When in doubt, we take soundings (measure the water's depth) with the same tool Hudson's crew would have used: a lead line (or sounding line). Flags attached to the lead line mark depth in 6-foot increments (fathoms). The Half Moon has a draft of 8-1/2 feet (extending that far underwater), so it needs at least a fathom and a half of water to stay clear of the bottom.
In Hudson's day, crews would even use their lead lines to take samples of the river bottom. They could fill a small hollow on the bottom of the line's lead weight with tallow, then observed what stuck to this goo when they retrieved the line. Silt or sand made for a fine anchorage, but clean tallow warned of rocks lurking below, making anchorage dangerous if not impossible.
On this Voyage of Discovery, Greg and Ross took soundings during our data collection layover at Grave's End Bay to track changes in the height of tide for their student presentation.