Near-Earth Asteroid Size Estimate Example


Quote of the Day

Knowledge consists in the search for truth ... it is not in the search for certainty.

Karl Popper. I have always found his work on the philosophy of science interesting. He is best known for his belief that scientific concepts must be falsifiable.

Figure 1: Deceptive Image of an Asteroid Passing Extremely Close to the Earth. (USA Today)

Figure 1: Deceptive Image of an Asteroid
Passing Extremely Close to the Earth.
(USA Today)

Newspapers often talk about Near-Earth Objects (NEOs) that are passing "close" to the Earth. To increase the number of clicks, the articles usually include an image implying that the NEO is very close to the Earth. I find these articles a bit irritating.

This morning at 2:53AM Eastern Standard Time, asteroid 2017 VR12 had its closest point of approach to Earth, which was ~4x the distance from the Earth-to-Moon. It is not considered an impact threat. USA Today published an article that included Figure 1, which implies a very close pass. That is simply not correct.

To give you some perspective, let's examine Figure 2, which is a picture of the Earth-Moon system as seen by an asteroid-sampling spacecraft called OSIRIS-REx.

Figure 1: Earth-Moon System.

Figure 2: Earth-Moon System from 3 million miles away. The Moon is 60 Earth radii distant from the Earth. Asteroid 2017 VR12 is ~4x this distance from the Earth at its closest point. (NASA)

The article also mentioned that the asteroid "could be as big as Empire State Building". I thought I would show how you can do that calculation for yourself (Figure 3). The Empire State Building is 443.2 meters tall, which is roughly the maximum equivalent spherical diameter  of 2017 VR12. The uncertainty in size is large because the albedo of asteroids is so variable.

Figure 3: Calculations That Show 2017 VR Could Have an Equivalent Radius Similar to the Empire State Building.

Figure 3: Calculations That Show 2017 VR Could Have an Equivalent Radius Similar to the Empire State Building.

US Today Article Minor Planet Data University of Iowa Astronomical Symbols Table of Asteroid Sizes
Posted in Astronomy | Leave a comment

Cabin Is Complete


Quote of the Day

The young man knows the rules but the old man knows the exceptions.

— Oliver Wendell Holmes Jr.

Figure 1: View of My Cabin as I Walk From My Garage.

Figure 1: View of My Cabin as I Walk From My Garage.

My cabin construction project is now complete. My wife and I are now beginning to furnish our new home, which will take some time. I continue to work on the garage construction myself, which will take until sometime in May to finish. Overall, our planning was good and there were no major surprises. The one area of difficulty that I did not fully appreciate is the remoteness of the site. Before you go to the site, you need to plan out every possible tool or part that you will need while there.

This is a huge, multi-year project that I am relieved to say the house portion is complete – the garage still needs a bit of work. My plan is to retire at this site in 5 to 10 years and spend my time designing hardware, writing software, and building furniture. I hope that my granddaughter will get to spend quite a bit of time here with her grandparents.

Some basic home details:

  • 2100 square feet
  • 2 floors
  • 3 bedrooms
  • 2 bathrooms
  • no basement, concrete slab on ground with in-floor heating
  • insulated with closed-cell foam
  • heated with propane (the only form of fuel that I could get locally)
  • designed for handicapped access (I want to live there when I am old)
    My wife and I can live on the ground floor and have our guests stay on the upper floor.

Some additional photos.

Figure 2: House View From Driveway.
Figure 3: Kitchen View.
Figure 4: Living Room View.
Figure 5: Master Bedroom (2nd Floor).
Figure 6: View of Stairway and 2nd Floor Hall (Bedroom on Left).
Figure 7: Handicap Access Shower (1st floor).
Figure 8: Living Room Fireplace.
Figure 9: Second View of Master Bedroom (2nd floor).


Posted in Construction, Personal | 10 Comments

Minnesotans In the Olympics


Quote of the Day

Yes, I should have given more praise.

Sir Winston Churchill, quoting the reply of the then elderly Duke of Wellington when a friend asked him, 'If you had your life over again, is there any way in which you could have done better?'

Figure 1: People Curling in Northern Minnesota. (Source)

Figure 1: People Curling in Northern Minnesota. (Source)

I spend a lot of time in northern Minnesota now that I have a home there. I have been surprised as to how popular curling is in the area (Figure 1). The US curling team at the 2018 Olympics is dominated by people from northern Minnesota. I also notice that there are quite a few Minnesotans participating in the games' other sports – the numbers are large enough that the New York Times has even written an article called "Team USA? More Like Team Minnesota" on the topic (PDF of the article). Our state does not have a huge population, ~5 million, and most of that population is concentrated around Minneapolis and St. Paul. The northern part of the state is only sparsely populated as it is covered with national forests and wilderness areas.

To understand the participation of Minnesotans in the Olympics, I grabbed an Excel file from the US Winter Olympic Team web site  and generated a couple of pivot tables, which I show below. My workbook is include here.

Figure 2: Top Ten Home States for US Olympic Athletes.

Figure 2: Top Ten Home States for US Olympic Athletes.

California contributes the most athletes to this year's Olympic team, followed by Colorado and Minnesota (Figure 2). Since Minnesota has no mountains, alpine events are not our strength – though Lindsey Vonn is from St. Paul and first skied here at Buck Hill.

The big snow sports here are hockey, cross-country skiing, and curling. You see this reflected in the athletes we send to the Olympics (Figure 3). Biathlon is a combination of cross-country skiing and shooting, which are two common passions here.

At this point, the Minnesota athletes have brought home medals in curling, hockey, and cross-country.

Figure 3: Minnesota Participation in Olympic Sports.

Figure 3: Minnesota Participation in Olympic Sports.

For my family, skating and hockey became a passion first for my children and then for me – this is the reverse for most families. My dad was a hockey player and ice dancer, but I never had any interest early on in either sport. My children saw the movie The Mighty Ducks, and they became driven to skate. I learned to skate and play hockey on the kiddie ponds next to the rinks where my children were practicing.

Table of Athletes

I included a subset of the Olympic spreadsheet here for any general searching that I want to do.

First NameLast NameGenderDisciplineAge (As of 2/8/18)HometownHome State
StaceyCookFAlpine Skiing33Mammoth LakesCalif.
BreezyJohnsonFAlpine Skiing22Jackson Wyo.
Tricia ManganFAlpine Skiing20BuffaloN.Y.
MeganMcJamesFAlpine Skiing30Park CityUtah
AliceMcKennisFAlpine Skiing28New CastleColo.
AliceMerryweatherFAlpine Skiing28HinghamMass.
LaurenneRossFAlpine Skiing29BendOre.
MikaelaShiffrinFAlpine Skiing22Eagle-VailColo.
ResiStieglerFAlpine Skiing32Jackson Wyo.
LindseyVonnFAlpine Skiing33VailColo.
JacquelineWilesFAlpine Skiing25PortlandOre.
BryceBennettMAlpine Skiing25Tahoe CityCalif.
TommyBiesemeyerMAlpine Skiing29KeeneN.Y.
DavidChodounskyMAlpine Skiing33Crested ButteColo.
RyanCochran-SiegleMAlpine Skiing25StarksboroVt.
MarkEngelMAlpine Skiing26TruckeeCalif.
TommyFordMAlpine Skiing28BendOre.
JaredGoldbergMAlpine Skiing26Salt Lake CityUtah
TimJitloffMAlpine Skiing33RenoNev.
NolanKasperMAlpine Skiing28WarrenVt.
TedLigetyMAlpine Skiing33Park CityUtah
WileyMapleMAlpine Skiing27AspenColo.
StevenNymanMAlpine Skiing36SundanceUtah
AndrewWeibrechtMAlpine Skiing32Lake PlacidN.Y.
ClareEganFBiathlon30Cape ElizabethMaine
MaddiePhaneufFBiathlon22Old ForgeN.Y.
LowellBaileyMBiathlon36Lake PlacidN.Y.
TimBurkeMBiathlon36Lake PlacidN.Y.
SeanDohertyMBiathlon22Center ConwayN.H.
LeifNordgrenMBiathlon28Marine Minn.
LaurenGibbsFBobsled33Denver Colo.
JamieGreubel PoserFBobsled34NewtownPa.
ElanaMeyers TaylorFBobsled33DouglasvilleGa.
JustinOlsenMBobsled30San AntonioTexas
CarloValdesMBobsled28Newport BeachCalif.
NathanWeberMBobsled31Pueblo WestColo.
EvanWeinstockMBobsled26Las VegasNev.
SadieBjornsenFCross-Country Skiing28WinthropWash.
RosieBrennanFCross-Country Skiing29AnchorageAlaska
SophieCaldwellFCross-Country Skiing27PeruVt.
JessieDigginsFCross-Country Skiing26AftonMinn.
RosieFrankowskiFCross-Country Skiing26MinneapolisMinn.
AnnieHartFCross-Country Skiing25StillwaterMinn.
KaitlynnMillerFCross-Country Skiing26ElmoreVt.
CaitlinPattersonFCross-Country Skiing28CraftsburyVt.
KikkanRandallFCross-Country Skiing35AnchorageAlaska
IdaSargentFCross-Country Skiing30CraftsburyVt.
LizStephenFCross-Country Skiing31East MontpelierVt.
ErikBjornsenMCross-Country Skiing26WinthropWash.
PatrickCaldwellMCross-Country Skiing23LymeN.H.
SimiHamiltonMCross-Country Skiing30AspenColo.
LoganHannemanMCross-Country Skiing24FairbanksAlaska
ReeseHannemanMCross-Country Skiing28FairbanksAlaska
NoahHoffmanMCross-Country Skiing28AspenColo.
TylerKornfieldMCross-Country Skiing27AnchorageAlaska
AndyNewellMCross-Country Skiing34ShaftsburyVt.
ScottPattersonMCross-Country Skiing26CraftsburyVt.
KarenChenFFigure Skating18FremontCalif.
MadisonChockFFigure Skating25Redondo BeachCalif.
MadisonHubbellFFigure Skating26SylvaniaOhio
MiraiNagasuFFigure Skating24ArcadiaCalif.
AlexaScimeca KnierimFFigure Skating26AddisonIll.
MaiaShibutaniFFigure Skating23Ann ArborMich.
BradieTennellFFigure Skating20CarpentersvilleIll.
EvanBatesMFigure Skating28Ann ArborMich.
NathanChenMFigure Skating18Salt Lake CityUtah
ZacharyDonohueMFigure Skating27MadisonConn.
ChrisKnierimMFigure Skating30San Diego Calif.
AdamRipponMFigure Skating28Los AngelesCalif.
AlexShibutaniMFigure Skating26Ann ArborMich.
VincentZhouMFigure Skating17Palo AltoCalif.
MaddieBowmanFFreestyle Skiing24South Lake TahoeCalif.
AshleyCaldwellFFreestyle Skiing24AshburnVa.
CarolineClaireFFreestyle Skiing18Manchester CenterVt.
AnnalisaDrewFFreestyle Skiing24AndoverMass.
TessJohnsonFFreestyle Skiing17VailColo.
JaelinKaufFFreestyle Skiing21AltaWyo.
DevinLoganFFreestyle Skiing24West DoverVt.
KeatonMcCargoFFreestyle Skiing22TellurideColo.
KileyMcKinnonFFreestyle Skiing22MadisonConn.
MadisonOlsenFFreestyle Skiing22Park CityUtah
MorganSchildFFreestyle Skiing20PittsfordN.Y.
BritaSigourneyFFreestyle Skiing28CarmelCalif.
DarianStevensFFreestyle Skiing21MissoulaMont.
MaggieVoisinFFreestyle Skiing19WhitefishMont.
CaseyAndringaMFreestyle Skiing22BoulderColo.
AaronBlunckMFreestyle Skiing21Crested ButteColo.
MacBohonnonMFreestyle Skiing22MadisonConn.
AlexFerreiraMFreestyle Skiing23AspenColo.
NickGoepperMFreestyle Skiing23LawrenceburgInd.
AlexHallMFreestyle Skiing19Park CityUtah
GusKenworthyMFreestyle Skiing26TellurideColo.
JonLillisMFreestyle Skiing23RochesterN.Y.
EricLoughranMFreestyle Skiing22PelhamN.H.
TroyMurphyMFreestyle Skiing25BethelMaine
EmersonSmithMFreestyle Skiing21DoverVt.
McRaeWilliamsMFreestyle Skiing27Park CityUtah
BradleyWilsonMFreestyle Skiing25ButteMont.
DavidWiseMFreestyle Skiing27RenoNev.
TorinYater-WallaceMFreestyle Skiing22BasaltColo.
CaylaBarnesFIce Hockey19EastvaleCalif.
KaliFlanaganFIce Hockey22BurlingtonMass.
HaleySkarupaFIce Hockey24Rockville Md.
MeganKellerFIce Hockey21FarmingtonMich.
EmilyPfalzerFIce Hockey24BuffaloN.Y.
NicoleHensleyFIce Hockey23LakewoodColo.
KendallCoyneFIce Hockey25Palos HeightsIll.
HannahBrandtFIce Hockey24Vadnais HeightsMinn.
DaniCameranesiFIce Hockey22PlymouthMinn.
KellyPannekFIce Hockey22PlymouthMinn.
LeeSteckleinFIce Hockey23RosevilleMinn.
AmandaKesselFIce Hockey26MadisonWis.
GigiMarvinFIce Hockey30WarroadMinn.
SidneyMorinFIce Hockey22MinnetonkaMinn.
MaddieRooneyFIce Hockey20AndoverMinn.
KaceyBellamyFIce Hockey30WestfieldMass.
JocelyneLamoureux-DavidsonFIce Hockey28Grand ForksN.D.
MoniqueLamoureux-MorandoFIce Hockey28Grand ForksN.D.
AmandaPelkeyFIce Hockey24MontpelierVt.
HilaryKnightFIce Hockey28Sun ValleyIdaho
MeghanDugganFIce Hockey30DanversMass.
BriannaDeckerFIce Hockey26DousmanWis.
AlexRigsbyFIce Hockey26DelafieldWis.
BrianGiontaMIce Hockey39RochesterN.Y.
ChrisBourqueMIce Hockey32North ReadingMass.
MattGilroyMIce Hockey33BellmoreN.Y.
JordanGreenwayMIce Hockey20CantonN.Y.
JohnMcCarthyMIce Hockey31Boston Mass.
JamesWisniewskiMIce Hockey33CantonMich.
DavidLeggioMIce Hockey33BuffaloN.Y.
ChadBillinsMIce Hockey28MarysvilleMich.
RyanDonatoMIce Hockey21ScituateMass.
NoahWelchMIce Hockey35BrightonMass.
RyanZapolskiMIce Hockey31EriePa.
JimSlaterMIce Hockey35LapeerMich.
BrandonMaxwellMIce Hockey26Winter ParkFla.
WillBorgenMIce Hockey21MoorheadMinn.
GarrettRoeMIce Hockey29ViennaVa.
BobbySanguinettiMIce Hockey29WilmingtonN.C.
JonathanBlumMIce Hockey29Ladera RanchCalif.
TroyTerryMIce Hockey20Highlands RanchColo.
ChadKolarikMIce Hockey32AbingtonPa.
RyanStoaMIce Hockey30BloomingtonMinn.
BobbyButlerMIce Hockey30MarlboroughMass.
RyanGundersonMIce Hockey32BensalemPa.
MarkArcobelloMIce Hockey29MilfordConn.
BrocLittleMIce Hockey29RindgeN.H.
BrianO'NeillMIce Hockey29YardleyPa.
SummerBritcherFLuge23Glen RockPa.
ChrisMazdzerMLuge29Saranac LakeN.Y.
TaylorMorrisMLuge26Salt Lake City Utah
MattMortensenMLuge32Huntington StationN.Y.
AndrewSherkMLuge25Fort WashingtonPa.
BenBerendMNordic Combined22Steamboat SpringsColo.
TaylorFletcherMNordic Combined27Steamboat SpringsColo.
BryanFletcherMNordic Combined31Steamboat SpringsColo.
JasperGoodMNordic Combined21Steamboat SpringsColo.
BenLoomisMNordic Combined19Eau ClaireWis.
MattAntoineMSkeleton32Prairie du ChienWis.
NitaEnglundFSki Jumping25FlorenceWis.
SarahHendricksonFSki Jumping23Park CityUtah
AbbyRingquistFSki Jumping28Park CityUtah
KevinBicknerMSki Jumping21WaucondaIll.
MichaelGlasderMSki Jumping28CaryIll.
CaseyLarsonMSki Jumping19BarringtonIll.
WillRhoadsMSki Jumping22Park CityUtah
JamieAndersonFSnowboarding27South Lake TahoeCalif.
KellyClarkFSnowboarding34Mammoth LakesCalif.
ArielleGoldFSnowboarding21Steamboat SpringsColo.
FayeGuliniFSnowboarding25Salt Lake CityUtah
HaileyLanglandFSnowboarding17San ClementeCalif.
NickBaumgartnerMSnowboarding36Iron RiverMich.
MickDierdorffMSnowboarding26Steamboat SpringsColo.
KyleMackMSnowboarding20West BloomfieldMich.
MikeTrappMSnowboarding29Marstons MillsMass.
HeatherBergsmaFLong Track Speedskating28High PointN.C.
BrittanyBoweFLong Track Speedskating29OcalaFla.
ErinJacksonFLong Track Speedskating25OcalaFla.
MiaManganelloFLong Track Speedskating28CrestviewFla.
CarlijnSchoutensFLong Track Speedskating23West JordanUtah
JericaTandimanFLong Track Speedskating23KearnsUtah
ShaniDavisMLong Track Speedskating35ChicagoIll.
JonathanGarciaMLong Track Speedskating31HoustonTexas
KimaniGriffinMLong Track Speedskating27Winston SalemN.C.
BrianHansenMLong Track Speedskating27GlenviewIll.
EmeryLehmanMLong Track Speedskating21Oak ParkIll.
JoeyMantiaMLong Track Speedskating32OcalaFla.
MitchWhitmoreMLong Track Speedskating28WaukeshaWis.
MaameBineyFShort Track Speedskating18RestonVa.
LanaGehringFShort Track Speedskating27GlenviewIll.
JessicaKooremanFShort Track Speedskating34MelvindaleMich.
J.R.CelskiMShort Track Speedskating27Federal WayWash.
ThomasHongMShort Track Speedskating20LaurelMd.
John-HenryKruegerMShort Track Speedskating22PittsburghPa.
RyanPivirottoMShort Track Speedskating22Ann ArborMich.
AaronTranMShort Track Speedskating21Federal WayWash.
Posted in Excel, Statistics | Leave a comment

Time for a Job Change


Quote of the Day

Be kind whenever possible. It is always possible.

— Dalai Lama

Figure 1: I have decided that it is time for a new job. (Source)

Figure 1: I have decided that it is
time for a new job.

My company is changing its approach to hardware development, and after much soul-searching, I have decided to volunteer for layoff. I do not have any immediate plans – it is just time for a change. I will continue to write on technical topics because math, electronics, and software are in my blood.

I fell in love with electronics when I was five-years-old after my neighbor showed me a schematic. I thought it was some weird language that I needed to figure out. My first projects involved building kits from Radio Shack, Heathkit, and Lafayette Radio that I paid for using my income as a paperboy. I also started doing circuit-based science fair projects. It all culminated with me studying electrical engineering and working in this field for my entire career. Even after these many years, my passion for technology of all sorts continues unabated.

If you know of any jobs that would be appropriate for someone like me, please leave me a note here or on my linkedin page. My wife's job is covering my benefits, so either a contract or employee position would work.

Figure 2: Interociter schematic from the movie This Island Earth. This schematic also interested me as aboy. I loved that movie. (Source)

Figure 2: Interociter schematic from the movie This
Island Earth
. This schematic also interested me as a
boy. I loved that movie. (Source)

Posted in Personal | 4 Comments

Smallest Rocket to Put Payload Into Earth Orbit


Quote of the Day

Our educational system is like an automobile which has strong rear lights, brightly illuminating the past. But looking forward, things are barely discernible.

Hermann Oberth, German rocket theoretician, describing the German education system in the 1920s. He was bitter because his doctoral thesis on rocket propulsion was deemed utopian. His work became the basis of all spaceflight today. In my opinion, his criticism of the German educational system could be applied to the US education system today.

Figure 1: Japan's SS-520 rocket. It is reported to be the smallest rocket capable of putting a payload into orbit. (Source)

Figure 1: Japan's SS-520 rocket. It is reported to
be the smallest rocket capable of putting a
payload into orbit. (Source)

I just read a news article about Japan launching a 3 kg satellite into orbit using a 9.7-meter-long, two-stage rocket called the SS-520 (Figure 1). The 9.7 meter length was interesting to me because I recalled an Air & Space magazine article from 1999 that stated that the smallest rocket capable of achieving Earth orbit would be "about 30 feet long." Since 9.7 meters is 31.8 feet long, it appears that Japan's SS-520 is very near the lower size limit for rocket that can put an object into Earth orbit.

The size limit for an orbital rocket is driven by the amount of momentum lost because of atmospheric drag. As with artillery projectiles, larger rockets are more efficient in retaining momentum against drag. For a given shape, larger rockets are more aerodynamically efficient because frontal area increases by the square of the linear dimensions and volume (and mass) scales by the cube of the linear dimensions (see this detailed discussion). Drag is a function of the frontal area of the rocket, thus larger rockets have more mass (and momentum) relative to their drag. Another challenge with implementing a small launch vehicle is the difficulty of efficiently implementing a high specific impulse, liquid-fuel system because of the overhead of all the pumps, plumbing, and cooling.

Because I am still tied up with my cabin project, I have not gone through the minimum-sized orbital rocket calculations myself. Air & Space magazine states that:

A terrestrial rocket has to push through a plug of air equivalent to a 30-foot column of water, and physics dictates that the smallest vehicle capable of moving all that atmospheric mass without paying a penalty in momentum is about 30 feet long.

Historically, the orbital launch market has been dominate by customers who want to put large payloads into space. The advent of CubeSats has created a market for these small rockets. For example, a company called  Rocket Lab uses their Electron rocket to launch small groups of CubeSats.

NASA has been researching the smallest rocket that can return a sample from Mars to Earth. According the Air & Space magazine article, the smallest orbital rocket is "about the size of a pencil" for essentially zero payload. NASA's Mars return mission is targeting a 1 pound payload and the mass is about 170 kg. Having lower gravity and a much thinner atmosphere make the job of getting into Mars orbit much easier than getting into Earth orbit.

People have been discussing these small rockets for many years. In fact, people have tried to motivate innovation in this area with the N-Prize, which is focused on putting a small payload (10 - 20 grams) into Earth orbit for less than 1000 £ . For an excellent discussion on micro-rocketry, see this forum thread. The following Google talk on microlaunchers is also useful.

Figure 2: Microlaunchers – The Case for a New Generation of Very Small Spacecraft.
Posted in Astronomy, Space | 4 Comments

Electrical Conduit Math


Quote of the Day

A leader is a dealer in hope.

— Napoleon Bonaparte

Figure 2: My Garage at Night.

Figure 1: My Garage at Night.

As I have mentioned in other posts, I am building a large garage in northern Minnesota (Figure 1). I would show you some pictures of the interior, but I have promised my son that I will not post anything that could ruin his surprise when he sees it in April. As part of this construction effort, I am using quite a bit of electrical conduit. Conduit consists of metal pipes (often called EMT) through which the wires pass and it must be bent to go around any barriers it encounters. Conduit is a very efficient way to wire a working area because it directly attaches to the wall and does not require opening holes in drywall and repairing the damage. Conduit can also be updated and modified easily by running new/additional wires through it.

Figure 1: 4 Point Saddle Bend Around An Obstacle.

Figure 2: 4-Point Saddle Bend Around An
Obstacle. (Source)

I am going to review the process for running conduit around an obstacle using a 4-point saddle bend, which entails bending the conduit into a trapezoidal shape for passing around the obstacle (Figure 1). Electrical handbooks contain tables that tell electricians how to measure along the conduit so that the bend will go around an object of a given depth. In this post, I will provide simple formulas for this bend and will use these formulas to regenerate a commonly seen table for conduit bending.

For those who like to follow along, my worksheet is here.


Reference Article

In this post, I will duplicate a conduit bending table that I saw in this excellent reference article. The table is shown in Figure 3, which has units of degrees for angles and inches for length.

Figure 4: Bend Table That I will Duplicate in Excel.

Figure 3: Bend Table That I will Duplicate in Excel.

Conduit Bending Video

Figure 4 shows a conduit bending video by a local trade school (Dunwoody) that I think is first-rate. The instructor covers both 4-point (trapezoid) and 3-point (triangular) bends. My focus in this post is the 4-point saddle bend because that is what I am dealing with in my garage construction right now.

Figure 4: Good Briefing on 3-Point and 4-Point Saddle Bends.

Conduit Bending Formulas

Conduit Bending Formulas Ignoring Bend Radius

There are two formulas that I need to generate: (1) shrinkage, which is the reduction in horizontal length caused by the bend; (2) bend distance, which is the horizontal length of the bend region. Figure 5 illustrates the geometry of the situation.

 Figure 5: Key Conduit Bending Formulas.

Figure 5: Key Conduit Bending Formulas Ignoring Bend Radius.

Applying basic trigonometry to Figure 5, we can derive Equations 1 and 2.

Eq. 1 \displaystyle \text{BD }=\text{BO}\cdot \text{cot}\left( \theta \right)
Eq. 2 \displaystyle \text{S}=\text{BO}\cdot \text{tan}\left( {\frac{\theta }{2}} \right)


    • BD, Bend Distance is the horizontal distance between bends.
    • BO, Bend Offset is the depth of the obstacle to be passed over.
    • Θ is the angle of the bend.
    • S, Shrinkage is the effective reduction in horizontal conduit length because of the bend. Essentially, it is the difference in length between the hypotenuse and the base of a triangle.

I will use these equations to generate the table shown in Figure 3.

Conduit Bending Formulas Compensating for Bend Radius

Again, there are two formulas that I need to generate: shrinkage (Equation 3) and bend distance (Equation 5). An additional formula for the straight pipe length is also provided (Equation 4). Figure 6 illustrates the geometry of the situation and the associated formulas. The radius of the conduit bender, called R, will vary for each conduit bender. It normally is stamped on the bender, or the information is available in the vendor's literature.

Figure 6: Key Conduit Bending Formulas (Compensating for Bend Radius).

Figure 6: Key Conduit Bending Formulas (Compensating for Bend Radius).

Applying basic trigonometry to Figure 5, we can derive Equations 3, 4, and 5. Note that BD is defined slightly differently in that it represents the center-to-center distance between the bends.

Eq. 3 \displaystyle S\text{ = }CL-HL=\left( {BO-4\cdot R} \right)\cdot tan\left( {\frac{\theta }{2}} \right)+2\cdot R\cdot \theta
Eq. 4 \displaystyle SL=\left[ {BO-2\cdot R\cdot \left( {1-cos\left( \theta \right)} \right)} \right]\cdot \csc \left( \theta \right)
Eq. 5 \displaystyle BD=R\cdot \theta +\left[ {BO-2\cdot R\cdot \left( {1-cos\left( \theta \right)} \right)} \right]\cdot \csc \left( \theta \right)

Equations 3 - 5 are functions of the bend radius of the conduit bender. Because conduit benders can have different bend radii (see Figure 7), this means that using a single table for all conduit benders may result in some error – particularly for large bend offsets. Ideally, we would build a table for the conduit bender being used. I include this table with bend radius as a parameter on a worksheet in the Excel workbook associated with this post.

Figure 7(a): Klein™ Conduit Bender with a 4" Bend Radius. Figure 7(b): Ideal™ Conduit Bender with a 5.25" Bend Radius.



My focus here is on generating the traditional conduit bend table. In my workbook, I also include a tool using a more exact model.

There are a number of ways I could generate this table using Excel. The approach I chose was to:

  • Generate a table of values for bend offsets of 1 inch. I call this my "reference table" because it is used for all subsequent calculations.
  • Generate separate tables of shrinkage and bend distances.
  • Collate shrinkage and bend distance columns by bend angle (Θ).

I chose this approach because I wanted to experiment with arranging columns by using a helper row containing the ordinal number of each column and doing a horizontal sort.

For demonstration purposes, I also included a tab where I used formulas to fill down the columns. A third tab was includes the conduit bender radius as a parameter.

Reference Table

Figure 8 shows the shrinkage and bend distance formulas evaluated for a 1-inch bend offset (i.e. obstacle height), rounded to the nearest 1/16th of an inch. These values can be used as scale factors for other obstacle heights, which is exactly how the table in Figure 3 was generated.

Figure 6: Reference Bend Table.

Figure 8: Reference Bend Table.

Full Table Generation

The table shown in Figure 3 is generated by multiplying the bend offsets by the scale factors in Figure 9. I used Excel tables to perform this action.

Figure 7: My Excel Version of the Conduit Bend Table.

Figure 9: My Excel Version of the Conduit Bend Table.


I was able to duplicate the original table. I will be using this table for some conduit bending this weekend.

Posted in Construction | 2 Comments

Minor Planet Eccentricity versus Perihelion Chart


Quote of the Day

Einstein repeatedly argued that there must be simplified explanations of nature, because God is not capricious or arbitrary. No such faith comforts the software engineer…

— Frederick P. Brooks Jr., The Mythical Man-Month– Essays on Software Engineering

Figure 1: Interesting Graph Showing Minor Planet Eccentricities Versus Perihelion Distance. (Source)

Figure 1: Interesting Graph Showing
Minor Planet Eccentricities Versus
Perihelion Distance. (Source)

The amount of information being gathered in recent years on objects in the outer solar system is amazing. Think about what has happened in recent years:

  • The New Horizons probe visited Pluto.
  • Many new bodies have been discovered that both bigger and further out than Pluto (example).
  • Strong evidence has been found for a large body in the outer solar system.
  • The New Horizons probe has been directed to a recently discovered body (2014 MU69) that may consist of two bodies in very close proximity.

While searching the web for information on the outer solar system, I encountered the graph shown in Figure 1. This graph is made using eccentricity and perihelion data for ~1000 outer solar system objects. As I looked at it, I though I could generate a similar chart using data from the JPL Small Body Database Search Engine – a wonderful tool for solar system data exploration efforts.

I used the JPL search engine to download a list of all outer solar system asteroids and trans-Neptunian objects, which provided me 25K data points to plot (search setup). I then used Power Query and Excel to plot the data in Figure 2. Clearly, Sedna and 2012 VP113 are outliers in the data set. For reference purposes, I also included the same points for Pluto, Neptune, and Uranus.

Figure 2: My Version of Figure 1.

Figure 2: My Version of Figure 1.

For those who are interested in duplicating this work, my workbook and data file are included here.

Posted in Astronomy, Excel | 1 Comment

A Funny Stock Photo Error


Quote of the Day

He respectfully requests six Cleveland Browns pall bearers so the Browns can let him down one last time

— Obituary of a Cleveland Browns fan

Figure 1: No Way to Hold a Hot Soldering Iron.

Figure 1: No Way to Hold a Hot Soldering Iron.

We have been laughing at some stock photos of people soldering. An engineer was looking for a stock photo of a person soldering, so she went out to Shutterstock to find something. The first photo she found was Figure 1, which she immediately passed around to the group. It turns out that she found a number of photos that were equally bad. Apparently, a lot of people have never soldered. I was raised with a soldering iron in my hand, so I was a bit stunned to see this.

She also found a T-shirt that showed how you should hold a soldering iron (Figure 2).  If you want to buy this T-shirt, you can find it on Amazon.

Figure 2: Soldering on a T-Shirt.

Figure 2: Soldering on a T-Shirt.


Posted in Humor | 1 Comment

Using Excel to View US Pre-School Attendance Rate


Quote of the Day

We see a lot of feature-driven product design in which the cost of features is not properly accounted. Features can have a negative value to customers because they make the products more difficult to understand and use. We are finding that people like products that just work. It turns out that designs that just work are much harder to produce than designs that assemble long lists of features.

Douglas Crockford, author of JavaScript: The Good Parts. I encounter many marketing people who view product definition as the mere listing of features. In reality, there is a balance that must be achieved.

Figure 1: Graph Being Discussed by Jeffery Sachs. (Source)

Figure 1: Graph Being Discussed by Jeffery Sachs. (Source)

Jeffrey Sachs was on CSPAN this weekend giving a talk on the competitive challenges the US faces with other nations. During his presentation, he showed a chart (Figure 1) that ranks the US as 30th among reporting OECD countries with respect to preschool participation rates for 4-year-old children. The discussion was interesting, but I found myself focusing on the technical aspects of the graphs he was using. I am always looking for good Excel examples for use in training my staff, and the y-axis in Figure 1 contains formatted text, which is something I have not shown my staff how to do.

Figure 2: My Excel Version of Figure 1.

Figure 2: My Excel Version of Figure 1.

In Figure 2, I show how my duplication of Figure 1 using Excel. For those who like to follow along, my workbook is here. To highlight the formatting of the y-axis, I used green and red colors instead of bold font.

My process was straightforward:

  • Use Power Query to grab the data from this web site.
  • Generate a bar chart.
  • Use the method of Jon Peltier to format the y-axis.

While this is not a sophisticated chart, it does provide an end-to-end example of web scraping and charting.

Posted in Excel | Leave a comment

Dealing with Furnace Condensate At Low Temperatures


Quote of the Day

If all printers were determined not to print anything till they were sure it would offend nobody, there would be very little printed.

— Benjamin Franklin


Figure 1: A Typical Condensate Pump. (Source)

Figure 1: A Typical Condensate Pump. (Source)

While working on my retirement home and workshop in northern Minnesota, I have noticed that my furnace is generating between five and seven gallons of condensate per day. The furnace is on quite often this time of year because the outside temperature is running about -30°F (-35°C). I currently pipe the condensate over to a floor drain, which is connected to my septic system.

I mentioned the amount of condensate to my General Contractor (GC), and he said that this condensate can be an issue with a septic system in a cold climate because septic systems work best when they receive significant amounts of water flow. He said that he trickle of water can create a blockage if the flow is so low that it can freeze. Frozen pipes mean broken/blocked pipes and condensate water backing up into the house. If you are a homeowner that is gone for long periods of time during the winter – like vacationing in a warmer climate – you could return to a house with water damage.

My GC  said that condensate pumps (Figure 1) resolve this issue by collecting the condensate water and releasing it in surges, which ensures that a significant amount of water is sent down the drain. These surges are very similar in size to that produced by a toilet and are very unlikely to freeze. I went online and confirmed that others use this solution to resolve their issues with a condensate pump (example).

This discussion generated a few questions that a bit of math can help me answer.

  • How much water is generated per BTU of furnace heat?
  • How much propane is consumed per BTU of furnace heat?


Propane Characteristics

I obtained my information on propane from the Wikipedia:

Where is the Water Coming From?

Burning hydrocarbons generates water. We don't think about this water much because it often floats away in the form of steam. In the case of a furnace like mine, this steam is condensed so that its heat of vaporization can be captured and used to heat the building. In the case of a propane system like mine, the amount of water produced by the propane combustion can be computed by looking at the chemical formula for propane combustion (Equation 1).

Eq. 1 \displaystyle {{\text{C}}_{\text{3}}}{{\text{H}}_{\text{8}}}\text{+5}{{\text{O}}_{\text{2}}}\to \text{3C}{{\text{O}}_{\text{2}}}\text{+4}{{\text{H}}_{\text{2}}}\text{O}

where the chemical symbols are:

    • Propane, C3H8
    • Oxygen, O2
    • Carbon Dioxide, CO2
    • Water, H2O

Equation 1 tells us that for every mole of propane burned, we generate four moles of water.


My Furnace Characteristics

To answer my questions, we need to discuss my furnace and how it is running during this cold snap. Here are the critical parameters:

  • Furnace heat output: H = 100,000 BTU/hour (hr)
  • Furnace efficiency: ϵ = 96.3%
  • Furnace duty cycle: dc = 30%


Figure 2 shows my calculations. The key results are:

  • A propane-powered furnace will generate about 1 gallon of condensate per every 100,000 BTU of heat generated.
  • My furnace under these cold conditions is generating between 6 and 7 gallons of water condensate every day.
  • During the cold spell, I am burning about 34 pounds of propane each day.
Figure 2: Analysis of Condensate Generation and Propane Consumption.

Figure 2: Analysis of Condensate Generation and Propane Consumption.

Propane Heat of Combustion Propane Molar Mass


I now understand why I am seeing so much condensate water now. I will be installing a condensate pump this weekend.

Posted in Construction, General Science | 10 Comments