The Army does not have "Rapid Deployment Units" anymore and has not used that as a doctrinal term for some time - although it keeps sticking around. In general, the 82d Airborne Division at Fort Bragg has a mission that used to be called rapid deployment. In conjunction with the 82d, certain other units of the 18th Airborne Corps keeps units on alert as well.
Within Special Operations, the Rangers, the 160 SOAR, and SF all have various alert missions. If I remember correctly, 15R is some sort of helicopter maintainer. The best places to go to in order to deploy early and deploy a lot for a 15R are the 82d's Aviation Brigade at Fort Bragg.
Of course, in today's Army, everyone gets to deploy sooner or later.
If you mean capable of deploying with x amount of hours: then socom units(82nd ad and 10th mountain ARE part of socom) and various airborne units have brigades with bags packed rdy to deploy if you mean back to back deployments...then the "light" infantry units. 25th ID, 10th Mountain, Airborne units, etc.
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