Path of an airplane in a 1G roll

Corky, you're right. Earlier the discussion was about a roll: I think I
can present a model for experiencing 1 g throughout what might be
called a roll, but that argument fails for a straight loop.

On Sun, 19 Jun 2005 11:04:39 -0500, Chris W wrote:

4 Groups?

Do we have any who is a math whiz here? I want to find a formula to
calculate the position of an airplane throughout a 1G roll. The reason

At any rate, do you want to maintain 1G, or just positive G? it's a
big difference.

You can do a barrel roll and maintain positive G all the way around.
It's a very simple maneuver and very easy to do. It's also probably
one of the easiest to screw up.

I'm doing this is so I can build a "roll track" for a remote control car

Remember that in straight and level flight you are pulling 1G. If you
start a roll you will have to start adding nose up stick to maintain
1G to the point of 1G when inverted. "
"Theoretically" as you rolled past inverted you would start reducing
back pressure until you were back wings level.

At this point it takes some one much more versed in aeronautic theory
(and practice) than I, but... A barrel roll comes the closest to what
you are asking. It, however starts out at more than 1G. Typically 2Gs
and it can be more. With a 2G pull up at the start, you will be
pulling 1G when passing inverted.

Remember you started out in a nose high attitude to get to this point.
So in the theoretically description you would most likely be way nose
low at the 180 degree inverted position and I think you will probably
get well past 2 Gs getting back to the wings level position.

so the car will alway have a positive g force on it to keep it on the

But, if it's just the positive Gs you need, shape the track like the
path a plane would take through a barrel roll. It would go up and
curve to the right forming a corkscrew shape with the end right back
at the same level as the beginning. You can add turns as well "as
long as the car is changing direction in relation to *its" own
vertical axis. For example if the car is on its right side the track
needs to be curving right, if on its left then the track needs to be
curving left. If the car is inverted the track needs to be curving
down.

Remember too that the car has to be going fast enough to maintain the
desired G forces and traction. Slow down and it'll just fall off.

Roger Halstead (K8RI & ARRL life member)
(N833R, S# CD-2 Worlds oldest Debonair)
www.rogerhalstead.com
track. Anyone have any ideas? So far my attempts have have all come up
short. They don't pass what my college calculus instructor called the
"warm and fuzzy" test. I think it has been too long since I took those
classes.

In article ,
Corky Scott wrote:


Tony, it doesn't matter where the plumb bob hangs, going up means
adding some force in excees of 1G to do it. No matter how gently you
do it, a sensitive enough G meter will detect the additional force
that is required.

It's kind of like trying to fake out a bathroom scale. No matter how
gently you step onto it, it will eventually read your weight.

Climbing is like pushing against an inverted scale.

Corky Scott

Corky,

"Net force = mass times acceleration" (Isaac Newton, ~1620)

"Acceleration = rate of **change** of velocity"

"Work done = force times distance"

If you're standing on a bathroom scale in a stationary elevator at the
ground floor, the scale will read your weight. Gravity (the invisible
gravitational field) is pulling down on you with a force mg (your mass
times the acceleration of gravity); the scale is pushing back up on you
with the same force mg (and that force is what its dial reads). The
total force on you (the sum of gravity pulling down on you plus the
scale pushing up on you) is thus zero, but it's zero not because you're
stationary, that is, remaining at a constant level; it has to be zero
because you're at a constant vertical speed, namely zero; you're not
*accelerating* (changing speed) -- not at this point anyway

The doors close, the elevator starts upward. For a brief initial
period, until the elevator reaches its steady-state upward speed, the
scales read more than mg. That's because the elevator (or whoever is
pulling on the elevator cable) is both pushing you upward with a force
equal to your weight (mg), which does work and adds to your potential
energy in the gravitational field; but there's also a slight excess
force at the start which is needed to accelerate you to the steady-state
speed of the elevator (and which therefore gives you a little kinetic
energy as well as your steadily increasing potential energy).

Once the elevator reaches its steady-state speed (around the 3rd floor,
let's say) from there up to the 104th floor you're traveling at a
*constant* vertical velocity: you're *not accelerating*. Therefore
there can't be any net upward force on you; the scales read mg.

[This does leave out the fact that the value of g changes very (very!
very!) slightly between the ground and the 104th floors, but this change
is so minute in going from the ground floor to the 104th floor that it's
just not in the discussion here.]

The rest of the way up, from the 3rd to 101st floors, the scales are
pushing up on you with a constant force mg; and that force eventually
acts through a distance h, the height from the ground floor to the 104th
floor. Total work done by the elevator on you is therefore force times
distance, or mgh. That work has gone into giving you an added potential
energy equal to mgh in the Earth's gravitational field.

[As you neared the 104th floor and the elevator slowed to a stop, you
also lost the kinetic energy you had gained between the ground and third
floors. The scales showed a small reduction below mg between 101 and
104 just as they showed a small increase between first and 3rd floors.]

You now own that extra potential energy of mgh; it's yours, as you step
off the elevator on the 104th floor. Want to get it back? Step outside
on the viewing deck and pop over the railing. Leaving aside questions
of air resistance, by the time you get back down to, say, the first
floor level you'll have all that potential energy converted into kinetic
energy -- a lot of kinetic energy! Unfortunately, one floor later all
that energy energy will pretty much have been converted into heat,
slightly warming up a small patch of sidewalk and some gunk on it.

Same deal in a plane: hang a seat from a butcher's scales hung from the
ceiling of a plane, and sit in it. Have someone fly the plane in a
constant forward speed, constant upward speed, straight line climb.
Except for a slight initial transient period when they begin the climb,
the scales will read your weight, mg, no more, no less.

--"Another Tony"

There is a path that, if followed by a vehicle, produces a
loop at exactly 1G. It can be visualized as a combination
of a path that accelerates downward to produce 0 G and a
path that makes a perfect circle at exactly 1 G in the 0 G
background field.

This is true as far as it goes. However, in order to do this in still
air, using wings, the aircraft has to assume certain attitudes that
preclude the 1G from being pointed in the same direction relative to the
cabin throughout the maneuver. To illustrate, consider the aircraft at
the bottom of a loop done in this manner, after completion. It would be
essentially horizontal (since it's the bottom of the loop and the
centripetal forces are pushing outward (downward w.r.t the cabin).
However, it is descending at whatever rate a freefall would be after
however long it takes to complete the maneuver. I bet that's pretty
fast - probably much faster than the forward speed of the airplane.

Consider the relative wind against the wings - I bet you'd see much more
than a 1G load on them were they to actually get into this configuration.

Now, it would work if the surrounding air were also freefalling.
However, the circumstance that would lead to freefalling air with an
airplane inside of it is not a circumstance in which I want to be the
pilot.

Jose
r.a.student snipped - I don't follow that group
--
You may not get what you pay for, but you sure as hell pay for what you get.
for Email, make the obvious change in the address.

Tod, your comment about free fall is on the money and it makes the
analysis easy. Great insight. If we define a roll as the airplane
rolling on its axis I think it's realizable. Think about flying a roll.
It's probably complete in say 5 seconds. 5 seconds of 1 G acceleration
is about 160 fps, or about 100 kts. That might be a dive something less
than 45 degrees, and I agree a straight pull back to level would induce
some Gs.



You'll need enough elevator authority and air speed to maintain the 1
G.

My take on this is that an airplane in a 1G roll would follow the same
path as any other object.

Imagine your in space. A 1G roll would be a perfect circle with a
constant 1G acceleration.

Now bring that path into the Earth's gravity well. Now the 1G roll is
all messed up by the Earth's 1G. How can we fix that? Just like the
Vomit Comet does, by accelerating down at 9.8m/s^2. Superimpose a roll
on top of a parabolic descent and you have the path of a theoretical
airplane in a 1G roll.

I don't think there is a plane that could actually perform this maneuver
in reality.

--
This is by far the hardest lesson about freedom. It goes against
instinct, and morality, to just sit back and watch people make
mistakes. We want to help them, which means control them and their
decisions, but in doing so we actually hurt them (and ourselves)."

On Wed, 29 Jun 2005 04:01:56 +0100, Ernest Christley
wrote:

My take on this is that an airplane in a 1G roll would follow the same
path as any other object.

Imagine your in space. A 1G roll would be a perfect circle with a
constant 1G acceleration.

Now bring that path into the Earth's gravity well. Now the 1G roll is
all messed up by the Earth's 1G. How can we fix that? Just like the
Vomit Comet does, by accelerating down at 9.8m/s^2. Superimpose a roll
on top of a parabolic descent and you have the path of a theoretical
airplane in a 1G roll.

I don't think there is a plane that could actually perform this maneuver
in reality.

Obviously, the quicker you can roll, the easier it would be, but
essentially it would be impossible to complete a constant 1G roll back to
S&L. You would have to end up in a nose-down attitude in order to
maintain 1G while inverted. The greater your roll rate, the less time
you'll need to maintain positive G while inverted, and hence the nose
won't need to drop as far. The closest you're going to get to this is a
simple aileron roll where you start nose high... but then you've pulled
more than 1G to get the nose in to that position!



--

PERCUSSIVE MAINTENANCE:
The fine art of whacking the cr*p out of an electronic device to get it to
work again.

T o d d P a t t i s t wrote:

There is a path that, if followed by a vehicle, produces a
loop at exactly 1G. It can be visualized as a combination
of a path that accelerates downward to produce 0 G and a
path that makes a perfect circle at exactly 1 G in the 0 G
background field. At the end of the maneuver, the object
following that path would be hurtling towards the ground at
high speed (the speed the object would have reached if it
had fallen towards the ground during the entire time it took
to fly the 1G loop.) I doubt any vehicle I'm familiar with
could actually traverse such a path through air.

I agree with all of the above, Todd, except the part about calling it
a "loop" g. The following is the vertical profile of such a "loop",
flown in the hypothetical 0 G free fall that you describe, and at a
constant "loop" speed of 100 kts.

http://www.airplanezone.com/PubDir/FauxLoop.php (9 KB gif file)

Note that the Y scale of the plot is about 10 times the X scale so the
path is exaggerated in the x direction. Also note that the resulting
path has no resemblance to a loop. Perhaps you already visualized the
path, but I am sure many others didn't (including me). Just trying to
add to the knowledge.

David Odum -- email: David at AirplaneZone dot com

T o d d P a t t i s t wrote:

Cool! Thanks for doing the math (what did you use?)

Well, I could have used Mathematica, my zillion dollar workhorse (and
toy), or I could have written a program in Delphi or one of the
several C variants at my disposal, but, alas, I used what I usually
use for quick and dirty analysis such as this, I used Excel.

Have you looked closely enough at this to figure out whether
you could get a more practical result with a non-constant
speed loop, or by using a different speed?

I can plug any constant loop speed I wish into the spreadsheet that I
made. Indeed, loop speed is the only input variable. Alas, however,
it doesn't matter what speed is input, the general shape of the
vertical profile remains the same, only the scale changes. As for
modeling a non-constant loop speed, I doubt whether it would make much
of a difference. Perhaps one day I'll do that too, but not now
because my new Canon D20 digital SLR has just arrived and I want to
play.

BTW, Todd, those "1 G free fall barrel rolls" proposed elsewhere in
this thread have about as much resemblance to a barrel as your "1 G
free fall loop" does to a loop, as I'm sure you can now well imagine.

Greetz,

David Odum - email: David at AirplaneZone dot com

On Mon, 27 Jun 2005 at 12:30:45 in message
, Corky Scott
wrote:

Tony, it doesn't matter where the plumb bob hangs, going up means
adding some force in excees of 1G to do it. No matter how gently you
do it, a sensitive enough G meter will detect the additional force
that is required.

Although it is true that a climb cannot be initiated without exceeding
1g in the transition from level flight to climb, a climb at a steady
speed and climb rate does not mean that more than 1g is felt in the
aircraft.

Why should it? If there is no acceleration there is no g other than the
gravitational one. Of course this does ignore the fact that the earth's
gravity is reduced as the aircraft moves further from the surface of the
earth!
--
David CL Francis