Explained: Why flying isn't impossible on a globe

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Provemewrong

Member
The earths curve is approximately 8 inches per mile squared. With planes flying at 500mph, the earth would curve beneath them around 31.5 miles every hour. In order for the plane to keep up with the curvature and not steadily head towards space, the plane would have to descend 2777 feet per minute or 46 feet per second!
Since there's at least one pilot here this should be an easy one to solve.

Spectrar Ghost

Senior Member.
Plane altitude is determined by hydrostatic forces; lift versus weight. Increasing altitude puts the plane out of equilibrium, causing it to descend. No active control is necessary.

Provemewrong

Member
Plane altitude is determined by hydrostatic forces; lift versus weight. Increasing altitude puts the plane out of equilibrium, causing it to descend. No active control is necessary.
So the plane actually does descend by a rate of at least 46 feet per second?

Trailblazer

Moderator
Staff member
So the plane actually does descend by a rate of at least 46 feet per second?
What do you mean by "descend"? Altitude is measured relative to sea level, or, if you prefer, lines of equal gravitational potential.

If you maintain the same altitude and move around a globe, then your path will describe a curve, following the curve of the Earth. If you followed a "straight line" as the Earth curved away underneath you then your altitude would be getting greater and you would have to supply additional energy to overcome gravity.

Why even bring planes into it? By your logic, if you drove a car along a straight road, then after one mile your car would be 8 inches off the asphalt, and after two miles it would be 32 inches, almost three feet up in the air! Why should gravity affect planes differently?

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Provemewrong

Member
What do you mean by "descend"? Altitude is measured relative to sea level, or, if you prefer, lines of equal gravitational potential.

If you maintain the same altitude and move around a globe, then your path will describe a curve, following the curve of the Earth. If you followed a "straight line" as the Earth curved away underneath you then your altitude would be getting greater and you would have to supply additional energy to overcome gravity.

Why even bring planes into it? By your logic, if you drove a car along a straight road, then after one mile your car would be 8 inches off the asphalt, and after two miles it would be 32 inches, almost three feet up in the air! Why should gravity affect planes differently?
... Cars drive on the earths surface, planes are in the air. I'll reword the question. Does the plane fly towards the surface of the earth at 46 ft per second while maintaining altitude?

Mick West

Staff member
... Cars drive on the earths surface, planes are in the air. I'll reword the question. Does the plane fly towards the surface of the earth at 46 ft per second while maintaining altitude?

No, it stays the same distance from the surface, which curves slightly.

Trailblazer

Moderator
Staff member
... Cars drive on the earths surface, planes are in the air. I'll reword the question. Does the plane fly towards the surface of the earth at 46 ft per second while maintaining altitude?

No, the plane maintains the same distance from the centre of the Earth (and therefore the surface, ignoring mountains, hills etc), so it "falls" at the same rate as the surface does.

The Earth's surface "falls away" (compared to a straight line). If your car falls away with it, then why wouldn't a plane? Maintaining level flight means maintaining the same gravitational potential. A gravitationally level surface on a round planet describes a curve.

In your view, what is holding the car down and making it follow the Earth's surface?

Provemewrong

Member
No, it stays the same distance from the surface, which curves slightly.
Sorry I'm just having a hard time wrapping my head around it. How does the plane stay the same distance from the surface which is curving away at 46 feet per second?

Mick West

Staff member
Sorry I'm just having a hard time wrapping my head around it. How does the plane stay the same distance from the surface which is curving away at 46 feet per second?

You can't measure curvature like that.

In one second, a plane traveling at 500mph travels 0.139 miles, (500/60/60)

The "drop" over 0.139 miles is just 0.15 inches.

The curvature is vastly less than the gentlest curve of a freeway.

Trailblazer

Moderator
Staff member
Sorry I'm just having a hard time wrapping my head around it. How does the plane stay the same distance from the surface which is curving away at 46 feet per second?

Because it is in level flight. If the lift from the wings exactly balances the pull of gravity, then the plane will maintain a constant altitude above the Earth (ie, a constant height above sea level).

Edit: and, as Mick says, you can't measure the drop that way. You are trying to measure the drop relative to a stationary starting point, with the plane disappearing off over the curve. Following that logic, by the time the plane was a quarter of the way round the world, it would be heading vertically downwards!

Provemewrong

Member
You can't measure curvature like that.

In one second, a plane traveling at 500mph travels 0.139 miles, (500/60/60)

The "drop" over 0.139 miles is just 0.15 inches.

The curvature is vastly less than the gentlest curve of a freeway.
I see. Thanks for the quick replies!

Provemewrong

Member
You can't measure curvature like that.

In one second, a plane traveling at 500mph travels 0.139 miles, (500/60/60)

The "drop" over 0.139 miles is just 0.15 inches.

The curvature is vastly less than the gentlest curve of a freeway.
You can't measure the curvature that way either, or there would never be enough to make a sphere. So let's make a more realistic scenario.
Airport A and B are 1500 miles apart. 1500 miles has about 1.5 million feet of curvature.
To make this easier we'll say the plane leaves point A at its full and constant speed of 500 mph, already at cruising altitude of 35,000ft.
At 500mph hour this trip would take 3hrs, equaling 500,000 ft of curvature every hour.
/60=8333.33 ever min
/60=138 feet per second.
The plane obviously doesn't adjust 138 feet per second so my question is ......
Where does the curvature go?

Mick West

Staff member
You can't measure the curvature that way either, or there would never be enough to make a sphere. So let's make a more realistic scenario.
Airport A and B are 1500 miles apart. 1500 miles has about 1.5 million feet of curvature.
To make this easier we'll say the plane leaves point A at its full and constant speed of 500 mph, already at cruising altitude of 35,000ft.
At 500mph hour this trip would take 3hrs, equaling 500,000 ft of curvature every hour.
/60=8333.33 ever min
/60=138 feet per second.
The plane obviously doesn't adjust 138 feet per second so my question is ......
Where does the curvature go?
Try drawing a scale diagram of this situation.

Z.W. Wolf

Senior Member.
The distance between the two airports is 1,500 miles along a curved line.

Instead of telling you things, maybe it's best to ask you some things. When you drop a bomb from a plane does it drop straight down? If you were the bombardier would you release the bomb when the plane was directly over the target? Or would you release the bomb before your plane was over the target?

This is germane to your problem.

To start, we have to think about:
1. Kinetic energy
2. Potential energy
3. Gravity
4. Gravitational potential energy (Important!)
5. Inertia

Something else to chew on. In this idealized (2 dimensional) problem, we should treat the horizontal and vertical motions independently.

What path would the dropped bomb follow? What shape would that path take? And - to quote the wonderful Dr. Julius Sumner Miller - "Why is it so?"

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Provemewrong

Member
The distance between the two airports is 1,500 miles along a curved line.

Instead of telling you things, maybe it's best to ask you some things. When you drop a bomb from a plane does it drop straight down? If you were the bombardier would you release the bomb when the plane was directly over the target? Or would you release the bomb before your plane was over the target?

This is germane to your problem.

To start, we have to think about:
1. Kinetic energy
2. Potential energy
3. Gravity
4. Gravitational potential energy (Important!)
5. Inertia

Something else to chew on. In this idealized (2 dimensional) problem, we should treat the horizontal and vertical motions independently.

What path would the dropped bomb follow? What shape would that path take? And - to quote the wonderful Dr. Julius Sumner Miller - "Why is it so?"
To simplify it, are you saying the difference in curvature is partially due to the difference between point a and b being measured on a curved line vs a straight one?

Mick West

Staff member
Again, draw a scale diagram. It will make things much clearer for you.

Imagine driving down a road that just curves a little to the left. A VERY little. So little that if it were on a flat plane, and the road curved around until it joined itself, it would be 24,000 miles long.

What would that road look like to the driver?

Henk001

Senior Member.
The plane doesn't have to adjust anything, because EVERYTHING is curved -- not just the Earth's surface, but also the directions! "Up/down";"straight ahead";"water level". All these directions are locally defined by Earth's gravity, which always points towards the centre of the Earth/perpendicular to the surface.

Provemewrong

Member
The plane doesn't have to adjust anything, because EVERYTHING is curved -- not just the Earth's surface, but also the directions! "Up/down";"straight ahead";"water level". All these directions are locally defined by Earth's gravity, which always points towards the centre of the Earth/perpendicular to the surface.
Actually I've heard pilots DO have to make adjustments, or a computer does it automatically in relation to the VSI (vertical speed indicator). Hoping for some input from TWCobra seeing as he's a pilot.

Trailblazer

Moderator
Staff member
Actually I've heard pilots DO have to make adjustments, or a computer does it automatically in relation to the VSI (vertical speed indicator). Hoping for some input from TWCobra seeing as he's a pilot.

Pilots (or autopilots) do make adjustments to altitude, but that is nothing to do with the curvature of the Earth. If you want to maintain level flight (a constant altitude), then you might have to adjust up or down to account for wind etc, or the aircraft trim not being set perfectly. You'd have to do the same whether the Earth was flat or curved, just like you have to make little corrections of the steering wheel even when driving along a straight road. It's not the case, as you seem to assume, that without corrections the plane would go flying off at a tangent from the Earth. Doing that would actually mean ascending at an increasingly steep angle (again, draw a diagram).

It seems to be a common misconception that curvature means the altitude somehow changes over distance. It doesn't. EVERYTHING is curved. "Level" is always at right angles to "down". You don't have to adjust for the curvature any more than you have to remember to turn yourself upside down before getting off the plane in Australia.

NoParty

Senior Member.
Actually I've heard pilots DO have to make adjustments, or a computer does it automatically...
That's an interesting thing to hear, in that something that a plane does automatically, in the background, seems quite different than a manual task that pilot would be forced to constantly perform.

Can you share the source where you heard this?

Provemewrong

Member
Pilots (or autopilots) do make adjustments to altitude, but that is nothing to do with the curvature of the Earth. If you want to maintain level flight (a constant altitude), then you might have to adjust up or down to account for wind etc, or the aircraft trim not being set perfectly. You'd have to do the same whether the Earth was flat or curved, just like you have to make little corrections of the steering wheel even when driving along a straight road. It's not the case, as you seem to assume, that without corrections the plane would go flying off at a tangent from the Earth. Doing that would actually mean ascending at an increasingly steep angle (again, draw a diagram).

It seems to be a common misconception that curvature means the altitude somehow changes over distance. It doesn't. EVERYTHING is curved. "Level" is always at right angles to "down". You don't have to adjust for the curvature any more than you have to remember to turn yourself upside down before getting off the plane in Australia.
I disagree with no adjustments needed. In Mick's example of the car, the wheel would have to be turned slightly to the left for the duration of the ride. Same thing should apply in any direction.

mm1145

Member
Actually I've heard pilots DO have to make adjustments, or a computer does it automatically in relation to the VSI (vertical speed indicator). Hoping for some input from TWCobra seeing as he's a pilot.

no the "adjustments" are made by gravity and because the instruments point to the centre of gravity (not at 90 degrees to a straight line) you fly a level curve

Provemewrong

Member
no the "adjustments" are made by gravity and because the instruments point to the centre of gravity (not at 90 degrees to a straight line) you fly a level curve
Lol a level curve! Level and constant curvature in relation to the ground to maintain altitude correct?

mm1145

Member
I disagree with no adjustments needed. In Mick's example of the car, the wheel would have to be turned slightly to the left for the duration of the ride. Same thing should apply in any direction.

ok if I asume you are thinking about a car driving in a cricle?

imagine if yo had a rope tieing you to a pole in the centre that rope keeps you going in a circle. but it is more than that because the rope dose not only effect the car but also all the things in the car at the same time.

I relay recommend playing kerbial space program for a bit if you want to really get a visualisation of how orbits (witch are all that level flying on a globe is) works because it is a realy visual/experimental learning and you can really get a feel for how you have to adjust some ways of thinking to account for a scale the human brain is not used to

mm1145

Member
Lol a level curve! Level and constant curvature in relation to the ground to maintain altitude correct?
yes you fall to the ground at the same speed as the ground falls away so you stay the same distance form it I will try to draw some diagrams later

jonnyH

Senior Member.
I disagree with no adjustments needed. In Mick's example of the car, the wheel would have to be turned slightly to the left for the duration of the ride. Same thing should apply in any direction.
Imagine the road has a slight incline towards the centre of the circle, do you still have to turn the wheel?

NoParty

Senior Member.
Thank you!

The source you cite begins with:
"A plane will fly at a constant altitude and will follow the curvature of the earth and would not gain altitude during a level flight."

Is that, in fact, the position you have been trying to argue for?

Provemewrong

Member
Thank you!

The source you cite begins with:
"A plane will fly at a constant altitude and will follow the curvature of the earth and would not gain altitude during a level flight."

Is that, in fact, the position you have been trying to argue for?
Yes it is! I guess I'm trying to understand the concept of a level curve.

Provemewrong

Member
Imagine the road has a slight incline towards the centre of the circle, do you still have to turn the wheel?
Yes? I think lol

NoParty

Senior Member.
Yes it is! I guess I'm trying to understand the concept of a level curve.
Okay...so when you say "Lol a level curve!" you're gently mocking Lim Khoy Hing, the ex-pilot you cited, yes?

Trailblazer

Moderator
Staff member
Yes it is! I guess I'm trying to understand the concept of a level curve.
The difference between "level" and "flat" is not an intuitive one. The plane flies level, but does not fly flat.

Think of a spirit level. If I hold a spirit level up in the air here in England so the bubble is centred, and someone in California, roughly a quarter of the way round the Earth, does the same, the two levels are at an angle to each other, right? But they are both level.

Now imagine a long line of spirit levels, placed end to end in the air, stretching from England to California. The plane will follow that line.

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Provemewrong

Member
Okay...so when you say "Lol a level curve!" you're gently mocking Lim Khoy Hing, the ex-pilot you cited, yes?
More so the idea in general. I see what you guys are though, just sounds very contradictory.

Provemewrong

Member
The difference between "level" and "flat" is not an intuitive one. The plane flies level, but does not fly flat.

Think of a spirit level. If I hold a spirit level up in the air here in England so the bubble is centred, and someone in California, roughly a quarter of the way round the Earth, does the same, the two levels are at an angle to each other, right? But they are both level.

Now imagine a long line of spirit levels, places end to end in the air, stretching from England to California. The plane will follow that line.
And THAT is a great description. Thanks a lot guys.

Senior Member
sI think the good analogy is a person walking around a pole whilst attached to the pole by a fixed/rigid link

so the question is "does the person have to walk in a circle" (if it help imagine they are blind folded)

the answer surely is "no" he/she walks in a "straight" line

the fixed link is acting the same as gravity

NoParty

Senior Member.
...a person walking around a pole whilst attached to the pole by a fixed/rigid link...

Will that be Trump's punishment for losing the election?
(well, c'mon, you did make the 'person' orange!)

NoParty

Senior Member.
The difference between "level" and "flat" is not an intuitive one. The plane flies level, but does not fly flat.

Think of a spirit level. If I hold a spirit level up in the air here in England so the bubble is centred, and someone in California, roughly a quarter of the way round the Earth, does the same, the two levels are at an angle to each other, right? But they are both level.

Now imagine a long line of spirit levels, places end to end in the air, stretching from England to California. The plane will follow that line.
That's an interesting visual, Trail. thanks.
I also learned that y'all call a bubble level a "spirit level." Thanks for that, too.

Trailblazer

Moderator
Staff member
I also learned that y'all call a bubble level a "spirit level."
I didn't know "spirit level" was a regionalism. One of these, anyway.

Mick West

Staff member
I disagree with no adjustments needed. In Mick's example of the car, the wheel would have to be turned slightly to the left for the duration of the ride. Same thing should apply in any direction.

The road example is to mentally illustrate just how LITTLE you need to turn the wheel. It's a thought experiment taking the great circle that a plane follows, putting it sideways (on an imaginary flat plane with gravity), and then driving a car around it.

Have you ever driven along a perfectly straight road without moving the steering wheel for a few minutes? Not a good idea.

Those normal corrections you'd have to do to simply keep a car going in a straight line would be vastly more than tiny tiny correction to keep it on the curve.

Provemewrong

Member
sI think the good analogy is a person walking around a pole whilst attached to the pole by a fixed/rigid link

so the question is "does the person have to walk in a circle" (if it help imagine they are blind folded)

the answer surely is "no" he/she walks in a "straight" line

the fixed link is acting the same as gravity

There are a few problems with this.
Let's say you can take 3 steps straight forward before reaching the end of the rope. After taking those 3 steps, what do you have to do to continue your way around the circle?
Also a plane flying at 35,000 feet still has plenty "rope" left to go.

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