A friend and I have been having an ongoing debate for years. We were at a pub on a wharf, watching shipping container ships and cruise ships come into dock, and he posed the question. With no wind, no waves, perfect conditions, could he move the ship at all?
In: Planetary Science
Yes. If you eliminate the slightest wind, waves, or current you could even pull it 5 miles per day once it’s moving.
For the nerds:
There is no static friction in water. That’s part of why ships have defined trade for millenia. No static friction means 0 force at 0 velocity so we can definitely do *something* to the velocity before drag gets in our way.
https://pubmed.ncbi.nlm.nih.gov/15028193/
This says a male human can pull 400N. Let’s just say we can do this indefinitely. Sleep is for people who don’t pull cargo ships.
http://www.diva-portal.org/smash/get/diva2:1449680/FULLTEXT01.pdf
This paper gives the drag coefficient and wetted surface area of a container ship in section 2.2 and 5.2. The drag coefficient plots don’t go down to 0 velocity and I expect it’s higher at 0 velocity, but this is a terrible approximation for the internet so I’m gonna just say it’s 4.4*10^-3. They give their formula for drag coefficient which is based on the wetted surface area, not cross sectional area like the normal non-naval-engineer drag coefficient. The wetted area is 19556.1m^2.
How fast could we eventually get it to go? At constant speed, the drag force and our pulling force are equal, so we just plug the 400N into the drag coefficient. I picked a middle-ish value from WolframAlpha’s seawater density of 1027kg/m^3 and I got a velocity of 95mm/s. That’s actually pretty good and adds up to just over 5 miles per day!
How long would it take us to get there? The paper says it’s a Capemax ship so from Wikipedia, 170000 tons (deadweight tons, but the actual boat is usually only a small fraction of the cargo.) From standstill, you will start moving it at 2.6e-6 m/s^2 which would have been enough to reach full speed in 10 hours. However, as the drag starts to ramp up your acceleration goes down until you’re barely accelerating. You never actually hit the full speed above because it’s asymptotic. If we assume it follows an exponential decay, you’re probably within 2% of final speed within like 40 hours.
Checking our assumptions, the drag coefficient is probably higher down in the stokes flow region, and the real world will never give you 2 days of no current, no wind, and no waves anywhere you can pull a Capemax ship. However, Capemax is really big so smaller boats will be easier. If you manage to salvage the Edmund Fitzgerald out from the bottom of Lake Superior, it’s less than 1/10 the weight and representative of Seawaymax vessels.
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