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iPhone As Artificial Horizon

Steve Jobs first said the iPhone would not be open to third party programming. Now, there are hints that they might allow some third party apps.
The first generation does not appear to include GPS, but the rumor mills are ripe with talk about GPS iPhones in January, 2008.
 
jsherblon said:
The first generation does not appear to include GPS, but the rumor mills are ripe with talk about GPS iPhones in January, 2008.
Click to expand...
Check again, I think all new cell phones have to have GPS thanks to OJ and our government's desire to track your location.
 
If all you want is an artificial horizon that shows you nice, straight, and level whenever you have the airplane well coordinated, even when you're upside down, then it will work fine ;)

You need gyros to do an AH. The accelerometers are used to get drift out of the gyros and are used for the ball.
 
rickmellor said:
But the iPhone should show you when you're in a VERY steep bank! :D
Click to expand...

DynonSupport is right.
It will not work. At all. Not even a little bit.
Very unfortunately, because accelerometer chips are now quite cheap and rather good.
I believe you can blame a guy called Albert Einstein for this. He said something to the effect that acceleration is indistinguishable from gravity. Since that day we have to use gyros.

Rainier
CEO MGL Avionics
 
Whiskey Charlie said:
Maybe it has a gyro then. http://www.apple.com/iphone/ads/ad1/
How else would it know to change video output from vertical
to horizontal as you turn the phone sideways?
Click to expand...
The accelerometers know which way is "down".
When you are standing on the earth, that is an easy calculation. Unfortunately in an aircraft, in well coordinated flight, "down" is always where your seat is planted, regardless whether it's pointing at the sky or the earth.
Again, it's a case of acceleration being indistinguishable from gravity (per Rainier and Albert):)
-mike
 
Got it. Thanks for the clarification.

Oh well I'll just have to use it as a:

phone/ipod/in-flight entertainment center/internet browser/back-up gps

:)
 
The software is easy...the physics is impossible

Whiskey Charlie said:
Since the iPhone has built in accelerometers, can any of you software writers do an application so I can use the iPhone as a back-up artifical horizon?
Click to expand...

Tempting, but not possible. Try holding a pendulum (a simple accelerometer) in the cockpit while you do a steep turn. As long as you keep the turn coordinated, the pendulum will be vertical. That's why artificial horizons have gyros in them, and not just accelerometers.
 
Big Bubba is watching you....

N941WR said:
Check again, I think all new cell phones have to have GPS thanks to OJ and our government's desire to track your location.
Click to expand...

Good point, they have GPS sort of....

As of 2005, new cell phones do have internal GPS as required by the FCC. But most models, including the first generation Apple iPhone, do not have any interface to the handset or the user. The required GPS is for use by 911 operators (and by fill-in your favorite, big brother, cloak & dagger agency here __________ ) to locate callers within 100 meters.

I'd be amazed if we don't see full access GPS on the iPhone later on. I'd bet that Apple had a hard time sticking the name "iPhone" on it because it's way more than just a phone.
 
jsherblon said:
Good point, they have GPS sort of....

As of 2005, new cell phones do have internal GPS as required by the FCC. But most models, including the first generation Apple iPhone, do not have any interface to the handset or the user. The required GPS is for use by 911 operators (and by fill-in your favorite, big brother, cloak & dagger agency here __________ ) to locate callers within 100 meters.
Click to expand...


so you can't get a cell phone without GPS, even if you want one?

I remain cell phone free and completely 802.11 ignorant.
 
Accelerometer in Cell phone

I'm totally bummed about the accelerometer that will automatically rotate the screen from vertical to horizontal. I mean c'mon...what if I'm dialing a number while driving around a corner...it will flip the screen causing me to mis-dial the number. ;)

just kidding everyone...I despise cell phone drivers. Although, you heard this scenario here first! I give it only 6 months before there is a lawsuit against apple for an accident when this happened. "You're honor, I was distracted by my phone's screen rotating when driving...that's why I got in an accident".

[sigh] only in America...
 
GPS Cell phone

Congress made it illegal for the cell phone companies to even activate a cell phone without GPS. This rule kicked in about 1.5 years ago. Even if you already own a cell phone without GPS, if you need to have it activated, no go without getting a phone with a GPS. This was enacted about 4 years ago after some woman who put her car in a ditch, called 911 for help, and she died because it still took something like 12 hours to find her. The media went on about how $40 dollars worth of GPS technology would have saved her life, blah blah blah... You get the picture.

So it wasn't a conspiracy, it was a bad woman driver who didn't know enough to tell the dispatchers the name of the road she was on.

Of course the popo aren't complaining mind you. All GPS phones that I have seen have an option to shut it off so it is only activated for 911 use. I can imagine that the assorted agencies have it worked out to turn that thing on remotely. Mine uses it to give you really bad directions to a a really bad database of destinations for a overly high fee.

:rolleyes:
 
gstopyra said:
I'm totally bummed about the accelerometer that will automatically rotate the screen from vertical to horizontal. I mean c'mon...what if I'm dialing a number while driving around a corner...it will flip the screen causing me to mis-dial the number. ;)

just kidding everyone...I despise cell phone drivers. Although, you heard this scenario here first! I give it only 6 months before there is a lawsuit against apple for an accident when this happened. "You're honor, I was distracted by my phone's screen rotating when driving...that's why I got in an accident".

[sigh] only in America...
Click to expand...

No Greg! The proper technique is to steer with both knees, thereby allowing you to hold your accelerometer phone with both hands - and compensating for any g's with opposite accelerations to flip it back.:D Seriously though, the Blackberry 8700 I've had for over a year has this feature. It's not that sensitive.
 
Corners...NO, RV...YES!

Whiskey Charlie said:
You need an RV bad if you like feeling those kind of g forces in corners. :)
Click to expand...

Yeah I do!! Unfortunately my '95 ford escort station wagon won't even deliver those forces. Most people have more power in their motorcycles than I have under the hood! It's all good though, if I have to make that sacrifice to save money (and get 30-40MPG) for the RV, then so-be-it!

can't wait for the day...

-Greg
 
jsherblon said:
Steve Jobs first said the iPhone would not be open to third party programming. Now, there are hints that they might allow some third party apps.
The first generation does not appear to include GPS, but the rumor mills are ripe with talk about GPS iPhones in January, 2008.
Click to expand...

jsherblon,

Are you familiar w/ OS X ?

I'm looking for someone to write and app that incorporates the eGYRO-BT (http://www.pcflightsystems.com/news.html) w/ the iPhone via Bluetooth.
 
I am actually a Cirrus owner (don't hate me just because I'm certified.) But I felt compelled to write:

With two - three axis accelerometers, you can calculate acceleration in any plane and rotation about any axis (6 degrees of freedom.) I assume this is what the iPhone has ( and the Wii for that matter.)

Acceleration is the second derivative of distance with respect to time (dx/dt^2). Velocity is the first (dx/dt). If you know the acceleration and the time to a sufficient precision, and you have a point of reference (hold it really really still and zero the accelerometers), your velocity in any direction as well as your angular velocity is a simple calculation (actually it in an integral over time so it's not THAT simple, but at least it is a linear function).

NB: A gyro simply resists angular acceleration by translating it to a 90 degree offset. Gyros require that the offset angle be held fixed otherwise they will rapidly precess.

By simply integrating the velocity over time you can summate your change in position, both in an X/Y/Z coordinate field AND in a rotational field. Thus you could know your attitude at any given time. Of course error would accumulate over time. EFIS systems use a gyro to generate error correction angles. Curiously a GPS could be used to do the same thing as your linear track could be plotted and your actual velocity and rate of turn calculated. This assumes coordinated flight (for an example of this see the instrument page on a GM396/496) but on an iPhone the degree of coordination could be read directly off the accelerometers.

Someone seems to be working on this http://iphoneavionics.com/.

Of course an iPhone is NOT an air data computer and has no way of knowing winds aloft. (So their promise of an ASI is a bit overstated) Although I suppose you could download ALL the winds aloft Everywhere prior to flight and make a pretty good guess! ;)

Shawn Clark

PS Maybe I should write this software and make some money but my day job keeps me pretty busy. PM me if you have some time.
 
SBClark said:
I am actually a Cirrus owner (don't hate me just because I'm certified.) But I felt compelled to write.
Click to expand...

Shawn, welcome to VAF.

You are not the only guy flying a non RV, all are welcome here.

The Cirrus is a nice plane, just dont ever let someone talk you into a ride in a
RV, might get expensive.:D
 
I am distressed to read that all of us AHRS designers have been so wrong for such a long time. Just use a cheap 3 axis accelerometer for a few $ and integrate. Why did I not think about that !
Seriously, you CAN measure acceleration. You CANNOT measure rotation this way. If you cannot measure rotation, you cannot propagate your estimated horizon.
We can all thank old Albert Einstein - it's his fault that acceleration is indistinguishable from gravity (gravity = acceleration !). You want to derive a vector to point towards the direction of gravity. Sadly, (and blame Einstein), this is impossible using acceleration measurements in isolation.

The only time you can use accelerometers to derive a vector as desired if they are mounted on a platform (your aircraft) and it is not accelerating in any direction (acceleration = 0 thus any acceleration measured is gravity).
AHRS systems use this to right the horizon whenever possible or at startup - so this is hardly new.

If you would like to delve into what makes AHRS tick and what the problems and issues are (and how to do something about them), I can recommend a good book:
"Strapdown Inertial Navigation technology" ISBN 0 86341 260 2
D.H. Titterton and J.L. Weston do a good job of explaining what you need to know.

Rainier
CEO MGL Avionics


SBClark said:
I am actually a Cirrus owner (don't hate me just because I'm certified.) But I felt compelled to write:

With two - three axis accelerometers, you can calculate acceleration in any plane and rotation about any axis (6 degrees of freedom.) I assume this is what the iPhone has ( and the Wii for that matter.)

Acceleration is the second derivative of distance with respect to time (dx/dt^2). Velocity is the first (dx/dt). If you know the acceleration and the time to a sufficient precision, and you have a point of reference (hold it really really still and zero the accelerometers), your velocity in any direction as well as your angular velocity is a simple calculation (actually it in an integral over time so it's not THAT simple, but at least it is a linear function).

NB: A gyro simply resists angular acceleration by translating it to a 90 degree offset. Gyros require that the offset angle be held fixed otherwise they will rapidly precess.

By simply integrating the velocity over time you can summate your change in position, both in an X/Y/Z coordinate field AND in a rotational field. Thus you could know your attitude at any given time. Of course error would accumulate over time. EFIS systems use a gyro to generate error correction angles. Curiously a GPS could be used to do the same thing as your linear track could be plotted and your actual velocity and rate of turn calculated. This assumes coordinated flight (for an example of this see the instrument page on a GM396/496) but on an iPhone the degree of coordination could be read directly off the accelerometers.

Someone seems to be working on this http://iphoneavionics.com/.

Of course an iPhone is NOT an air data computer and has no way of knowing winds aloft. (So their promise of an ASI is a bit overstated) Although I suppose you could download ALL the winds aloft Everywhere prior to flight and make a pretty good guess! ;)

Shawn Clark

PS Maybe I should write this software and make some money but my day job keeps me pretty busy. PM me if you have some time.
Click to expand...
 
There for a minute I thought I had wasted the last 20 years or so fooling around with those pesky gyro things and all I needed were more accels. Rainier you can be such a killjoy.

Don't blame it on Albert. The real problem is that our "accelerometers" don't really measure acceleration. One only has to look at the output of a free-falling 'accel'; it will measure 0 while accelerating at 32 ft/s/s (9.8 m/s/s for Rainier) toward the Earth. Once it stops it will measure gravity (if it didn't measure 0 for too long - splat).

Current accelerometers measure specific force not acceleration, a subtle but very important difference. Gyros also help us remove errors generated by the accels during rotation. Turns out they can't distinguish centripital force from acceleration either.

Dave
 
Einstein

I think Newton would be very upset that you are all crediting Einstein for his "discovery."

And I think y'all are missing the point. Near the planet surface, the acceleration of gravity is nearly constant (9.8m/s^2) DOWN. If you are free falling (discounting the resistance of the atmosphere) you ARE NOT ACCELERATING. The accelerometer is correct. You would not experience acceleration and would be, essentially weightless. Some people make big bux selling plane rides that use just this phenomenon.

Orbiting spacecraft are counteracting the acceleration of gravity by spinning arount the planet core really fast. The centrifugal acceleration (v^2/r) is equivalent to the gravitational acceleration. Therefore, again, weightlessness.

The thing is, the acceleration due to gravity is pretty constant (actually it falls off as the square of the distance a(g)=G/(r^2) from the center of the source, but so long as you are confined to the atmosphere, it will be pretty constant.

Therefore if you are "still" you can expect to experience a constant acceleration (9.8m/s^2) down. All the time. This is easy to compensate for mathematically - just subtract it from the Z component of both accelerometers.

If you have two accelerometers connected together by a fixed distance, and one experiences less acceleration than the other, the assembly has begun rotating in the vertical plane. On the other hand, if one experiences more horizontal acceleration than the other, the assemply has begun rotating in that plane. If they are both experiencing the same acceleration they are RELATIVELY not moving. It is that relationship to one another that can be used to derive the attitude. Gravity cancels out. An attitude indicator will still read straight and level if the plane is falling, so long as it in falling level - as in under a parachute.

Really.

I don't mean to start up an argument and I respect the knowledge of the members here, but two accelerometers and a clock are all you need. Really.

Shawn Clark
[email protected]

http://en.wikipedia.org/wiki/Isaac_Newton
http://en.wikipedia.org/wiki/Gravity
 
Kalman filters &c

Here's an ongoing discussion of the problem:

http://forum.sparkfun.com/viewtopic.php?p=38750&sid=df77b3b71ccb6fee31487947b0416b45

Basically a double integration of acceleration to obtain position introduces a lot of error. A gyro provides constant angular position data and, therefore, is doing a lot of the computation for you.

The error correction can be accomplished by referencing an external source of linear position from time to time (GPS) or angular position (Gyro).

The limiting factor, however, is computational speed and mathematical precision, not the nature of the time-space continuum itself.

As I wrote originally, it could be done. I'm not sure the 400-600MHz CPU in an iPhone is up to the task, but it is possible.

SBC
 
Gravity is not acceleration. Gravity is mass attraction. Gravity is one of those "external forces" that acts on an object when we talk about inertia (thanks, Mr. Newton) and can cause that object to accelerate. We use the same units to describe both mass attraction and acceleration but that is about the only similarity between the two. You touched on this when you talked about the fact that the effect of gravity changes as you move away from the center of mass. Acceleration does not change based on location. An acceleration of 1 m/sec^2 for 1 second will result in the same change of velocity whether it is here on earth or somewhere else in the cosmos.

Following your formulas, an accelerometer on the earth's surface should read 0 not 1g (9.8 m/sec^2). The change of velocity over time is 0, (it is just sitting there with it's input axis normal to the earth's surface) yet it will output a signal as though it were changing velocity (accelerating) at the rate of 9.8 m/sec^2. It is indicating the effect of mass attraction on the proof mass. Take that accelerometer out to about 22,000 miles, still normal to the earth's surface and it will no longer indicate 9.8 m/sec^2 of "acceleration". It still won't read 0 but darn close.

If I ignore the effect of atmospheric resistance a free falling body will accelerate at the rate of 9.8 m/sec^2 until it hits the earth. It is atmospheric resistance that defines the terminal velocity of a free falling object. Once the free falling object reaches terminal velocity an accelerometer on that object will indicate a portion of the mass attraction (proportional to the terminal velocity) but from the time the object begins it's free fall until it reaches terminal velocity the accelerometer will not indicate the actual acceleration (yes you can derive it by subtracting the effect of gravity but that's not what the accelerometer will be indicating). Of course this is again incorrect, change of velocity over time is 0 therefore it is not accelerating just measuring mass attraction.

Dave
 
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DrHolling said:
There for a minute I thought I had wasted the last 20 years or so fooling around with those pesky gyro things and all I needed were more accels. Rainier you can be such a killjoy.

Don't blame it on Albert. The real problem is that our "accelerometers" don't really measure acceleration. One only has to look at the output of a free-falling 'accel'; it will measure 0 while accelerating at 32 ft/s/s (9.8 m/s/s for Rainier) toward the Earth. Once it stops it will measure gravity (if it didn't measure 0 for too long - splat).

Current accelerometers measure specific force not acceleration, a subtle but very important difference. Gyros also help us remove errors generated by the accels during rotation. Turns out they can't distinguish centripital force from acceleration either.

Dave
Click to expand...

Ah yes, you have a point of course. But that is exactly where Albert comes in ! You are actualy talking about relativity. There is not telling that the accelerometer is falling. It may be that the rest of the universe is merely moving relative to the acceleometer which is standing still. Just depends on the observer. But let us not get into that - I'm sure there are dedicated forums for Albert.
Centripetal force does not exist. It is acceleration. We just use it as a convenience. Like when using aiding...

****, I've been playing around with all sorts of crazy (and not so crazy) ideas to get rid of (or reduce) the need for gyros. Magnetometers, accelerometers, stupid combinations of one or two gyros augmented by the above. Anything...
The closest I got was the "mattitude" mode of our now discontinued SP-3HC system. This realy did provide a horizon based on accelerometers and magnetometers - but still using gyros as I needed gyro stabilized magentic heading in the calculations.

In the end I gave up - just no getting away from three gyros, love or hate them - it seems to be the only way to make a good system.

Rainier
CEO MGL Avionics
 
Yes - but have a closer look.
All you are really doing with two accelerometers seperated by distance is making a gyro - sort of. It's a gyro that measures changes in rotation - which you want to integrate to get actual rotation rates. Trouble is, with current accelerometer technology, they are not good enough to give you the required accuracy to give you accurate rates over any length of time. Integration in the real World has some nasty issues.
You need "real" gyros - at least until somebody comes up with a real clever idea.

Newton "discovered" acceleration. Einstein put in the clincher - "Gravity IS acceleration - the two are the same thing". I was not crediting Einstein for discovering acceleration.

Rainier
CEO MGL Avionics

SBClark said:
I think Newton would be very upset that you are all crediting Einstein for his "discovery."

And I think y'all are missing the point. Near the planet surface, the acceleration of gravity is nearly constant (9.8m/s^2) DOWN. If you are free falling (discounting the resistance of the atmosphere) you ARE NOT ACCELERATING. The accelerometer is correct. You would not experience acceleration and would be, essentially weightless. Some people make big bux selling plane rides that use just this phenomenon.

Orbiting spacecraft are counteracting the acceleration of gravity by spinning arount the planet core really fast. The centrifugal acceleration (v^2/r) is equivalent to the gravitational acceleration. Therefore, again, weightlessness.

The thing is, the acceleration due to gravity is pretty constant (actually it falls off as the square of the distance a(g)=G/(r^2) from the center of the source, but so long as you are confined to the atmosphere, it will be pretty constant.

Therefore if you are "still" you can expect to experience a constant acceleration (9.8m/s^2) down. All the time. This is easy to compensate for mathematically - just subtract it from the Z component of both accelerometers.

If you have two accelerometers connected together by a fixed distance, and one experiences less acceleration than the other, the assembly has begun rotating in the vertical plane. On the other hand, if one experiences more horizontal acceleration than the other, the assemply has begun rotating in that plane. If they are both experiencing the same acceleration they are RELATIVELY not moving. It is that relationship to one another that can be used to derive the attitude. Gravity cancels out. An attitude indicator will still read straight and level if the plane is falling, so long as it in falling level - as in under a parachute.

Really.

I don't mean to start up an argument and I respect the knowledge of the members here, but two accelerometers and a clock are all you need. Really.

Shawn Clark
[email protected]

http://en.wikipedia.org/wiki/Isaac_Newton
http://en.wikipedia.org/wiki/Gravity
Click to expand...
 
Read Einstein. Forget Newton. The World is not real. It's an illusion. All quarks and quanta. (Pretty convincing illusion I might add).

Rainier


DrHolling said:
Gravity is not acceleration. Gravity is mass attraction. Gravity is one of those "external forces" that acts on an object when we talk about inertia (thanks, Mr. Newton) and can cause that object to accelerate. We use the same units to describe both mass attraction and acceleration but that is about the only similarity between the two. You touched on this when you talked about the fact that the effect of gravity changes as you move away from the center of mass. Acceleration does not change based on location. An acceleration of 1 m/sec^2 for 1 second will result in the same change of velocity whether it is here on earth or somewhere else in the cosmos.

Following your formulas, an accelerometer on the earth's surface should read 0 not 1g (9.8 m/sec^2). The change of velocity over time is 0, (it is just sitting there with it's input axis normal to the earth's surface) yet it will output a signal as though it were changing velocity (accelerating) at the rate of 9.8 m/sec^2. It is indicating the effect of mass attraction on the proof mass. Take that accelerometer out to about 22,000 miles, still normal to the earth's surface and it will no longer indicate 9.8 m/sec^2 of "acceleration". It still won't read 0 but darn close.

If I ignore the effect of atmospheric resistance a free falling body will accelerate at the rate of 9.8 m/sec^2 until it hits the earth. It is atmospheric resistance that defines the terminal velocity of a free falling object. Once the free falling object reaches terminal velocity an accelerometer on that object will indicate a portion of the mass attraction (proportional to the terminal velocity) but from the time the object begins it's free fall until it reaches terminal velocity the accelerometer will not indicate the actual acceleration (yes you can derive it by subtracting the effect of gravity but that's not what the accelerometer will be indicating). Of course this is again incorrect, change of velocity over time is 0 therefore it is not accelerating just measuring mass attraction.

Dave
Click to expand...
 
Zero G vs Free Falling vs Terminal Velocity...

SBClark said:
Near the planet surface, the acceleration of gravity is nearly constant (9.8m/s^2) DOWN. If you are free falling (discounting the resistance of the atmosphere) you ARE NOT ACCELERATING. The accelerometer is correct. You would not experience acceleration and would be, essentially weightless. Some people make big bux selling plane rides that use just this phenomenon.
Click to expand...

Accelerometers do not measure acceleration. Accelerometers measure Specific Force. (Thanks for pointing that out, Dr Holling. :))

Sit on your chair. Sit still. Are you accelerating (relative to the earth)? (look at simple F=ma if you are not sure. Ask yourself if the resultant force on you is zero or not... The forces are due to gravity and floor keeping your chair stationary.) So, no: you are not accelerating. Are you experiencing "weightlessness"? Nope. (you could repeat this standing on a scale and check your Weight... not zero)

Now let's jump out of a stationary hot air balloon from 10kft. Is the wind/air resistance applying a force the moment you get out of the balloon? No. The force (air resistance) is proportional to the square of your velocity. Since your velocity is zero, you acceleration is approximately 9.8m/s^2 down. Are you feeling weightless for that moment you exit? Yes! Are you accelerating: yes!

You continue accelerating, and your velocity increases, and the force due to the wind/air increases until you reach terminal velocity.

Are you accelerating? No. Terminal velocity, by definition is: no longer accelerating. No change in velocity. Are you feeling weightless? Nope.

Now get into the Zero G aircraft (http://www.gozerog.com) : are you accelerating at the time that you experience weightlessness? Most definitely! You are accelerating towards earth at a heck of a rate! (don't pull out of the parabolic flight path and see what happens!!)

And you will have to continue accelerating to maintain the feeling of being weightless...

"The airplane produces weightlessness by following a parabolic vertical flight path. A parabolic flight path is the same path that would be taken by an object in free fall, such as a cannonball fired into the air. As a result, the aircraft does not exert any G force on its contents, so the contents have zero apparent weight relative to the aircraft.

The aircraft heads upward at an angle of 45 degrees. As soon as the pilot begins the rotation into the parabolic trajectory, weightlessness is achieved. This lasts all the way "up-and-over the hump", until the craft reaches a declined angle of 30 degrees. At this point, the craft has lost a significant amount of altitude, and must begin to pull into a hard upward turn. The forces are then roughly twice that of gravity on the way down, at the bottom, and up again. This lasts all the way until the aircraft is again half way up its upward trajectory, and the pilot again initiates the zero-g parabola."

Taken from http://en.wikipedia.org/wiki/Vomit_Comet

My point: you are accelerating at 1G when you are experiencing weightlessness in a "Zero G" aircraft. Be careful when comparing free fall (accelerating) and falling at terminal velocity (no acceleration) and Zero G parabolic flight (accelerating)...
 
Acceleration

I don't mean to belabor the point, but I just thought it was worth a quick explanation...

Acceleration in classical physics requires a reference point. In the case of aviation this is typically the earth surface, specificaly mean sea level in the vertical plane.

The confusion comes in in calculating gravity into the equation. Gravity produces a spherical "acceleration field" which diminishes with distance from the center point.

In this case there is not a convenient point of reference. If you choose MSL, then you would still be accelerating at 9.8 m/s^2. The airplane "accelerating" down in a parabolic course is, actually, simply compensating for gravitational acceleration and therefore NOT accelerating at all. This is counter intuitive, but true.

The key point made by Einstein in his paper "Special Relativity" was that gravity and acceleration are not similar, they are the same. Gravity is not simpy an attractive force between two bodies with mass - it is an abberation in the shape of space. To prove this, Michaelson and Morely demonstrated that light, which has no mass, is deflected by gravity.


OOps gotta line up for a Southwest flight. I'l try to write more later...
 
The problem is really quite simple if one accepts Newton and make use of the earth as an inertial reference. (Which is 100% acceptable in my opinion on this one, and commonly used in flight dynamics. Even for analysis of significantly more complex flight dynamics problems.)

But I get the feeling that the real problem here is not the physics, but the definitions of the terms at stake... For example (Newton says): gravity is a force... Acceleration is the rate of change in velocity caused by a non-zero resultant force...

But if you look at the world from Einstein's point of view, it is all relative! :p

It’s been fun. :)
 
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