# Birds flying in a plane, does the weight change?

1. Oct 9, 2004

### rcgldr

My turn for a troll question.

Take a sealed box that contains air and an object in it that is either hovering, flying or gliding. The object within the box maybe be moving, but it has no vertical component of acceleration. Does the box weigh less if than it would if the object within the box were resting on the bottom of the box?

2. Oct 9, 2004

### ZapperZ

Staff Emeritus
Hint: the object needs a medium to "fly", in this case, air. Do you think if it pushes on the air to obtain lift, would the air also needs to be "supported" by something else so that there's a push back?

Zz.

3. Oct 9, 2004

### Zuryn

If you are referring to the box as it is opposed to what it contains then the mass would be no different.

4. Oct 10, 2004

### rcgldr

Oops, I meant the entire system, box, air, object, the total weight of all three. Assume the box is resting on a scale that measures the total weight.

For an example case, assume the box weighs 50 lbs, the air in the box weighs 49 lbs (big box), and the object weighs 1 lb. With the object resting at the bottom of the box, the scale indicates 100lbs, total weight of this closed system.

When the internal object is hovering or flying within the box, and with no vertical acceleration, does the weight as measured by that scale change?

Last edited: Oct 10, 2004
5. Oct 10, 2004

### rcgldr

I also mentioned hover. Could be a small gondola attached to a helium balloon. Could be a magnet controlled to hover near the top of the box. Slightly different cases than say a small model plane or helicopter. However the answer is the same for all of these cases.

I'm looking for an explanation to cover these various cases.

Last edited: Oct 10, 2004
6. Oct 10, 2004

### ZapperZ

Staff Emeritus
The SAME hint applies. Your "helium balloon" will NOT be afloat in vacuum. It requires a surrounding air to obtain its loft.

Zz.

7. Oct 10, 2004

### rcgldr

The magnet controlled hovering wouldn't need any air, but it's a different case than all the others, and a bit more obvious, so ignore that one for now.

8. Oct 10, 2004

### ZapperZ

Staff Emeritus
But there is STILL an action=reaction forces as dictated by Newton's 3rd Law. It doesn't matter if it is air, magnetic field, electric field, etc. In each of these cases, the "floating object" WILL act against something in the box to exert its weight. The total weight will not be any different.

Zz.

9. Oct 10, 2004

### saksham

I think that the apparent weight of the enclosure would increase because I bird's wings pushes the air particles which have downward acceleration and the force>force of gravity.

10. Oct 10, 2004

### rcgldr

Next hint is yet another question:

If a hp-80 scuba tank, which weighs $$26lbs$$ "empty" (air at atmospheric pressure inside), has $$6lbs = 80 ft^3$$ of air forced into it, (pressure at $$3500 lbs/in^2$$ is how this is done), and then is weighed by placing the tank (with the pressurised air in it) on a scale, what weight does the scale indicate?

No fair doing web searches for scuba tanks to find out the answer.

Last edited: Oct 10, 2004
11. Oct 10, 2004

### rcgldr

I limited this case to no vertical acceleration, so if it's birds inside the tank, just assume that they're gliding at a constant rate of descent (no vertical acceleration in this case).

12. Oct 10, 2004

### ZapperZ

Staff Emeritus
Again, you are forgetting that these things that are "gliding" have WEIGHTS! Unless you want to throw out basic newtonian laws, "no vertical acceleration" means that there HAS to be something else that balances out the weights of these "gliding things". Where do you think this would come from?

Zz.

13. Oct 10, 2004

### rcgldr

That's what I wanted others on this thread to figure out. It's apparent that you know know the correct answer to the original question. The helium balloon case is a bit trickier to explain how it works. Rather than post any spoilers here, you can email me at jeffareid@jeffareid.net.

14. Oct 10, 2004

### rcgldr

Ok, not getting any responses, so I'll provide the answers to this question, spoiler space follows, don't scroll down if you don't want to read this.
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For the second question the weight increases the same as the weight of the air added. The result is 32lbs, 26lbs from the tank, 6lbs more from the air inside.

The real question is how to gases exert their weight within a closed system. The answer is pressure differential. Pressure decreases with altitude within a closed system acted upon by gravity (or equivalent acceleration). Using the scuba tank as an example, the pressure at the top is less than that the pressure at bottom, with a net downforce exactly equal to the weight of the gas inside the tank. It doesn't matter what the shape of the tank is, or how it's oriented, the pressure differential within the tank always results in a net downforce equal to the weight of the gas inside the tank.

The same thing applies to the original closed system. Lets remove the object and add 1 lb of air so we have a 50 lb box with 50lbs of air in it. Again, the pressure differential will create a net downforce within the box of 50lbs, exactly the weight of the gas inside the box. Again, the shape, size, or orientation of the box doesn't matter, (as long as the size isn't so large that changes in the pull of gravity or cetripetal reaction to rotation of the earth isn't an issue), there will always be a net downforce equal to the weight of the gas within the box. One factor to note is that the smaller the box, the higher the pressure and denstiy of the gas inside, the rate of pressure change versus altitude is greater than that of a larger lower pressure, lower density gas filled box.

Getting back to the flying / gliding object case, we have 50lbs of box, 49lbs of air, and 1 lb of object. Well it's a closed system, gravity doesn't stop pulling down on the object just because it's flying. As long as there are no net vertical acceleration, the system will always weigh 100lbs. So while the object is flying/gliding, it has to create a pressure differntial that creates a net downforce of 1 lb within the box. This is one way to argue that wings produce lift by accelerating air downwards.

In the case of the helium balloon. Lets start with the balloon defalated and with the helium inside a tank on the model balloons gondola. As the balloon is inflated with helium, the pressure within the box increases. As the pressure within the box increases, so does the density, which in turn, increase the pressure diffferential. Once the balloon is hovering, the density of the surrounding air has been increased so that the higher density air's pressure differential results in a 1lb gain in net downforce, exactly equal to the weight of the helium balloon model. If the helium balloon is continued to be inflated, it rises upwards into lower density (lower pressure) air and hovers again. The over all increase in pressure remains constant as long as the balloon is hovering. The balloon can continue to be inflated to increase the pressure that creates a differential of more than 1 lb, but in this case it's risen to the top of the box, and pushes upwards at the top, exactly canceling out any further gain in net downforce due to increase in air density within the box.

Lastly is the magnetic case, which isn't as intersting, since it simply pulls downward on the top of the box.

In all cases, as long as there is no vertical acceleration of the center of mass of the closed system, the weight of the system is constant.

Once the birds flying in a plane end their vertical acceleration, the weight of the system remains the same as before when the birds were resting.

Last edited: Oct 11, 2004
15. Oct 12, 2004

### rcgldr

The answer was posted in the previous post, just scroll down to look at if interested.