Conventional headers have four individual tubes from the head flange to the collector.
Tri Y headers have short (about 10")tubes from the flange to a Y, pairing two tubes to a larger tube about 20" long that then Ys together at the larger final collector. Doug Thorley was the most popular supplier of these headers for 30+ years.
They were popular when older engines had smaller heads and valves that didn't breath as well as more modern heads do. These headers enhanced the available power curves of the time. With bigger heads, cams, carbs, and intakes, the midrange and upper end enhancing 4 tube headers became more useful and popular.
TRI Ys enhance power at and below an engines torque peak 4 tube headers enhance above the torque peak to the shift point.
Today, tri Ys are primarily used for rock crawlers, 4 WDs, fuel economy, and towing vehicles. They were extensively used in cast iron and factory installed headers in the 70s , 80s, and 90s.
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