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For my project, I need to create a lock gate which will be used for the Panama Canal. One of the many thing my teacher said, was that for the design of the lock gate, the gate should not fail when it gets bumped by a large ship (like a cruise ship).

All the information that we need to calculate, like the mass of a common cruise ship can be found on the internet or other places. We came to the conclusion that the mass of a cruise ship, in the worst case scenario, is equal to $65.000.000 \text{ kg} + 158.200.000\text{ kg} = 223.200.000\text{ kg}$.

The $65.000.000$ is the mass of a common cruise ship and the $158.200.000$ is the maximum mass a cruise ship can hold. The average speed of a cruise ship is equal to about $7 \text{ m/s}$.

We can now calculate the kinetic energy, which is:

$$E_k = \frac12mv^2$$

$$E_k = \frac12\cdot223.200.000\cdot7^2$$

$$E_k =5.468.400.000\text{ J}$$

But after this, I got stuck. A tip from my teacher was that we also need to use the formula $W = F\cdot s$, whereas $s$ is the indentation of the lock gate. How do I know that the lock gate will not fail? I wanted to try something like this:

$$\frac12mv^2 = F \cdot s$$

But I'm not sure if this is right. What is the right approach to know if a lock gate will fail or not against a bump of a cruise ship?

Edit

Here is the information about the lock gate:

The lock gate itself is 31 m x 10 m x 57 m and is hollow in the inside. This leaves a 30 m x 9 m x 56 m gap:

enter image description here

The thickness of the edge is 0,5 m everywhere. The outer case is made of steel and has crossed steel beams.

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closed as off-topic by ACuriousMind, Kyle Kanos, user36790, Bill N, Gert Mar 14 '16 at 1:12

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  • $\begingroup$ What's all the information you have about the lock gate? $\endgroup$ – lemon Mar 11 '16 at 15:49
  • $\begingroup$ @lemon I have added the information about the lock gate. The layout for the steel beams is not known yet. $\endgroup$ – Adnan Mar 11 '16 at 16:17
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    $\begingroup$ Ships maneuvering in or near a lock will not get anywhere near 7 m/s speed. The question one has to ask is - what absorbs the energy in the collision? Is it the ship, the lock door, or some third element (buffer). If it is the ship, it will be damaged; ditto the hole. I think you need to design a deliberate "bumper". $\endgroup$ – Floris Mar 11 '16 at 16:24
  • $\begingroup$ @Floris Ohh, that is quite logical. A ship always slows down when it gets near the lock gate. About the bumper, it is very logical and I would have probably done the same thing, but this is not allowed for the design. I think this has to do something with the s, which needs to be as small as possible. For this, I need to know the F, but I have no idea how to do that. $\endgroup$ – Adnan Mar 11 '16 at 17:27
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    $\begingroup$ The force that the ship exerts on the gate depends not on the ship's momentum, but on how quickly the momentum changes (i.e., on how quickly the moving ship comes to a stop.) The more quickly it stops, the more the force. The "bumper" that @Floris suggested is something that the ship can crush, and it reduces the impact force by spreading it out over the amount of time that it takes to crush the bumper. $\endgroup$ – Solomon Slow Mar 11 '16 at 18:12
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I don't know what source you used to get the masses of a "common" cruise ship and its contents. 158,000 metric tons seems like a lot of stuff to cram into one ship. What happened? Did all the passengers bring lead suitcases on this trip?

The Spirit-class cruise ships can fit in the canal locks and they have a deadweight of only 7500 tons. I estimate the empty weight of one of these ships at about 37,500 tons, or about 45,000 tons for the fully-loaded vessel.

https://en.wikipedia.org/wiki/Spirit-class_cruise_ship

You can't use the gross tonnage figures to estimate weight since the gross tonnage is a measure of the internal volume of the vessel.

https://en.wikipedia.org/wiki/Gross_tonnage

Many of the largest cruise ships cannot fit in the lock chambers of the canal because they are physically too large. The lock chambers are 1000 feet long by 110 feet wide, and the widest vessel which is normally accommodated cannot be wider than 105 feet.

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