30th November 2010 - 06:19 PM
following it, we can take a case when a giant aquarium is taken on a very sensitive scale, and the air is not allowed to escape. If by some Magic Spell we could transfer a fly inside it, we would see that the scale equivalently shows an increase in the weight.
Ahh... yes, I agree. Very good example! So the fly's weight is transferred to the airplane not necessarily through aerodynamic forces such as downwash, but though buoyancy considerations (an increase in static pressure) which can be viewed statically, and are independent of whatever method the fly (or airplane in the other example) actually uses to stay in the air (this line of thinking even works for a hot air balloon).
So that answers my question b) for any objections I previously posed, and to answer my own question a) about the airplane in a theoretical universe of air and downward gravity: this imaginary universe is itself not consistent with our universe's physical laws for a single reason... what keeps the air (which itself has mass and weight) from accelerating downward under the influence of this universal 'downward' gravitational field? Something has to, and I wrongly didn't address this in my air-only universe.
Back in reality on Earth, the ground serves this purpose. So the combination of ground and gravity (or something similar to contain the air, such as your giant sealed aquarium or a 747 with a pressurized cabin) is
required for an airplane to fly at any altitude, no matter how far away from ground effects.
Interestingly though, does this mean that whatever air container is used to hold the suspended flying object (fly or airplane) must be airtight in order for the weight to be transferred? "Airtight" meaning a container able to withstand an increase in pressure needed for buoyancy. (Of course, I mean when using the buoyancy explanation PatGhosh came up with and neglecting dynamic considerations such as ground effects and downwash.) In this case, the suspended weight and volume (buoyancy) of the fly in an unpressurized cabin would result in an (minuscule) increase in pressure in all of the world's atmosphere (which would be the only container that is 'airtight' in this thought experiment). Put another way: does a unsealed
box weigh more with a hot-air balloon inside of it? A sealed box would weigh more, as PatGhosh explained with buoyancy (repped), but it seems to me an unsealed box would simply loose the weight-equivalent amount of displaced air to the atmosphere, so the box would not feel the difference if there was, say 8 oz of balloon compared to if 8 oz of air occupied that same space.
So to summarize my current stance on the original question: the fly would add weight to the airplane only if it had a pressurized cabin
, neglecting dynamic considerations such as the ground effect or whether or not the cabin is big enough to let the air move around freely (as likely wasn't the case with the MythBusters experiment).
Awesome question by the way, enord. Thoughts?