A Moment of ???

[Minotaur]

 

Originally posted by wells:
To understand moment of inertia, you should first understand torque  (Force * distance).  The force part of that formula is the 'impulse' force or the change in momentum (mass * velocity) over a time interval.  <snip>
 

Thanks!

This is starting to click now I hope.  

To guess the meaning of a moment.  I kind of now realize that a moment has to do with momentum.  Just as momentum can be related to inertia, a moment can be related to the force, that is in the form of torque, that is effecting inertia.

Or to put it simpler, a moment is a force that effects momentum.   Or possibly it is a rate of force change that effects a rate of momentum change.  

Now we have the the term "Long Moments" to confuse me.  Meaning that forces that are effecting torque are farther away from the CG.  By the same token the weight that is effecting the moment is also farther away so the inertia changes.

Example:
Picture an ice skater spinning in one place.  With their arms extended their rotation is slow.  With their arms tightly alongside their body their rotation is fast.  Moving their arms out, they slow.  Moving their arms back in, they speed up.

The total energy or inertia, of their body and its motion has not changed.  What has changed is the energy is simply positioned or stored farther or closer to their CG.  To maintain the same energy state, the rotation must increase as the arms are pulled in and vice versa.

However in either case, it requires an equal amount of torque to effect a porportional change in inertia.  What is different is the change in speed of rotation.  The slower rotation would have less speed change than the higher rotation.  IE:  For the arms out position there would be a much less change in speed than for the arms in position.

Am I getting closer to this concept?



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Mino
The Wrecking Crew
Trainer

[niklas]

Mino, i said if both aircraft have the same Torque produced by the aillerons, THEN yes. If you read my posting again, youīll see that the P38 can produce more Force with itīs aillerons.

I made a quick picture to explain my model. You can see that the engine in the wing is not only in a rotation, itīs also moving around in the space- THATīs the big difference that leads to the "steinerterm".
At the bottom i tried to demonstrate the difference between F,m,a  and M(=F*x),J,u

Hope that helps.

good example with the ice-skater mino. Itīs a question of Energy, Energy=constant for this example.
When she pulls her arms out, J (moment of inertia) increases. If she spins with the same speed (compared to "arms in") , her Energy (safed in the rotation) would be much bigger now. But Energy=const therefor she must slow down.
Again, look how fast they accerlate when they make themself "small"- Believe me, the difference between "mass in the middle" and "mass far outside" is huge!

   

niklas

[This message has been edited by niklas (edited 03-07-2000).]

[funked]

Mino:
Here's another pair of equations for you:

Force = Rate of Change of Linear Momentum

Torque = Rate of Change of Angular Momentum

Niklas:
In the spinning skater example it is Angular Momentum that is conserved, not Kinetic Energy.  Her kinetic energy increases by the amount of work required to pull her arms in.  However since there is no external torque on her body, angular momentum remains unchanged.  Assuming of course, an ideal frictionless environment.

[indian]

Mino heres a discription of inertia found on the web.
 http://library.thinkquest.org/12632/motion/index.html

check it out it might help.

Law of inertia

Abody that is in motion continues in motion with the same velocity (at constant speed and in a straight line), and body at rest continues at rest unless an unbalanced forc acts upon it. (Physics for Career Education)

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Tommy (INDIAN) Toon
  1st Aces High Trainer Crew
Home of The Allied Fighter Wing A.F.W.
A.F.W. Homepage

[This message has been edited by indian (edited 03-07-2000).]

[bloom25]

EEEEEEKKK, I'm getting flashbacks from Statics class.    (Well actually.   )  As far the the p38 goes, I believe that you need to take into account that by the engines are able to push air directly onto the control surfaces themselves.  Not only that, only roll acceleration would be affected I believe.  (This seems to be evident in the p38 in AH, it takes quite a while to get the thing really rolling.)  Moment is a general term describing the tendancy of an object to rotate about an axis perpendicular to the axis of the moment arm.  (Eek, another flashback.    Ok, that's enough for me, I'm an EE, not a ME afterall.  Now ... if anyone want to start a post about fun Electrical fundamentals stuff like Mutual Induction, or Bandpass filters, now that would be different.   )

bloom25
THUNDERBIRDS

[funked]

Mino:  I think you are correct that when he said "stalling moment" he meant a "momentary stall" or something like that.

[Minotaur]

Going off the deep end here, I hope there is water in the pool!              

Newton: An object at rest tends to stay at rest and and object in motion tends to stay in motion.

This statement describes the term "Inertia".  IE: The property of matter that resists changes is motion

Mass is the measurement for the property of Inertia.

Force is the measurment of an effect that attempts to make a object move (For this dissussion)

Gravity is the attraction (pull) by the earth on an object.  This is an expression of the force applied on the object directly toward the center of the earth.

Weight is the measurement of an objects mass under the force of gravity.

To make an object move a force has to be applied to it.  This force can be applied from only one direction, or from multiple directions.  Opposing forces will cancel out each and a "Net Force" will be applied to make the object move.  

Example:

• A rope "Tug-of-War".  The center point moves in the direction of greatest force.
• An aircraft wing produces an upward force called lift.  If the aircraft is flying level this force equals the force of gravity and the forces cancel out.  The net force is zero

Momentum describes the mass of an object while it is motion.  An object moving in a a straight line is said to be in "Linear Momentum".  An object moving in rotational motion is said to be in "Rotational Momentum".

Momentum is the measurment of the mass of an object in motion.  It is the combonation of mass the object at rest and the net force that was required to put to the object into motion.  Basically this a way to say that the mass of the object is now changed.  The change in this mass is equal to the force that effected change in the motion.  IE:  Applied force = {Mass in motion) - (Mass at rest)

Torque is the measurement of the force that causes an object to rotate on an axis called a "Pivot Point".

Moment Arm is the measurement of distance between the pivot piont and how far away from the pivot point the force is acting. IE: The distance would be the radius of the circle

Moment of Intertia is the measurement that describes how much mass is effectively at the distance for which the force of the moment arm is acting.  IE: Effective mass at the radius

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Now to get back to airplanes.              

Airplanes rotate on 3 axis.  Because we are dealing with a rotation, in comes our topic about "Moment".  

From my discussion, I will consider the airplanes CG to be the pivot piont, relating to how torque is applied.

Concerning balancing the aircraft for pitch.  This really means you are equalizing two forces.  Weight in the nose and weight in the tale, which are torque forces applied straight down.  

This means that there is actually two moment arm's in play here.  One fore and one aft of the CG.  The length of these two moment arms is different and the weight at the radius is not the same.  

What puts the airplane in balance is that each respective torque,  which is force in form of weight, exactly opposes the other one.  There is no net torque and the plane is in balance.

As there are two moment arms fore and aft for pitch rotation, there are also two for yaw and roll.  Roll being the more important one for this discussion as roll directly effects the agility of the airplane.

For discussion I will only discuss one wing or just one of the moment arms associated about the roll axis.

To make the aircraft roll, torque must be applied on the roll axis.  This torque is applied as the result of a force being applied by the deflection of an aileron.  This force attempts to make the wing move in one direction.

What attempts to prevent this movement is the effective mass at the point of the wing where the force is applied or the Moment of Inertia.  

Once the aircraft begins rolling it now has "Rotational Momentum", which is the sum of force that was applied and the moment of intertia.

To stop the rotation, a force must be applied in the opposite direction.  This force must equal the mass of the rotational momentum.

Therefore, airplanes with shorter moment arms and / or less moment of inertia roll faster, with an equal amount of torque aplied.  This is because the moment of inertia is less and requires less force to start rotation.  Additionally, less force is required to be applied to oppose rotational momentum, to stop rotation.

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Whew, did I get it?    

Mino

[This message has been edited by Minotaur (edited 03-08-2000).]

[wells]

More roll torque = faster final roll rate and faster roll acceleration.

less moment of roll inertia = faster roll acceleration but same final roll rate.  

All moments of inertia for roll, also count for yaw.  All moments of inertia for pitch, also count for yaw.  You can tell that the greatest moment of inertia is about the yaw axis, while the fin/rudder combo are much smaller than the hstab/elevator for the same 'moment'.  Result = airplane is more sluggish in yaw than in pitch.  So why not just put a bigger fin/rudder on?

Good question!

If the lift from the rudder/fin exceeds that of the body/fuselage (they lift opposite to each other), then you start getting really weird yawing motions.  Take, for example, the pilot applies left rudder. The nose will yaw left (at first) and then start yawing right, requiring left wing drop to maintain heading!  Not natural at all.  So generally, fins are kept smaller and fuselage area is increased to provide the necessary directional stability, while meeting a specific sideslipping requirement.  The added resistence of the fuselage to yawing motion makes for even less response and smaller yaw angles to be achieved.

[This message has been edited by wells (edited 03-08-2000).]

[SC-GManMP]

Geeez guys, i'm just here to have fun, not earn a degree!!!!!!!

You guys are pickin this apart like a turkey carcas the day after thanksgiving!!!!!!!

Very informative tho, thnx

[Minotaur]

niklas;

Thanks!    Those diagrams really helped me out.

Something dawned on me.  I think that you are using the wrong r value.  

The torque application point is at the end of the moment arm.  This value should be at the mean center of the ailerons, I believe.

Throw these numbers into your calculations.

• For the P-38 with a wingspan of 52 feet, use an r value of 23 feet.
• For the 190A-8 with a wingspan of 34.5 feet, use an r value of 15 feet.

Maybe fudge the torque up a hair for the P-38 due to larger sized ailerons, say 125% of the torque for the 190.  But, not fudging this might approximatly account for the larger wing mass of the P-38 as compared to the 190.
 
Additionally do two more calculations just for fun, to compare powered and unpowered ailerons.  Use the same r values as above.  

Assuming that at airspeed Vp, which is about 50% Vmax, the aileron torque is equal between the 190 and P-38.  Do one calculation showing roll acceleration at Vp.

Assuming that at airspeed Vmax aileron torque for the P-38 is 200% of Vp, and for the 190 it is 35% of Vp.  Do another calculation showing roll acceleration at Vmax.

Thanks again!  


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Mino
The Wrecking Crew
Trainer

[funked]

Mino, I think you have the idea now.  I could go through and nitpick your language but I think you get it.

One thing:

Linear momentum is mass times velocity.
Angular (rotational) momentum is moment of inertia times angular velocity.  Angular velocities are things like roll rates and pitch rates.

Also as to these calculations for the P-38 and the Fw 190, I think Wells has already done them.  

[This message has been edited by funked (edited 03-08-2000).]

[niklas]

mino, r is not the moment arm of the ailleron, itīs the radius of my engine model. I need it for the calculation of my moment of inertia. I added now the moment arm and the force of an ailleron in the picture, have a look again.

wells, do you agree, that if an aircraft has a wingspan twice as big compared to another aircraft, and has a Force produced by the aillerons twice as big (compared to the other one), both have same maximum roll rate?

Of course the bigger one has more inital roll torque, but the wingtip is moving around twice as fast compared to the smaller aircraft (when both have the same rollrate) - so drag increases twice as fast, and the Force of your aillerons decreases twice as fast, right?

niklas

[indian]

Mino you can go to Nasa's site they have a paper thier if you search it right on the p38 .

But glad to see you found the answer Its been so long sence I went to school on this stuff forgot how to discribe it. But the moment arm is what I was getting at. They actualy figure this stuff out by putting plane on a pendulum (old way that is) ne wway they calculate it. thats info is on nasa web site also.

------------------
Tommy (INDIAN) Toon
  1st Aces High Trainer Crew
Home of The Allied Fighter Wing A.F.W.
A.F.W. Homepage

[wells]

 

wells, do you agree, that if an aircraft has a wingspan twice as big
                compared to another aircraft, and has a Force produced by the
                aillerons twice as big (compared to the other one), both have same
                maximum roll rate?

Yes, that would be the case.  The reason the roll rate is the same though, is because the counter-torque (the angle of attack produced by the rotation of the wing) is also located further out (sqrt of 1/3 span).  For the most part, the ailerons are of the same proportion on most planes (about 10% of the wing area), so the maximum roll rate is predominantly a function of wingspan and forward speed.  A plane with twice the wingspan, travelling twice the speed of another plane will have the same maximum roll rate, given equal aileron proportions.

Take a P-51 and a P-38 for example, wingspans are 37' and 52'.  For any given speed (within the stick force limits for full deflection), the P-38 should roll about 70% as quicly as the P-51, give or take a small amount.

[Minotaur]

 

Originally posted by indian:
Mino you can go to Nasa's site they have a paper thier if you search it right on the p38 .

But glad to see you found the answer Its been so long sence I went to school on this stuff forgot how to discribe it. But the moment arm is what I was getting at. They actualy figure this stuff out by putting plane on a pendulum (old way that is) ne wway they calculate it. thats info is on nasa web site also.

Can you point me in the right area, the NASA is huge.  Thanks!



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Mino
The Wrecking Crew
Trainer