Monday, October 01, 2007

Conversion Factors

Units are nifty. Most non-science people are rather frustrated by them, but typically, it's a very nice, quick way to check equations to make sure they'll actually give you the sort of quantity you're looking for. After all, you don't want a distance coming out with seconds as the unit. Rather, you'd want something in meters, or parsecs, or furlongs, etc....

In astronomy, we tend to switch between units quite often. Meters are perfectly fine for describing diameters of planets, but aren't ideal for the size of solar systems. For that we use Astronomical Units (AU). Those work great on that scale, but fall short (har har) for sizes of galaxies. Lightyears or parsecs are much better there. For cosmological distances, we like megaparsecs.

Quite often in classes, professors like to make sure you're paying attention to your units and will give you something in a unit that needs to be converted to something else before it will cancel with the units of a particular universal constant. Most of us students that have been doing this for awhile realized that having to look up the conversion factor and do the conversion by hand gets tedious.

Fortunately, the great Google can do every unit conversion known to man. Need to know how many megaparsecs 245 AU is? Just type in "245 AU to megaparsec" and BAM! Google spits out your answer: "245 Astronomical Units = 1.18779352 × 10-9 megaParsec". Nifty. Now let's try to figure out what the hell the rest of this problem this professor is asking us actually means...

Pretty straightforward. But Google sure does know some weird conversions. I mean, who the hell asks for the "number of horns on a unicorn acre in tea spoons per light year"?

7 comments:

mollishka said...

*shrug*. Just use centimeters. (Who the hell measures the sizes of planets in meters anyhow?!)

Wayne said...

Thanks a lot, I just got sucked into the wacky world of unusual units for the last microcentury. Shesh.

Michael said...

I've been using this feature for a long time. What's really cool about Google is that you can do math also, and as long as you know what type of units the answer will be in, you can leave the conversion 'til the end.

For instance, (bore / 2) ^ 2 * pi * stroke * cylinders in cubic inches will get you the piston displacement of an engine if you know the bore, stroke and number of cylinders. The great part is that you can change in^3 to cm^3 or liters or parsec^3 or whatever volume unit you want without having to change the bore/stroke units. You can even mix units, say 4.04 inches for bore and 8.636 cm for stroke.

Piston displacement (probably not the official term) is what you'll see advertised on TV. The full displacement, used alongside piston displacement when you're calculating what parts to use when building a motor, also takes into account piston dome/dish volume, head chamber volume and head gasket volume. Google is especially handy for this, as dome/dish can add between -15 and +15 cc per cylinder, head chamber volume can add 30 to 80 cc per cylinder, and the head gasket can add 1 to 1.5 mm of height or as much as 6 cc total displacement (top-of-my-head typical Ford V8 small-block values that I'm sure you noticed are in a zillion different units).

If you want to know the compression ratio of your motor you divide the full displacement by the difference between full and piston displacment. This can be simplified to ((bore / 2) ^ 2 * pi * stroke) / (head + piston + (bore / 2) ^ 2 * pi * headgasket); substitute the values in whatever units you have, plug it into Google, and you've got your ratio. In this case, it's about 12.5:1, which tells you it probably needs midgrade or premium gas, and won't handle a ton of boost.

Completely not astronomy-related, but that's the stuff I use Google math for. As an aside, I was using Google searches to make sure I was using the right values, and found it interesting to note that some people use '(bore/2)^2 * pi' while others use bore^2 * (pi/4)'.

Jon Voisey said...

Precisely why we should all join the .

Stephen said...

Linux (freeware) usually comes with a command line app called "units". Very handy for this sort of thing.

Thomas Antonsen said...

I'd be more impressed if they had rearranged the "number of horns on a unicorn" coefficient to be

horn-acres in unicorn-teaspoons per light year

Thomas Antonsen said...

I'd be more impressed if they had rearranged the "number of horns on a unicorn" coefficient to be

horn-acres in unicorn-teaspoons per light year