My boat has a large displacement-hull. Where should I place the transducer? I am using a Garmin model.

Do you mean the transducer for a depth sounder?

This answer has come straight off the Garmin website:

For large displacement-hull powerboats, Locate the transducer 1/3 aft LWL and 15-30 cm (6-12) off the centerline of the boat on the side of the hull where the propeller is moving downward.
For small displacement hull and planing-hull powerboats, mount the transducer well after and near the centerline of the boat to ensure that is in contact with the water at high speeds. Mount the transducer on the side of the hull where the propeller is moving downward.

inboards mount well ahead of the propeller(s) and shaft(s).
I/Os and outboards mount close to the engine(s).
On fin keel sailboats the transducer is best located to the side of the keel and forward of the fin keel 30-60 cm (1-2').

I may be wrong but I guess the object for both log and depth sounder [more critical for former?] must be to avoid areas where there is most turbulent rather than smoothly running water and this would seem to depend on the underwater profile. Can your class club, or if one-off, the designer not direct you?