Date: 202104
Local time of day: 1201-1800
Location: MDW.Airport, IL
Aircraft: Medium Transport; Low Wing; 2 Turbojet Eng
Operator: Fractional
Operating under: Part 135
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class C MDW
ATC / advisory: Tower MDW
Reporter organization: Contracted Service
Reporter function: Captain
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Confusion; Communication Breakdown
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Result: Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Contributing factors: Chart Or Publication
Primary problem: Chart Or Publication

Narrative: We were flying the Midway 5 departure off [Runway] 04R. Tower gave us a left turn 250 degree along with our takeoff clearance. We misunderstood the SID instructions and began an initial right turn to 100 degrees (with intention to turn left 250 degrees at 2400 ft; which is what we specifically discussed and briefed. Tower called us as we were turning right and stated that he wanted a left turn 250 degree. We immediately corrected and turned left 250 degrees.  I told Tower that we were flying the SID initial turn and he said that the SID was misleading. Poorly worded SID. We had a discussion about these instructions on our pre-departure briefing and both pilots misinterpreted the instructions. The SID is worded: 'Assigned heading clockwise 360 degrees through 080 degrees climbing right turn to 2400 heading 100 degrees before proceeding on course.' I would suggest rewording the SID; perhaps add 'all other turns; fly as assigned'. I will not make this mistake again; but it sounded like it was a somewhat common misinterpretation (according to tower's response).


Second narrative: Was assigned Midway5 departure from runway 4R; maintain 3000'.   Captain and I extensively briefed this departure and we both agreed that the depiction and narrative is confusing.  Do you turn to the assigned heading before or after the depicted 100 deg heading at or above 2400'?  That's the question and discussion we had.  I recalled a previous departure I flew from this airport; which I believed was the same runway; where the controller turned us into a TCAS RA.  So; in my mind I was on heightened alert.  With takeoff clearance; the tower controller instructed left turn; heading 260; cleared for takeoff.  Captain and I had agreed during brief that the depicted route had to be flown before turning.  Normal initial climb; heading mode was selected at 400'; power came out of the takeoff detent as I am preparing to start getting ready for a 3000' leveloff as assigned.  Started the right turn.  Immediately tower said left turn; left turn 260.  I was not yet on autopilot so continued to hand fly and smotthly rolled the wings in the other direction and continued without further incident.  Captain responded to ATC that we were turning as indicated on the SID depiction.  Tower controller replied 'yes; it's a confusing procedure' or words to that effect.It's a confusing depiction and textual narrative on the chart for the MIDWAY5.  I think a review of the narrative and better description of the procedure is warranted; given that ATCT reported 'it's confusing'.This SID assigned concerned me from the start.  Sitting on the ramp before engine start and before briefing; I thought it would be a left turn scenario as it happened last time.  But they turned us into an RA back then.  I discussed my concerns with the Captain; who BTW is an FAA Line Check Airman.  So there is a bit of built-in deferral from me to his decisions and input; even though it was my leg to fly.  I stated that I think we fly the heading as assigned prior to takeoff; so we'll fly the departure in HDG and PITCH at 200 knots up to 3000.  The Captain said we should fly the chart depiction of 100 degrees; and he would reset the heading bug after takeoff from  runway heading to 100.  Again; I had a built-in bias to defer to him as an LCA .. but really; it was on me.  I think the simplest solution to prevent this is; if I/we had any confusion/questions/concerns about the route depicted and what was expected of us on the departure; the person to ask was ATC..and we had multiple opportunities to do so: clearance delivery; ground; and tower at departure.


Synopsis: Medium Transport Crew reported conflicting departure instructions issued by ATC verses the MDW3 SID narrative; resulted in a deviation.