TXWY EXCURSION WHEN A C172 PVT PLT LOSES R BRAKING CAPABILITY ON THE TAXI-OUT TO RWY 28 AT DPA; IL.

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ON MAR/FRI/02; C172 WAS PREFLTED INSIDE THE HANGAR. I FOUND THE AIRPLANE TO BE IN AIRWORTHY CONDITION. THE PLANE WAS THEN PULLED OUT OF THE HANGAR AND STARTED WITH SUPPORTING CHKLISTS. AFTER RECEIVING ATIS; THE BRAKES WERE RELEASED; A LITTLE THROTTLE GIVEN; AND THEN BRAKES WERE REAPPLIED TO VERIFY THEIR OP. THEY WERE FINE SO I CONTINUED TO TAXI ON THE RAMP TO THE EDGE OF TXWY E. I STOPPED AT TXWY E AND CONTACTED GND CTL. THEY GAVE CLRNC TO TAXI TO RWY 28 VIA TXWY E. WHEN THE PLANE STARTED TO ROLL; I APPLIED L BRAKE TO ASSIST IN TURNING AROUND THE BEND. THE L BRAKE PERFORMED FINE. I APPLIED THE CORRECT WIND CORRECTION TO THE AILERONS; A L QUARTERING TAILWIND. I CONTINUED TO TAXI DOWN TXWY E WITH AN RPM SETTING OF 900 RPM AND A SPD OF THAT OF A BRISK WALK. AFTER XING TXWY C THERE WAS A BEND/ZIGZAG IN TXWY E. AS I APCHED THE BEND I APPLIED R BRAKE AND HAD NONE. I TRIED AGAIN AND STILL HAD NONE. I APPLIED SOME L BRAKE TO TRY TO SLOW DOWN OR STOP BEFORE THE EDGE OF THE TXWY. IT SLOWED THE PLANE; BUT NOT BEFORE ROLLING ABOUT 5-10 FT OFF THE TXWY. AS IT ROLLED OFF THE TXWY; THE L REAR MAIN GEAR PUSHED A TXWY LIGHT BACK SLIGHTLY. I THEN USED THE L BRAKE TO BRING THE PLANE BACK ONTO THE TXWY TO CONTACT GND. I CONTACTED GND AND EXPLAINED THE SIT. THE PLANE WAS THEN TAXIED VERY SLOWLY BACK TO THE HANGAR. THE INCIDENT HAPPENED AT EARLY XA05 AM. THE PROB WAS CAUSED BY A FAULTY R BRAKE. ANOTHER FACTOR TO THE SIT WAS THE TAILWIND WHICH MADE THE RUDDER THAT MUCH LESS EFFECTIVE. IN THE FUTURE I PLAN TO TEST THE BRAKE BEFORE APCHING ANY SHARP TURNS. HOPEFULLY THEN THERE WILL BE MORE THAN A FEW FEET TO DEAL WITH THE SIT.