Cp - Prismatic Coefficient Fore & Aft

[idkfa]

Hello everyone,

Simple question really, how relevant is dividing Cp into Cp_fore/Cp_aft in yacht design? And is it preferable to have fore smaller than aft at the various heel angles.

Thanks,

idkfa

[rxcomposite]

Cp is the fineness of the boat (displacement) in relation to the prism dictated by the cross sectional area x length.

What is distrubuted fore and aft (from the midship section) called the area curve is the sectional area coefficient Cx which in turn leads to location of longtitudinal center of buoyancy (LCB) which is usually measured forward or aft of midship.

[Skippy]

Fore-aft differences in Cp would affect the location of where drag occurs. For instance, if you have a hull that's canoe-shaped forward with a short boxy after half, the drag will be mostly aft at low speeds. But I have no idea what good that would do you.

[idkfa]

Thanks guys,

Skippy, you're saying wave drag will develop further aft? but at lower speeds, the increased wetted drag of the canoe bow will hurt?

Cp only tells you average of fineness/fullness of the fore and aft volumes. So, shouldn't a good yacht design be concerned with the distribution of that volume ie. area curve, but then how do you numerically compare one curve with another? fore / aft Cp???

I've been trying to collect data on the relative split on fore aft, and it seem that a finer bow and fuller aft is favourable. Any ideas on what that ratio should be? Know it is limited by what fair-shape can be created.

eg Cp = 0.54, Cp_fore = 0.52, Cp_aft = 0.56?

I've attached a zip file (iges & 3dm) of and ideal canoe? not a legal or possible hull form having hollows and will not work heeled, but it shows the fore/aft volume split. lcg approx midship, cp 0.578, fore 0.54, aft 0.605.

[nero]

Hull Resistance Calculator in the software section of boat design.net. Writtten by Fiona Sinclair. This program splits the cp fore and aft.

[rxcomposite]

I have not encountered fore and aft Cp in design procedures but thanks, i will look into that one. It is my understanding that Cp is = displacement/ (largest cross sectional area x length.)

What i use is the distribution or section area curve plot along the length. Sometimes it is plotted as a section area coefficients. This way you can easily see if the hull displacement distribution is symetrical or not.

Slightly full hull fore and aft increases stability but has more resistance in wavemaking and frictional resistance. A finer, longer entrance with slight reverse curve waterline decreases resistance. This leads to the aft being fuller. However, a too full aft will decrease directional stability. This applies to canoe and paddle boats.

Dinghys and sailboat offen have the largest cross sectional area forward, near the mast, as a general rule.

[Skippy]

idkfa: at lower speeds, the increased wetted drag of the canoe bow will hurt?
No, the angular lines of the stern will be terrible at low speeds, while the canoe bow is ideal.

idkfa: it seem that a finer bow and fuller aft is favourable.
The stern is often flatter to provide stability, generate weather helm when heeled, and/or promote planing. The aft Cp doesn't necessarily have to be higher. Notice that a canoe is almost as fine aft as it is forward, and many are exactly symmetric.

[sorenfdk]

Originally Posted by Skippy

...the location of where drag occurs...

AFAIK, Drag doesn't occur at some specific location.

[JonathanCole]

It has been stated in various threads on this forum, that the most effecient hull has a fine bow and stern, a high L/B ratio (for example, 20:1) and with the largest section about 2/3 aft. This makes sense when you think about it. It is related to Cp but Cp doesn't tell the whole story. When the water is divided by the hull, you want the division to be as gradual as possible to avoid pushing a wave up. Lifting water is work which requires energy. But you also need it (the water) to gradually return to its meeting place at the stern or else you will create eddies and counterflows which also have a lot of resistance to the movement of the hull.

[Leo Lazauskas]

Originally Posted by JonathanCole

It has been stated in various threads on this forum, that the most effecient hull has a fine bow and stern, a high L/B ratio (for example, 20:1) and with the largest section about 2/3 aft. This makes sense when you think about it. It is related to Cp but Cp doesn't tell the whole story. When the water is divided by the hull, you want the division to be as gradual as possible to avoid pushing a wave up. Lifting water is work which requires energy. But you also need it (the water) to gradually return to its meeting place at the stern or else you will create eddies and counterflows which also have a lot of resistance to the movement of the hull.

Cp certainly doesn't tell the whole story. Changes in Cp will also affect dynamic sinkage and trim which in turn affects the resistance of the vessel.

Leo.

[idkfa]

leo.

Approx. how large are these effects before & after Fn 0.4? And is this where Cp aft should rise above 0.7 ie. submerged transom?

idkfa

[Leo Lazauskas]

Originally Posted by idkfa

leo.

Approx. how large are these effects before & after Fn 0.4? And is this where Cp aft should rise above 0.7 ie. submerged transom?

idkfa

In general, dynamic sinkage and trim (or "squat") effects are small for Fn below about 0.35. For Fn > 0.35 the effects depend on the shape of the hull. I calculate squat from the actual hull geometry, not from formulae that use Cp as a parameter, so I can't help you much with the last question.

Good luck!
Leo.

[rxcomposite]

I am ignorant on this matter. What is the methology for finding fore and aft Cp. Do i find the largest cross sectional area first and use that as a point to locate distances fore and aft or do i locate LCB to have fore and aft distances.

Thanks.

[rxcomposite]

The most efficient hull is where the the wave making and frictional resistance meet when plotted at different speeds.

Frictional resistance accounts for the majority of resistance at low speed. At higher speed, wavemaking resitance increases until it becomes a dominant factor.

Increasing lenght to reduce wave making resistance is not always a boon as frictional resistance increases with lenght. There is an optimum combination for every speed.

Leo's hull optimization program is great for analyzing hull for frictional and wave resistances. Also wave interference.

[Leo Lazauskas]

Originally Posted by rxcomposite

... Frictional resistance accounts for the majority of resistance at low speed. At higher speed, wavemaking resitance increases until it becomes a dominant factor.

And then at still higher speeds (strictly, Froude numbers), wave resistance decreases and viscous resistance again becomes the dominant contribution.

Regards,
Leo.