Assuming you are not going for a full out physics simulator:
Your plane needs to have a position, velocity, direction(angle), acceleration and various maximum values. On each game step:
velocity += acceleration * dt;
velocity = clamp(velocity, 0, max_velocity);
acceleration = 0;
position += velocity * dt;
On (de)acceleration:
acceleration = getVecFromMagnitudeAndDirection(accelerationRate, direction);
On moving north/s/e/w:
direction += (desired_direction - direction)*rotationRate;
- note that you probably want a calcAngleDifference function to handle various edge cases.