The name hornpipe dates back as far as the early 16th century, but originaly for a very different dance. The modern rhythm bearing the name evolved around mid 18th century.
Basic hornpipe rhythmThe modern hornpipe is usually notated in cut or in common time:
sometimes in 2/4 time with the 8th note as the beat: 
Tempo and FeelA hornpipe is slightly slower than a reel (about 180 beats per minute) with strongly accentuated beats and very distinctive triplet or even dotted feel. Sometimes the eight note rhtyhm is notated with dotted notes:
sometimes they're notated as even ones: 
This is just a matter of notation though. You play the hornpipe with the same feel in both cases. The 2/4 hornpipe notation is also just a case of notation. Everything is notated with half the note values - fourth notes in common time becomes eight notes in 2/4 time, eight notes become sixteenth notes and so on. Some musicians tend to play 2/4 horpipes with a slightly faster beat, but the difference isn't that big and it's not an absolute rule anyway.
Rhythm patternsThe two most useful basic strumming patterns for a hornpipe is the bass note-chord pattern:
the "Drunken sailor" pattern: 
and a combination of the two: or 
just like the reel. You may also want to add eight notes on the third beat: 
VariationsOf course you don't have to stick to the same rhythm pattern throughout. Don't be afraid to add or remove an egth note offbeat here and there. Triplets can be very effective in a hornpipe too - as long as they're not overdone.
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