SPI BECOMES DISORIENTED AND ENTERS CLASS C AIRSPACE WITHOUT CLRNC.

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MY STUDENT PLANNED A XCOUNTRY TRAINING FLT FROM MDH TO UCY AND RETURN. I CHKED HER PLANNING BEFORE SHE LEFT AND GAVE HER THE APPROPRIATE ENDORSEMENTS IN HER LOGBOOK AND SENT HER OFF. LATER THAT AFTERNOON; I CALLED COLUMBIA FSS TO SEE WHAT HER INBOUND TIME TO MDH WAS AND THEY TOLD ME AB15Z. AT AB45Z COLUMBIA CALLED US BACK BECAUSE SHE WAS OVERDUE. WE STARTED MAKING PHONE CALLS TO FIND OUT WHERE SHE WAS. WHEN WE FOUND OUT WHERE SHE WAS LOCATED; SHE HAD BEEN IN CONTACT WITH ZKC (127.7) AND THEY MANAGED TO GET HER TO THE MARION ARPT (MWA) WHICH IS APPROX 11 MI E OF CARBONDALE (MDH). WE WANTED HER TO LAND ASAP BECAUSE WE WERE UNSURE OF THE AMOUNT OF FUEL SHE HAD REMAINING. SO SHE LANDED IN MARION AND I WENT TO PICK HER UP WITH ANOTHER INSTRUCTOR. WHEN WE RETURNED I TOOK A LOOK AND TRIED TO FIGURE OUT HOW SHE GOT SO DISORIENTED. I DISCOVERED AN ERROR IN HER PLANNING THAT I DID NOT DETECT BEFORE SHE LEFT. BASICALLY; SHE ADDED HER WIND CORRECTION ANGLE INSTEAD OF SUBTRACTING IT AND ENDED UP FLYING WAY OFF COURSE. HER PREDETERMINED INCORRECT HDG COMBINED WITH THE REDUCED VISIBILITY DUE TO HAZE CAUSED HER TO BECOME LOST. WHILE SHE WAS LOST WE BELIEVE THAT SHE PENETRATED THE EVV CLASS C AIRSPACE UNKNOWINGLY. WHEN SHE FINALLY WAS ABLE TO CONTACT THE EVV APCH CTL; SHE WAS ALREADY WITHIN 5 MI OF THE PRIMARY ARPT. SUPPLEMENTAL INFO FROM ACN 295308: ON MY WAY BACK FROM UNION CITY; I LOST TRACK OF MY POS IN PART BECAUSE OF THE HAZE OUTSIDE; BUT ALSO BECAUSE OF A COMPUTATIONAL ERROR WHEN PLANNING. I ENDED UP FLYING TO THE NE AND WAS IN CLASS C AIRSPACE. I WAS NOT SURE WHERE I WAS UNTIL I CONTACTED TERRE HAUTE FLT SVC. THEY TOLD ME I WAS ABOUT 5 MI TO THE NE OF EVV ARPT AND TO CONTACT EVV APCH. EVV APCH HAD ME SQUAWK A CODE; TOLD ME MY LOCATION; AND TO FLY BACK TO CARBONDALE; IL; AT A HDG OF 240 DEGS. I THEN MONITORED EVV APCH FOR ABOUT 20 MI; WHERE AGAIN THEY GAVE ME ANOTHER HDG OF 230 DEGS TO FLY BACK TO CARBONDALE.