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As mentioned in a few questions and answers (1,2,3,4), US astronauts receive their astronaut wings upon crossing the 50 mile altitude mark.

Are these statute miles (1609.344 m, 5280 ft) or nautical miles (1852 m, 6076-ish ft)?

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According to an authoritative-sounding post on collectspace here, it's statute (which matches my recollection).

Edit: OP @costrom found an FAA document Fact Sheet – Commercial Space Transportation Activities which confirms it.

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Are these statute miles (1609.344 m, 5280 ft) or nautical miles (1852 m, 6076-ish ft)?

TL;DR Neither. Or rather, it is 50 statute miles, but a statute mile is not 1609.344 meters. That is the length of an international mile, and U.S. statutes have intentionally not made the conversion from survey miles to international miles. A statute mile is a synonym for a survey mile, which is exactly 6336/3937 kilometers. This differs from an international mile of 5280 feet by two parts per million. 50 international miles are shorter than 50 statute miles by about 16 cm.


Excessive pedantry follows

The problem is the parenthetical (1609.344 m, 5280 ft). A statute mile is neither 1609.344 meters nor 5280 (international) feet.

Most people in the US don't know this, but a statute mile is not 5280 feet long. This hasn't been the case since 1959.

The United States was an early adopter of the metric system. (Seriously!) Congress made the metric system optional in the Metric Act of 1866. The 1893 Mendenhall Order made the optional Metric Act of 1866 official. In particular, the Mendenhall Order made the metric system the official basis of all weights and measures. It also established the conversion factors between the customary units that the US used (and still uses) and metric units.

In particular, the Mendenhall Order defined an inch as 100/3937 meters, exactly, with a foot retaining its definition of 12 inches, a yard retaining its definition of 3 feet, and a mile retaining its definition of 5280 feet (or 6336/3937 kilometers, exactly).

Other English speaking countries developed their own metric-based standards. A foot in Great Britain, India, South Africa, Australia, New Zealand, and the United States slightly differed from one another. This created problems with regard to international commerce. These English speaking countries agreed upon an international yard and international pound via a treaty in 1959. An "inch" is now exactly 2.54 centimeters long.

Inches, feet, and yards are important measures with regard to international commerce. Miles are not. Miles on the other hand are important internally, particularly so to a country that is 2800 miles across. The 1959 treaty would have made a mess of precise surveying. The end result is that a statue mile has not been 5280 feet long since 1959. A statue mile remains 6336/3937 kilometers long to this day. Quoting from From NIST Handbook 44, Appendix B,

From 1893 until 1959, the yard was defined as equal exactly to 3600/3937 meter. In 1959, a small change was made in the definition of the yard to resolve discrepancies both in this country and abroad. Since 1959, we define the yard as equal exactly to 0.9144 meter; the new yard is shorter than the old yard by exactly two parts in a million. At the same time, it was decided that any data expressed in feet derived from geodetic surveys within the United States would continue to bear the relationship as defined in 1893 (one foot equals 1200/3937 meter). We call this foot the U.S. Survey Foot, while the foot defined in 1959 is called the International Foot. Measurements expressed in U.S. statute miles, survey feet, rods, chains, links, or the squares thereof, and acres should be converted to the corresponding metric values by using pre-1959 conversion factors if more than five significant figure accuracy is required.

This means that 50 (statute) miles, the elevation above sea level at which becomes a candidate to receive astronaut wings, is a bit higher than 80.46720 km (50*1609.344). It is instead ~80.46736 km.

That 16 centimeter difference is of course a difference that doesn't matter. Moreover, there are moves afoot (pun intended) to make the mile once again be 5280 feet long. If no reasonable objections are posted to a recent National Institutes of Technology proposal, the survey mile (statute mile) will become toast in 2022.

Editorial

The above provides yet another example of why the US should convert to the metric system.

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    $\begingroup$ I read somewhere (I think it was another SE, either History or World Building) that Thomas Jefferson had ordered a set of metric standards shipped from France back in the day, and that ship was waylaid by a storm and sacked by pirates, and thus never arrived. So there were plans to go fully metric right from the early days. $\endgroup$ – Darrel Hoffman Aug 7 at 13:24
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    $\begingroup$ Practically, there isn't a difference WRT internal use (e.g. as a layperson, not a surveyor or someone needing exact precision), as 5279.986877ft is so close to 5280ft that most people would not be able to notice a difference if you showed them up close (that's a 5/32 of an inch difference over a mile, to put it in more common expression). Even traveling 2800 miles, you'd only end up 1/6th or so of a mile off from someone using the other measurement, or less than one lap around a high school track. $\endgroup$ – TylerH Aug 7 at 13:40
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    $\begingroup$ Wikipedia calls the "6336/3937 km mile" a US survey mile. Though I guess there won't be many cases where an astronaut reaches 50 international statute miles and not 50 survey miles, given that the difference is just 36 cm. $\endgroup$ – Paŭlo Ebermann Aug 7 at 19:29
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    $\begingroup$ Downvoted for excessive pedantry. The survey foot and the international foot are so close in length that even surveyors have trouble measuring the difference. $\endgroup$ – Mark Aug 7 at 20:37
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    $\begingroup$ +1 for excessive pedantry. That said, a short summary at the top would probably be good. $\endgroup$ – Nat Aug 8 at 19:32
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They use statute miles (50) or feet (264,000). 50 miles are 43.4488120950325 nautical miles so it's hard to convert.

If you mean whether they use 50 statute miles or 50 nautical miles, it's easy to e.g. find out on Wikipedia the U.S. use a value that converts to about 80 km, therefore statute miles. But if you say "mile" only you usually don't mean a nautical mile anyway, you mean the statute/imperial/US customary mile (1.609344 km or 5280 ft).

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    $\begingroup$ The US does not use imperial units. For example, an imperial pint is 25% larger than is a US pint. The US uses US customary units. $\endgroup$ – David Hammen Aug 7 at 7:57
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    $\begingroup$ @DavidHammen The imperial mile or statute mile or US customary mile is one and the same (1.609344 km or 5280 ft). America uses the survey mile, as its name states, only for land surveying, otherwise they use the statute mile. $\endgroup$ – Giovanni Aug 7 at 15:16
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    $\begingroup$ The statute mile is called that because there is a statute (aka a law) dictating what the statute mile is. The relevant law is the 1893 Mendenhall Order as the 1959 treaty that changed the definitions of the yard and the pound intentionally did not address longer units of measurement used by surveyors. Interstate wars (e.g., the Toledo Strip) have been fought over surveying conflicts. The US statute mile retains its 1893 definition, at least for now. $\endgroup$ – David Hammen Aug 8 at 6:09

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