Inclining Experiment: a more simple way

[quequen]

I was searching for a simplest way to do an Inclining Experiment on small vessels and (roughly?) determining KG. I came to this simple deduction, and wish to know if this is right. If right, this can be easily inverted to get Heeling Angle for a given excentric weight, having KM, KG, and Disp. as data (I suspect it's not correct as it's too simple and I couldn't find something similar on many stability books). Comments will be appreciated...

[quequen]

Attached is a little spreadsheet using formulas from previous post. I'll appreciate if someone could compare outputs with some Inclination Experiment taken on real life.
I wonder if it's accurate-enough for small vessels like sailboats, kayaks etc.
Again, comments will be appreciated...
Thanks

[Paul Kotzebue]

Originally Posted by quequen

I was searching for a simplest way to do an Inclining Experiment on small vessels and (roughly?) determining KG. I came to this simple deduction, and wish to know if this is right. If right, this can be easily inverted to get Heeling Angle for a given excentric weight, having KM, KG, and Disp. as data (I suspect it's not correct as it's too simple and I couldn't find something similar on many stability books). Comments will be appreciated...

Assuming the weight will move parallel to the deck line, as opposed to the heeled waterline as you have shown, then GM = Weight * Distance / Displ / tan (angle).

[quequen]

Thanks Paul, your formula is what I've seen on stability books, I will add it to the spreadsheet. What I thought is than when a small boat return to equilibrium, weight's movement line is no longer parallel to waterline, assuming that load comes from center deck. Also, I guess where the center of load's moment should be located: just from where it comes, or the vertical line passing CB and CG?
Your designs are cool, by the way

[Paul Kotzebue]

Originally Posted by quequen

Thanks Paul, your formula is what I've seen on stability books, I will add it to the spreadsheet. What I thought is than when a small boat return to equilibrium, weight's movement line is no longer parallel to waterline, assuming that load comes from center deck. Also, I guess where the center of load's moment should be located: just from where it comes, or the vertical line passing CB and CG?
Your designs are cool, by the way

In an inclining experiment the heeling moment is always the weight multiplied by the distance moved. If I understand your question correctly, the answer is: just from where it comes.

[quequen]

Attached is a spreadsheet having this simplified Inclining Experiment.
And two images showing two different metods that produce exactly the same results. One of them uses tg(heeling) and G moves to G' over a line parallel to deck (the standard formula). The other uses sin(heeling) and cos(heeling) to correct Weight moment. In this second case, G moves to G' over a line wich is perpendicular to B'M.

In reality, G moves to his new position G' over the stright line GW, wich is not parallel to deck nor perpendicular to B'M. I wonder if this produces a significant error