# natural period(Tn) and yacht motion

Discussion in 'Stability' started by urisvan, Mar 8, 2007.

1. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

in some books i am reading things like that: "if one makes a very deep hull and add the weight at the very bottom of the boat, he will rise the GM and the boat will make some quick motions in the seaway."
in the same books it is written that "if the natural period of the boat about the center of rotations is high, she makes easy motions in the seaway"
isn't it a conflict?
in the literature i saw that: Tn=1.108*k/sqrGM(seaworthiness, marchaj)
so natural period increases by the weight location being apart from the axis of rotation. in a way it reduces because it is inversly proposional with the GM. but it is inversly propotional with GM's squareroot. but directly propotional with the gyradius.
please ease my mind. which one is true? will a boat will make quick motions so will be uncomfortable if she is deep and her ballast is located deep? or will the boat will be comfortable, by her ballast located deep so she will have a high natural period so will make easy motions.

2. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

hiii

consider two boats that are equal(the shape, ballast ratio vs..)but the ballast of one boat is lower than the other one.
which one will make easy movements or which will roll quickly?

3. Joined: Mar 2002
Posts: 1,585
Likes: 43, Points: 58, Legacy Rep: 779
Location: Minneapolis,MN, USA

### duluthboatsSenior Dreamer

"if one makes a very deep hull and add the weight at the very bottom of the boat…..”
In this case it requires a lot of force to cause movement, but when the force is removed you can get a very quick righting movement.

"if the natural period of the boat about the center of rotations is high….”
In this case it requires less force to cause movement, and when the force is removed the righting movement is less.

There is a much more technical description of this but I have to keep things simple or I don’t understand them. I hope it helps.

Gary

4. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

hi, thank you for your reply. you are the only person who interested me.
but as my grandfather says: "you got me wrong and also you are the only person who got me".
the boat which is deeper and ballast located down also has a bigger natural period value. isn't it?

5. Joined: Mar 2002
Posts: 1,585
Likes: 43, Points: 58, Legacy Rep: 779
Location: Minneapolis,MN, USA

### duluthboatsSenior Dreamer

urisvan,
It is your bad luck to get me as the one to help you. I am only an aging man who is interested in small boats. I have read most of the books available on the subject. I have only a basic understanding stability. Hopefully one of the engineer types will chime in and better answer your question.
Gary

6. Joined: Mar 2005
Posts: 3,644
Likes: 188, Points: 63, Legacy Rep: 2247
Location: Pontevedra, Spain

### GuillermoIngeniero Naval

urisvan,
generally speaking wide beams (higher stability of forms) and/or low centers of gravity (higher stability of weights) induce shorter rolling periods, so higher accelerations and more uncomfortable movements. A boat with very short rolling period may become very uncomfortable at sea, while one with a too long one may be dangerous, as this may indicate poor stability.

Using the formula Tn=1.108*k/GM^.5, we see Tn increases with gyradius (so with the spreading of weights outwards) and decreases with increasing GM, which is dependent on beam and the vertical position of CoG. The beamier a boat is, the higher the GM and so the shorter the Tn. On the other hand, the higher the CoG is, the lower the GM and so the longer the Tn, although variations in the vertical position of CoG may significatively affect gyradius (depending on masses distribution), and so its effect in Tn may not be so evident as in the case of beam.

There is a formula used to estimate a boat's natural rolling period (roughly, for a 'usual' one) as a function of displacement, Lwl and beam as follows:
Tn = 6.28*(disp^1.744/35.5) / (82.43*Lwl*(.82*beam)^3))^.5 (Imperial units)
You can see the big effect of beam.

Cheers.

7. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

thank you very very much
do you mean that, one who tries to increase gyradius by adding weigth and locating it to the bottom so to increase Tn, unwillingly can increase GM, so decrease Tn?

please consider this: there is a boat, which has a bulb keel, that you can lower and rise up. in which case the Tn of the boat will be higher? when you lower the bulb keel or when the bulb is up?

8. Joined: Mar 2005
Posts: 3,644
Likes: 188, Points: 63, Legacy Rep: 2247
Location: Pontevedra, Spain

### GuillermoIngeniero Naval

With the bulb in the low position Tn most likely will be higher, as the effect of gyradius (which varies with the square of distance), will be usually greater than the effect of the increased GM due to the lower CoG.
Cheers.

9. Joined: Sep 2004
Posts: 368
Likes: 7, Points: 0, Legacy Rep: 75
Location: Bangkok, Thailand

### MikeySenior Member

Tn = 6.28*(disp^1.744/35.5) / (82.43*Lwl*(.82*beam)^3))^.5 (Imperial units)

Beam entered in that formula is overall beam and the 0.82 is to get an average waterline breadth. If the boat has flare or hard chines, then this should be compensated for

Guillermo has explained it well, another observation is that Big bulbs on real cruising boats are not popular (although beam is by far the dominating factor).

Mikey

Last edited: Mar 12, 2007
10. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

a quotation

hi
a different scenerio;
now we don't lower the ballast, but increase it.
let me introduce you a quotation from "Lars Larsson and Rolf Eliassons" famuous book "principles of yacht design", page 89:
"....a very severe problem of this kind was experienced when the first large ships for carrying ore were taken into service. when the ore was loaded on the bottom of the hull, its stability became so large that excessive accelerations were created...."
cheers

11. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

hi mikey,

12. Joined: Sep 2004
Posts: 368
Likes: 7, Points: 0, Legacy Rep: 75
Location: Bangkok, Thailand

### MikeySenior Member

The iron ore ships are a very extreme case indeed, these boats have extreme form stability (high BM and GM), they simply had to load higher to reduce stability (reduce GM). Although the principle as Guillermo explains it is the same, these extreme effects cannot realistically be duplicated on a sailing boat.

The reasoning still stands, adding say a huge bulb very low would increase stability and make the boat less comfortable, just adding ballast by increasing the weight of the keel would make it more comfortable

13. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

hi,
mikey you approve guillermo, but you are in a conflict with him and also with me. you say that, vessel with a high keel and heavy bulb at the end of the keel will be discomfortable. you say like that, because all bulb keel boats you saw also have a nearly flat bottom, light displacement for speed. so they have high GM and low Tn, despite their low and heavy bulbs.

14. Joined: Mar 2005
Posts: 3,644
Likes: 188, Points: 63, Legacy Rep: 2247
Location: Pontevedra, Spain

### GuillermoIngeniero Naval

urisvan
I'm not in disacordance with Mikey. Either I'm not explaining myself properly or you are not understanding my posts and Mikey's. Please read again carefully.
Cheers.

15. Joined: Nov 2005
Posts: 225
Likes: 5, Points: 18, Legacy Rep: 53
Location: istanbul

### urisvanSenior Member

hi guilermo, the words below are yours:
"With the bulb in the low position Tn most likely will be higher, as the effect of gyradius (which varies with the square of distance), will be usually greater than the effect of the increased GM due to the lower CoG."

and these are mikey's words:
"The reasoning still stands, adding say a huge bulb very low would increase stability and make the boat less comfortable, just adding ballast by increasing the weight of the keel would make it more comfortable"

isn't there a disacordance?
bye

Forum posts represent the experience, opinion, and view of individual users. Boat Design Net does not necessarily endorse nor share the view of each individual post.
When making potentially dangerous or financial decisions, always employ and consult appropriate professionals. Your circumstances or experience may be different.