Army basic trining called "Jumping Jacks"- "side shuttle hops" - how
come? Can't find any real information on the web about "side shuttle
hops".

I think I can help you with this question. I remembered back many
years ago what coaches called them in workouts. You have misunderstood
what the trainer in the Army said, or he had it wrong himself. The
correct term is "side straddle hop" and that is why you could find no
references in your searches. I am certain that you can search now, but
here are a few I found too:

http://www.askmen.com/sports/bodybuilding_60/96b_fitness_tip.html

Conditioning drills are recommended to develop the four components, as
well as motor skills. Five repetitions are recommended, progressing to
10 as one increases strength and endurance. The drills are conducted
in a rhythmic cadence, and in order. Form is not to be sacrificed for
a faster speed.
The first drill consists of:

Sit and reach 
Lunges 
High jumps 
Crunches 
Knee bends 
Side straddle hops 
Swimmer 
Supine bicycle 
Pushups
The second conditioning drill is designed to increase endurance, joint
mobility, and upper body strength via:

Pull-ups 
Sit-ups 
Pull-ups 
Sit-ups 
Pushups

http://www.tradoc.army.mil/pao/Web_specials/H_and_PWB/cofer14.htm

Calisthenic exercise is returning from the 1950s and ?60s as a
training mode. The Army Physical Fitness School is currently
incorporating various exercises into the physical-training program to
simulate the Soldier?s tasks, reduce training injuries and prepare
them for the physical demands of the battlefield.

Side straddle hops (four-count jumping jack) 
Starting position: Relaxed position of attention.

Count:
1. Jump to side and swing arms overhead.

http://www.teenbodybuilding.com/brent5.htm

Army Special Forces Workout 


2. Return to starting position.
3. Repeat #1.
4. Return to starting position.

I have done many side straddle hops in my time and can't see that they
have hurt me any. Hope this clears things up for you.

Redhoss

Thanks for the quick answer.