BE35 FLT CREW ENCOUNTERS STRONG HEADWINDS ENRTE AND LANDS WITH LESS FUEL THAN PLANNED.

Narrative

I WAS GIVING FLT INSTRUCTION TO A GENTLEMAN WHO ALSO HAD A NUMBER OF BUSINESS FLTS TO COMPLETE THAT DAY. WE ORIGINALLY DEPARTED WILMINGTON; DE; AND HAD ACCOMACK COUNTY ARPT AS OUR FIRST STOP FOR THE DAY. AFTER ARRIVING AT ACCOMACK; WE WERE ON THE GND FOR ABOUT 2 HRS BEFORE SETTING COURSE FOR GREENSBORO. THE WX THAT DAY WAS CLR AND VISIBILITY WAS MORE THAN 10 MI. HOWEVER; THE WINDS WERE VERY STRONG AND VARIABLE UP THROUGH 10000 FT. WE ELECTED TO FILE 8000 FT AS OUR CRUISING ALT AND THE FLT PLAN HAD 4 HRS OF FUEL LISTED. THIS WAS THE FIRST MISTAKE. IN REALITY; THE PLANE ONLY HAD ABOUT 2 1/2 HRS OF FUEL. DESPITE THIS; WE STILL CALCULATED OUR FLT TO ONLY TAKE 1 HR 15 MINS. WE DEPARTED ACCOMACK AND CLBED TO 8000 FT. AFTER BEING IN CRUISE FOR ABOUT 30 MINS; WE DISCOVERED THAT WE HAD FOUND OURSELVES IN SEVERE WINDSHEAR AT 8000 FT. OUR AIRSPD WAS CHANGING RAPIDLY. IT WOULD READ ANYWHERE FROM 170 KTS TO 85 KTS WITHIN A MATTER OF 1 MIN. AT ONE POINT WE HAD TO REQUEST LOWER FROM ATC DUE TO THE FACT THAT WE COULD NO LONGER MAINTAIN ALT. WITH THIS CONSTANT SHIFTING OF WINDS AND SHEAR; WE FOUND OURSELVES BEHIND ON OUR CALCULATED TIME ENRTE AND FUEL BURN. UPON GETTING TO WITHIN 55 NM OF GSO; MY STUDENT TOOK IT UPON HIMSELF TO DECLARE MINIMUM FUEL. WHILE I WOULD HAVE PREFERRED A DISCUSSION ON THE MATTER BEFORE WE HAD ATC GIVING US SPECIAL ATTN; THE CALL WAS WELL DESERVED. OUR AIRSPD CONTINUED TO FLUCTUATE AND PLAYED HAVOC WITH OUR PLANNING. DESPITE THE FACT THAT WE HAD A NUMBER OF ARPTS TO LAND AT ALONG THE WAY; OUR FINAL CALCULATION PUT US ON THE GND AT GSO WITH A 30 MIN RESERVE. SINCE THE WX WAS VMC; WE DECIDED TO CONTINUE. WE ACTUALLY ENDED UP LNDG AT GSO WITH AROUND A 35 MIN RESERVE. THIS PROB WAS CAUSED BY INACCURATE PLANNING AND A LACK OF AWARENESS. WE COULD HAVE FUELED AT ACCOMACK AND HAD A PLEASANT FLT WITH THE EXCEPTION OF THE MODERATE TO OCCASIONAL SEVERE TURB; BUT WE ELECTED TO NOT PLAN FOR THE UNEXPECTED. FOR PREVENTION: REFUEL EVERY CHANCE YOU GET; AND PLAN FOR THE UNEXPECTED.