that's not true, it's not entirely accurate. The anchor itself is what holds a ship in place, but the chain plays a key role in keeping the ship in place, it's a team effort between both.
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Given a long enough chain, his statement would be true.
No need to dwelve into catenary physics, though.
Correct. Which for large ships, you need extremely long chains.
Anchors alone just slide in the seabed. It's the weight of several meters of chain close to the soil that holds the anchor in place.
Actually, it’s the anchor, not the chain, that holds the ship in place. The anchor’s flukes dig into the seabed to grip it, while the chain adds weight to keep the anchor set. Without the anchor, just the chain wouldn’t stop the ship from drifting. I know this because I own a ship an I have to use an anchor to keep it in place