In the previous handout we discussed how the air pressure in the lift air cushion lifts the hovercraft off the ground. We assumed that the hovercraft was hovering above solid ground. Now let’s investigate what happens when the hovercraft travels over water. In order to lift the hovercraft, the pressurized air must now push against the surface of the water. If you tried pushing your hand into a sink full of water, your hand would sink into the water. What keeps the hovercraft from sinking as well? The answer to this comes from one of the oldest established principles in the history of science: Archimedes’ Principle or the Law of Buoyancy.
Archimedes of Syracuse
(287 BC - 212 BC)
According to legend Archimedes was struck by this principle while taking a bath when he noticed that the volume of water displaced was equal to the volume of his body. Overjoyed by his discovery, he jumped out of the bathtub and ran through the streets naked shouting, “Eureka! Eureka!” (Greek for “I’ve found it! I’ve found it!”) Developed in 250 BC, this principal explains why some objects float in water while others sink. The principle states the following:
‘When a body is immersed in fluid at rest it experiences an upward
force or buoyant force equal to the weight of the fluid displaced by the body’.
Notice when you get into a bathtub, the level of the water rises. This is because your body is now taking up some of the space where the water used to be. The water has to go somewhere else when it is pushed out of the way, so it goes up, making the water level rise. You’ve just displaced that amount of water. Archimedes’ Principle says that a buoyant force will push upwards on you when you’re in the water, and the strength of the force will be equal to the weight of the water that you pushed out of the way when you got in.
The same thing happens with boats. When a boat is placed in water, part of the boat goes beneath the surface of the water and pushes the water out of the way. According to Archimedes’ Principle, this results in a buoyant force that pushes up on the boat. The magnitude, or strength, of the force is equal to the weight of the water that would have filled the space that is now taken up by the boat. The boat floats in the water because this upward buoyant force is equal to the downward weight of the boat.
In order to do calculations using this principle, we need to know the weight of a certain volume of water that is displaced, or the weight density of water.
Weight Density = Weight ÷ Volume
The weight density of water is about 62.42 pounds per cubic foot ( lb/ft3).
A cubic foot is a unit of volume equal to the volume inside a box whose sides
are 1 ft long. In SI units (System International), the weight density of water
is about 9806 Newtons per cubic meter ( N/m3).
Weight Density = Weight ÷ Volume
A boat that displaces 0.5 m3 of water weighs 4903 N [1102 lb].
When a hovercraft travels over water, it acts a little differently than a boat, because the hovercraft itself doesn’t actually displace any water. It is the pressurized air inside the lift air cushion that pushes down on the water, causing some of the water to be displaced. If you blow into a sink full of water, you can see that you create a small dimple in the water. Hovercraft do the same thing, except they create a larger depression in the water. In fact, we know that for every 5.2 lb/ft2 [24.9 N/m2] of pressure in the lift air cushion, the water underneath the hovercraft is depressed one inch [2.54 cm]. In the previous handout, we discussed how the pressurized air in the lift air cushion pushes the hovercraft up and causes it to hover. Now we see that not only does the pressurized air push up on the hovercraft, it also pushes down on the water.
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