One final attempt to expain
– Last Updated: Sep-18-10 12:02 AM EST –
The problem with this whole discussion is that you have not actually been applying the principles of buoyancy to the internal floatation in the hull of your canoe. You know that the stuff floats, but you are forgetting that it only floats by displacing water. Therefore, when it is part of a floating boat, its weight is fully supported by the water and therefore it must displace a volume of water having a weight that is equal to the weight of the floatation material itself. The only way it can displace that much water while an integral component of a floating boat is to depress the hull of that boat into the water a little deeper, enough to displace a quantity of water having a weight equal to its own. I'll try an example that might help, using only the principles I've already described, but this time applying them to an imaginary boat.
EXAMPLE
Imagine that we have a canoe that weighs 85 pounds, and that this canoe has a buoyant layer built into the hull. For simplicity, let's say that the buoyant layer consists of the material on the inner half of the hull instead of being sandwiched in the middle. If you don't like that idea, feel free to imagine that the floatation layer is sandwiched in the middle, because that won't change anything about this example except for the difficulty of the modifications to the boat that we are about to perform.
1. Place the empty canoe in the water. Would you agree that when floating freely, the canoe sinks just a little ways into the water, just enough to displace a volume of water having the same weight as the canoe, which is 85 pounds? Good.
2. Now, let's get our hands dirty. We will strip out that inner floatation layer of the hull, leaving the outer, structural layer of the hull intact and in perfect condition. That means that the outside dimensions of the hull are exactly the same as before. Imagine that we put all that stripped-out floatation on a scale and find that the total weight of that material is 30 pounds (that may not be an unreasonable figure if it was taken from a big, 85-pound canoe, but if you want to pretend it weighs a lot less, that won't change anything except the magnitude of the changes described below). Would you agree that after removal of the floatation layer, the canoe now weighs 55 pounds? Good. It's still a perfectly good canoe - the outside surface of the hull is exactly the same as before - so let's put it back in the water.
3. Okay, so this same canoe, with the exact same external hull dimensions as before, is floating in the water again, but now it only weighs 55 pounds instead of 85. Would you agree that when floating freely, the canoe now displaces less water than before, and that in fact, the weight of the water it is displacing equals the current weight of the canoe, which is 55 pounds? Good.
4. Now, if the canoe has the same external hull dimensions as before, but it is displacing 55 pounds of water while floating instead of the original 85 pounds of water, that means the hull must be embedded in the water by a smaller amount than before, or in other words, it is floating higher in the water. After all, the deeper the hull is pushed into the water, the more water it displaces, and we know it is displacing less water than before, so it must be floating higher than before (If this were a real-life experiment, we could just measure the difference in waterline depth).
5. Therefore, the floatation that was originally built into the hull actually caused the hull to sink more deeply into the water, rather than make it float higher. This is actually very simple, and the laws of buoyancy are obeyed perfectly. When comparing hulls that are exactly the same size: 1. The heavier you make the boat, the deeper it will sink into the water. 2. The more weight you load into the boat, the more deeply it will sink into the water. 3. The less weight you load into the boat, the less deeply it sinks into the water. 4. The lighter you can make the boat, the less deeply it sinks into the water.
6. If we could build this same canoe with magic floatation material that was totally weightless, the removal of the floatation would not change the depth to which the canoe embedded itself in the water while floating, but by the same token, installing the material would not make the canoe float any higher simply because installing the material would not reduce the weight of the canoe. Taking this experiment one step farther will illustrate the other way to affect buoyancy, but we will use the "real" floatation material of the original canoe, not the magical weightless stuff.
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Let's re-install all that floatation back into the hull, returning the boat to its original weight of 85 pounds. However, this time, let's install the floatation layer on the outside of the structural layer of the hull instead of its original location on the inside.
1. Now the canoe looks funny, but let's put it back in the water and let it float again. Since the canoe weighs the same as it did at the very beginning of this experiment, it is once again displacing 85 pounds of water while floating. Is the canoe floating higher, deeper, or at the same depth as it did before we moved the floatation layer to the outside of the hull?
2. Answer: The canoe is floating higher than it did originally. Sure, it weighs 85 pounds, just like it did originally, and it still displaces exactly 85 pounds of water while floating, but now the external dimensions of the hull are greater than before because we put the floatation layer on the outside. Since the hull only sinks into the water deeply enough to displace 85 pounds of water, it sinks into the water less deeply now. The bigger hull does not need to be embedded as deeply as the original, smaller-size hull to displace the same amount of water.