SMA LANDS AT MAJOR ARPT WITHIN TCA WITHOUT CLRNC OR CONTACT OF ANY KIND.

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I WAS NAVING FOR THE PLT. WE WERE N OF MEIGS FIELD; NBOUND ALONG THE SHORE OF LAKE MICHIGAN. OUR INTENTION WAS TO LAND AT PAL-WAUKEE AND TRADE ROLES (PLT/COPLT). WE DIDN'T WANT TO TRANSITION THE TCA SO I GAVE THE PLT DIRECTIONS USING A TCA CHART. MY DIRECTIONS WERE AS FOLLOWS: FLY N ALONG THE COAST; INTERCEPT AND FLY INBOUND ON THE 115 DEG RADIAL TO N BROOK VORTAC; AT 15 DME; TURN L HDG 240 DEGS; WHEN ARPT IS IN SIGHT; CALL LEGS ON CTAF AND LAND ON RWY 16. I MADE THE MISTAKE BY USING A SCALE THAT MEASURES NM ON A SECTIONAL CHART RATHER THAN THE APPROPRIATE SCALE. USING THE CORRECT SCALE THE DIRECTIONS SHOULD READ TO SAY 'AT 7 DME; TURN L HDG 240 DEGS.' THE INTENDED COURSE WHEN PLOTTED ON THE CHART LEADS TO PAL- WAUKEE. THE COURSE GIVEN (MEASURED WITH THE WRONG SCALE) LEADS TO CHICAGO O'HARE INTL. UNAWARE OF OUR ACTUAL LOCATION; WE LANDED THE ACFT. I REALIZED MY MISTAKE WHILE ON THE GND BY NOTICING AIRLINES; A NUMBER OF HVY JETS AND (WHEN WE TOOK OFF) THE RWY MARKED RWY 14L. AFTER TAXIING TO THE RUN-UP PAD; WE TRADED ROLES (I WAS NOW PLT). I TOOK OFF RWY 14L AND DEPARTED (MAKING L TFC) TO THE N.