## Something Blue

I was at a wedding over the weekend for some friends. During dinner, there was a trivia game and each table (ours was a table of five UPC folk) were able to submit their own questions for round :

• After the 2012 earthquake in Haiti, what type of plane was JoEllen evacuated on?1
• What is Chuck Noris’ first name?2

Round two was an entire section on wedding trivia — who knew weddings cost so much and people married so late in life. This one in particular stood out for the comment delivered with such comedic timing half a beat later:

“In the phrase ‘Something old, something new, something borrowed, something blue,’ what does blue signify?” (half-beat) “Balls.”

The correct answer is actually purity, love, and fidelity3. I liked the first answer better — which also indicates that I’m apparently still 12 years old.

1. DC-3)

2. What is the tallest building in the US? ((Willis Tower

3. Carlos

## Lifecycle Costs of Lightbulbs

Scientific American had an article on the costs of light bulbs1. I wanted to figure out a way to fairly compare the rough lifecycle costs of the bulbs to the consumer. I figured the best way to do that would be to determine the cost per an operating lux-hour.

We’re going to figure out the cost to buy and operate lights that emits 1600 lumens for 20000 hours $(3.2 \times 10^{7} lm \mbox{-} h)$ given that energy costs $\0.085\ kWh^{-1}$2:

Cost of energy:
$\frac{100 W}{1600 lm} = 0.0625 W \cdot lm^{-1}$
$0.0625 W \cdot lm^{-1} \times \0.085 kW \mbox{-} h^{-1} = \5.313\times 10^{-6} lm \mbox{-}h^{-1}$
$\5.313\times 10^{-6} lm \mbox{-} h^{-1} \times 3.2 \times 10^{7} lm \mbox{-} h = \mathbf{\170.00}$

Cost of bulbs:
$\frac{\0.37}{750 h} = \4.933\times 10^{-4} h^{-1}$
$\4.933\times 10^{-4} h^{-1} \times 20000 h = \mathbf{\9.87}$

Total Cost:
$\170.00 + \9.87 = \mathbf{\179.87}$

You can do the same math for the rest of the bulbs (substituting the proper numbers in) to get a chart that looks like this:

Incandescent
Halogen
Incandescent
Compact
Fluorescent (CFL)
LED
Watts (W) 100 77 23 20
Lumens (lm) 1600 1600 1600 1600
Cost/bulb $0.37$1.59 $2.23$45
Life span (hours) 750 1000 10000 20000
W/lm 0.0625 0.0481 0.0144 0.0125
$/(lm-h) 5.313E-06 4.091E-06 1.222E-06 1.063E-06 Cost to run$170.00 $130.90$39.10 $34.00$/h 0.493E-04 1.590E-04 2.230E-04 2.250E-04
Cost to buy $9.87$31.80 $4.46$45.00
Total cost $179.87$162.70 $43.56$79.00

Here’s the thing I found amazing: there’s a big push to implement LEDs, probably because of the ‘cool’ factor. However, they don’t save that much more energy over CFL — about 13% — and they cost almost twice as much to operate right now. Manufacturers are going to have to have to drop the cost of LED lights a lot in order to make a change worth it…or the government will have to ban mercury in lights3.

Graphic by George Retseck and Jen Christiansen
Sources: U.S. Department of Energy and Efficacy calculations based on currently available bulbs (traditional, halogen and compact fluorescent); SWITCH LIGHTING (led)

1. How to Buy a Better Lightbulb, John Matson, Scientific American, January 6, 2012

2. CFLs contain about 4mg of Mg, per Energy Star

## Approach for 2012

I’m cleaning up my room and came across this note. I wrote it a few months ago as I was doing my planning for 2012.

For 2011, my word was “Pace“. This year, I picked four words about how I’m going to approach this year: Explore, Focus, Finish, Fun.

I didn’t just pick these four words out of thing air, there was a process to get there and this piece of paper was my thought process. Click to embiggen.

## @rands To err is human; to check is engineering.

@rands To err is human; to check is engineering.

## Foiled

The printer was hole-punching my printouts at work (on the wrong side of the page, to boot). I was mystified by why it was doing this.

I tried changing the print settings.
I tried restarting my computer.
I tried restarting the printer.
I tried uninstalling and reinstalling the printer driver.
I tried that rain dance I learned middle school.1

Nothing worked.

I went to call the help desk, expecting the agony of having to cater to their pedantic troubleshooting guide. I started to imagine what they might ask me, and began to mentally reply to their invisible questions, “Yes, I did that… Yes, I tried that… No, that didn’t work either.”

I was dreading the thought of another 30 minutes wasted. I decided to get one more data point by verifying with my coworker that he had the same issue.

His words of wisdom: “Oh, the printer must be loaded with the wrong paper again.”

“The wrong paper? Again?”, I thought to myself.

I quizzically walked back to the printer and furiously opened all the trays in an attempt to locate the non-compliant source.

And there it was. The paper punched for a three-ring binder.

1. I made this up, but I should have tried it

## Empire Builder 8

Rachel’s grandmother passed away last week, so we’re making the trek to Montana for the funeral service. We were going to visit Portland this weekend, but that trip has been preempted by this.

Since the funeral isn’t until Monday, we decided to inject some fun and take the train to Montana and then fly back.

We’ve never ridden on a train for travel, except when I was in Europe. So this will be a first for both of us in the US, which Rachel calls Darjeeling Limited-style.

The train ride takes 23 hours, so I’m hoping to provide some updates en route.

Cheers!

4.3 mm || f/2.4 || ISO160 || iPhone 4S
Seattle, Washington, United States

## Omnipotence

Emailing and IMing with people while I cross the country in an airplane gives me an odd sense of omnipotence. So does posting on the blog.

## Sorting through “My Documents” sometimes feels lik…

Sorting through “My Documents” sometimes feels like opening an unexpected time capsule.

“A common example of Simpson’s Paradox involves the batting averages of players in professional baseball. It is possible for one player to hit for a higher batting average than another player during a given year, and to do so again during the next year, but to have a lower batting average when the two years are combined.”

## Napkin Analysis of the Sand Flea Jumping Robot

I shared this video1 with Peter, who then asked:

I saw that a couple days ago. Awesome! And has some cool practical applications. I [couldn’t] quite tell if the pitch of the robot was adjustable by the user, or of it always jumped in the same direction. Did you get a sense for that?

It was a good question and one I didn’t have an immediate answer to.

I would actually guess that I don’t have immediate answers2 to at least 50% of questions people ask me3. I have to do some amount of thinking, and sometimes even some research. I think people tend to think I know the answer off the top of my head, I assure you: I am not that smart.

I do have an inquisitive mind, I do know where to look, and I do know how to ask the right question.

I decided to remedy this question though by talking it through, instead of just giving an answer. This is basically my thought processes as it occurred. Except that I got Sin and Cos mixed up and didn’t realize it until I had finished my conclusion. So I had to redo my entire analysis, and that’s what you see here. Please note this is still really just a paper napkin answer:

As far as angle, I’m not sure. I suspect there would be some angle change.

Elevation angle can affect two things, how high it goes and how far it goes forward, and these two things are intrinsically linked through SohCahToa. Height and forward distance can also be affected by the force applied (ceteris paribus4). This gives a problem with two independent input variables (angle and power) and two dependent output variables (height and forward distance/range).

Since my primary goal is to jump, I’m going to put most of my energy into that. If I want to jump higher, I can either apply more force or make my elevation angle higher (as long as it’s < 90°). As the elevation angle nears 90° $\left (\frac{\pi}{2} \right )$, more of my energy goes into going up than going forward. The proportion of energy applied to going up is defined by Sin and the proportion of energy applied to going forward is defined by Cos. Also worth remembering is that the Sin[x] + Cos[x] is not a straight line, it's another parabola that peaks at 45 degrees. The biggest bang for your average buck is to angle yourself at 45 degrees and shoot. Additionally, Cos (forward) angles that are near 90° have a high rate of change (i.e. going from 80° to 81° has more of a difference than going from 10° to 11°), thus little changes in elevation angles near 90° have relatively larger impacts on how far forward I go. Conversely, Sin (height) angles that are near 90° have very low rates of change. The cross over point for rates of change between Sin and Cos is - you guessed it - at 45° . Since the goal of the robot is to jump high (not far), it would make sense to only use high angles (above 45° ). To vary height significantly though, you are going to have vary power. Going from 46° to 90° only increases height by ~93% if the force remains the same. In comparison, going from 1 degree to 45 degrees increases height by 164,000%. Math is great, but if you can't implement it, it doesn't matter so let's turn to what's practical: One of the underlying assumptions is if the robot can vary the force it uses and if it could accurately set it's elevation angle. Setting the angle is pretty easy using encoders, and accelerometers to determine which way is down (if you were jumping from an angled surface, for instance). We've also already seen that the jumping leg can move, so adding functionality for precision angle measurements (within a degree, let's say) is pretty trivial. The real question, I think, is how does it jump? Delivering energy quickly has always been a problem. Delivering a measured amount of energy quickly even more so. Based on jumping from the ground to the loading dock (1.5 meters in height at most) and then from the loading dock to the roof (probably at least 4 meters), that's about a 166% increase in height, which is not quite enough as could be accomplished by just varying the angle from 46° to 90°. Since you can't gain that height just by altering the angle alone, it makes sense to assume that the jump force setting can be altered. However, if you change the jump force setting, what does that do to the forward movement (we know it will make the robot jump higher)? It will, of course, move the robot forward even more. How much more? I don't know exactly, but probably enough to make some minor angle tweakage worth it. We would have to sit down and work on the math to verify the exact amount. I think it involves something with squaring the derivative of the force divided by the mass. Squaring always make numbers bigger, so I tend to think it would be significant. Suffice it to say, if you don't want to proportionally more forward when you jump significantly higher, you would have to adjust your jump elevation angle. Thus I would assume there may be small changes in angle elevation, but that's hard to estimate given the view-point the videos were shot at. It's also pretty easy to solve for power required and angle needed to reach a particular height while moving forward only a certain amount (once you figure out what the maths are), so at least the implementation factor is pretty easy from a computing standpoint. And I've spent way to much time on that answer.5 As always, please check my work.

1. answers that only involving recalling a specific outcome

2. I just made that number up, really

3. all other things being equal or held constant

4. One of the reasons I decided to blog about it, the work was pretty much a sunk cost