This is copied from the Brodak web site.  I have always used .012" stranded with no complaints.

Carrier .15
15 profile is an un-official event. Models may be Electric or Glow.  The rules are summarized below.

Maximum engine size, .15- glow/diesel, .20- 4 cycle or .20 total displacement for multiple engine models.  Electric 2.5lb weight limit.  See Detailed Electric Rules below.
This is a speed limit event. Maximum high speed points are for 70MPH, no penalty for exceeding 70 MPH. 
No model size limit, Glow; 4 lbs weight limit, Electric; 2.5lbs weight limit.
No movable controls except throttle, elevator, and hook.(i.e. no line sliders)
Muffler pressure is allowed, no crankcase or other timed pressure systems allowed
Lines: .012 stranded stainless steel, 52 feet to 52 ft 6 in from center of handle to airplane centerline.
No bonus points except 10 bonus points for using a Brodak kit.
Scoring is per AMA Navy Carrier except flights are timed for eight ( laps vice seven (7).
Airplanes are encouraged to be finished and marked with naval color schemes
All other AMA carrier regulations apply.

The rules came from "Denver club" and were adopted by NCS.   I have never been able to find a legitimate way that electric wormed its way in.

Bob,
 I am the one who put the line rule on the Brodak site. I thought it was clear , but maybe not. The rule is .012 for a 3 line setup and .014 for a two line setup, electric throttles and such. It is a bit old, I put that up before 2.4Ghz was allowed. There were coated .014 lines back then. Today it should read .015. The last time I was at the NATS that is the way we flew 15.
I'll review the Brodak posting.


John Vlna

what law is that Paul? For all carrier events in the AMA rule book , line size is different for 3 and 2 line setup's. Of course 15 is a non-rule book event, but at the NATS and every other 15 contest i have been to use .012 for 3 line and .015 for 2 line.

This is also copied and pasted from the website(focus should be on the General part):


General:
All AMA Safety and general CL rules observed. Please note line lengths are specified differently than most other AMA events. Scale and AMA/Sportsman are 60ft. to 60 ft. 6 in. Not 60 ft. plus or minus 6 in. Similarly 15 profile is 52 ft. to 52 ft. 6 in. All are measured from the aircraft centerline to the handle grip center. (Where your palm rest on the handle.) Lines diameters (for three line systems) are .012 for 15, .015 for AMA/Sportsman and Class I, .018 for Class II.  For 2 line systems line diameters are .014 for 15 Profile, and per AMA rules for AMA/Sportsman and Class I & II.

Carrier Profile
Per AMA rulebook

Carrier Sportsman
Sportsman is an un-official event. Models may be Electric or Glow.  It is intended as an entry level event, or one for fliers who do not primarily specialize in Navy Carrier. Rules are the same as AMA Profile carrier except:

Muffler Pressure is allowed
10 bonus points are given if a Brodak kit is used.
Nitro content is limited to 10%
Models may be Electric or Glow Powered
Electric 3.5lbs Weight Limit, 42 volts maximum.  See Detailed Electric Rules below.
Carrier, I & II Combined.
Per AMA rules except:

One award for first through third place.
Carrier .15
15 profile is an un-official event. Models may be Electric or Glow.  The rules are summarized below.

Maximum engine size, .15- glow/diesel, .20- 4 cycle or .20 total displacement for multiple engine models.  Electric 2.5lb weight limit.  See Detailed Electric Rules below.
This is a speed limit event. Maximum high speed points are for 70MPH, no penalty for exceeding 70 MPH. 
No model size limit, Glow; 4 lbs weight limit, Electric; 2.5lbs weight limit.
No movable controls except throttle, elevator, and hook.(i.e. no line sliders)
Muffler pressure is allowed, no crankcase or other timed pressure systems allowed
Lines: .012 stranded stainless steel, 52 feet to 52 ft 6 in from center of handle to airplane centerline.
No bonus points except 10 bonus points for using a Brodak kit.
Scoring is per AMA Navy Carrier except flights are timed for eight ( laps vice seven (7).
Airplanes are encouraged to be finished and marked with naval color schemes
All other AMA carrier regulations apply.
Control Line Electric Sportsman and .15 Electric Navy Carrier
Applicability. All pertinent AMA regulations for Control Line Navy Carrier and unofficial rules shall apply. In places where the term “engine” is used in the AMA regulations, the term “motor” shall be understood for purposes of applicability and pertinence to the electric Navy Carrier events.
Power Systems. Models shall be propelled only by one or more electric motors which receive their power from one or more onboard battery packs. Size or type of motors and battery packs are unrestricted. Maximum battery voltage is 42 volts. Electrical signals for control may be transmitted through the control lines but electrical power to power the motors or recharge the battery packs may not be transmitted through the control lines.
Sportsman; Weights. The model weight shall not exceed 3.50 pounds ready for flight, including batteries. Pull test will be 20G
.15 profile; Weight. The model weight shall not exceed 2.50 pounds ready for flight, including batteries. Pull test 25 lbs.