INSTRUCTOR WITH SPI HAS NMAC IN TFC PATTERN WHEN A SECOND ACFT DEPARTS BELOW THEIR ACFT AT NON TWR ARPT.

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I WAS CONDUCTING TFC PATTERN OPS WITH A STUDENT IN THE RWY 24 TFC PATTERN AT HWV. WE MADE POS RPTS ON EACH LEG OF THE PATTERN; AND THE STUDENT INITIATED A GAR LATE IN THE FLARE. ON CLBOUT; THE STUDENT NOTICED A WHITE WITH RED STRIPED C172 SLIGHTLY TO OUR L AND BELOW. THE CESSNA TURNED SLIGHTLY L; CAUSING ME TO KEEP OUR ACFT ON RWY HDG LONGER THAN PRESCRIBED BY AIM. THERE WAS NEVER A RADIO CALL MADE TO ANNOUNCE DEP BY THIS ACFT; ALTHOUGH THE PLT APPARENTLY MADE AN ANSWER TO OUR GAR CALL 'THAT'S PROBABLY A GOOD CHOICE.' THERE WERE SEVERAL OTHER RADIO CALLS MADE BY A PERSON ON THE GND WHO COMPLAINED THAT THIS PLT HAD TAKEN HIS KEYS WITH HIM; AND BLOCKED THE CTAF FOR THE DURATION OF 1 TIME AROUND THE PATTERN. CORRECTIVE ACTION: SHORT OF FAA ENFORCEMENT; I DON'T KNOW WHAT ACTION WOULD BE APPROPRIATE. I DOUBT EDUCATION OF THIS INDIVIDUAL WOULD CHANGE HIS CARELESS DISREGARD FOR SAFETY. I WILL POST A COPY OF THIS RPT ON THE LCL BULLETIN BOARD; AND ENCOURAGE THE ARPT MGR TO TALK TO HIM. SUPPLEMENTAL INFO FROM ACN 335815: I SPOTTED A C172 (WHITE WITH RED STRIPE) A LITTLE TO MY L SIDE AND BELOW. AT THIS TIME THE C172 BANKED L AND CONTINUED TO CLB CAUSING ME TO ABORT THE L TURN I NEEDED TO MAKE TO BE ON THE XWIND LEG.