A GRUMMAN AMERICAN TIGER IN CRUISE AT 6000 FT DIVERTED DUE TO THE FUEL QUANTITY INDICATORS READING EMPTY CAUSED BY INDICATORS READING ZERO WHEN TANK ACTUALLY ONE QUARTER FULL.

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MY INST STUDENT AND I WERE ON HIS LONG XCOUNTRY FLT DEPARTING BDR TO ACK TO ORH RETURNING TO BDR. WE HAD; ACCORDING TO OUR FLT PLAN; SUFFICIENT FUEL ON BOARD TO FLY THE RTE IF NEEDED WITHOUT A FUEL STOP BUT PLANNED A FUEL STOP AT ORH. WE ARRIVED AND DEPARTED ACK AS PLANNED AND WERE FLYING AT 6000 FT ON V146 FROM PVD TO PUT VOR AND HAD JUST BEEN TURNED OVER TO BDL APCH. WE HAD RECEIVED A SPECIAL ON ORF THAT THE CEILING AT ORF WAS 100 FT. I ASKED BDL TO CONFIRM AND WHILE DOING THIS; NOTICED THAT BOTH FUEL GAUGES SHOWED EMPTY. FUSES AND ELECTRICAL WERE CHKED AND GAUGES WERE TAPPED TO SEE IF ANY MOVEMENT OCCURRED. A QUICK ESTIMATE OF TIME AND DISTANCE AND FUEL BURNED DICTATED THAT WE HAD BURNED ABOUT 22.5 GALLONS AND HAD ABOUT 15 GALLONS LEFT VERSUS A BURN RATE OF 8.5 GALLONS OR CONSERVATIVELY 10 GPH. I WAS CONFIDENT WE HAD ENOUGH FUEL TO FLY FOR AT LEAST 1.5 HRS AND COULD GET SOMEWHERE SAFELY; BUT HAD NO WAY TO VERIFY THAT WE IN FACT WERE NOT OR HAD NOT EXPERIENCED A FUEL LEAK (THE PLT HAD NOT SWITCHED TANKS AS HE SHOULD HAVE SO ONE OF THE TANKS HAD BEEN ON THE LOW SIDE ANYWAY) AND THEREFORE FELT WE SHOULD LAND AS QUICKLY AS POSSIBLE TO VERIFY THE TANKS. BDL APCH WAS ADVISED WE HAD A FUEL GAUGE PROB AND WANTED VECTORS TO THE NEAREST ARPT WITH AN APCH. HFD WAS SELECTED AND WE WERE GIVEN VECTORS TO THE HFD LDA 2. UPON PICKING UP ATIS; WE DISCOVERED HFD WAS BELOW MINIMUMS AND ADVISED BDL APCH. BDL APCH SUGGESTED IJD AND THE LOC 27 APCH AND TURNED US OVER TO PVD APCH WHO ADVISED US THAT IJD WAS NOW AT 500 FT OVCST. SINCE WE NEEDED 920 FT FOR THE APCH; I ASKED FOR THE CLOSEST ARPTS WITH WX WHICH WOULD ACCOMMODATE US. I WAS TOLD TMU (40 MI) AND PVD (30 MI) WERE THE 2 CLOSEST AND WAS ASKED WHAT I REQUESTED. I ASKED FOR VECTORS TO IJD LOC 27 AND IF WE COULD NOT GET IN FOR VECTORS DIRECT TO PVD AND HOPE WE DID NOT HAVE A FUEL LEAK. WE WERE ABLE TO MAKE THE APCH AT IJD BECAUSE OF A BRIEF BREAK IN THE OVCST LAYER AND LANDED SAFELY. UPON REFUELING; WE FOUND THAT WE DID IN FACT HAVE 10 GALLONS OF FUEL LEFT AND THAT OUR CALCULATIONS AT THE TIME WE DISCOVERED THE EMPTY GAUGES; WERE PRETTY CLOSE AND SUFFICIENT FUEL EXISTED AND THE FUEL GAUGES WERE INOP. EVEN THOUGH WE BELIEVED WE WERE RIGHT; THE FACT THAT WE COULD NOT VERIFY THE OP OF THE FUEL GAUGES CAUSED GREAT ANXIETY IN A VERY HVY AND DETERIORATING IMC CONDITION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE ACFT WAS A GRUMMAN AMERICAN TIGER AND THE FUEL QUANTITY INDICATORS WERE IN NEED OF CALIBRATION. THE RPTR SAID WHEN THE TANKS WERE 1/4 FULL THE INDICATORS READ EMPTY. THE RPTR STATED THE FAA INVESTIGATED THE INCIDENT AND THE RPTR'S FUEL BURN FIGURES WERE THE SAME AS THE FAA CALCULATION.