Watching for nomograms

Cleaning out drawers last weekend, I took a minute to fiddle with two slide rules that I inherited, one from each of my grandfathers. I’ve always found them to be a mysterious link to the past, where clever tricks made all kinds of things possible that we take for granted today. I’d like to be able to make more use of them, but they’re just not that practical any more.

Yesterday I stumbled on a link to a gallery of similarly outdated but intriguing tools called nomograms, which are graphical solutions to equations. Ron Doerfler assembled a calendar for 2010 featuring a number of intricate nomograms. He updates his site infrequently, but I certainly hope he is able to put together a similar calendar for 2011. I will definitely check back later in the year! It will be good for engineer‐cred.

As an electrical engineer, I still have nightmares about trying to understand Smith charts in college. The Smith chart is another type of nomogram used for a number of purposes, including matching components, transmission line characteristics, and other high‐frequency uses. Again, the chart is fascinating to look at, but it’s really a product of the black arts. Stay away.

Thinking more about where I’ve seen nomograms, I recall on highway maps there used to be a fuel economy calculator. There were two horizontal lines and a diagonal line between them. On one horizontal scale, you would select how many gallons it took to fill the tank, and on the other, you would choose how far you went on that tank. The center scale showed the car’s fuel economy for that tank. For the life of me, I can’t find any examples online, so I tried out PyNomo to create one of my own.

In the example above, I went 650 miles on a tank of fuel, and it took 14.5 gallons to refill the tank. The line between those two points intersects the MPG scale at about 45 MPG.

The PyNomo site has some additional examples that fly way beyond my comprehension, but they are neat to look at.

I also found a nomogram for homebrewers to calculate IBUs, and one illustrating the operation of planetary gear set in a Prius.

Wind Rose

I wanted to find a way to show which direction the wind normally comes from, but wasn’t sure of the best way to show that information. A histogram is close, but it would be nice it could be shown in a circular representation. I stumbled on exactly the type of plot I was looking for. Turns out that R has a nice package called “climatol” that has a function to show this perfectly.

Whose turn is it?

We’ve been working for a long time to teach our son how conversation works: we take turns talking and listening.

Similarly, the activities of said 4‐year‐old are represented thus:

Mileage way down

Getting married, moving closer to work, and having a baby all have a way of reducing the number of miles one puts on a car in a year!

Photo statistics

Playing around more with the Google Charts API, I found some interesting insights into our photo albums.

  1. Cameras
    Still lots more pictures taken on the two Sony cameras we’ve owned: a CyberShot DSCS70, and a CyberShot DSCF707. The Canon Digital Rebel XT is next by volume, and it is our primary camera. We also use a Samsung L830 and a Motorola Motozine.
  2. Years
    We started dating in 2001 and were married in 2002. It was new and exciting to have a digital camera, but then our camera use settled down for the next couple years. David was born at the end of 2005, and surprise, the number of pictures doubled!
  3. Months
    I think this chart speaks a bit to our seasonal happiness levels: February is the depth of the wintertime experience, and there is less to be excited about, or to take pictures of. As spring emerges, the number of photo‐worthy events increasesand keeps going through the summer. Fall then arrives, and we start to withdraw into our hibernation routine. December brings a spike because of the holidays, and there is some inertia that carries through to January. And then our cycle repeats.
  4. Weekdays
    Google Chart
    This one isn’t too surprising, either. Naturally, we take more pictures on the weekends!

So there are some fun insights into our picture‐taking habits.

Electric update

electric-meter

In the last 24 hours, where the temperature did not go over 2°F, we racked up another $15 in electricity usage. And our thermostat was set to 60°F for much of that time.

cold-nws-graph-2009-01-16

Wicked cold snap

kdk_0226bThis cold snap is crazy. Out of curiosity, I wanted to figure how much it costs to heat our house on days like these, where the temperature hovers around 0°F all day long. The answer turned out to be about $7.

If you’re curious too, I arrived at this number by separating the portions of our electric bills that have to do with heating and cooling from the rest. We have a heat pump with supplemental electrical resistance heat, so it’s not quite as straightforward as looking at a gas bill.

The first step in doing that is to figure out how much of the bill to attribute to heating and cooling. I started with the assumption that the heat pump uses roughly the same amount of energy to heat the house one degree in the winter as it does to cool the house one degree in the summer. This isn’t really true, but we have to start somewhere.

Next, we need a way to correlate each bill with how hard the heat pump had to work that month. The National Weather Service keeps climatology records that make this pretty simple. Among the monthly statistics that they maintain are the number of heating and cooling degree days. (For each day, add or subtract the average temperature from 65°F to get the number of degree days. For example, if the day’s high was 20°F, and the low was 10°F, then the average temperature was 15°F. That’s 50 heating degree days, because the heat pump had to keep the house 50° warmer than the outside air.) The more degree days, the harder the heat pump has to work. The National Weather Service gives us the number of degree days each month, so we can show how hard the heat pump had to work each month. The graph below shows our electric bills plotted against the number of degree days that month.

electric-bill-by-degree-days

Another assumption is that aside from heating and cooling, our electricity use is constant throughout the year: above a certain baseline, all of our additional energy use is for heating and cooling. The linear approximation in the graph above shows that in a hypothetical month with zero degree days, meaning that the heat pump did not have to do any cooling or heating all month long, our electric bill would be about $55. Anything above $55 on our electric bill is a result of heat pump use. Specifically, each degree day adds 9¢ to our electric bill. 

Given yesterday’s official high of 29°F and this morning’s low of -4°F observed on my car’s thermometer, the past 24 hours are worth 52.5 heating degree days, or $4.73. Tomorrow we might get more official data from the NWS’s observed weather history graph.

I need to revisit one of my assumptions, though. Heat pumps do not work very effectively at very cold temperatures. The heat pump can only maintain a certain maximum differential between the outdoor and indoor temperatures. Below this point, it needs to use the electric resistance backup heat, which is much less efficient than the heat pump operating alone. Since yesterday was extremely cold, and we used resistance heat rather than the heat pump, we can simply subtract the difference between the past two mornings’ electric meter readings, and find 99 kWh used in the last day. At our current average rate of 7.6¢/kWh, that’s $7.52. How much of that was due to heating, as opposed to normal electricity use?

hwh-by-dd

The graph above shows that a hypothetical month with zero heating or cooling degree days would have us using 313 kWh of electricity. However, for the past 24 months, our baseline figure has been 164 kWh, or 5.4 kWh/day. So, if we take out 5 kWh for regular household use, we used 94 kWh to heat the house yesterday, which comes to $7.14.

2008 in race distances

More experimenting with the Google Chart API. I found a nice Google Chart Generator GUI that is a more polished and complete implementation of what I started with my state mapper project. 

At any rate, the highlights are 7 5ks and 3 halfs in 2008. I have decided that the half is my favorite distance: long enough to be a significant effort, but not quite as consuming as a full marathon.

Google Chart

See some other Indianapolis‐area upcoming road races in my race calendar. You can subscribe to the calendar for automatic updates, as well.

2008 running mileage

Running 1,226 miles in a year has a way of wearing out shoes. We ran in 20 races this year, and we had a lot of fun doing it!

2008-mileage