Fort Woodbury was part of the Arlington Line, an extensive network of fortifications erected in present-day Arlington County, VA to protect Washington, D.C. from Confederate attack. Construction began on the Arlington Line in May 1861, shortly after war broke out, and accelerated after the Union’s defeat at the First Battle of Bull Run in July 1861. It stood atop one of Arlington’s highest hills, and was named for Major Dwight P. Woodbury, the engineer who designed and constructed the Line.

(This clarification comes from Tracy Brown) There were two D.P. Woodburys, the architect that desined Arlington Line who gets credit and then there's the one who the fort is truly named for, this being D.P Woodbuty commander of the 4th Michigan Infantry. The 4th Infantry constructed the fort, then named it after their commander. Wiki got it wrong as most understandably do. Letters home from the soldiers themselves as well as communications from General McClellan contribute to this fact. See "hell on a wooden bridge" for these references.

from Wikipedia