C560 PLT MADE A HARD LNDG AND BOUNCED BACK IN THE AIR 4 TIMES BEFORE COMING TO A STOP IN THE RWY OVERRUN AREA RESULTING IN DAMAGE TO THE NOSE GEAR. ACFT WAS STRANDED AND TOWED OFF THE RWY.

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ON APR/THU/02 AT APPROX XA30 WE WERE ON OUR FINAL APCH INTO 3CK; LAKE IN THE HILLS. THE OTHER PLT WAS FLYING FROM THE L SEAT AND I WAS THE PNF IN THE R SEAT. THE CONDITIONS THAT DAY WERE CLR AND THE RWY WAS DRY. THE WINDS WERE STRONG OUT OF THE W AND GUSTY. (I BELIEVE THEY WERE 280 DEGS AT 22 KTS GUSTING TO 36 KTS). AS PER THE MANUAL (1/2 OF THE GUST FACTOR IN EXCESS OF 5 KTS). WE ADDED 7 KTS TO VREF AND OUR TARGETED AIRSPD WAS 103 KTS (96 + 7=103). PF HAD ABOUT 22 HRS IN THE ACFT AND HAD LANDED IT SEVERAL TIMES. HE HAD SEEN SEVERAL LNDGS BEFORE; BUT THIS WAS HIS FIRST ATTEMPT AT LNDG THERE. WE HAD DISCUSSED THIS APCH AND LNDG AT 3CK AND I TOLD HIM MY HANDS WOULD BE VERY CLOSE TO THE CTLS AS A BACK-UP. THE APCH WAS NORMAL AND ON-SPD AND THE FLARE WAS AT THE NORMAL HT. THEN THE PF PUSHED FORWARD TO MAKE THE LNDG; WHICH RESULTED IN A FIRM 3-POINT LNDG. AS SOON AS THE AIRPLANE TOUCHED DOWN; PF EXTENDED THE THRUST REVERSERS. DUE TO THE FIRM LNDG; THE ACFT BOUNCED SLIGHTLY OFF THE GND; CAME DOWN AND BOUNCED AGAIN. AT THIS POINT; THE BOUNCE WAS NOT SEVERE ENOUGH TO WARRANT A GAR; HOWEVER; EACH BOUNCE GOT PROGRESSIVELY WORSE. MY GUESS IS THAT WE BOUNCED ABOUT 3-4 TIMES. AFTER THE SECOND OR THIRD BOUNCE; I CAME ON THE CTLS BUT COULD NOT CTL THE ACFT. AT THIS POINT; THE ACFT WAS TOO SLOW AND BEHIND THE PWR CURVE TO ATTEMPT A GAR. THE LAST BOUNCE WAS VERY HIGH AND RESULTED IN DAMAGE TO THE NOSE GEAR. WHEN THE ACFT CAME TO A STOP; WE SHUT IT DOWN AND WERE EVENTUALLY TOWED OFF THE RWY. I DON'T REMEMBER POSITIVELY IF I EXTENDED THE SPD BRAKES OR NOT; BUT I DON'T THINK I EVER DID BECAUSE WE WERE NEVER ESTABLISHED ON THE RWY WITH POSITIVE BRAKING. IN MY OPINION; THE REVERSERS WERE EXTENDED TOO SOON. YOU DO NOT WANT TO EXTEND THE SPD BRAKES OR THRUST REVERSERS UNTIL THE ACFT IS ON THE RWY; WITH THE NOSE GEAR DOWN; AND BRAKES HAVING BEEN APPLIED. TO QUOTE THE MANUAL FOR SHORT-FIELD LNDGS: 'FOR LNDG UTILIZING THRUST REVERSERS; AFTER TOUCHDOWN ON THE MAINS; LOWER THE NOSE; APPLY WHEEL BRAKES; EXTEND THE SPD BRAKES; AND DEPLOY THE THRUST REVERSERS.'