American fighters never used the 'European' type roundels as national markings.
Flypast July 2008 - Evolution US National Insignia
Not until the Mexican Punitive Operation of April to May 1916 did US aircraft adopt any national insignia. A red star was hand painted on the rudder of Curtiss R-3s and R-4s. The insignia varied in size, had curved sides more akin to a leaf and were only in use for three months. The Signal Corps continued to apply this
style of marking, with straight sides and sometimes on a white circle until 1917.
The US entry into the Great War in 1917,hastened the need for a suitable national insignia and the design submitted by the 1st Aero Squadron, New York National Guard, when called to Federal service, was
adopted in May of that year. This comprised a blue circle containing a white star with a red centre circle, to be marked on the upper and lower wing surfaces. The red circle was later enlarged but was to clear the inner points of the star by 1/24th of the overall diameter. In October 1917a standard 60in (152.4cm) size was adopted and the red circle was to touch the tangent lines of the star sides. Where the wing chord was smaller than 60in, a small insignia equal to the chord was authorised. At the same time, rudder striping was introduced, comprising equal widths, from the rudder post, of blue/white/red stripes.
In France, the American Expeditionary Force found that the star insignia could, at a distance, be indistinguishable from the curved outline of the German Cross and advised that it was going to adopt a circle insignia, similar to that already in use by the French Air Force and the Royal Flying Corps and Royal Naval Air Service. This consisted of a wing chord width red outer, an inner 2/3rd diameter blue and 1/3rd diameter
white circles, to be marked on the upper and lower wing surfaces. This roundel was authorised for use on Navy and Army aircraft on January 11,1918and later amended, on March 5, 1918,by the Signal Crops to standardise on the 60in insignia, in use by the Navy. At the same time the rudder striping was amended to red (forward)/white/blue. On May 17,1919,the insignia reverted to the 'star in circle' design as authorised in October 1917with the rudder stripes reverting to blue(forward)/white/red.