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Probably because volume increases faster than surface area.

Edit: To expand on that, assume the Queen Mary is an airtight cube. A small model of the cube might have 1m sides, with a volume of 1m³. If the real cube had sides of 3m, it would have a volume of 27m³. Buoyancy is a function of the volume of water displaced by an object, so since volume increases so much faster than surface area (and, by extension, weight), the larger cube would displace enough water to overcome its weight where the smaller one wouldn't.

Good on you for challenging that and bad on me for repeating that without knowing precisely. Heard that decades ago and use it as a general reference to the fact that functional models are absolutely not scalable. I'm not a trained engineer and I don't know if the 1:6 part is right but there is a scale where that design would capsize because it was designed to function at the scale it was built for. At sufficiently different scales different properties of water would become dominate and upset the intended function.

At a super small scale it might just kind of stick in the water. That's a funny image. With water I just imagine it as kind of like 'resolution'. Take a small boat and a cup of water, then scale that up 10,000x. You're not really 'scaling' everything because the molecules aren't growing, there's just more of them, and the dynamics that govern the interactions of 10 molecules are very different from 10,000.

I also remember something about Gulliver's Travels- proportionately scaled giant's bones couldn't support the weight because square-cube law. I should have used that reference because I do know how that works. Could just be that with the Queen Mary too but I vaguely remember it being something about water itself.

But again good on you for asking. And since you are the kind of person that challenges things you probably already understand everything I just babbled about but thanks for giving me a minute to pretend I remember stuff I sort of learned once.

Can't help myself so I'll take a total guess that maybe the Queen Mary thing something about friction of water not having enough effect at smaller scales to provide resistance the keel needs? idk- that was probably an embarrassing guess but I'm just a dilettante so who cares.