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Moments of Inertia derivation

S

Simon853

Messages
516
I think I'm way out of my depth here... This isn't strictly an FS problem, but I figured you guys maybe the folks to ask!

I need to provide Moments of Inertia of a small air vehicle to a subcontractor who is going to simulate it on a pro simulator. I have only basic weight and dimension details from the airframe supplier.

I did a (whole host of) web searches and turned up a FS related web page citing a process by Dr Jan Roskam for deriving approximate MoI's based on aircraft weight, length and wing span, when factoring in a rough mass axis offset based on the generic aircraft type.

i.e.

The roll MoI is defined as:

Ix = (W/g)*(Rx*b/2)^2

Where W is weight, g is geforce, b is wingspan and Rx is 0.242 as defined for a single engined high-wing aircraft.

What I (and my company's mathematicians) don't understand is: why does he divide by g? If weight is the static weight of the aircraft, then 1 Kg weight = 1 Kg mass, surely? So it appears if I divide by g it would give me a grossly incorrect answer.

Anyone ever had to calculate MoI's like this?

Thanks,

Si
 
arno

arno

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Staff member
FSDevConf team
Resource contributor
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netherlands
Hi,

Must be become weight is a force in Newton, while the mass is in kg. See this quote I found on the internet:

Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object.
Click to expand...

So by dividing it by g you actually get the mass of your aircraft. So I guess you could also simply to formula to:

Ix = m*(Rx*b/2)^2
 
B

Brother23

Messages
184
Country
germany
Please could you Post...

...the Web address or other aerodynamical terms here.

I would like to try some out.

Are there books by Dr. Roskam that I should buy?

Of course some, with things I can put in my aircraft.cfg.

And one other thing: How can I edit the air.file? Are there

graphical programs where I can edit the peformance curves?




Greetings
 
R

rightnumberone

Messages
123
Country
us-massachusetts
arno said:
Hi,

Must be become weight is a force in Newton, while the mass is in kg. See this quote I found on the internet:



So by dividing it by g you actually get the mass of your aircraft. So I guess you could also simply to formula to:

Ix = m*(Rx*b/2)^2
Click to expand...

What a wonderful explanation.

It is why people shouldn't really care what they weigh. In fact, people "weigh" differing amounts depending solely on what is nearby to them.

For example: I'm currently located very close to a rather large object ... the Earth, so I weigh about 185 pounds. This is significantly more than if I was currently located closer to some less massive object - such as the Moon - producing much less of a gravitational force.

A good explanation of why you would divide by G would be located here:

http://www.astronomicaltours.net/ZeroG/how.htm

This page demonstrates how negative G forces can "overcome gravity" and make us weightless even though we are very close to the Earth - relatively speaking.
 
B

Brother23

Messages
184
Country
germany
Hey Hey!

That is also not the end of the story.

Nature is all in all very simple.

Its only about dimensions.

All that many things you can see in nature come of the dimensions.

We have three we can see directly. The space.

We have one we can imagine directly. Time. Past. Present. Future.

And then we have what we call forces: Gravity, Electromagnetism, Strong and
Week Nucleus Forces.

These 4 things we can feel every day. But they are dreams of reality, that for
today, work good for us.

But especially Gravity is a nice thing.

It is told, that newton while overthinking his theories, was hat by an apple.

And the he had his enlightment of the gravity concept. Sure this is only a

story, but he made a gravity concept.

That two masses, with 1kg in size, that are 1 Meter appart, attract each
other with 1 Newton Force. Sure this is now crude force.

But planets are much greater. Especially earth is

596 000 000 000 000 000 000 000 kg in mass.

Wow. I think that attraction force is much higher.

When we are on the surface the force, a acceleration force, an that is that

interesting, is 1 G. It is 9.81 m x sec exp 2.

This means that when we jump in a hole near the ocean after 1 second

we descend with 9.81 meter per Second. After two Second with 20 meter

per second and so on.

Common airplanes travel most from an Altitude at 0 Kilometer to and Altitude

up to 20 Kilometer.

With newtowns formula G (Weight) is Mass1 (earth) x Mass2 (Airplane) divided

through RadiusxRadius when dont need to calculate much. The common sports

aeroplane is 2x10 EXP3 Kg in Mass. The earth was 5.96 x 10 EXP24 kg in

Mass.

So earth has 10 000 000 000 000 000 000 000 times more mass the the

airplane.

So it is like an elephant that should feel a single atom the just landed on

his back.

And while earth has so much influence on all earthlings and their little airplanes cool people made the 1 G Formula.

Your Mass on this world, is almost your weight.

But an small excurs: Why do you think, are masses accelerating in gravitational fields. Thats what really interesting and the next step of
understanding!

Then you see, that also complicated formulas, are only the feelings of
the fingertips of a blind man, wandering through a world of shiny colorful
things he cant see.

Greetings
 
B

Brother23

Messages
184
Country
germany
Next Part...

As a little child I drove with a train the first.

I only saw the train standing in the little railyard.

I had no clue what will happen.

When I sat inside, suddenly their were vibrations

AND

the railyard started to move!

I shouted out to my father - HE, THE RAILYARD DRIVES AWAY...WHAT

HAPPENS HERE-!

Later, when I better understood physics I saw that I had become a victim

of the phsychological relativity. My standpoint in mind was not so correct and

my brain misinterpreted the input of my biological sensors.


And now, we see masses that attract each. Or simplY: When a mass

occupies space, I attracts almost anything, also light that has actual

NO mass. Only energy. So we understand space itself is altered. Its bend

and scratched. The light not takes a turn. For itself its traveling straight.

Yeah, space is more complicated then a Utah village. But EVERYONE can

manage to understand that, when he has no brain damage and is open.

It is gods creation. He loves us. And he wants us to understand and receive

the great joy when we do.


So we have to ask brave in return: Could it be, that the manipulated space

itself creates the masses, creates the matter, the energy,

the galaxies

the star clusters

the planets

life

human beings


and little aircraft we have THE GREATES JOY to loiter the sky with.

What is an aircraft?

Yeah it is made of metals and other things.

But this chemical things were all around this world. Millions of years.

But some day a human being had a dream. IT WAS ONLY IS HIS HEAD.

And this dream altered again things in space.

It formed a wunderful machine. A flying machine.

And now this dream is in everyones head you have see this machine.

He knows how it works.


Isnt that wunderful?

And out of this, respect human dreams.

When real respect evolves, the conflicts vanish.

And a synthesis is possible, that owns only the best.

And this is the reason of evolution.

Existense of the best.

And what get dirty vanishes.

Ideas.

Armies.

Empires.

Lets hope, that in the common years more wisdom reaches the people that manage the world.

Greetings
 
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