WHILE PRACTICING INST APCHS NEAR LAF; A C172 PLT AND INSTRUCTOR EXPERIENCED AN NMAC WITH A LIGHT TWIN ACFT.

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I WAS FLYING WITH A CFII APPLICANT ON A FINAL REVIEW FLT BEFORE THE CHKRIDE. THE STUDENT WAS IN THE R SEAT; I WAS IN THE L. WE WERE TRACKING TO THE BOILER VOR FROM THE N IN ORDER TO PRACTICE A VOR HOLD. THE STUDENT WAS WEARING A VIEW-LIMITING HOOD; AND THE ALT INDICATOR AND DIRECTIONAL GYRO HAD BEEN COVERED WITH PIECES OF PAPER TO SIMULATE A VACUUM SYS FAILURE. A STRONG WIND ALOFT (FORECASTED AS 310 DEGS AT 30 KTS) HAD CONTRIBUTED TO US BEING SLIGHTLY E OF BOILER AS WE CROSSED THE VOR. I LEANED BACK AND LOOKED OUT THE R WINDOW TO VISUALLY SEE OUR LOCATION WITH RESPECT TO THE VOR. AS I WAS DOING THIS; THE STUDENT INDICATED SHE WAS NOTING THE TIME ON THE ACFT CLOCK AND BEGINNING THE 1 MIN TURN TO ENTER THE HOLD. GLANCING AT THE ACFT CLOCK MUST HAVE ALLOWED MY STUDENT TO SEE OUTSIDE ENOUGH TO NOTICE ANOTHER AIRPLANE CONVERGING FROM ABOUT OUR 10 O'CLOCK POS; APCHING NEARLY HEAD-ON. THE STUDENT LOOKED UP; EXCLAIMED THAT SHE SAW AN AIRPLANE AND IMMEDIATELY BEGAN A STEEP R TURN AWAY FROM THE OTHER ACFT. I LOOKED FORWARD AND THEN L JUST IN TIME TO SEE THE OTHER ACFT PASS TO OUR L AND SLIGHTLY BELOW US. THE ACFT WAS A LIGHT TWIN SIMILAR TO A SENECA OR BARON. WE WERE COMMUNICATING WITH THE LAF ATCT DURING OUR DEP AND HAD MONITORED THE FREQ LISTENING FOR OTHER TFC FROM LAF THAT MIGHT BE IN THE AREA. I DID NOT ANNOUNCE THAT WE WOULD BE PRACTICING A HOLD OVER BOILER -- SOMETHING I NORMALLY DO. IT DID NOT APPEAR THIS OTHER ACFT WAS PART OF THE LCL TRAINING FLEETS AS WE NEVER HEARD ANY RADIO XMISSIONS OF RECEIVED ANY ADVISORIES INDICATING THIS ACFT WOULD BE IN THE AREA. BOILER VOR IS 10 NM FROM THE LAFAYETTE ARPT; SO THIS ACFT NEED NOT HAVE BEEN IN CONTACT WITH LAF TWR. WITH POOR RADAR COVERAGE FROM ZAU AND NO RADAR SVCS AVAILABLE AT LAF ATCT; IT IS UNLIKELY EITHER ACFT COULD HAVE BEEN ADVISED OF THE OTHER'S PRESENCE BY ATC. I FEEL MY INATTN TO VISUALLY SCANNING FOR TFC; ALTHOUGH MOMENTARY; IS THE PRIMARY REASON FOR THIS OCCURRENCE. I ALSO FEEL SEVERAL OTHER FACTORS CONTRIBUTED: 1) LACK OF RADAR SVCS AT LAF PREVENTED A POSSIBLE TA BEING ISSUED TO ME. 2) POOR RADAR COVERAGE BELOW 5000 FT FOR ZAU MAY HAVE PREVENTED A TA FROM BEING ISSUED TO THE OTHER ACFT (IF HE OR SHE WAS COMMUNICATING WITH ZAU). 3) THE AREA OF INTENSIVE FLT TRAINING OPS THAT EXISTS AROUND THE LAF ARPT; INCLUDING THE BOILER VOR; IS NOT CHARTED ON ANY AERO CHARTS. 4) NEITHER THE OTHER ACFT NOR I ANNOUNCED TO LAF ATCT THAT WE WERE APCHING THE BOILER VOR. NO PROC EXISTS TO ANNOUNCE YOUR POS AS YOU NEAR BOILER; IT IS A COMMON LCL PRACTICE. LAF IS HOME TO OVER 35 TRAINING ACFT BELONGING EITHER TO THE UNIVERSITY OR THE FBO'S FLT SCHOOL. MOST OF THESE ACFT FLY MULTIPLE TIMES A DAY WHICH OFTEN RESULTS IN OVER 8 ACFT IN THE TFC PATTERN; A FEW ON PRACTICE INST APCHS; AND A FEW MORE ARRIVING OR DEPARTING. THE LAF ATCT DOES AN OUTSTANDING JOB KEEPING TRACK OF EVERYONE AND ISSUING TA'S WHEN POSSIBLE. HOWEVER; IN MY OPINION THE CTLRS ARE OVERBURDENED AND; WITHOUT RADAR; ARE POORLY EQUIPPED.