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Good point Vance. The two hang tests are used to establish two different tasks.
 
The double hanging test should normally be done with all the masses of the rotorcraft attached.
However, each hanging does not change if you remove the element from which it is hung, due to the nul force moment this element produces.
Thus, the hanging line by the rotor will not change if you only remove the rotor, the hanging line by the front wheel will not change if you only remove the front wheel, the hanging line by the rear wheel will not change if you only remove the rear wheel.

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A single test gives only one line on which GC is certainly situated. The second test gives a second line on which GC is certainly situated.
The crossing of the two lines gives the exact position of GC
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Very clear and instructive, JC.

I can't understand why is there so much discussion on this subject. After all, it's the time-honoured method for obtaining the CG of an irregular body.

If I remember correctly, the CG of a human body was determined in that way, using frozen bodies. That was done in France, in the 19th century, again if I remember correctly...

Correction... No, that work was due to two German anatomists. An English translation of their findings is available in the internet:

 
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A single test gives only one line on which GC is certainly situated. The second test gives a second line on which GC is certainly situated.
The crossing of the two lines gives the exact position of GC
View attachment 1146063


I would love to see someone do the second hang (line 3 and line 4) exactly like that with a pilot in there :)
 
Very clear and instructive, JC.

I can't understand why is there so much discussion on this subject. After all, it's the time-honoured method for obtaining the CG of an irregular body.

If I remember correctly, the CG of a human body was determined in that way, using frozen bodies. That was done in France, in the 19th century, again if I remember correctly...
I believe that the forces involved in the stability of an object being shoved through the air have greater forces applied to that object than the forces involved in the difference in moment arm and mass from the thrust line. I feel that the measurement of a static body to find a center of mass to determine the stability of an which will be subjected to other forces perhaps is a bit simplistic. At what point of axis will the frozen Frenchman spin when dropped from great height?About the CG or area or both? Also I must add, that questions bring us greater understanding and answers. No stupid questions isn’t that correct?
 
So to describe an object in space, it requires a certain amount of vectors. It is clear to me the initial hang test is to establish a balance from an point at or very near the place of lift the rotor will be of influence on the fuselage. This is a good thing to do and I have read/heard and therefore understand, a nose down slight angle ( 3 degrees ) is about right. This can also be used to adjust and center the control stick. I could be mistaken. Once this is established and a plum line is drawn, this becomes the first vector. This line is obtained by allowing the fuselage to pivot under the point of suspension. This a Similar point of suspension which the fuselage will be allowed to pivot when in flight. Agreed? If a hang strap is fashioned to where the attached rotor becomes the point of suspension or we could construct something to support all of the lengths of the rotor blades and the entire gyro was lifted from the floor, the first pivot line would be the same. Wither the rotor off or the rotor on be used to suspend, it is the balance of the fuselage which is measured by drawing the plumb line. Now what is the purpose of the second vector but to show where the CG of the fuselage is, after all it will be suspended by the rotor in flight. Adding the tilted weight of the rotor with all of the moment arm involved will not give a true reading of the center of gravity of the fuselage as a component alone. Apples need to be compared to apples.
 
So to describe an object in space, it requires a certain amount of vectors. It is clear to me the initial hang test is to establish a balance from an point at or very near the place of lift the rotor will be of influence on the fuselage. This is a good thing to do and I have read/heard and therefore understand, a nose down slight angle ( 3 degrees ) is about right. This can also be used to adjust and center the control stick. I could be mistaken. Once this is established and a plum line is drawn, this becomes the first vector. This line is obtained by allowing the fuselage to pivot under the point of suspension. This a Similar point of suspension which the fuselage will be allowed to pivot when in flight. Agreed? If a hang strap is fashioned to where the attached rotor becomes the point of suspension or we could construct something to support all of the lengths of the rotor blades and the entire gyro was lifted from the floor, the first pivot line would be the same. Wither the rotor off or the rotor on be used to suspend, it is the balance of the fuselage which is measured by drawing the plumb line. Now what is the purpose of the second vector but to show where the CG of the fuselage is, after all it will be suspended by the rotor in flight. Adding the tilted weight of the rotor with all of the moment arm involved will not give a true reading of the center of gravity of the fuselage as a component alone. Apples need to be compared to apples.

A single hang test from the teeter is used to center the controls.

Experience has shown what the hang angle for a specific model of gyroplane works best so some people try to achieve that by moving the rotor head. The best hang angle range is different for different models of gyroplane.

Typically at around 60kts the rotor will be tilted back around seven degrees so a three degree hang angle will be flying nose up in relation to whatever is used for the hang angle unless some aerodynamic device is used to change it.





On a separate and unrelated subject.

The double hang test is used to determine the vertical center of gravity.

If the rotors are left off the measurement of the vertical center of gravity will not be correct.

Some people feel the location of the vertical center of gravity is important and some could not care less.

Most gyroplanes today have a thrust line well above the vertical center of gravity.

Most modern gyroplanes have the fuel tank(s) below the center of gravity so the vertical center of gravity changes as the fuel is exhausted.

If you feel the vertical center of gravity is not important then there is no reason to do a double hang test.
 
The video of Gabors Behemoth being hang tested had a very convincing conclusion. First we secured a posterboard alongside the mast. Then we suspended the gyro from the teeter bolt with the rotor off..with Gabor sitting in the seat. A vertical laser line was I intersecting the teeter bolts center, then a vertical line was drawn on the posterboard where the laser beam was shining.

Next we installed the rotor and did a 2nd hang somewhat offset from the teeter bolt. This gave another vertical line which intersected the first line. You can see this intersection marked in the video.

Then I had them balance the gyro on its mains right at its point of tipping either way. The vertical laser beam was then aimed coming up from the axle centerline..
and a third line was marked. Guess what? Check the video. That like intersected exactly at the CG intersection of the first two lines. All three lines intersected at one point absolutely verifying the original CG plot as being accurate. Nothing like real world techniques proving themselves.
 
The problem I had was, getting the mains on the Dominator high enough off the ground so the tail would clear the ground.
 

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