Ten Linear Miles: What does it mean?
It is, in fact, ambiguous. The term linear [unit] is most often used to distinguish from square [unit], and most often refers to things that are already straight. For example:
Linear footage is a measure of length, 1 foot is 1 linear foot. Linear footage measurements do require a straight line measurement. Lumber, fencing, and fabrics are commonly sold by the linear foot.
—"How to calculate linear feet", InchCalculator.com
However, as is implied by the usage above, a total linear measurement amount can aggregate several individual measurements; for example, if you were building three shelves that were each four feet long, you would need twelve linear feet of shelving.
Linear miles is subject to similar ambiguity. It can mean X miles-in-a-straight-line:
The Middle 1 Route (68.73 miles, or 110.6 km long) will cross 8 linear miles (12.9 km) of sensitive biological habitat
—Northwest Regional Power Facility (NRPF), Near the Town of Creston: Environmental Impact Statement, 1996
Here, we are told that the Route is 68.73 miles long, so the only possible interpretation of it crossing "8 linear miles" is that this is a measurement, in a straight line, across the total terrain covered.
However, it can also mean X miles-if-you-stretched-all-the-measurements-into-a-straight-line. For example:
The Storm Water Division oversees the maintenance and repair operations of approximately 500 linear miles of storm water drainage systems within the City of Green.
—"Storm Water Management", City of Green, Ohio, 2014
Here, unless the City of Green is absolutely enormous, and all on one long, straight street, the 500 linear miles must be an amalgamation of the many twists and turns of sewer pipes and ditches that make up the city's storm water drainage system.
Unfortunately, this means that there isn't an easy way to know what is meant by linear miles; it just has to be determined from context, and careful writers should include an explanation of how they are using the term.
Other answers give the meaning of the linear in linear miles, but with these explanations, they are missing the explanation why one would use an apparently redundant expression. After all, a mile is a length or distance, which is measured in a single dimension.
When you encounter something that is normally referred to by its size in some number of dimensions, it is common practice to be emphatic when another measurement is also discussed involving a different number of dimensions.
Therefore:
- Your brick wall may span 200 feet, and you might need 9 yards of concrete to build it. Unless you are doing this every day for a living, you might not know that's 9 cubic yards and 200 linear feet, which might give you a wall of 1800 square feet.
- You might buy firewood in cubic feet, but you would buy fence posts in linear feet (once you have settled on the other dimensions).
- A wildlife preserve may cover 100 square miles, but the road through it covers 10 linear miles. Of little interest may be the fact that the road takes up less than 1 square mile.