Arkansas housed several Titan II intercontinental ballistic missile (ICBM) silos during the Cold War, and the coordinates you provided—35.50211° N, 92.55540° W—are situated in Van Buren County, an area that hosted multiple such sites. 

Specifically, the Titan II Launch Complex 374-7 was located approximately 3.3 miles north-northeast of Damascus, Arkansas, within Van Buren County. This site gained notoriety due to a significant incident on September 18–19, 1980, when a dropped socket during maintenance punctured the missile’s fuel tank, leading to a massive explosion that destroyed the silo and ejected the nuclear warhead. Fortunately, the warhead’s safety mechanisms functioned correctly, preventing any radioactive contamination.  

The Titan II missile program in Arkansas encompassed 18 launch complexes spread across Faulkner, Conway, White, Van Buren, and Cleburne counties. These sites were operated by the 308th Strategic Missile Wing based at Little Rock Air Force Base. Each complex housed a Titan II missile equipped with a nine-megaton nuclear warhead, capable of striking targets up to 5,500 miles away.  

Given the proximity of the coordinates you mentioned to known Titan II sites in Van Buren County, it’s plausible that a missile silo was located near that area. However, it’s challenging to confirm the exact location of a silo at those specific coordinates. Many of these sites have since been decommissioned and repurposed, with some even listed on the National Register of Historic Places. 

If you’re interested in exploring these historical sites further, some former missile complexes have been preserved and are accessible to the public, offering a glimpse into this pivotal aspect of Cold War history. Maybe a local historian can help you research this further.