A B727-200 STRIKES ITS TAILSKID DURING A XWIND TKOF FROM LGA; NY.

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STRUCK TAILSKID ON TKOF DURING INITIAL CAPT IOE/FAA CHK FLT. FAA SAFETY INSPECTOR WAS RIDING OMC TO CONDUCT INITIAL CAPT FAA CHK. TKOF FROM RWY 31 AT LGA. STRONG L XWIND (APPROX 20 KTS) WITH GUSTING RPTED ON ATIS. I ELECTED TO USE REDUCED THRUST BECAUSE TWR RPTED STEADY WIND AT TKOF. RAN UP ENGS NORMALLY USING XWIND TKOF PROC. EXPERIENCED ONE BRIEF COMPRESSOR STALL ON ENG #2 AS ENG #2 APCHED 1.4 EPR. REMAINING ENG #2 PARAMETERS CHKED NORMAL AND NO FURTHER ENG #2 ABNORMALITIES NOTED DURING TKOF. DURING TKOF ROLL I NOTED A VERY ROUGH RWY SURFACE ESPECIALLY AT THE INTXN OF RWYS 31/22. ROTATED AT VR USING L WING DOWN AILERON. EXPERIENCED A WIND GUST AT ROTATION WHICH CAUSED YAW; SOME WING ROCK AND POSSIBLY SOME SETTLING OF THE ACFT AT TKOF. NOTED TAILSKID LIGHT REMAINED ON AFTER GEAR RETRACTION. UPON LATER QUERY; THE FLT ATTENDANTS RPTED HEARING AN ABNORMAL BUMP AT LIFTOFF. PERFORMED TAILSKID EXTENDED WITH LNDG GEAR UP IRREGULAR PROC. NOTIFIED DISPATCH; ASKED FOR ADJUSTED FUEL FIGURES AND ASKED DISPATCH TO COORDINATE WITH MAINT. CONTINUED THE FLT TO ORD AFTER VERIFYING THAT WE HAD ADEQUATE FUEL ON BOARD. NOTIFIED THE FLT OPS DUTY MGR BY TELEPHONE AFTER LNDG. THE FAA SAFETY INSPECTOR SAID THAT HE NOTED NO INDICATION OF AN IRREGULARITY DURING TKOF; AND HE WAS SURPRISED THAT WE BELIEVED THAT WE HAD HAD A TAILSKID STRIKE. HE STATED THAT THE IRREGULAR PROC WAS HANDLED PROFESSIONALLY AND SIGNED MY INITIAL CAPT FAA CHK AS SATISFACTORY. I BELIEVE THAT THE ROUGH RWY AND WIND GUST WERE CONTRIBUTING FACTORS. IT IS POSSIBLE; BUT NOT CERTAIN; THAT I ROTATED TOO FAST. INSPECTION OF THE ACFT AFTER LNDG AT ORD SHOWED NO NORMAL EVIDENCE OF COMPRESSION OF THE CRUSHABLE CARTRIDGE. THERE WAS NO ANNULAR RING MARK OF DISPLACED GREASE ON THE TELESCOPING SLEEVE; AND THE SHEAR CLIP WAS INTACT AND IN PLACE. HOWEVER; THE TAILSKID RUB PLATE WAS MISSING; AND THE UPPER PORTION OF THE TAILSKID STRUT (ABOVE THE CRUSHABLE CARTRIDGE) HAD SHEARED RIVETS AND WAS HANGING DOWN ABNORMALLY. SINCE THE CRUSHABLE CARTRIDGE SEEMED NOT TO HAVE COMPRESSED; I AM GUESSING THAT THE DAMAGE WAS CAUSED BY SIDELOADS DURING THE TAILSKID STRIKE. SUPPLEMENTAL INFO FROM ACN 438384: GUSTS HAD BEEN RPTED BTWN 25-35 KTS. AT START OF TKOF ROLL; TWR ADVISED WINDS ONLY AS 14 KTS. JUST AS LIFTOFF OCCURRED; HOWEVER; WE EXPERIENCED A STRONG GUST FROM THE L; THE ACFT SLEWED SOMEWHAT AND THE MAINS TOUCHED DOWN AGAIN. AT THE SAME TIME; THE CAPT IN TRAINING INCREASED PITCH ATTITUDE; AND I FEEL WITH THE ASSOCIATED STRUT COMPRESSION; THAT THE TAILSKID CONTACTED RWY AT THE SAME TIME.