Saturday, May 10, 2008

Toll Avoidance, and Gain Conversions

I occasionally look at my referers to see what people are searching for when they find my blog. There were two in the recent list that stuck out to me: "convert dB to gain" and "chicago route around no tolls". I've obviously touched on these before, or else people wouldn't be finding my blog so easily, but I haven't talked about either directly, so here we go.

Decibels are a dimensionless unit used to relate a measured level against a reference standard. The actual unit is the "bel"; one bel represents a tenfold increase in level as compared to the standard. A decibel is a tenth of a bel, and therefore represents an increase of about 25%, since 100.1 is approximately 1.25. To convert decibels to an absolute gain figure, one simply raises ten to the power of the gain ratio expressed in bels. If G is the gain in decibels, then g=10G/10 is the absolute gain multiplier. The reverse is done with logarithms and is left (for now) as an exercise for the reader.

As for finding a route around Chicago that avoids tolls, this is more complicated. In part, it depends on where you're trying to get and from where. The most common situation where this comes up is when someone is going east to west (or west to east) on I-90 and is routed through Chicago. (I-80 doesn't actually go into Chicago.) Interstate 90 is toll from the Wisconsin state line to just outside Chicago, and then again on the south side of Chicago; avoiding it is not easy. In addition, using the freeway part of I-90 to go through Chicago is not terribly fun; the Dan Ryan is widely regarded as one of the least pleasant freeways on which to drive.

Avoiding the the Skyway toll is easy; just enter Illinois on I-80/94 instead of on I-90. If you're already avoiding tolls you've done this anyway since I-90 in Indiana is the western end of the Indiana Toll Road. Avoiding the Jane Addams toll is much harder as there are no suitable alternative routes for most of its length. (You can avoid the east terminus toll by using I-290.) A lower-toll alternative is I-80 and I-39; you only pay one toll on the portion of I-80 that is overlaid on the Tristate and one on the portion of I-39 that is overlaid on the Jane Addams. You could avoid these by using lesser surface routes, but none of these alternates is very enjoyable. If you're heading far enough west, consider taking I-80 all the way to I-35 (in Iowa) to reconnect with I-90 in Minnesota. If you're coming up from central Indiana, consider using I-74 to I-39 (in Bloomington) or I-80 (in the general area of the Quad Cities). If you are heading up into the Wisconsin coast (Kenosha or Milwaukee), you can try using US 41 instead of I-94 from the north side of Chicago.

Hope this helps someone. If not, oh well.