EMB ERJ 145 ER/LR
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
We did our standard brief at the gate. We were in the middle of our before takeoff checklist when tower issued a new clearance. I read back his clearance correctly but was a bit confused at what I just read back because I was thinking about my other task of the checklist. I finished the checklist and the flying pilot asked tower for a clarification of a left or a right hand turn out after takeoff? The tower told us right turn after takeoff; direct ZZZ VOR; climb and maintain 15000. The flying pilot assumed that ZZZ VOR was to our left after takeoff and the tower wanted us to go the long way around for the direct (If you look at the SID; the VOR appears to be a left turn and that's where we went wrong). So the flying pilot said he would direct me up when we get turned back to it and just following the heading bug; which he spun around 90 degrees to the right to get us going in that direction. As we were in our initial turn ATC questioned us and said the fix was to our left and we told him the tower told us to take a right and then the controller said it was basically a direct after takeoff and that it might have been confusing when the tower gave us those instructions. He then amended our clearance and told us to continue our turn and when able direct ZZZ VOR; and that traffic was no factor and everything was okay.We should have told the tower to stand by and completed our checklist then received our changes in our clearance and reviewed it in the FMS and on the SID. We also should have had FMS selected and perhaps that would have alerted us that it was basically directly in front of us. So; the threat and error was our situational awareness. The other threat was how it looks depicted on the SID. If you look at the SID; it's clearly to the left of centerline of the runway; however when you look at it depicted on your screen it was slightly to the right; perhaps 5 degrees to the right. What I learned was to always question the controller when unsure of a clearance.
EMB-145 First Officer reported their ATC clearance was to turn right after takeoff; but the VOR they needed to cross was actually just slightly to the left of runway heading.