# Fly, flying inside a plane

I know this may seem elementary to many on this forum so please forgive me if it does.

We are having a late Christmas celebration and this question has arisen.

If a fly is in a plane and flying does the plane weigh more than before the fly entered the plane? Assume the fly continues to fly, never touching anything. Also assume that the fly only displaces it's volume of air and then the plane is perfectly sealed.

My hypothesis is that the plane will actually weigh less because of displaced air while the mass goes up because of increased density. As long as the fly keeps flying.

I am alone and everyone else thinks the plane will weigh more.

Also would the answer change if there were many many flies?

Any input will be greatly appreciated.

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dst
It depends on what you mean. Inside the plane, there will be more mass for obvious reasons. A weighing scale measures the reaction force of the plane's weight. If a fly is close to the floor of the plane such that there is no increase/change in pressure from its wings then its weight (the flapping of its wings counteract gravity and through Newton's third law) will be transferred to the plane and the plane will 'weigh more'.

"Weigh" is too vague to really say anything about.

I guess you could say that if the plane is in flight, then its weight is zero, regardless of how many flies or chubby tourists are aboard!

But, while it's on the runway waiting to take off, I'd venture to say that the plane should weigh more, by the weight of one fly (or to be more precise, the weight of one fly minus the weight of the air it displaced), since something is supporting it (the air under its wings), and something on the plane is supporting that (the hull, or fuselage).

DaveC426913
Gold Member
The plane does have weight even when it's flying. It displaces the air underneath it. (Consider: If the plane suddenly weighs more for whatever reason, say a tyrannosaur lands on it, it may not be able to stay airborne. The engines will have to work harder to keep it in level flight.)

The plane will weight more with a fly in it than it will without a fly in it. It makes absolutely no difference whether the fly is at rest or in flight.

This is a twist on the classic puzzle about a truck full of pidgeons crossing a rickety bridge. Banging on the truck to get the birds flying has no effect on the weight of the truck.

The fly displaces a volume of air that counterbalances its weight, called lift. This flow of air has a pressure that pushes down on the floorboard of the airplane. If you put the plane on a scale, the mass of the fly would be recorded. Period.

Have you ever stood under a helicopter? It pushes the air, and a hell of a lot of it, down on the ground below. Its called prop wash, and it can blow you away. A fly is just a small version of a helicopter hovering above the ground (A/C floorboard).

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The plane does have weight even when it's flying. It displaces the air underneath it. (Consider: If the plane suddenly weighs more for whatever reason, say a tyrannosaur lands on it, it may not be able to stay airborne. The engines will have to work harder to keep it in level flight.)
MMMM, you should be very careful on that. You are correctly, but its an indirect effect that the engines have to work harder, and its not proportional to the weight of the T-rex.

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I guess you could say that if the plane is in flight, then its weight is zero, regardless of how many flies or chubby tourists are aboard!
The weight of the airplane is w=mg in level flight. This is non-zero and is certainly affected by its occupants/cargo.

PS, do you work at APL?

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The directionality of the fly's lift becomes randomized with the air inside the plane, so that the force of flying is converted into thermal pressure, eventually acting evenly on the plane's interior. The fly's "buzz," the signature of its flight, is mostly omnidirectional, and otherwise interferes with sounds of wavelength similar to its wingspan, ~1 cm.

Please draw a control volume around the inside of the A/C cabin. The wings must product an amount of lift $$\Delta L$$ that supports the weight of everything inside said control volume.

The air might be randomized and spread out inside the cabin, but the net dynamic presssure still has to act downwards (despite being spread out).

Think of a helicopter: If it hovers 2 feet above your head, you are going to get blasted with downwash (Lots of force, little area). If that same helicopter hovers 2 miles above the ground, the downforce from the blades will spread out over several miles laterally. This means the pressure will be very minute and you wont 'feel' the downforce (Lots of force, LOTS of area). Integrated over those several miles, it still has to add up to the weight of the A/C.

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russ_watters
Mentor
A fly is a lot smaller then a helicopter, Loren Booda, so it is easy to dismiss the effect of its wings, but the effect is still there. The pressure gets spread-out, yes, but it is still greater below the fly than above. Just like for the helicopter. It does not completely randomize.

The energy dissipated by the airflow, on the other hand, slowly increases the air temperature of the air in the plane, but that's not the same thing. A hovering fly/helicopter and a plane in level flight are essentially static force situations.

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rcgldr
Homework Helper
Perhaps it would to explain that air or any gas exerts it's weight inside a closed container via a pressure differential that decreases versus altitude in the container. For 80 cubic feet of air into a scuba tank, and there's an increase of about 6 pounds corresponding to the weight of the 80 cubic feet of (sea level pressure) air. The pressure change versus altitude within a container is enough to create a net downwards force exactly equal to the weight of the air or gas within the container.

In the case of the fly within the air plane, the fly increases the net pressure differential, so that net downforce applied by the air is equal the weight of the air plus the fly, as long as the fly doesn't have a vertical component of acceleration.

The weight of the airplane is w=mg in level flight. This is non-zero and is certainly affected by its occupants/cargo.

PS, do you work at APL?
Sorry, I was being silly, just saying that if we call the "weight" the net sum of all the forces acting on the plane, including gravity, weight of the passengers, force of the fly's downdraft, and lift on the planes wings, then that all appears to sum to zero. A normal person wouldn't call that "weight", however.

And yes, I do.

DaveC426913
Gold Member
MMMM, you should be very careful on that. You are correctly, but its an indirect effect that the engines have to work harder, and its not proportional to the weight of the T-rex.
I'm merely pointing out that, whether on the ground with a weigh scale, or in the air with the strain of the engines, extra weight is extra weight.

I know. I just want to make it clear that the engines dont directly carry the extra weight of the T-rex in your example. The added weight means the wings have to create more lift, which in turn causes more drag. The increased drag due to lift is what the engine has to overcome and is not necessarily a 1:1 ratio to the added weight.

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Sorry, I was being silly, just saying that if we call the "weight" the net sum of all the forces acting on the plane, including gravity, weight of the passengers, force of the fly's downdraft, and lift on the planes wings, then that all appears to sum to zero. A normal person wouldn't call that "weight", however.

And yes, I do.
What building you at, 17?

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What building you at, 17?
Nope, only when I'm using the locker room/shower facilities. I'm in Bldg. 1 - how about you?