Hello,

I have been working on a jet fighter model for over 6 months now and I have come
to the point where it is worthy to be animated.  The only thing is, I have no
idea where the rotation point of the plane should be.  Let me elaborate.  From
my understanding, an airplane may rotate along the yaw axis (the rotation the
rudder controls), the roll axis (which is controlled by the ailerons), and last
the pitch axis (controlled by the elevators).  In most diagrams I've seen these
three axis of rotation meet at a single point and this is the point I don't
know how to find.  My only guess is that it would be the centroid.  Any help
would be greatly appreciated.

Bridgeofstraws

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Bridgeofstraws wrote:
> Hello,
> 
> I have been working on a jet fighter model for over 6 months now and I have come
> to the point where it is worthy to be animated.  The only thing is, I have no
> idea where the rotation point of the plane should be.  Let me elaborate.  From
> my understanding, an airplane may rotate along the yaw axis (the rotation the
> rudder controls), the roll axis (which is controlled by the ailerons), and last
> the pitch axis (controlled by the elevators).  In most diagrams I've seen these
> three axis of rotation meet at a single point and this is the point I don't
> know how to find.  My only guess is that it would be the centroid.  Any help
> would be greatly appreciated.
> 
> Bridgeofstraws
> 

It should be the center of mass.  However, there's no obvious way to find the center
of mass unless you know the mass density of each element of the aircraft.

For each element of the aircraft, of center of mass position r_i, and unit mass m_i,
you can calculate the net center of mass r-com:

r-com = sum_i { r_i m_i } / sum_i { m_i }

where r-com and each r_i are spatial vectors with x, y, and z components.

Dan

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I've made a probably a much simpler jet model than yours.
  And I put the center point just a little toward the tail from the 
midpoint of the front and back of the main wing and in the middle of
the thinkness of the wing.
Have Fun!

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> I have been working on a jet fighter model for over 6 months now and I 
> have come
> to the point where it is worthy to be animated.  The only thing is, I have 
> no
> idea where the rotation point of the plane should be.  Let me elaborate. 
> From
> my understanding, an airplane may rotate along the yaw axis (the rotation 
> the
> rudder controls), the roll axis (which is controlled by the ailerons), and 
> last
> the pitch axis (controlled by the elevators).  In most diagrams I've seen 
> these
> three axis of rotation meet at a single point and this is the point I 
> don't
> know how to find.  My only guess is that it would be the centroid.  Any 
> help
> would be greatly appreciated.

Use the centre of mass, as it will make the calculation of rotations easier 
when forces are applied to the control surfaces on the plane.  But really 
you can use any point because there is no such thing as a fixed "rotation 
centre" in real life - eg while doing a loop the rotation centre is at the 
centre of the loop, while flying across the atlantic it is at the centre of 
the Earth etc.

I would imagine that for a jet fighter the centre of mass will be about 1/3 
of the way from the main landing gear towards the front landing gear, 
judging by the beefyness of the wheels :-)

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> I would imagine that for a jet fighter the centre of mass will be about 
> 1/3 of the way from the main landing gear towards the front landing 
> gear, judging by the beefyness of the wheels :-)
> 
> 

On a bicycle, the center of mass is approximately 40-45% of the distance from the rear
tire patch to the front tire patch.  Since the first airplane is commonly attributed
to bicycle builders, I'd say a plane is probably similar.


Dan

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Dan Connelly wrote:
> 
>> I would imagine that for a jet fighter the centre of mass will be 
>> about 1/3 of the way from the main landing gear towards the front 
>> landing gear, judging by the beefyness of the wheels :-)
>>
>>
> 
> On a bicycle, the center of mass is approximately 40-45% of the distance 
> from the rear tire patch to the front tire patch.  Since the first 
> airplane is commonly attributed to bicycle builders, I'd say a plane is 
> probably similar.
> 
> 
> Dan

A more serious analysis may be considered by consulting a reference such as the
following:

<http://books.google.com/books?id=RDZUG--o9HMC&pg=PA5&lpg=PA5&source=bl&ots=H1uZSIsNVR&sig=zJKCWYYoT4TYBGJ6Wyay8hJgANg&hl=en&sa=X&ct=result#PPA10,M1>

There's a nice figure on page 10 which shows the center-of-mass approximately between
the wings, within the fuselage.

Dan

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> A more serious analysis may be considered by consulting a reference such 
> as the following:
>
>
<http://books.google.com/books?id=RDZUG--o9HMC&pg=PA5&lpg=PA5&source=bl&ots=H1uZSIsNVR&sig=zJKCWYYoT4TYBGJ6Wyay8hJgANg&hl=en&sa=X&ct=result#PPA10,M1>
>
> There's a nice figure on page 10 which shows the center-of-mass 
> approximately between the wings, within the fuselage.

Yeh, I think it is going to be roughly in the geometric centre, but of 
course it needs to be infront of the main landing gear by a suitable margin, 
otherwise the plane will fall over backwards while sat on the ground!

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Just so everyone knows, I haven't been working on my jet for 6 months straight.
Not even close.  I started it 6 months ago and have been very slowly adding to
it.  So, Leroy I'm sure your airplane is just as good as mine is.  Dan and
Scott, I'm so grateful for all of your help so far.  I'm looking at the google
books article right now and it looks like exactly what I need.

Also, in case anyone is interested here is some background on my jet fighter:

The jet fighter is a cross between a F22 and F15.  It is called an M22 (atleast
for now) which is because M is my first initial and 22 is my favorite number.
The plane has three versions, a CSG version, an isosurface version and a mesh
version that is generated from the isosurface by an include file made by
someone else (whose name I can't remember now but I have it written down
somewhere).
Just last week I added an exhaust nozzle and a flame, and I'm working on adding
a smoke trail using Rune Johansen's particle system.  The smoke trail is
actually the entire reason I started this topic because in order to generate a
smoke trail you need an animation.  And this seemed like the perfect time to
figure out where the center of the aircraft should be located so that when I
tell the jet to follow a spline, its flight will look realistic.

Anyways, thanks again for the help.  I'll hopefully post a picture of my jet
with a smoke trail before Christmas.

Bridgeofstraws

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"Bridgeofstraws" <bri### [at] inboxcom> wrote:
> Hello,
>
> I have been working on a jet fighter model for over 6 months now and I have come
> to the point where it is worthy to be animated.  The only thing is, I have no
> idea where the rotation point of the plane should be.  Let me elaborate.  From
> my understanding, an airplane may rotate along the yaw axis (the rotation the
> rudder controls), the roll axis (which is controlled by the ailerons), and last
> the pitch axis (controlled by the elevators).  In most diagrams I've seen these
> three axis of rotation meet at a single point and this is the point I don't
> know how to find.  My only guess is that it would be the centroid.  Any help
> would be greatly appreciated.
>
> Bridgeofstraws

CG is somewhere in the wings depending on the sweep. I don't see why you need
perfection here. somewhere behind the wing's leading edge is your pivot point

hold a model by its wing tips, it should be fairly well balanced.

Here's my CSG transport (3hrs total more or less), looking forward to another.
links are here, pic and mpg:
http://home.earthlink.net/~openuniverse/

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"alphaQuad" <alp### [at] earthlinknet> wrote:
>
> CG is somewhere in the wings depending on the sweep. I don't see why you need
> perfection here. somewhere behind the wing's leading edge is your pivot point
>
> hold a model by its wing tips, it should be fairly well balanced.
>
> Here's my CSG transport (3hrs total more or less), looking forward to another.
> links are here, pic and mpg:
> http://home.earthlink.net/~openuniverse/

I am only looking for the aircraft's approximate center of gravity.  Perfection
isn't important to me.  I just want to make sure that once I set a whole bunch
of variables with relation to this center of gravity that I won't have to redo
it anytime soon.  By the way, I like your CSG transport.  You must be very
talented to have made that in 3hrs.  I can't even make a simple scene within a
week.

Bridgeofstraws

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