Honestly, as an old Naval Officer, you are better off towing with either: (a) a full tank, or (b) an empty tank, than with a partly filled tank; because of what we call "the free surface effect". With a full tank, the center of gravity of the water in the tank will stay pretty close to the center of gravity of your trailer. With a partially filled tank, the center of gravity will shift every time you turn or swerve while driving. This could cause unwanted and unstable swaying of your rig as the water sloshes back and forth in the tank.
This "free surface effect" applies equally to black water and grey water tanks. Best to drain all tanks as dry as possible before heading out on the highway.
Anchors Away!!
This makes sense to me, as a railroad conductor on freight trains. When hauling tank cars, we can tell if they aren't quite completely loaded, as the sloshing effect is worse and causes slack action in the train to hit us in the ass end of the locomotive when slowing/stopping.
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