Saturday, October 4, 2008

A Bit about Map Scales

...of which most of the geologists reading this will already know.

Geologists will often talk about the scale of a map - a topographic map or the geologic map they happen to be creating - by saying something about the size of the scale: a large scale map or a small scale map. Large and small in this case are quite relative and refer vaguely to the absolute scale of the map, which is usually stated somewhere toward the bottom of the map near the bar scale. The bar scale will give a visual indication of the map scale, and every map should have one, along with a north arrow. Without those two things, it's not really a map (or at least you won't know it's a map).

The absolute scale, though, is usually shown as something like 1:1,000,000, 1:250,000, 1:24,000, 1:10,000, 1:6000, or 1:1000. These are actually fractions, so 1/1,000,000 is a much smaller fraction than 1/1000. That means that a map of 1 to 1 million scale (1:1,000,000) is a small scale map compared to a map of 1 to 1000 scale (1:1,000).

Another way of looking at these map scales is to see what they really mean! A 1:1,000,000 scale means 1 unit (inches or centimeters) equals 1,000,000 units (one million inches or one million centimeters). That translates into 1 inch = 1 million inches or 8333.33 feet or 15.78 miles. It also translates into 1 centimeter = 1 million centimeters or 10,000 meters or 10 kilometers. If you happen to want to mix types of measuring systems (yikes!) then 1 inch will equal 25,400 meters or 25.4 kilometers. A small scale map such as this one will easily show a whole state like Nevada on a piece of paper under 1 meter on each side.

A large scale map, compared to the last example, might have a scale of 1:1000. In this second example, 1 unit equals 1000 units. So 1 inch = 1000 inches, which is the same as 1 inch = 83.33 feet. On the same map of scale 1 to 1000, 1 centimeter = 1000 centimeters, which is the same as 1 centimeter = 10 meters. This sort of large scale map can be used to map a smaller area at much greater detail than the first example of a small scale map.

The scales are called large or small because of the size of the fractions used to represent them: 1:1,000,000 (1 to 1 million) is a very small fraction compared to 1:1,000 (1 to one thousand).

Now, just to be a little confusing, many outfits will map at a strangely combined scale, using non-metric and metric units. I have mapped at a scale of 1 inch = 50 meters. To figure out the absolute scale, you have to work backwards. You first have to either convert inches and meters to centimeters and compare those, or you have to convert the meters to inches and compare those. It happens that, using this handy online conversion site, 50 meters = 1,968.5 inches. That means that our absolute scale is 1 inch = 1,968.5 inches or 1:1,968 (I'll round down). That scale also means that 1 inch = about 164 feet.

Figuring out this strange, bizarre scale using metric units, you would have 2.54 centimeters (1 inch) = 5,000 centimeters, which is the same as 1968.5 meters (surprise! they work out to be the same thing!). This 1 inch = 50 meters is similar to the old U.S. mapping scale (pre-metric) of about 1 inch = 150 feet. Working backwards, our old, pre-metric scale of 1 inch = 150 feet goes to 1 inch = 1800 inches, which is an absolute scale of 1:1,800.

Okay, I never mapped at 1 inch = 150 feet. We were actually more likely to map at 1 inch = 500 feet, an absolute scale of 1:6,000. At a larger scale, I've seen very detailed maps of 1 inch = 50 feet, which is 1:600.

And that's probably enough map math for this early in the morning! Just remember that large scale maps show the smallest area and the most detail compared to small scale maps, which show a larger area with less detail.


Anonymous said...

nice post ... I haven't thought about map scales in a long time

Anonymous said...

A common mistake my students make is to include a map (or part of one) in a report, expanding or contracting to fit the page, but forgetting to revise the scale in the figure caption.

Silver Fox said...

Thanks, Brian - I had noticed small v. large scale used incorrectly somewhere, and was thinking about it.

Hypocentre, that's why maps should really have bar scales. But even then, if there is an absolute scale written somewhere, then it has to be changed - and that can be hard to remember!

I've had maps changed to almost unusable scales by reduction or enlargement - to scales that there aren't any rulers/scales for.

Suvrat Kher said...

very useful discussion. i am just thinking how flexible the concept of scale has become with people now using images as a backdrop in a GIS software and zooming in and out and drawing geological overlays on it!

any thoughts on that?


Silver Fox said...

Suvrat, my one big thought is you need some kind of bar scale on those kinds of images. Also, it is with GIS-type software that I have seen air-photo images created that are difficult to use: the UTM grid is visible, but it's at a scale that requires making up some kind of paper scale to measure anything.

The software can be used to create images at certain "real" or standard scales, but sometimes that's hard to do, especially when using the software for the first time. That's my limited experience with GIS programs - I don't even know what program it was.

Another thing - all/most mines usually have their own mine grids for location, which goes back to pre-GPS days - so sometimes there are two locating grids in use: UTM and the mine grid. I'm hoping mines will all go to just UTM sometime (soon!). Of course, this is all from the U.S. I don't know about other countries.