A C177 PLT VIOLATED THE RESTR AIRSPACE INVOLVING A RESEARCH CTR.

Narrative

I DEPARTED ZZZ ARPT ON NOV/TUE/01 SOMEWHERE BETWEEN XA30-XB00 LCL TIME. IT WAS A VFR FLT TO ZZZ1 NEAR ZZZ2. AS I CLBED OUT OF ZZZ TOWARDS THE E I NEEDED TO CLB AS FAST AS POSSIBLE TO AVOID MOUNTAIN TERRAIN. HOWEVER A CESSNA 177 CARDINAL DOES NOT HAVE A GREAT CLB PERFORMANCE SO AS I CLBED I MEANDERED AROUND THE PEAKS TO GAIN ALT. WHEN I WAS OUT OF ZZZ LCL ARPT AREA I SWITCHED TO ZZZ3 TRACON. THE RADIO TFC WAS SUCH THAT I COULD NOT GET A XMISSION IN EDGEWAYS. FOR SAFETY I WANTED TO GET TO AT LEAST 5000 FT ON MY WAY TO 5500 FT TO FINISH CLRING ANY MOUNTAINS IN THE AREA. I HAD TUNED INTO THE ZZZ4 VORTAC; BUT WAS NOT YET RECEIVING A CLR SIGNAL. I NEEDED TO KNOW WHAT RADIAL I WAS ON SO I COULD STAY OUT OF THE TFR THAT WAS 9 MILES E OF ZZZ4. BY NOW I WAS NEARING THAT EASTERN EDGE OF THE MOUNTAINS AND THE WESTERN EDGE OF THE VALLEY. ALSO NOW RECEIVING A CLR VOR SIGNAL FROM ZZZ VORTAC. IT WAS NOW TO THE BEST OF MY RECOLLECTION TO BE AROUND XB30 LCL TIME. I MENTIONED TO MY PAX THAT IT LOOKED LIKE ZZZ4 OFF A LITTLE WAYS TO OUR LEFT. I SAID THAT I DID NOT KNOW EXACTLY WHERE THE TFR WAS; BUT I WILL CONTACT ZZZ4 APCH TO MAKE SURE I WAS CLR OF THE TFR; AS THE ZZZ4 VORTAC RADIAL I WAS ON I WAS AFRAID I MIGHT HAVE PENETRATED THE TFR. ZZZ4 APCH CONFIRMED MY FEARS; I WAS IN THE TFR. ZZZ4 APCH TOLD ME TO TURN IMMEDIATELY TO 040 DEGS; WHICH I DID. I OFFERED TO TURN EVEN MORE IF THAT WOULD HELP ME TO EXIT THE TFR QUICKER. HE EMPHATICALLY REITERATED TO TURN TO 040 DEGS AS DIRECTED; WHICH I HAD ALREADY DONE. THE REST OF THE FLT TO ZZZ1 WAS QUITE PEACEFUL WITH THE GREAT ASSISTANCE OF BOTH ZZZ4 APCH AND ZZZ5 APCH CTLS. I MIGHT ADD THAT THIS WAS THE FIRST MAJOR FLT I HAVE TAKEN SINCE ALL THE NEW RULES HAVE GONE INTO EFFECT. IT WAS DEFINITELY A NEW AND LEARNING EXPERIENCE FOR ME. I DID NOT INTENTIONALLY FLY INTO THE TFR. IT WAS DUE TO MEANDERING AROUND THE MOUNTAINS TO AVOID A COLLISION WITH RISING TERRAIN. I TEND TO ERROR ON THE SIDE OF CAUTION AND SAFETY. WHEN DIRECTED TO TURN TO THE HDG I DID SO IMMEDIATELY AND EVEN OFFERED MORE IF IT WOULD HELP. THE TFR COORDINATES WERE NOT GIVEN EXACTLY; BUT ONLY GIVEN BY GENERALITY. I TOOK THE TFR AREA TO BE AREA ZZZ WHICH I THOUGHT I WAS S OF WHEN I CLRED THE MOUNTAINS.