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Apr 09, 2016, 10:57 AM
F3B and F3K
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# harmonic oscillator to determine changes in yaw inertia

Hi Guys

I performed an experiment to compare the moment of inertia for different DLG setups.

I applied it to see if a different arrangement of the radio gear has a measurable effect.

I tried to compare the overall moment of inertia of a conventional Flitzebogen to a new setup where everything is moved closely to the CG. I have used an unbuilt fuselage and I added a finished wing and tails to it.

Then I stuffed the radiogear either in the front of the nose or at a location closer to the CG and added 100gr of Tungsten to balance it. In the normal setup, that amount of Tungsten went into the CG as we would do with conventional ballast.

Then I hanged the model on two strings from the ceiling, exactly balancing it on the model's CG.

The system is now a harmonic oscillator around the yaw axis with a weak torsional spring constant. Its resonance frequency is the square root of the spring constant, K_T, divided by the moment of inertia, I_Flitz.

Thus an oscillation period is T= sqrt(I_Flitz/K_T)

Now I measured the oscillation period over two oscillations and ensemble averaged over multiple realizations of the experiment.

I found:

2*T_FlitzOld=20.23+-0.173s

2*T_FlitzNew=19.49+-0.075s

T_FlitzOld is the oscillation period of the conventional setup

It is important that the mass of the system is exactly the same (else the spring constant is changed) and that the model is hanged up exactly the same in each experiment.

If we now divide T_FlitzOld by T_FlitzNew, we can get rid of the unknown spring constant.

One can then find that I_FlitzNew=T_FlitzNew^2 / T_FlitzOld^2 * I_FlitzOld

With the experimental values, it follows that the new setup has 93% of the inertia of the conventional setup.

This 7% reduction will increase launch height (in a nonlinear fashion), and with all optimization of current airplanes, it is an easy gain that lays there for grabs.

Reto

PS: the measurement is related to this method published by Mark Drela: https://www.rcgroups.com/forums/show...&postcount=104

However, I derived it differently and avoided modelling the torsional spring (as I am not interested in the absolute moment of inertia).

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Last edited by RetoF3X; Apr 10, 2016 at 12:10 PM.