This ordnance hat insignia is a redesigned version introduced in 1873. The Civil War version has a larger flame.
The 1873 version was used until 1896 when it was replace by a screw back insignia. It measures one and five-eighths
by one and one-eighths.
Reference: Emerson, Encyclopedia of United States Army Insignia and Uniforms p. 246
Ordnance insignia used during the Civil War had much larger flame as seen in this 1866 Quartermaster photograph and the original insignia.
This illustration appears in the Specifications for Clothing, Camp and Garrision Equipage published by direction of the Quartermaster General of the Army 1889 shows an insignia similar to our example.