midship coefficient - Cm

[mcollins07]

I'm using freeship software which calculates a midship coefficient (Cm). Can you describe what this is and how it is used in design work?

thanks,
michael

[Raggi_Thor]

It's the area of the midship section (or the largest station) divided by the area of a rectangle with the same beam and draft. A rectangular barge with sharp corners will have 1 or 100% while a V bottom will have 0.5 or 50%.
If deplacement is midship area x length x prismatic coefficient
Depl=Am x Lwl x Cp,
and Am = Bwl x D
and Depl = Bwl x D x Lwl x Cb
then Cb = Am x Cp

[mcollins07]

Raggi_Thor,
your definition makes sense, but the numbers that I get from FreeShip don't seem to fit. I'm working with a wedge. Thus, the midship section would always be a rectangle. Cm = Am / (Beam midsection x Draft midsection). Cm would always be 1? Freeship calculates zero for the flat bottom wedge. Freeship calculates from 0 to about .58 for a bottom with an upward sloping stern. Since the midship section is always a rectangle, shouldn't it always be one?

[fcfc]

The problem is the "midship" section definition.

Sometimes, it defines the section at the widest beam overall, or the widest waterline beam (raggi definition), or the station at 50% length (Freeship definition).

Cm may also refer to the section with the biggest undewater area. Which may be not the beamiest, neither the one at 50% len....

[Raggi_Thor]

I think we have to ask Martinj about this :-)

[SailDesign]

Michael,
At the risk of being perceived as EXTREMELY rude, can you check that your "bow" is indeed the bow? The only way you should be able to get those numbers would be if your wedge was out by 90degrees, and the bow is really the staboard beam.
Humour me....
Steve

[mcollins07]

Originally Posted by SailDesign

.. "bow" is indeed the bow? ...

Steve,
I did not find it in the manual, but my notes have that the X coordinate is the longitudinal direction and that the bow is the highest number. This is what I have.

One thing that I'm doing a little strange, I have the Loa = 1 meter. I'm looking at different scales and the unit of one is convenient.

[Raggi_Thor]

I looked at your picture again.
You have the Bmax at the stern, X=0.
What is the area of the hull (underewater) if you look at it from behind (or front)? That is not a vertical section (Dmax and Bmax is at different positions), but rather
Bmax X Dmax
How does this area compare to the midship section, X=0.5 ?

[mcollins07]

After generating a new set of offsets in excel, the Cm results looked reasonable. Cm started at .7 and went down to .5 Must have been something wrong with my input as you suggested.

Are you defining Cm:

Cm = Area@midShip / Bmax x Dmax

[Raggi_Thor]

yes, that was a thought, in your case Bmax = Bmax_lwl.