A FLC FAILED TO COMPLY WITH A SID TURN RADIUS RESTR; WHEN DEPARTING CHICAGO MIDWAY. THE FMS; AND IT'S ASSOCIATED FLT DIRECTOR COMMANDS; WERE ILLOGICAL.

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CLRNC WAS MDW 4 DEP; WITH AN ATC ASSIGNED HDG OF 260 DEG; L TURN ON DEP FROM RWY 04R. WX WAS APPROX 3000 FT OVCST; WINDS (TWR) WERE 100 DEG; GUSTING TO 25 KTS ON ARR 2 HRS PRIOR; INS WINDS (ON APCH) WERE 40 KTS AT 1000 FT AGL; HOWEVER; TURB WAS LIGHT; AT THAT TIME. DEP PROCEEDED NORMALLY UNTIL FMS WENT TO ALT CAPTURE MODE AT APPROX 2500 FT MSL. FO WAS AT CTLS AND FO'S FLT DIRECTOR LESSENED THE BANK ANGLE FROM 30 DEG TO 10 DEG. I NOTICED THE SHALLOWING OF THE TURN AND COMPARED MY FLT DIRECTOR; WHICH INDICATED A STANDARD L TURN COMMAND. AT THIS TIME; ORD ATC STERNLY CALLED FOR AN INCREASE IN BANK. TURB WAS MODERATE AND THE RADAR INDICATED LEVEL 3 RETURNS; WE WERE; ALSO; IN VERY HVY RAIN AND WORKLOAD WAS HIGH; TO KEEP ACFT UNDER CTL. THE AUTOPLT WAS DISCONNECTED AND FO DISREGARDED COMMAND BARS AND INCREASED BANK ANGLE. THE AUTOTHROTTLES STARTED SURGING DUE TO THE WIDE AIRSPD VARIATIONS; AND WE HAD TO DISCONNECT. ATC APPARENTLY HAD TFC AND WAS YELLING AT US (REMEMBER THE 4 MI RADIUS RESTR) BUT WE COULD NOT SAFELY INCREASE BANK ANGLE BEYOND 30 DEGS DUE TO THE TURB. WE STATED THIS TO ATC; BUT HE TOLD US (CORRECTLY) THAT WE HAD TO INFORM BEFORE DEP IF RESTR COULDN'T BE MADE; ETC; WE WERE GIVEN A CLB TO 4000 FT; AND I SELECTED VNAV FOR CLB; HOWEVER ALT HOLD REMAINED ENGAGED ALSO; AND NEITHER MODE WOULD DE-SELECT. FO'S FLT DIRECTOR WAS COMMANDING A SHALLOW BANK AND DSCNT; WHILE MINE WAS GIVING CORRECT INDICATIONS. WE SELECTED THE CTR FLT DIRECTOR ON FO'S SIDE AND PROB WAS CORRECTED. THE AIRSPACE PROB WAS A COMBINATION OF AN EQUIP FAILURE AND WINDS; TURB; A NARROW TURN RADIUS AND PROB RESOLUTION TIME (RECOGNITION); ALL AT THE MOST INOPPORTUNE TIME. FO; IN MY OPINION; PERFORMED THE CORRECT ACTION OF DISENGAGING THE AUTOFLT AND IGNORING AN ERRONEOUS COMMAND BAR.