I would like a URL for one or more web pages describing a system where
the US military would rescue a downed airman by having him send up a
small balloon on a rope and then flying over him with an airplane that
grabbed the rope and lifted the man off the ground.  He was then
winched into the airplane.

vincecate..

Thank you for your interesting question.  What you are referring to is
known as the Fulton Extraction.  They way it works(ed) was a downed
pilot who manages to evade the enemy establishes radio contact with
friendly forces. A package is dropped to the pilot. The package
consists of a harness, a helium-inflatable miniature blimp, and a long
coiled tether connecting the harness and the blimp. The downed airman
gets into the harness and inflates and releases the blimp with tether
attached. The specially configured C-130 homes in on the balloon and
snags the tether with a "V" shaped device attached to the nose of the
aircraft. The downed man is jerked into the air and reeled up to the
open cargo hatch of the aircraft. Now, there are several problems with
this method.  First, an inflated balloon is pretty much a dead
giveaway to the enemy of a persons location.  Secondly, the aircraft
is moving, unlike a hovering helicopter, therefore, once the man was
snatched up, he would be moving forward and there would be several
immovable objects, mainly trees, that might cause some problems.
Therefore, the person would need to be in an open field.  Again, a man
standing in an open field with a helium ballon attached to his back is
a pretty easy target.

The system was developed in 1966, however, with the avaialability of
long range, air refuelable helicopters, the Fulton recovery was
discontinued by the Air Force in 1996.

Thanks again for a very interesting question.  Having served in the
military, I thoroughly enjoyed researching your question.  If you need
any additional clarification, please let me know.

Regards,

-THV

Search Strategy:
downed airman rescue balloon
Fulton Extraction
Fulton rescue

References:
Global Security.org
MC-130P Combat Shadow HC-130P/N Combat Shadow
http://www.globalsecurity.org/military/systems/aircraft/mc-130p.htm

VegSource
View from d'Isle
http://www.vegsource.com/articles/john41.htm

United States Air Force Rescue Service - Fulton Surface-to-Air
Recovery System
http://www.wpafb.af.mil/museum/history/rescue/res12.htm

Fulton Surface-To-Air Recovery System
http://www.wpafb.af.mil/museum/history/rescue/res12.htm

Very good answer.  Thanks.