What font is used in these wooden trail signs?
I originally thought the standard was Helvetica, but looking at these examples we see the font is narrower and the 'R' doesn't look like Helvetica.
Also, these signs are typically routed -- so the router will give a rounded profile to sharp corners.
Does anyone know what font is used here, or anything that comes close?
The type used by the Forest Service is referred to as ASA Series C in the FS docs. The FHWA more commonly refers to the type as FHWA Series fonts but they appear to be the same. That name is applied to both the routed and printed type. You can read up on some of the specs at the Sign and Poster Guidelines for the Forest Service (PDF) page. Section 14.4 speaks to the routed signs.
The FHWA type is available in Series A-F, A being the narrowest, F being the widest. The document Standard Alphabets For Traffic Control Devices (PDF) shows the types in all their glory with the spacing parameters.
Tobias Frere-Jones produced a full-featured replica under the name Interstate.
Generally these are single line/stroke fonts for Computer Numerical Control (CNC) machines. Most don't have a specific name or foundry. They simply are supplied with CNC software from the manufacturer.
CNC machines are computer driven cutters/engravers used in manufacturing many items which need to be custom shaped or carved. I suspect signs such as those are carved by machines. Most likely CNC machines, but there is a possibility that laser engravers were used. In the case of laser engravers, any font will work.
You can find several single stroke fonts if you google for "CNC Fonts"