Stabilization line
The first line to set is the stabilization line. This is critical to success in most pin rescues. The stabilization line basically helps support the trapped boater so they can conserve their strength and breathe freely. In some cases, extra equipment can be quickly sent to a rescuer that is with the victim, sort of like a zip line. When setting a stabilization line, don't forget how powerful a vector pull is - set a low angle V in the line. The deep V also provides more support for the trapped boater. For maximum support where it is needed, the line should cross the paddler right around their nipples and under their arm pits. This set-up makes it much easier for the paddler to support themself in an upright position where they can breath easily without fighting the current. Nearly all pin/entrapment rescues use a stabilization line because it works. If the person is unconscious, this technique isn't as effective. Their arms may flop out of the way causing the rope to ride too high. When the person is unconscious, you really need to get someone to the victim quickly to render assistance.
Fundamental tool for entrapment and pin rescues
Stabilization, snag, and cinch lines each have their uses in freeing trapped boaters and their equipment. These rope techniques allow rescuers to work from safe locations, perhaps on shore to buy rescue time (stabilization line), transport equipment or a rescuer to the victim (zip line), free a trapped foot (snag line), dislodge a pinned boat or paddler (cinch line). These techniques are amongst the safest alternatives for rescuers in a pin or entrapment rescue and typically are your first choice.
Consider what happens when the victim is freed; consider pre-set live bait
Once the victim is freed, they will head downstream - perhaps pretty quick. If this was a foot entrapment, they will probably be injured. If they have been trapped for awhile, they may be too tired to grab a throw rope. Be ready with a pre-set live bait rescuer. Basically, a rescuer wears a rescue vest and is attached to a line with a fair amount of slack. The rescuer needs to time a shallow water entry and potential quick ferry to meet the victim and safely grab them. The line will get taught real quickly and the belay person better be in a good brace so they can pendulum both quickly to shore. Consider having an extra person assist with a vector pull.
This film from the 2010 Green River Race shows several "Live Bait" rescues: Green River Race Live Bait Rescues.
Upstream and downstream safety is essential
Think positive, in most cases you should be able to free the victim. What happens then? The victim and equipment will float downstream and need to be retrieved somehow and that means downstream safety. On a serious foot entrapment, there is a very strong likelihood that the victim is seriously injured. Chances are also high they will not be able to swim effectively - they are certainly going to need some help. Downstream safety is essential. Ropes that cross a river can be quite dangerous for unsuspecting boaters entering the rapid. We certainly don't want to clothesline anyone. Anytime you work with ropes, set safety upstream as well and make certain rescuers have a safety knife that is easy to access on their person.
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