A BE55 had an airborne conflict with another aircraft while departing 39N.

Narrative

During taxi for Princeton (39N) Runway 28; there was an aircraft departing; and an aircraft in the downwind. As I prepared to take Runway 28; the landing traffic declared a simulated engine out on base. I saw the aircraft; and had already completed my run-up and made an immediate departure. During the takeoff roll; I took notice of the upwind traffic to the right of centerline; and it appeared to be departing to the north. I checked the engines; monitored my takeoff; raised the gear and flaps. I began to clean up the aircraft as it passed through blue line. I checked traffic display and it showed an aircraft to the left of centerline. The upwind traffic had corrected course and I was startled to see it now to the left of centerline. The apparent distances did not seem correct between the traffic display and the visual. I began to wonder if another aircraft had appeared as often occurs at uncontrolled airports. With my speed building rapidly; I looked right quickly turned right and departed to the north; making a departure call as I did. As I made the right turn to the north; I realized I was turning at a rather low altitude; near the departure end of the runway. I could have avoided this by allowing the landing aircraft to finish; thus providing space with the departing aircraft.