN load has 5 of these series components in parallel.
Feed Resistance
All phone circuits need to have protection circuit on their inputs. These circuits protect against nasty realities like AM radio interference (I have frequently heard radio stations on phone lines), lightning, and foreign voltages (e.g. high voltage inadvertently put on phone lines because of an errant nail or screw). These protection circuits have a resistance associated with them that I model with the feed resistance.
Line Resistance
The resistance of the phone line. The resistance of the phone line is related to its length (500 feet or 1000 feet), wire gauge, and temperature.
Symmetrical Ringing
A ring voltage waveform that is symmetrical about 0 V. Some older systems used a sine wave with a DC level added to it, which was referred to as asymmetrical ringing. I do not see this type of ringing very often today.
SLIC Voltage Drop
The voltage drop in the POTS supply voltage as it passes through the SLIC on the way to the tip and ring lines. In general, it is a function of the current being placed on the tip and ring lines.

Circuit Model

A ringing phone circuit modeled using the equivalent circuit shown in Figure 2. I will assume that the phone is the only circuit element with a reactive component.

Figure 2: Phone Ringing Circuit Model.

Figure 2: Phone Ringing Circuit Model.

Analysis

Approach

I am using this analysis as a reference example for a new engineer to use for a design he is working on. I am not using any particular hardware, but instead I am using typical values that I have seen over the years. I will be assuming a symmetrical ring voltage with a sinusoidal shape. Personally, I like to use trapezoids for ring voltage waveforms on short phone lines, but this particular application will use sinusoidal waveforms.

Power System Model

Figure 3 shows how I modeled both the power supply output voltage (VSupply) and the voltage drop (VSLIC_Drop) through the SLIC.

Figure 2: My Model of the Power System Voltages Versus Current.

Figure 3: My Model of the Power System Voltages Versus Current.

Ring Voltage Model

Figure 4 shows my calculation for the ring voltage RMS value. I do mention some measured ring voltage values in the calculation that I have from a circuit we designed years ago for comparison with my calculations.

Figure 4: Calculations of Ring Voltage For Two Configurations.

Figure 4: Calculations of Ring Voltage For Two Configurations.

Conclusion

My rough model put together from memory gave me results similar to those of a deployed system, so I feel that the model is pretty close to accurate. The analysis should provide our new telephony engineer a model for how to proceed with his application.

Posted in Electronics, Telephones | Comments Off on Estimating the RMS Ring Voltage at a Telephone

New Telescopes Coming Online In the Next Ten Years

Posted on 10-November-2014 by mathscinotes

I am just amazed at the new technology in telescopes today. Take a look at this article – these are the kinds of instruments that will change our view of the universe. If you have trouble getting access at PhotonicsSpectra, try this lower-quality version.

The Wikipedia has a great chart that show the relative sizes of the major telescopes, which I include below.

Comparison_optical_telescope_primary_mirrors.svg

Posted in Astronomy | Comments Off on New Telescopes Coming Online In the Next Ten Years

A Little Queueing Math

Posted on 8-November-2014 by mathscinotes

Introduction

Figure 1: Model of a Fiber-To-The-Home Network.

Figure 1: Model of a Fiber-To-The-Home Network.

Queues arise naturally in many circumstances and networking products are no exception. We use queues for many tasks in our networking products and this post discusses our need to store packets while we wait to be granted access to our fiber network. This post will show you a simple queueing problem and how its solution perfectly modeled the performance we measure during testing.

The basic problem discussed here is a common one. When a home PC needs to transmit information onto the Internet (e.g. email), it starts by sending its data to the home's Internet gateway, which is often a DSL or cable modem. In the case of a Fiber-to-the-Home network, that gateway is called an Optical Network Terminal (ONT). The ONT must place the data it receives from the PC onto its FTTH Passive Optical Network (PON) network, but it cannot do that until it receives a receives an allotment of transmit time from the FTTH network manager called the Optical Line Termination (OLT). This allotment of time is required because FTTH systems share the fiber between multiple homes and only one ONT can transmit at a time (see Figure 1). While the ONT is waiting for its time allotment on the network, it must store the data it is receiving from the PC so that no data is lost. This storage drives the number of queued packets which our system must manage, which is one of the cost drivers of the ONT.

The analysis I present here was performed by an engineer in my group, Chris Bernard, and I am presenting it here as an example of how little bit of analysis can provide insight into the performance we see in data networks.

Background

Definitions

It is helpful to begin with a couple of definitions.

bandwidth request
A request for fraction of a network's available transmit time.
packet drop
A packet drop occurs when a packet arrives at the ONT and there are no resources available to store or transfer it, so it must ignored and its information is lost. The PC must retransmit it, which is inefficient and slows the PC's operation.

Objective

I want to compute the maximum number of packets that I will need to manage when holding data at the ONT while we request and are granted transmission time on the PON. You want to provide all the resources you need to manage the maximum number of packets so that the PC's data can be transferred without dropping any. Allocating any resources above the maximum you need is wasteful and results in unnecessary costs.

Process for Transmitting Data

Figure 2 illustrates the six-step process for a PON bandwidth request.

Figure 2: Bandwidth Request Process

Figure 2: Bandwidth Request Process

If define the six-step bandwidth request process as follows:

  1. PC begins transferring data to the ONT at 1 Gigabit Per Second (Gbps)

    Most PCs support 1000BaseT Ethernet and its data rate is 109 bits per second, which we call 1 Gbps.

  2. The ONT begins queueing the PC data coming in.

    A PON is a fiber network that is shared between many subscribers – as many as 64 – and only one subscriber can transmit at a time. To ensure that only one subscriber can transmit at at a time, ONTs must request from the OLT  an allotment of time to transmit its data. We refer the request ONT's request for transmit time as a request for bandwidth.

  3. The ONT requests permission to transmit on PON – because the speed of light is finite, the signal takes time to get to the OLT (τ Flight).

    The fiber can be as long as 40 km and the light must travel on the fiber from the ONT to the OLT. The ONT transmits to the OLT using 1310 nanometer (nm) light.

  4. The OLT must recognize the ONT is requesting bandwidth (τSampling).

    The OLT creates an opportunity for every ONT to request a time allotment on the PON once every millisecond (msec). Since the PC can start to transmit at any time, the ONT may have to store as much as 1 msec of data before the OLT even considers its request for bandwidth.

  5. The OLT must determine how to allot the ONT time for transmitting data (τDBA).

    There is an algorithm in the system referred to as Dynamic Bandwidth Allocation (DBA). This algorithm requires a fixed unit of time to determine the ONT's bandwidth allotment.

  6. Because the speed of light of light is finite, the bandwidth allotment takes time to get to the ONT (τ Flight).

    The transmission time from the OLT to the ONT is roughly the same as from the ONT to the OLT (step 3). The difference in time is because the speed of light on a fiber varies slightly with its wavelength. The OLT transmits to the ONT at 1490 nm, which is a slightly longer wavelength the ONT's 1310 nm value.

The ONT now has time allocated to it and it can begin transmitting data and emptying its queue, which will shrink the queues size and the number of packets in storage.

Analysis

Figure 3 shows the analysis for number of packets that we must be able to queue so that we do not have to drop any data arriving from the PC.

Figure M: Maximum Number of Queued Packets Calculation.

Figure 2: Maximum Number of Queued Packets Calculation.

We need to be able to manage as many as 2973 packets to ensure that we do not need to drop any packets from the PC.

Conclusion

It turns out that we needed the ability to store 2973 packets, otherwise we began to drop data coming from PCs. While this was a simple analysis, it turned out to be very accurate.

Posted in Fiber Optics, Networking | Comments Off on A Little Queueing Math

Cow Productivity

Posted on 7-November-2014 by mathscinotes

Quote of the Day

The good thing about science is that it is true whether or not you believe in it.

— Neil deGrasse Tyson

Many of my blog posts are motivated by lunch-time conversations with our engineering staff. During lunch a few days ago, several of us were sitting around a table and trying to estimate the number of cows in the US, their daily milk production, and how much they eat per day – it might sound boring, but actually was pretty interesting.

After we finished doing our estimates, I did a bit of web searching to determine what the truth was. Our estimates turned out to be fairly accurate, but what shocked me was how the number of cows in the US has been dropping while milk production per cow has been increasing. This is an amazing tale of productivity improvement. Consider the following figure from this source.

CowPopulationThe population of cows in the US has been declining since 1944, while milk production per cow has increased to nearly 10,000 kg per cow, which is about 2550 gallons per cow per year or ~7 gallons per day.  I show the conversion calculations below.

CalculationThe productivity variation between cows is substantial. The record milk producer is a Wisconsin cow that produced 8,295 gallons of milk in a single year – more than 3 times the average cow's annual milk production.

Density of Milk Wikipedia

The improvement in the milk production per cow also comes with a reduction in the amount of food needed to produce each 100 pounds of milk, as shown in the following chart (source).

productivity3_thumb

Posted in General Science | Comments Off on Cow Productivity

Wood Hardness Versus Moisture Content

Posted on 5-November-2014 by mathscinotes

Introduction

Figure 1: Wood Hardness Scale.

Figure 1: Wood Hardness Scale.

I have long been told that wood hardens as it ages, but I have anecdotal evidence that this is not always true. I also know that some species are far harder than others (Figure 1).

I read the following forum post that I thought presented really good information on wood hardness and moisture content that I would like to research a bit more and present here. The key point of the forum discussion was that wood gets harder as its moisture content decreases, which can happen to wood as it ages. Other factors, like insects and mold, will decrease the hardness of wood. I am only concerned with moisture here – the other factors are unpredictable.

I will present two numerical models for how the hardness of wood varies with moisture content. These two models will be shown to be roughly equivalent.

Background

Concept

There are many wood properties that vary with the moisture content of the wood. Here are a few examples:

  • hardness
  • shear modulus
  • tensile strength
  • compressive strength

I have seen two approaches to modeling the effect of moisture on these properties: (1) a power law relationship (USDA) and a linear model (Bozkurt Y, Göker Y [1987]). I will show that the two approaches produce similar results over a narrow moisture content range.

Definition of Hardness

My post here will focus on Janka hardness, which is a commonly used wood hardness measure. Here is the definition of the Janka measurement process and how moisture content is defined.

Janka Side Hardness
Janka side hardness is the load required to embed an 11.28-mm (0.444-in.) ball to one-half its diameter.
Moisture Content (M)
The percentage of wood mass consisting of water. It is often measured in the field using electrical test equipment. In the lab, it can be measured using by measuring the mass of a test sample before and after drying and computing M\triangleq \frac{{{m}_{water}}}{{{m}_{dry}}}=\frac{{{m}_{wet}}-{{m}_{dry}}}{{{m}_{dry}}}
where

  • mwater is the mass of water in the wood sample.
  • mwet is the mass of the wood sample before drying.
  • mdry is the mass of the dried wood sample.

Figure 2 illustrates the Janka test.

Figure 2: Illustration of the Janka Test (Wikipedia).

Figure 2: Illustration of the Janka Test (Wikipedia).

This post is focused on hardness, but the approach can be used for many other parameters.

Forest Products Laboratory Model (USDA)

Equation 1 shows the model from the Forest Products Laboratory (FPL). I will use data from the FPL to model wood hardness.

Eq. 1 P(M)={{P}_{12}}\cdot {{\left( \frac{{{P}_{12}}}{{{P}_{g}}} \right)}^{\frac{\left( 12-M \right)}{\left( {{M}_{p}}-12 \right)}}}

where

  • P a property of wood (e.g. hardness)
  • P12 the property value at 12% moisture content.
  • Pg is the property value under green conditions.
  • M is the moisture content of the wood expressed as a percentage.
  • MP is defined in Chapter 4 of the 1999 Wood Handbook as the moisture content percentage at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood. They then say to assume 25% if MP is not known. I can explain why they say assume 25% if you do not have information otherwise. The intersection statement does not seem correct. I go into detail here.

Linear Model

Equation 2 shows a model that I have seen in many publications (example, sect 2.3) for normalizing data gathered from wood at various moisture contents to 12%, which is the industry standard for moisture content.

Eq. 2 \displaystyle P\left( M \right)=\frac{{{P}_{12}}}{1+\alpha \cdot \left( M-12 \right)}\approx {{P}_{12}}\cdot \left[ 1-\alpha \cdot \left( M-12 \right) \right]

where

  • P12 is estimated value of a parameter at 12% moisture content.
  • P is measured value of a parameter at a moisture content of u%.
  • α is a constant that in general varies with the species of the wood under test. It can be calculated using \displaystyle \alpha =\frac{\ln \left( \frac{{{H}_{12}}}{{{H}_{g}}} \right)}{{{M}_{p}}-12}. This relationship is derived in Figure 3.

Analysis

Objective

I will show how Equations 1 and 2 are related in that they produce similar results for wood hardness in the typical range of wood moisture contents.

Calculations

For my work here, I will work with the wood hardness normalized to the hardness at 12% moisture content. Normalizing allows me to work with numbers that are in the neighborhood of 1. Figure 3 shows my analysis.

Figure 3: Comparison of Exact and Linear Approximation.

Figure 3: Comparison of Exact and Linear Approximation.

FPL Paper FPL Paper

Conclusion

I was able to show that Equations 1 and 2 produce similar results in the typical range of wood moisture contents (6% to 14%). I also see that the model states that wood gets harder as moisture content decreases, which is something that I have observed.

To centralize the data that I use for my personal work, I have included a list of the hardness parameters for common North American Species (Table 1).

Appendix A: MP Values for Common North American Species.

MP is an important parameter for estimating wood hardness and its value varies by species. The Wood Handbook states that its value is normally near 25%. Figure 4 shows some common MP values and you can see that they are near 25%.

Figure 4: Table 4-13 from the Wood Handbook.

Figure 4: Table 4-13 from the Wood Handbook.

Appendix B: MP Definition Discussion.

The definition of Equation 1 includes some phrasing that is difficult for me to figure out. I will try to provide some additional clarification here. Here is how MP is defined.

MP [is the] moisture content at the intersection of a horizontal line representing the strength of green wood and an inclined line representing the logarithm of the strength–moisture content relationship for dry wood.

I actually could not understand this statement as written, although I do think I can explain how you determine MP. Figure 5 shows my explanation, which assumes you have (1) a plot of the hardness versus moisture content of the wood in question, and (2) you know the green hardness.

Figure 5: Explanation for Mp Determination Statement.

Figure 5: Explanation for Mp Determination Statement.

Figure 5 shows that the if we graph Equation 1, MP is the moisture level at which the wood strength equals the green strength. Figure 6 illustrates the relationship between MP and the Fiber Saturation Point (FSP). Observe that the "green" strength is reached before the FSP. This means that Equation 2 does not hold above MP.

Figure 6: Relationship Between Mp and FSP.

Figure 6: Relationship Between Mp and FSP.

Appendix C: Table of Hardness Values (Dry/Green/Ratio) for Common Species.

Table 1 is from a US Forest Service publication, which I have augmented with a column of common tree names. The scientific names are not of much use for me – I only know the common names of trees. Note that the hardness levels are specified in units of Newtons (metric measure) and there are 4.448 Newtons in a pound. For example, the hardness of Black Cherry is rated at 4210 Newtons, which is ~950 pounds.

Table 1: Hardness (Dry/Green) and Dry/Green Ratio By Species
Type Common Name Species Dry Hard. (N) Green Hard. (N) Dry/Green Ratio
Hardwood ALDER, COMMON ALNUS GLUTINOSA 2940 2220 1.32
ALDER, RED ALNUS RUBRA 2620 1950 1.34
ASH, BLACK FRAXINUS NIGRA 3770 2310 1.63
ASH, EUROPEAN FRAXINUS EXCELSIOR 6140 4270 1.44
ASH, GREEN FRAXINUS PENNSYLVANICA 5320 3860 1.38
ASH, OREGON FRAXINUS LATIFOLIA 5140 3500 1.47
ASH, WHITE FRAXINUS AMERICANA 5850 4260 1.37
ASPEN, QUAKING POPULUS TREMULOIDES 1550 1330 1.17
BEECH, AMERICAN FAGUS GRANDIFOLIA 5760 3770 1.53
BEECH, EUROPEAN FAGUS SYLVATICA 6410 4270 1.50
BIRCH, BLACK BETULA LENTA 6520 4300 1.52
BIRCH, PAPER BETULA PAPYRIFERA 4040 2480 1.63
BIRCH, YELLOW BETULA ALLEGHANIENSIS 5590 3460 1.62
BUTTERNUT JUGLANS CINEREA 2170 1730 1.25
CHERRY, BLACK PRUNUS SEROTINA 4210 2930 1.44
CHERRY, SWEET PRUNUS AVIUM 5780 4140 1.40
CHESTNUT, AMERICAN CASTANEA DENTATA 2390 1860 1.28
CHESTNUT, SWEET CASTANEA SATIVA 3070 3160 0.97
COTTONWOOD, BLACK POPULUS TRICHOCARPA 1550 1110 1.40
COTTONWOOD, EASTERN POPULUS DELTOIDES 1910 1510 1.26
CUCUMBERTREE MAGNOLIA ACUMINATA 3100 2310 1.34
GUM, BLACK NYSSA SYLVATICA 3590 2840 1.26
HACKBERRY, NORTHERN CELTIS OCCIDENTALIS 3900 3100 1.26
HONEYLOCUST GLEDITSIA TRIACANTHOS 7010 6160 1.14
HORNBEAM, EUROPEAN CARPINUS BETULUS 6980 5470 1.28
HORSE CHESTNUT AESCULUS HIPPOCASTANUM 3340 2580 1.29
MAGNOLIA, SOUTHERN MAGNOLIA GRANDIFLORA 4520 3280 1.38
MAPLE, BIGLEAF ACER MACROPHYLLUM 3770 2750 1.37
MAPLE, BLACK ACER NIGRUM 5230 3730 1.40
MAPLE, RED ACER RUBRUM 4210 3100 1.36
MAPLE, SILVER ACER SACCHARINUM 3100 2620 1.18
MAPLE, SUGAR ACER SACCHARUM 6430 4300 1.50
MAPLE, SYCAMORE ACER PSEUDOPLATANUS 4850 3830 1.27
OAK, AUSTRIAN QUERCUS CERRIS 8270 6180 1.34
OAK, SCARLET QUERCUS COCCINEA 6210 5320 1.17
OAK, SWAMP WHITE QUERCUS BICOLOR 7180 5140 1.40
OAK, WHITE QUERCUS ALBA 6030 4700 1.28
PECAN CARYA ILLINOENSIS 8070 5810 1.39
PLANETREE, LONDON PLATANUS ACERIFOLIA 5650 4270 1.32
POPLAR, TULIP LIRIODENDRON TULIPIFERA 2390 1950 1.23
SWEETGUM LIQUIDAMBAR STYRACIFLUA 3770 2660 1.42
SYCAMORE PLATANUS OCCIDENTALIS 3410 2710 1.26
TUPELO, WATER NYSSA AQUATICA 3900 3150 1.24
WALNUT, BLACK JUGLANS NIGRA 4480 3990 1.12
WALNUT, PERSIAN JUGLANS REGIA 3600 2970 1.21
POPLAR, CANADIAN POPULUS CANADENSIS 2220 2050 1.08
POPLAR, SILVER POPULUS CANESCENS 2360 1730 1.36
Hardwood
Average		 4474 3343 1.34
Softwood BALDCYPRESS TAXODIUM DISTICHUM 2260 1730 1.31
CEDAR, ALASKA CHAMAECYPARIS OOTKATENSIS 2570 1950 1.32
CEDAR, ATLANTIC WHITE CHAMAECYPARIS THYOIDES 1550 1290 1.20
CEDAR, PORT ORFORD CHAMAECYPARIS LAWSONIANA 2790 1690 1.65
FIR, BALSAM ABIES BALSAMEA 1770 1290 1.37
FIR, CALIFORNIA RED ABIES MAGNIFICA 2220 1600 1.39
FIR, DOUGLAS PSEUDOTSUGA MENZIESII 2930 2260 1.30
FIR, GRAND ABIES GRANDIS 2170 1600 1.36
FIR, NOBLE ABIES PROCERA 1820 1290 1.41
FIR, PACIFIC SILVER ABIES AMABILIS 1910 1380 1.38
FIR, SILVER ABIES ALBA 2850 1910 1.49
FIR, SUBALPINE ABIES LASIOCARPA 1550 1150 1.35
FIR, WHITE ABIES CONCOLOR 2130 1510 1.41
HEMLOCK, EASTERN TSUGA CANADENSIS 2220 1770 1.25
HEMLOCK, MOUNTAIN TSUGA MERTENSIANA 3020 2080 1.45
HEMLOCK, WESTERN TSUGA HETEROPHYLLA 2390 1820 1.31
INCENSE CEDAR LIBOCEDRUS DECURRENS 2080 1730 1.20
LARCH, EUROPEAN LARIX DECIDUA 3770 2450 1.54
LARCH, JAPANESE LARIX KAEMPFERI 2940 2140 1.37
LARCH, WESTERN LARIX OCCIDENTALIS 3680 2260 1.63
PINE, AUSTRIAN PINUS NIGRA 2890 1910 1.51
PINE, CLUSTER PINUS PINASTER 2670 1690 1.58
PINE, EASTERN WHITE PINUS STROBUS 1690 1290 1.31
PINE, JACK PINUS BANKSIANA 2530 1770 1.43
PINE, LOBLOLLY PINUS TAEDA 3060 2000 1.53
PINE, LODGEPOLE PINUS CONTORTA 2130 1460 1.46
PINE, LONGLEAF PINUS PALUSTRIS 3860 2620 1.47
PINE, MONTEREY PINUS RADIATA 3330 2130 1.56
PINE, PONDEROSA PINUS PONDEROSA 2040 1420 1.44
PINE, RED PINUS RESINOSA 2480 1510 1.64
PINE, SCOTCH PINUS SYLVESTRIS 2980 2220 1.34
PINE, SHORTLEAF PINUS ECHINATA 3060 1950 1.57
PINE, SPRUCE PINUS GLABRA 2930 2000 1.47
PINE, SUGAR PINUS LAMBERTIANA 1690 1200 1.41
PINE, VIRGINIA PINUS VIRGINIANA 3280 2390 1.37
PINE, WESTERN WHITE PINUS MONTICOLA 1860 1150 1.62
REDCEDAR, EASTERN JUNIPERUS VIRGINIANA 4000 2880 1.39
REDCEDAR, WESTERN THUJA PLICATA 1550 1150 1.35
REDWOOD, COAST SEQUOIA SEMPERVIRENS 2130 1820 1.17
SPRUCE, BLACK PICEA MARIANA 2310 1640 1.41
SPRUCE, ENGELMANN PICEA ENGELMANNII 1730 1150 1.50
SPRUCE, NORWAY PICEA ABIES 2110 1420 1.49
SPRUCE, RED PICEA RUBENS 2170 1550 1.40
SPRUCE, SERBIAN PICEA OMORIKA 2710 1470 1.84
SPRUCE, SITKA PICEA SITCHENSIS 2260 1550 1.46
TAMARACK LARIX LARICINA 2620 1690 1.55
WHITE CEDAR, NORTHERN THUJA OCCIDENTALIS 1420 1020 1.39
Softwood
Average		 2470 1722 1.43
Grand Average 3472 2533 1.38
Posted in Construction | Comments Off on Wood Hardness Versus Moisture Content

Spy Camera Math

Posted on 3-November-2014 by mathscinotes

Introduction

Figure 1: Hexagon Satellite (Wikipedia).

Figure 1: Hexagon Satellite (Wikipedia).

I just listened to a very interesting interview of Philip Pressel, a retired Perkin-Elmer mechanical engineer and satellite surveillance camera designer. The interview was conducted by Vince Houghton of the International Spy Museum. Philip discussed how the recently declassified KH-9 Hexagon (Figure 1)  camera system was designed and I found his information very interesting. The general public may not be quite as interested because Philip does dive into low-level details, but I love low-level detail as my life is a celebration of detail.

My goal here is to see if I can derive some of the camera operating characteristics based on the information that Phil mentioned during the interview. The analysis shown here will be approximate. My main interest in cameras is for astronomy, and I find these cameras interesting because NASA has been looking at using non-film versions of them for other purposes, like imaging Mars.

I do want to mention the excellent job that Vince Houghton does for the International Spy Museum. If you want to see him at his best, check out this CSPAN video of his lecture on the espionage Russia conducted on the Manhattan project during World War 2. I am a big CSPAN/BookTV fan and I  consider Vince's "Atomic Spies" video one of the best I have seen.

Background

Interview

Figure 2 shows the Youtube interview that I watched.

Figure 2: Interview with Phil Pressel of Perkin-Elmer.

He also gave the following audio interview, which also is interesting. Unfortunately, I could not find the presentation material that he refers to in the audio.

Spy Satellite Basics

Here is some general information on the KH-9 Hexagon satellite. For more of the detail, see the links, audio, and video I discussed above.

  • KH-9 Hexagon was designed in the late 60s and was the last of the film satellites.

    Film created all sorts of issues because it had to be returned to Earth. The KH-9 Hexagon contained four reentry vehicles so that it could return its images throughout its long mission time – the final mission lasted 275 days. Film does have an amazing information density and it proved to be a good medium for storing large amounts of data. This data is now being used by archeologists for finding ancient ruins, but that is another story.

  • The satellite has two cameras that are synchronized to take stereoscopic images.

    Stereo images allow photo-interpreters to derive all sorts of properties from the objects that were photographed, like their heights, distances between objects, and slopes.

  • The satellite is in an elliptical polar orbit with an perigee of ~155 km and an apogee of ~240 km.

    The polar orbit allows the KH-9 to photograph the entire Earth's surface, while using a low earth orbit means that they are close enough to the ground to achieve good resolution.

  • The camera uses strip photography

    These cameras would rotate and project their image through a slot onto moving film. I will not go into the technology in the post, but there Wikipedia article that has a good discussion on the topic. Figure 3 shows a crude illustration. Notice how the camera is constantly rotating, but only exposes film when the Earth is in view.

    Figure M: Ilustration of KH-9 Scanning (Ambivalant Engineer).

    Figure 3: Illustration of KH-9 Scanning (Ambivalent Engineer).

  • To obtain clear images, the camera must compensate for the motion of the satellite over the Earth.

    Since the satellite was in a polar orbit, the camera would "nod" to cancel out the motion in the direction of travel (called the in-track direction). This meant that the camera would then scan side-to-side (called across-track direction) to generate a panoramic image.

  • The KH-9 Hexagon used film that had to be returned to Earth.

    The satellite had four reentry vehicles for returning film. The film was picked up while hanging from a parachute using a cargo aircraft with a special device (Philip called it a 'trapeze') to grab the film reentry vehicle. Figure 4 illustrates the film recovery process.

    Figure M: Film Canister Reentry Vehicle Recovery.

    Figure 4: Film Canister Reentry Vehicle Recovery.

Camera Types

Figure 5 shows the two types of cameras carried by the Hexagon satellite.

Figure 4: Hexagon Carried Two Types of Cameras.

Figure 5: Hexagon Carried Two Types of Cameras.

My discussion here will focus on the pan cameras, which was used for obtaining detailed images of the ground.

Analysis

Reference Table

The Ambivalent Engineer blog gives the following table of KH-9 Hexagon parameters and I thought it might be useful to see how much of this table I could  derive with a bare minimum of inputs. As part of my job, I spend much of my day deriving requirements and I always find it interesting how little information you need to determine many of the characteristics of complex systems.

Table 1: KH-9 Hexagon Satellite Camera Parameters.
Parameter Value
Focal length 1524 mm (60 inches)
Aperture 508 mm (f/3.0)
Cross-track Field of View 120 degrees
Film width 168 mm (6.6 inches)
Film length 70,000 m (230,000 feet)
Format 155 (width) x 3190 mm (length)
Film resolution 1000:1, contrast: 3.7 micron;1.6:1 contrast: 7.4 microns
Depth of focus +/- 11 microns
Format resolution 42k x 862k = 36 Giga-pixels
Frames 21000
Nominal Altitude 152 km (82 nautical miles)
Center ground  resolution 37 cm
Swath 555 km
In-track field of view, center 15 km
Nominal overlap 10% (each camera)
Area collected 2x 80m km2
Nominal ground velocity 7,800 m/s
Cycle time 1.73 sec
Film velocity at slit 5.5 m/s
Maximum slit size 22? mm
Max exposure time 4? ms

I can only guess how certain system parameters were determined. For example, film speed has to do with the chemistry of the film. Orbital characteristics would probably be determined by the improved resolution you get with lower orbits balanced with the need to avoid air resistance in order to stay in orbit.

Here are the values that I will assume:

  • Film size: 155 mm x 3190 mm

    The film height (155 mm) can be determined knowing the resolution you want and the in-track distance that will be imaged on it. The film width (3190 mm) is more complicated to determine because the resolution is a function of the scan range. Philip mentioned the system supported a 120° scan range, but I noticed in other documents that they also used 90° and 60° scans. This would increase the resolution at the less swatch width.

  • Film speed: ASA 4000

    The Ambiguous Engineer blog states that earlier camera systems had used ASA 4000 films and that these films may have been used for the KH-9 Hexagon.

  • Film resolution: 3.7 μm

    The concept of resolution for film is a complex one, mainly because it is function of contrast. I will use the Ambiguous Engineer's assumption of a 1000:1 contrast range.

  • Overlap percentage: 10%

    All imaging systems I have worked on included overlap. In sonar systems, I often had 50% overlap so 10% overlap does not seem excessive to me all.

  • Number of film frames: 21,000

    This number is determined by the amount of land area you want to image and the packaging limitations of the satellite – I would have no idea what these requirements were.

  • Orbit characteristics: 155 km x 240 km

    The orbit is very important because the closer you can get to your photographic subject, the better the resolution you can obtain. However, if you get too close you will not be able to stay in orbit.

Computations

Figures 6-8 show my calculations. I have verified all the items in Table 1. Items highlighted in yellow are listed in Table 1.

Figure 6: Calculations (Page 1).

Figure 6: Calculations (Page 1).

Figure 7: Calculations (Page 2).

Figure 7: Calculations (Page 2).

Figure 7: Computations (Page 3).

Figure 8: Computations (Page 3).

Conclusions

I think I have a pretty good understanding of how a small number of system parameters, in particular orbital velocity and in-track swath, drove the hardware characteristics of this system.

Strip cameras are new to me and I think I will research them a bit more.

Posted in History of Science and Technology, optics | 3 Comments

Good Examples of Underwater Pressure

Posted on 1-November-2014 by mathscinotes
Figure 1: Styrofoam Cup Shrunk By Pressure 150Figure 1: Styrofoam Cup Shrunk By Pressure 1500 Meters Underwater.0 Meters Underwater.

Figure 1: Styrofoam Cup Shrunk By Pressure 1500 Meters Underwater.

I used to work on ships that were used to test undersea equipment. When we had visitors on the ship, we would put a Styrofoam cup on some of our test gear when lowered the equipment to our test depth. The pressure at depth would compress the air in the Styrofoam and shrink its volume to a fraction of its volume at the surface (Figure 1). The Styrofoam provided a nice demonstration of the effect of pressure on a common object.

No discussion about the impact of underwater pressure would be complete without mentioning one of the most dangerous occupations in the world either. Hyperbaric welding (or wet welding) is used in subaquatic construction and technologies and is essentially the process of fusing metals at elevated pressures. If you have aspirations of becoming an underwater welder, then a professional qualification is crucial to ensure you have the necessary skills to carry out the job correctly. For more information about hyperbaric welding, including where to find the Top rated welding schools, go to weldinginsider.com. Who knows, maybe this could be the start of an exhilarating new career for you.

I always thought the most dramatic demonstration of the pressure was when we would put an Integrated Circuit (IC) packaged in a Ceramic Dual-In-Line Package (CERDIP) at depth. When brought to the surface, the IC appeared to have a perfectly rectangular indentation over the air-gap that used to exist over the chip. Unfortunately, I did not keep any of those pictures.

Figure 2: William Beebe and Otis Barton.

Figure 2: William Beebe (L) and Otis Barton (R).

I have always been interested in the deep ocean. There is something mysterious about a place that is so difficult to visit. As a boy, I remember reading about William Beebe, an early undersea explorer who pioneered the use of the bathysphere for deep sea exploration . While he was an accomplished ornithologist, he is best known today for his undersea exploration work with a man named Otis Barton, who designed the bathysphere (Figure 2).

The bathysphere was an interesting, though very limited, ocean exploration tool. It was limited because it was suspended from a mother ship by a cable and had to be towed over to and lowered down on the location being examined. Anyone who has done ocean survey work that involves aligning something on the surface with a point location possibly miles below knows how difficult that task is. Underwater vehicles today are much more flexible than a bathysphere because they can easily move to where interesting things are without having to precisely position the mother ship over that location.

Figure 3: High Pressure Water Bursting Out of a Flooded Bathysphere.

Figure 3: High Pressure Water Bursting Out of a Flooded Bathysphere.

I was shown a movie in my grade school that showed a bathysphere having been flooded at depth during an early test. As the bathysphere was raised, the water and compressed air within it somehow became trapped. When the bathysphere was put on deck, its hatch was difficult to open because of the tremendous internal pressure. As it was opened, the hatch violently came off and a jet of water shot out of the bathysphere's hatch . I wish I could find the movie, but all I can locate is this one still image (Figure 3).

Figure 4: Bathysphere from Jonny Quest's Closing Credits.

Figure 4: Bathysphere from Jonny Quest's Closing Credits.

Even before seeing this movie in grade school, I had an interest in the bathysphere. My first contact with the bathysphere was the image of a bathysphere during the closing credits of "Jonny Quest" (Figure 4). Yes – I loved that cartoon and it provided me the motivation I needed to go to the Osseo Public Library and learn about bathyspheres.

In many ways, I have led a cartoon-driven life. I still marvel at how well Woody Woodpecker could teach us about how a rocket works – Woody's part starts about 1.5 minutes into the video.

Posted in Underwater | 1 Comment

Home Insulation Math

Posted on 29-October-2014 by mathscinotes

Introduction

Figure 1: Heat Flow from a House.

Figure 1: Heat Flow from a House.

One of the engineers in my group asked if I could help him understand the tradeoffs between the different kinds of house insulation and their relative economic value. We also spent quite a bit of time talking about where all the heat goes (Figure 1) during the winter. Poor heat efficiency can be really detrimental to the environment. This is why many people are looking to ensure they have a spray foam roof over their home or at least thicker insulation, or even a Gasfitting that avoids this.

To quantify these kinds of discussions, I have found the energy cost calculator at this site useful for making heating system and insulation decisions. As we talked about these calculations, it became clear that it would be useful to work through a simple example in Mathcad to show all the formulas used in estimating a home's energy cost and to make the various unit conversions clear. With overall rising energy costs, homes and businesses are looking for any method of reducing costs possible. Many businesses are deciding to switch energy supplier in order to save hundreds on energy costs. You might want to check out this page if you are looking to switch energy provider and save some money for your home or business.
– in the US, unit conversions are always a big deal. This post summarizes this discussion.

Background

There is a lot of material on the web on predicting home energy use (example), so I will not repeat a physics discussion done better elsewhere.

Here is my approach to duplicating the output from my reference web page:

  • I will only be looking at the energy use in January.

    I just wanted to use a month where I was assured we would be heating every day – January was as good as any other mid-winter month.

  • For my example, I will use a simple home with four walls and a ceiling.

    Since my intent here is to illustrate how the calculation is done, creating a more complex house is not necessary. I also should point out that this type of analysis is approximate – I would not expect great accuracy. At best, the analysis will provide me an reasonably accurate relative performance comparison.

  • I assumed air with a 50% humidity level.

    This is too high for winter here, but it seemed to give me the same answers as the web page I was using as my reference.

  • I am going to ignore things like
    • loss through the slab.
    • heat generated by occupants.
    • door losses.

Beginning with a simple model meets checking my results easier and these constraints/limitations are not significant with respect to my verification of the heating cost model.

Analysis

Unit Definitions

Figure 1 shows some units that I defined for this analysis. Note that the definition of R is different in the US than other countries because of the unit differences.

Figure M: Unit Definitions.

Figure 1: Unit Definitions.

Determination of Constants

Figure 2 shows the constants that were used in this analysis and where they come from. I used a couple of web-based calculators to assist me. The image has embedded links that will allow you to access the calculators and the Wikipedia reference by clicking on them.

Figure M: Determination of HVAC Constants.

Figure 2: Determination of the Analysis Constants.

Humid Heat Specific Humidity Moist Air Density

Home Characteristics

Figure 3 shows the characteristics of an example house that I used to illustrate how the web-based calculator worked. My Mathcad model and the calculator both gave the same results.

Figure M: Energy Calculation.

Figure 3: Energy Usage Calculation.

Air Infiltration Degree-Days in MN

Costs and Graphical Results

Figure 4 shows how I determined the heating cost for a typical January in Minnesota. I used January-2014 as my temperature reference.

Figure M: Cost Calculation and Graphical Result.

Figure 4: Cost Calculation and Graphical Result.

Conclusion

I was able to generate a Mathcad model that I plan to extend for investigating other insulation and heating options for a cabin I will be building next year in northern Minnesota – a place where insulation and heating are extremely important.

Posted in Construction | 2 Comments

Rule of Thumb for Wood Shrinkage

Posted on 24-October-2014 by mathscinotes

Introduction

As winter comes, I often see homes where gaps develop in the wood flooring, molding, or ceilings (Figure 1) – things are drying out. While I have never actually spent any time investigating the mechanism of wood's movement or magnitude, I see its effects all the time.

Figure 1: Examples of Seasonal Wood Movement.
Ceiling Crown Door
Source Source Source

Recently, I read a forum discussion in Fine Homebuilding magazine that got me interested in working through a numerical example of wood movement. The article did a great job explaining how a wood floor can develop a "bump" in it (Figure 2, left) and the simple remedy of setting the joists a bit lower (Figure 2, right) to prevent the joist from poking through. This drawing explains the occasional bumps in flooring I have encountered in new homes (i.e. ones with LVL beams). The key issue is that engineered beams and standard dimensional lumber beams have different expansion/contraction characteristics – dimensional lumber moves much more.

Figure 2: Fine Homebuilding Explanation For a Seasonal Floor Bump and the Fix.
Bump Fix

My objective in this post is to understand how moisture affects wood, with respect to its physical dimensions. Whilst many have found that looking to check out the floor sanding and polishing options available by leading floor sanding companies on this page helps them keep this in check, there are other measures that should be considered long before this. Since I like to focus on a specific problem to drive my inquiry, I have decided to verify a rule of thumb from the Fine Homebuilding article mentioned above. The rule of thumb is:

By checking the moisture content of the lumber before it's installed, framers can predict the amount of movement that will occur across the grain of dimensional lumber. It's not an exact science, but a good rule of thumb is that if the moisture content of a board changes by 4%, the board will shrink across the grain by approximately 1% of its width. You may need termite control los angeles services called in as some people experience termites in their furniture if there is any water damage or if a large amount of moisture comes into contact. If you have water damage it is a good idea to contact a service like ServiceMaster Restoration by Zaba to help before the problem gets worse. And getting rid of the furniture is all well and good, but you want to stop this from affecting anything else within the house. This is why it may be best to look into something like Termite Control Kansas City to help return your property back to its original state. Tho/blockquote>
I will take a quick look at this rule of thumb and see if I can explain how it was derived. I also derive a relationship between two common formulas used to estimate the movement of wood and the coefficients used in these formulas for the different species.

Background

Some Definitions

Moisture In Wood

The following definitions all refer to Figure 3. The information here comes from this web page, which I strongly encourage you to visit.

Figure M: Section Drawing of Wood Structure.

Figure 3: Section Drawing of Wood Structure.

Bound Water
Water is this hydrogen bonded to the cellulose of the wood cells.
Free Water
The water filling the wood cell cavities. For more details on these cavities, refer to the Wikipedia on xylem and phloem.
Fiber Saturation Point (FSP)
The wood moisture content level at which all the free water is gone, but the bound water is still present. We usually assume that the number is 30%, but the number actually varies with temperature and species of tree. For example, the Wikipedia states that the FSP=0.30-0.001\cdot (T-20), where T is the wood temperature.
Moisture Content (MC)
The percentage of wood mass consisting of water. It is often measured in the field using electrical test equipment (example). In the lab, it can be measured using by measuring the mass of a test sample before and after drying and computing MC\triangleq \frac{{{m}_{water}}}{{{m}_{dry}}}=\frac{{{m}_{wet}}-{{m}_{dry}}}{{{m}_{dry}}}, where

  • mwater is the mass of water in the wood sample
  • mwet is the mass of the wood sample before drying
  • mdry is the mass of the dried wood sample.

Directions in Wood

Wood literally has a grain (aka growth ring) to it and the amount of movement varies with respect to the gain. Figure 4 illustrates the three directions in which wood's expansion are usually specified.

Figure M: Illustration of Moisture-Driven, Growth Directions (from J Gibson McIlvain).

Figure 4: Illustration of Moisture-Driven, Growth Directions (from J Gibson McIlvain).

Tangential Direction
Wood movement along the growth ring, which is the direction of greatest movement.
Radial Direction
Wood movement perpendicular to the growth rings. Expansion in this direction is often smaller than in the tangential direction by a factor of 2 to 5.
Longitudinal Direction
Wood movement parallel to the grain of the wood (i.e. up and down for a standing tree). This is usually a small number (0.1% to 0.3%) and often ignored (source).

Types of Lumber Cut

Figure 5 shows the best drawing I could find of the types of saw cuts and how they change dimensionally with moisture variation. You can see why the different cuts expand differently if you visualize the wood expanding the most in the direction along the grain. I do find it interesting that the quarter sawn wood expands in thickness rather than width – this explains why I have had better luck with it in certain applications than others with respect to expansion.

Figure M: Cut Types and How They Change Dimensionally.

Figure 5: Cut Types and How They Change Dimensionally (from Popular Woodworking).

Modeling Shrinkage

For modeling purposes, the relationship between MC and FSP controls how wood expands or contracts:

  • MC ? FSP, have no impact on the physical and mechanical properties of wood.

    The additional water is filling up the air voids within the wood and it is not causing any dimensional changes.

  • MC < FSP, does impact on the physical and mechanical properties of wood.

    The additional water is filling up the air voids within the wood and it is not causing any dimensional changes.

In actual fact, the transition is a bit more subtle than implied by this simple model. The following quote from Wood Handbook does a good job describing what happens. Note that the Wood Handbook uses MCfs instead of FSP for the Fiber Saturation Point.

Moisture can exist in wood as free water (liquid water or water vapor in cell lumina and cavities) or as bound water (held by intermolecular attraction within cell walls). The moisture content at which only the cell walls are completely saturated (all bound water) but no water exists in cell lumina is called the fiber saturation point, MCfs [FSP]. Operationally, the fiber saturation point is considered as that moisture content above which the physical and mechanical properties of wood do not change as a function of moisture content. The fiber saturation point of wood averages about 30% moisture content, but in individual species and individual pieces of wood it can vary by several percentage points from that value.

Conceptually, fiber saturation distinguishes between the two ways water is held in wood. However, in actuality, a more gradual transition occurs between bound and free water near the fiber saturation point. Within a piece of wood, in one portion all cell lumina may be empty and the cell walls partially dried, while in another part of the same piece, cell walls may be saturated and lumina partially or completely filled with water. Even within a single cell, the cell wall may begin to dry before all water has left the lumen of that same cell.

I should note that while I will focus in this post the on the dimensional changes in the width and thickness of a rectangular board, shrinkage can appear to change the angle of wood joints that are not 90°. This is because the width of wood along these joints vary, which means that the amount of shrinkage varies along the joint. See Appendix B for more details.

Analysis

Model

There are two equations that are commonly used to model the movement of wood as a function of moisture content. I will review them both here.

Equation 1 is used to model the dimensional changes when the wood's moisture content changes from 6% to 14%.

Eq. 1 \displaystyle \delta=\left\{ \begin{array}{*{35}{l}} {{D}_{I}}\cdot {{C}_{R}}\cdot \left( {{M}_{F}}-{{M}_{I}} \right) & \text{Tangential Direction} \\ {{D}_{I}}\cdot {{C}_{T}}\cdot \left( {{M}_{F}}-{{M}_{I}} \right) & \text{Radial Direction} \\ \end{array} \right.

where

  • ? is the change in dimension.
  • DI is the initial dimension.
  • CT is tangential change coefficient.
  • CR is radial change coefficient.
  • MF is the final moisture content (%).
  • MI is the initial moisture content (%).

For a more detailed discussion of Equation 1, see chapter 12 of the Wood Handbook (Equation 12-2). I am not going to spend much time analyzing this result because it is just a linear approximation – everything is linear if you restrict the dynamic range (i.e. range of application) sufficiently.

When the moisture change is outside the range of 6% to 14%, Equation 2 is used.

Eq. 2 \displaystyle \delta =\frac{{{D}_{I}}\cdot \left( {{M}_{F}}-{{M}_{I}} \right)}{\frac{30\cdot 100}{{{S}_{T or R}}}-30+{{M}_{I}}}

where

For a derivation of Equation 2, see Appendix A. I have not seen many examples of Equation 2 being used by woodworking practitioners. I cover it here because it is mentioned in the Wood Handbook, but most examples use Equation 1. I assume this is true because most wood is used in applications where its moisture content does not vary outside the range of 6 % to 14 %.

While Equations 1 and 2 use different sets of coefficients, it turns out that there is a relationship between these coefficients for many species (I have not checked them all out). Appendix C goes into the gory details.

Rule of Thumb Verification

I am going to make the following assumptions:

  • The rule of thumb uses Equation 1 because it is applicable to the typical range for the MC of wood under normal conditions.
  • The rule of thumb will use the tangential change coefficient CT because it is the largest coefficient, which means that the rule of thumb gives a worst-case estimate of the dimensional change.

To verify the rule of thumb, I will work with the mean of all the CT data from the Wood Handbook. Figure 6 shows my analysis.

Figure 1: Verification of the Rule of Thumb.

Figure 1: Verification of the Rule of Thumb.

Conclusion

I was able to verify the rule of thumb mentioned in the Fine Homebuilding forum discussion. This give me a pretty good idea as to how to determine the potential impact of moisture variations on my carpentry projects, especially molding.

Appendix A: Derivation of Equation 2.

I always find formulas expressed like Equation 2 confusing because it is not obvious (at least to me) where they come from. I thought I would play with Equation 2 a bit and figure out where it came from. Here is what I found.

  • Unlike Equation 1, Equation 2 is based on coefficients (ST : tangential coefficient, SR : radial coefficient) that represent the percentage length difference between green wood (30% moisture) and oven-dried wood (0% moisture).
  • Equation 2 is based on the following linear approximation: L\% = S_{R/T} \cdot \left(\frac{30-M}{30}\right), where M is the moisture percentage, "30" represents the assumed moisture content of green wood (30%), and L% is the percentage change in length. This is Equation 3-4 in the Wood Handbook.

Figure 7 shows my derivation of Equation 2.

Figure 7: Derivation of Equation 2.

Figure 7: Derivation of Equation 2.

Appendix B: Why Are There Gaps in Molding During the Winter?

Figure 8 shows a figure I have modified from Gary Katz that I have annotated to suit my needs here.

Figure M: Inside Corner Gap.

Figure 8: Inside Corner Gap.

You force the joint to stay together by using biscuits, splines, or dowels. Figure 9 shows an example from Craftsmanspace.

Figure M: Spline Example.

Figure 9: Spline Example.

Appendix C: Relationship Between S and C Coefficients

The fact that two tables of coefficients are specified bothers me – they should be related somehow. As it turn out, the coefficients are related. See Figure 10 for a demonstration.

Figure 10: Relationship Between S and C Coefficients.

Figure 10: Relationship Between S and C Coefficients.

Posted in Construction | Comments Off on Rule of Thumb for Wood Shrinkage

Frogs Love Fiber Optics -- At Least in the Winter

Posted on 24-October-2014 by mathscinotes

I was doing some installation inspections when we disturbed the following creatures in two different fiber optic enclosures. Winter is coming and everyone wants to find a nice, warm place to wait it out.

Frog1 Frog2
plains leopard frog tree frog
Posted in Fiber Optics, Humor | Comments Off on Frogs Love Fiber Optics -- At Least in the Winter