Good morning Vanderlay. 3.4 nm (just under 20700 ft) gives you a lot of room to turn at 160 knots. At 15 deg of bank and a 160 knot ground speed, you'd need approx 8500 feet.
A few questions, though.
Is your goal to stick precisely to a radius, stay inside it, or stay outside it?
Are we looking at a sea level location?
Is the airspeed going to be constant through the turn, and
What is the wind like in the area you are considering? For the arc you are describing, for a constant airspeed, the wind may signficantly decrease the groundspeed (and with it, radius) at one point in the turn and increase both for the other.
Cheers
Vs