# Navigaton system based on Fn

Discussion in 'Boat Design' started by zzerachiel, Jun 4, 2010.

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### zzerachielJunior Member

Hello,

Hope I've chosen the right section.

So, i'm studying for an exam and i bumped into something called "Navigation system ( regime ) based on Fn number"

Fn = v/sqrt(g*nabla^0.33) where nabla is the real hull volume.

It sais

FN < 1 : the ship weight is balanced by the push force ( Arhimede's principle )
Fn in ( 1,3) - ship's draft and trim are changing
FN > 3 : the ship's weight is balanced by the portant force.

I don't really understand the Fn in (1,3) case.

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### daiquiriEngineering and Design

A Froude number is defined as Fn = V / sqrt (g*L), where L is some reference length. Dimensionally, a displacement (D) is a length cubed (L^3), so D^0.333 is dimensionally a plain length and hence can be used as a reference length in the Fn formula. A Fn calculated with D^0.333 as reference length is called "volumetric Froude number".

Now, take a look at the Figure n.9 (page 5) in this paper:
http://nparc.cisti-icist.nrc-cnrc.gc.ca/npsi/ctrl?action=rtdoc&an=8895319&article=1&lang=en
It shows the sinkage and trim of a planing hull model at various speeds.
The model design weight is 30 kg, which means that displacement is 0.03 m^3. This information allows you to substitute the values of velocities in the X-axis of the graph with the correspondent volumetric Froude numbers.

You will find that up until Fn=0.6-0.7 circa, trim and heave are more or less constant. From Fn = 0.9-1.0 circa the values start to change. It happens because in this Fn region the distance between the bow and stern wave crests is higher than the hull length. The hull kind of "climbs" on the bow wave. This causes an increase in trim, with maximum trim angle attained in the region around Fn=1.8-2.0 . The change in heave will depend on the point where measurements are taken (by definition, Heave is the vertical movement of the Center of Gravity, so it should be measured there). In this case, heave is measured at a point placed at 15% of the LOA, from the stern. The result is that for Fn=0.7-1.1 the hull sinks into the wave trough, and then climbs up again for Fn > 1.2-1.3, up to the maximum value at Fn=2.9, after which it remains constant.
You can observe when the hull is in full planing mode, (Fn > 2.7-3.0 ) the draft remains pretty much constant as the speed goes up, while the trim continues to decrease.

Hope it was clear enough...
Cheers!

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### zzerachielJunior Member

Yep, very clear.

Thank you.

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