# The Naked Scientists Forum

### Author Topic: Does an aeroplane weigh less when flying at high altitude?  (Read 8687 times)

#### Airthumbs

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##### Does an aeroplane weigh less when flying at high altitude?
« on: 16/03/2012 21:01:38 »
Apparently the manned record for a propeller aircraft in altitude was 17,000mt by Lieutenant Colonel Mario Pezzi in 1938!  As space starts at 100km I wonder if he actually weighed less at that height.

following some digging.......

"Gravity decreases with altitude, since greater altitude means greater distance from the Earth's centre. All other things being equal, an increase in altitude from sea level to the top of Mount Everest (8,850 metres) causes a weight decrease of about 0.28%."source - http://en.wikipedia.org/wiki/Gravity_of_Earth
I am going to have to say my reference is poor as is states "all things being equal", maybe the author of this Wiki article knew that Air density is .4 x standard atmosphere and Air pressure is .3 x standard atmosphere at the top of Everest. Maybe I am barking up the wrong mountain!

So a Boeing 747 is around 480 tons.  Even flying at the height of Everest it's going to weigh just under 2 tons less then if it was on the ground, "all things being equal"! Maybe this is why planes use less fuel at higher altitude........

Ok, forget it, here is a more exciting question..........

How fast would you have to travel at ground level to experience zero g?    :P
« Last Edit: 16/03/2012 21:11:39 by Airthumbs »

#### wolfekeeper

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #1 on: 17/03/2012 00:59:48 »
Centrifugal force = m v^2/r = m 9.81

Rearranging v = sqrt(9.81 r)

At the earth's surface r=6,371km.

v = 7.9km/s

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #2 on: 17/03/2012 20:20:58 »
Centrifugal force = m v^2/r = m 9.81

But, but, but, there ain'ta no sanity clause, and there ain'ta no centrifugal force either.

(You must have "signatures" disabled.)

#### syhprum

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #3 on: 17/03/2012 20:27:05 »
I did not know you were still sensitive to the C word I see many examples of its use and have not bothered pointing them out as I thought you were now inured to its use.
7.9kms/s the same speed as the gravity train will hit as you pass through the centre of the Earth

« Last Edit: 17/03/2012 20:30:59 by syhprum »

#### CliffordK

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #4 on: 17/03/2012 20:42:12 »
Wouldn't the centrifugal force, and thus the weight of the airplane, and everything in it depend on whether you were travelling East or West?

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #5 on: 17/03/2012 21:00:04 »
I did not know you were still sensitive to the C word I see many examples of its use and have not bothered pointing them out as I thought you were now inured to its use.
7.9kms/s the same speed as the gravity train will hit as you pass through the centre of the Earth

I realize I am fighting a losing battle, but I still feel a moral obligation to science to point it out from time-to-time.

For those who don't know what I'm on about, if there actually was such a thing as centrifugal force, a rock spun around on a string would take off at right angles to its former path when you let go of the string. It doesn't. It follows a tangential path.

#### Airthumbs

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #6 on: 17/03/2012 21:30:04 »

For those who don't know what I'm on about, if there actually was such a thing as centrifugal force, a rock spun around on a string would take off at right angles to its former path when you let go of the string. It doesn't. It follows a tangential path.

I thought the reason the rock does not fly off at right angles is because gravity is stronger then the centrifugal force.  However should you manage to attach a flea to the surface of the rock with an electronic release device, it will surely fly off at right angles when you get the rock up to speed :) (I guess that's plain old inertia)!

If there is no such thing as centrifugal force then what is happening when someone spins a cycle wheel quickly and you notice resistance when you try to alter the axis it is rotating on?

Thanks for having a go at answering the question on zero g at the Earths surface, it puts things into perspective for me that this is even possible... :)

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #7 on: 18/03/2012 01:49:55 »

I thought the reason the rock does not fly off at right angles is because gravity is stronger then the centrifugal force.  However should you manage to attach a flea to the surface of the rock with an electronic release device, it will surely fly off at right angles when you get the rock up to speed :) (I guess that's plain old inertia)!

If there is no such thing as centrifugal force then what is happening when someone spins a cycle wheel quickly and you notice resistance when you try to alter the axis it is rotating on?

Thanks for having a go at answering the question on zero g at the Earths surface, it puts things into perspective for me that this is even possible... :)

The real force in the string is centripetal force. That's the force that causes things to move in a circular orbit.

When you go round a corner in a car, you might think something trying to force you out of the car, but there is only a centripetal force that is making you follow a circular path, rather than allowing your inertia to keep you moving in a straight line. Centripetal force acts in a direction towards the center of rotation. The mythical centrifugal force would act in the opposite direction, but if there really was such a force, things would tend to fly off along a radial path, which is not what happens at all.

There are cases where it might be convenient to talk about centrifugal force as if it's a real force as a sort of scientific shortcut, but the danger is it can easily cause people to misunderstand what is really going on in the general case.

#### Cheese2001

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #8 on: 18/03/2012 16:37:59 »
Pardon my confusion, but someone asked how fast you'd have to travel to experience zero g and was answered with a velocity?  As g is a unit of acceleration, the answer can't be a velocity.

Gravity does vary with altitude, so the airplane will weigh very slightly less, though the mass of the airplane will be exactly the same at both altitudes.

By setting the angular acceleration equal to g, I believe Wolfkeeper solved for the tangential velocity of hoop the size of the radius of the earth imparting a centripetal acceleration of 9.81 m/s/s.
« Last Edit: 18/03/2012 16:57:34 by Cheese2001 »

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #9 on: 18/03/2012 19:48:38 »
That's because it's not zero g. At that velocity g is still g and the object is in freefall.

Whoever it was that started talking about "micro gravity" in orbit has a lot to answer for. Gravity in orbit will be slightly less than on the surface of the Earth, but there is nothing "micro" about it.

#### Cheese2001

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #10 on: 18/03/2012 21:46:44 »
The answer, it seems, is at best incomplete.  If you are traveling 7.9 km/s tangentially to the orbit of the earth, you will follow a near circular path around the earth.  The same 7.9 km/s directly away from the center of the Earth will fall back to the surface without orbiting.  This is a question in which the velocity vector is equally important as the magnitude.

There is a great flash demonstration of the importance here:
http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Escape_Nav.swf::Escape%20Velocity%20Interactive [nofollow]

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #11 on: 18/03/2012 22:20:56 »
But you don't need any vertical velocity component. You only need a tangential component. Of course, that's assuming you don't bash into a mountain or a tree.

Imagine the earth was perfectly smooth and you were accelerating on a railway track on its surface. By the time you got to 7.9km/s, you would be in a freefall orbit around the Earth (except that wind resistance would slow you down again PDQ, so you would not be in orbit for long.)

Rockets go "up" as well as "along" so that they can escape from the Earth's atmosphere, but if you eliminate the atmosphere (as would be the case on the Moon) you can wizz along in a really low orbit as long as you don't bump into something.

#### yor_on

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #12 on: 19/03/2012 17:42:55 »
Nah nah it's simple. Just stand under it and then lift.
Just go by feel me man.

See what I mean..

Btw, what about those pesky flies, inside, flying. Do they add weight to the areoplane?
==

There are a lot of reasons why a aircraft saves fuel at higher altitudes, less resistance (drag), less turbulence, you can catch those jet streams ('exceeding 400 kilometers (250 miles) per hour at altitudes of 10 to 15 kilometers (6 to 9 miles)') and get that tail wind, getting over 36000 feet you lose thrust due to the falling density of air so it seems that this is the optimum 'flight height', it also gives you more time to fix a problem before meeting the ground, I don't know if the 'dead weight' of the aircraft plays a role for going high but , maybe?

http://www.skybrary.aero/index.php/High_Altitude_Flight_Operations
« Last Edit: 19/03/2012 18:02:21 by yor_on »

#### wolfekeeper

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #13 on: 20/03/2012 22:56:40 »
Centrifugal force = m v^2/r = m 9.81
But, but, but, there ain'ta no sanity clause, and there ain'ta no centrifugal force either.
Wrong, actually, there's at least two different ones that are defined, one is a pseudo force in a rotating reference frame (such as being in orbit around the center of the Earth), the other is a force that exists due to Newton's third law, and is equal and opposite to the centripetal force.

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #14 on: 20/03/2012 23:46:36 »
the other is a force that exists due to Newton's third law, and is equal and opposite to the centripetal force.

That's a reaction to centripetal force. If we went around giving special names to every reaction we would be even more confused than we are now.

And "pseudo" means not real, although I agree it can be be convenient to use pseudo-forces in calculations.

My objection to the use of the term centrifugal is that it can confuse people who might have a bit less understanding of mechanics/physics. TNS is about the de-obfuscation of science, not the opposite. I'm pretty sure half the people on the planet believe that, if gravity stopped working, they would shoot straight up into the air because of "centrifugal" force.

#### wolfekeeper

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #15 on: 21/03/2012 00:04:34 »
The term centrifugal just means 'towards the center' and it's used in mechanics, for example in bearing design, and helicopters. In roller bearings the rollers create a centrifugal force on the races.

Quote
I'm pretty sure half the people on the planet believe that, if gravity stopped working, they would shoot straight up into the air because of "centrifugal" force.
Yes, they pretty much would, because the surface of the Earth is a non inertial frame of reference due to the spin. Except it wouldn't be straight upwards, it would be parallel to the Equatorial plane, away from the Earth's axis.

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #16 on: 21/03/2012 00:58:12 »

The term centrifugal just means 'towards the center' and it's used in mechanics, for example in bearing design, and helicopters. In roller bearings the rollers create a centrifugal force on the races.

Centripetal force is the force that "acts toward the center". The mythical centrifugal force would act away from the center. The outer race actually exerts a centripetal force on the rollers to keep them moving in a circle instead of flying off at a tangent. If you suddenly removed the race, the rollers would not have any radial velocity at all, so there was no "centrifugal force". "Centrifugal force" does nothing to help explain what is really going on. It only creates confusion.

The purpose of science is to enlighten, and scientists do need to have some shorthand to make their lives simpler, but we should at least try to avoid making science any more difficult for the layperson to understand than it has to be, at least on TNS.

#### graham.d

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #17 on: 21/03/2012 08:43:22 »
Geezer as per another post - it depends on the frame of reference you choose. If I choose to take, as a frame of reference, the accelerated frame, then I feel a force which, if I understand what is going on, I can call a centrifugal force. It is mid-20th century teaching that tried to wipe the term from existence because it was thought to confuse pupils. It is better, and I think less confusing, to explain the nature of the force than to try to deny that there is one when every child on a roundabout can experience and feel it.

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #18 on: 21/03/2012 17:52:36 »
They feel it alright, but what they are feeling is the reaction to the centripetal force that is causing their mass to follow a curved path rather than the path that their mass would prefer to take, and most people are quite capable of appreciating that if it's explained properly.

Have we decided that moving objects no longer travel in a straight line in the absence of other forces?

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #19 on: 21/03/2012 20:55:17 »
After more reading to make sure I'm not any more bonkers than I previously thought, you can call it centrifugal force in an accelerated frame with the understanding that centrifugal force is a fictitious force that appears in an accelerated frame referenced to an inertial frame. It is useful to use it and other fictitious forces to predict certain behaviors, but that does not mean that it is a real force.

If the accelerated frame is not referenced to an inertial frame, you can't call it centrifugal force because you don't know you are in an accelerated frame. Within that frame, it is just a force. You might infer it is a consequence of acceleration/rotation but I don't think you can prove that without referencing the inertial frame.

So, the force felt is either the consequence of motion in an inertial frame, in which case it's definitely a reaction to centripetal force, or it's a mysterious force that cannot be called centrifugal.

Phew!

#### Airthumbs

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #20 on: 22/03/2012 19:59:28 »
Why do I get the feeling my science education was somewhat lacking in facts and in some cases seems to be more science fiction!

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #21 on: 23/03/2012 07:54:23 »
Why do I get the feeling my science education was somewhat lacking in facts and in some cases seems to be more science fiction!

Believe it or not, that's the reason I tend to get a bit "crusty" about this stuff. Most of it can be explained by the simple fact that large physical objects that we are familiar with "want" to keep traveling in a straight line, and I'm pretty sure you are quite familiar with that concept.

So, if an object is made to follow a path that is not straight, a force is being applied to it to keep it on that path. The force required to keep an object traveling along a circular path is called centripetal force. That's it. There is no other force, and that's my point.

Why introduce a lot of discussion about frames and fictitious forces? They may be convenient methods that can be used to solve particular problems in more advanced Physics, but they only confuse the fundamental points that should be grasped first.

#### wolfekeeper

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #22 on: 23/03/2012 16:51:39 »
Ummm. Well.... you've heard of the coriolis force/effect?

That comes out of the same equation that the centrifugal force comes out of! The coriolis force gives really obvious effects, and everyone knows about it, but most people, and many of the same people, will insist that the centrifugal force "DOESN'T EXIST!!!", even though it's the same equation and exists every bit as much as coriolis force does.
« Last Edit: 23/03/2012 16:57:25 by wolfekeeper »

#### wolfekeeper

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #23 on: 23/03/2012 16:54:01 »
Oh yeah, although it's described as a 'pseudoforce' it can kill you, and so no discussion on this topic can be complete without this xkcd:

#### Geezer

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##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #24 on: 24/03/2012 07:22:40 »
The Coriolis force is a fictitious force, just as centrifugal force is a fictitious force.

I don't have any objection to using fictitious forces, as long as we remember that that's what they are.

#### The Naked Scientists Forum

##### Re: Does an aeroplane weigh less when flying at high altitude?
« Reply #24 on: 24/03/2012 07:22:40 »