I was giving my son a bath and stuck a little paddle wheel with a suction cup to the tub wall. Neither by my hand nor my son's would this thing pop loose... how confounding! How.... HARD... can it.... POSSIBLY... STICK!!? (pop.)
The answer to how hard a suction cup can stick is related really to two things: How good is its ability to hold a seal when you pull on it, and what is the ambient pressure of the environment. For instance, if a suction cup is dry, it doesn't hold as well because air will slip under it, allowing it to pop off. If it's wet, you might still pull it off by pinching it or pulling it so hard it deforms or wrinkles, which again compromises that seal. Engineering problems.
I guess I'm more interested in theoretical maximum pulling force. If you're talking a perfectly engineered suction cup with a great soft seal and a body that won't warp when you pull it, the theoretical maximum force is determined by the ambient pressure and the surface area of the cup. ( It is literally ambient pressure times area of suction cup. ) This is because, if you can reach and exceed the pressure that's holding the cup to the surface, you can make that seal separate, letting the air or water in behind it... suction cups aren't glued on, they're just held there by pressure.... but I digress..
The tub drained and for some reason I was still thinking about it. What if the tub was deeper... how much more force would it take to pull the cup free? Here are some calculated examples, based on a spreadsheet I made for this very problem:
Force to remove suction cup with 1 square inch area:
( 2.88 cm dia or 1.13 inches dia)
Force at air pressure:101,325.00 Pa or 14.70 PSI
Force at 33 ft:202,650.00 Pa or 29.39 PSI
Force at 100 ft:408,370.45 Pa or 59.23 PSI
Force at 1300ft:4,092,915.9 1Pa or 593.63 PSI (HOLY CRAP THAT'S A LOT OF FORCE!)
Then I got to thinking, how big of a suction cup would I need to, say, stop a submarine?
I won't go into the work in this post, but if you want to see it, it's in this shared google spreadsheet. Feel free to clone it and try different things.
I decided I wanted to stop a Soviet Typhoon class submarine, ala Hunt for Red October. Wikipedia had lots of good info about the dimensions and maximum speed, and I applied the drag force calculation to determine that it would need such-and-such thrust. I compared this thrust with the rated power capacity of the twin nuclear reactors (also on Wikipedia, by the way!) and the numbers were pretty close. That is to say, the the thrust I calculated was reasonable: A little over 140 US TONS of forward thrust.
Then I used my suction cup holding force equation, plugged in the maximum running depth of a Typhoon class submarine (1300 ft) and Bam! A 25 inch diameter suction cup should do it! (Provided you can somehow stick it directly to the back of the submarine in some way that it won't slide off or get caught in the propellers. Navy SEALs could do it.)
I just think that's interesting. A suction cup the size of a serving platter could stop a Soviet sub from escaping.
Who knew suction cups were so effective at ocean depths?