CL65 CREW CLBED ACFT TOO HIGH FOR THE ACFT GROSS WEIGHT; GOT ON THE BACK SIDE OF THE PWR CURVE; AND WITH SLOWING AIRSPD; HAD TO DSND TO PREVENT A STALL IN ZKC CLASS A.

Narrative

A FLT OPERATED BTWN DEN AND KBNA. DUE TO CONTINUOUS CHOP/TURB AT OUR PLANNED CRUISING ALT OF FL330 I ELECTED TO REQUEST A HIGHER ALT WHERE WE ANTICIPATED A BETTER (SMOOTHER) RIDE. WE WERE INITIALLY ASSIGNED FL350 BUT FOUND CONDITIONS TO BE MUCH THE SAME. AFTER CONSULTING THE OPTIMAL/SAFE ALT CHARTS FOR OUR CURRENT WT AND CHKING THE ISA DEV AND FORECAST WINDS ALOFT; WE REQUESTED FL370. (THE CHART INDICATED FL380 AS THE MAX ALT FOR OUR WT.) WHILE CLBING TO FL370 AT MACH 0.70 (OUR CLB PROFILE) THE CLB RATE DECREASED TO ZERO. I CHANGED TO VERT SPD MODE AND SELECTED 500 FPM. AS WE CLBED; THE AIRSPD DECREASED UNTIL WE WERE LEVEL AT FL370; HOWEVER; THE AIRSPD DID NOT INCREASE AS EXPECTED; BUT CONTINUED TO DECREASE. I INSTRUCTED THE FO TO REQUEST A LOWER ALT WITH ATC; AS THE AIRSPD WAS DECREASING TOWARDS STALL THE AUTOPLT DISCONNECTED AND A DSCNT INITIATED. WE HAD DSNDED APPROX 800 FT WHEN ATC FINALLY CLRED US TO MAINTAIN FL330. IN HINDSIGHT; I FEEL THAT WHILE THERE WAS NO LACK OF ATTN IN THE SIT (IE; NO DISTRS); I WAS CAUGHT BY SURPRISE WHEN THE ACFT WOULD NOT ACCELERATE ONCE IT HAD LEVELED OFF. IN THE FUTURE; I WILL NEVER ALLOW THE AIRSPD TO DECAY BELOW THE CLB PROFILE 0.70 MACH; ASSUMING THAT ONCE WE LEVEL IT WILL INCREASE. ALSO; I WILL BE EVEN MORE SKEPTICAL OF THE SAFE ALT CHARTS ESPECIALLY IN A HVY ACFT.