Conservation of angular momentum - Page 2 - SailNet Community
 Seamanship & Navigation Forum devoted to seamanship and navigation topics, including paper and electronic charting tools.

Old 03-01-2012
Bristol 45.5 - AiniA

Join Date: May 2006
Posts: 4,501
Thanks: 5
Thanked 121 Times in 109 Posts
Rep Power: 11

One question

Quote:
Originally Posted by davidpm View Post
That was exactly what was thinking.
I seriously doubt that hoisting an anchor to the top of the mast in a storm will help prevent a capsize.
Would it help if the anchor was a Rocna? (Could not resist)

After the refit we have decided to sell Ainia. We want something smaller that would be could for the light summer winds of Lake Ontario, although we plan to spend at least a couple of winters in the Caribbean before heading north.
killarney_sailor is offline

Old 03-01-2012
Junior Member

Join Date: Apr 2011
Posts: 19
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 0

pendulum effect

Conservation of angular momentum can be visualised in a playground by watching how kids slow themselves spinning by shifting their centre of mass outward on those spinning poles.

On a sailing vessel the principles are the same but you're not rotating continuously you're oscillating like a pendulum. Polar moment of inertia is the term used in vehicle dynamics but dynamic oscillation of sailing vessels is less well understood.

While you could in theory dynamically balance your vessel by changing its mass moment of inertia you are subject to somewhat random frequency and amplitude inputs in a real ocean making it a tail chasing exeecise. You already have sails with near infinite adjustment. When you've dropped all canvas you are left with the vessels design and configuration.
Leftbrainstuff is offline
Old 03-01-2012
Senior Member

Join Date: Jul 2000
Location: Pennsylvania
Posts: 4,336
Thanks: 41
Thanked 235 Times in 222 Posts
Rep Power: 18

Quote:
Originally Posted by killarney_sailor View Post
Would it help if the anchor was a Rocna? (Could not resist)
It all depends how far from the deck you raise your Rocna on a halyard!!!!! :-o
RichH is offline

Senior Member

Join Date: Oct 2007
Posts: 4,473
Thanks: 360
Thanked 76 Times in 67 Posts
Rep Power: 10

No one has addressed the specific condition.
Your at a protected anchorage. There is no danger of large continuous waves.
On occasion a single 1 foot roller comes in caused by the wake of of boat.

In this specific case would some extra weight in the rigging have the effect of damping the sloshing?

Any natural motion would have the probability of causing the boat to oscillate so weight aloft would only help for the first couple of seconds then would cause even worse oscillation.

But with a single wave caused by a boat wake, what do you think?

Last edited by davidpm; 03-01-2012 at 08:45 PM.
davidpm is offline
Old 03-01-2012

Join Date: May 2007
Location: Santa Cruz
Posts: 396
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 10

Quote:
Originally Posted by davidpm View Post
No one has addressed the specific condition.
Your at a protected anchorage. There is no danger of large continuous waves.
On occasion a single 1 foot roller comes in caused by the wake of of boat.

In this specific case would some extra weight in the rigging have the effect of damping the sloshing?

Any natural motion would have the probability of causing the boat to oscillate so weight aloft would only help for the first couple of seconds then would cause even worse oscillation.

But with a single wave caused by a boat wake, what do you think?
I haven't done the math, but I can tell you that riding on a mooring with no mast is much worse than with a mast--the frequency of the roll is much higher, and so is the acceleration in response to a boat wake--enough to slide the coffee cups off the table. Seasickness is a strong function of frequency of oscillation, and it is one of the common complications of dismasting at sea.

I also think that the most common stability scenario is the dynamic response to being hit by a breaking wave from the side, where the taller and heavier masts give a distinct advantage. At one point I contemplated going to a carbon fiber mast, but the disadvantages at anchor and in storms made me decide to stick with the heavier aluminum.
Old 03-01-2012
Senior Member

Join Date: Sep 2011
Location: Michigan
Posts: 319
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 6

Quote:
Originally Posted by davidpm View Post
In a real dynamic situation however the mass of the mast had a tendency to keep the boat from capsizing due to the conservation of angular momentum
No doubt you could calculate this using momentum, energy or inertia calculations. I find inertia calculations to be more intuitive.

If I look at my boat, I see the predominant inertias (around waterline) as:

Keel at 8200 lbs (3727 kg) , at about 1.5 m gives 8400 kgm^2 inertia
Mast 60 feet, 550 lb, 250 kg, at 10 m gives 25000 kgm^2 inertia
Fiberglass hull 11,000 lb or 5000 kg at 1 meter gives 5000 kgm^2

First I notice that the mast and rigging determine the predominant inertia, so yes the mast is the most important inertia that will resist acceleration. So if we have a fixed torque applied to this inertia, it will cause an angular acceleration much higher if the mast is missing.

The sum of inertias is 38400 kgm^2

Now lets put a 100 lb mass or 45 kg at the top of the 18 m mast. This gives an inertia of 45 * 18^2 = 14580 kgm^2

Just for kicks:

The derivative of my stability diagram is about 100,000 Nm/rad at zero. This is the effective spring rate of the water against the boat.

So the natual frequency of my boat is:

so the natural period of my boat is about 4 seconds.

Without the mast, the natural frequency is:
Sqrt(100000/13400) = 2.73 rad/s = 0.434 hz or 2.3 second period

So if we just consider inertias, the angular acceleration will higher when the mast is missing. On the other hand, the angular displacement is the same with or without the mast because the frequency has changed.

However, the problem comes that we have neglected damping. When you reduce the inertia, the acceleration is higher, the velocity is higher, so the damping is higher. Since damping is proportional to angular velocity, the damping is going to be higher by about the ratios of natural frequencies: 0.434/0.257 = 1.7 times higher without the mast.

When we consider the higher damping and the higher frequency without the mast we find that the heeling angle goes down without the mast because the damping is higher.

Here is a simulink model that illustrates the effects.
Attached Thumbnails

Last edited by BryceGTX; 03-01-2012 at 10:25 PM.
BryceGTX is offline
Old 03-01-2012

Join Date: Jul 2008
Posts: 3,820
Thanks: 14
Thanked 51 Times in 50 Posts
Rep Power: 10

Quote:
Originally Posted by Barquito View Post
So, say you are motoring in a seaway where the wave train (or a harmonic) is the same frequency as your boats roll rate. Would it reduce roll if you hoist some weight up the mast until the roll rate of the boat is different than the waves?
I think Bryce just answered that one extremely well. The answer (tongue in cheek) is to send a friend aloft. A 100 kg person at the top of Bryce's mast has this effect:

Quote:
Originally Posted by BryceGTX View Post
With mast:
so the natural period of my boat is about 4 seconds.

Without the mast, the natural frequency is:
Sqrt(100000/13400) = 2.73 rad/s = 0.434 hz or 2.3 second period
With 100kg buddy at the top, this adds an additional 100 * 18^2 = 32,400 kgm^2
so the new natural period is about 5.29 seconds.

But if you are motoring and your friend won't go aloft, you could change your angle to the waves, thereby changing their apparent frequency and preventing oscillation. It's David's anchoring scenerio that makes you want to hoist something aloft.

Regards,

.
.
Great minds discuss ideas;
Average minds discuss events;
Small minds discuss people.
.
The best minds discuss sailing (and a little bit of politics). I don't know why. It's a mystery!
.

Last edited by Bene505; 03-01-2012 at 10:22 PM.
Bene505 is offline
Old 03-01-2012
Senior Member

Join Date: Sep 2011
Location: Michigan
Posts: 319
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 6

So now we run the Simulation with the mast. We see the natural frequency period of about 4 seconds and we notice that the damping causes the rolling to die out after about 5 cycles.

We notice a peak angular displacement of about +-4 degrees. THis is with a 5 degree step forcing function.
Attached Thumbnails

Last edited by BryceGTX; 03-01-2012 at 10:03 PM.
BryceGTX is offline
Old 03-01-2012
Senior Member

Join Date: Sep 2011
Location: Michigan
Posts: 319
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 6

Now we remove the mast inertia. We notice the natural frequency increases and so does the damping. The damping causes the rolling to die out after only about 3 cycles. And because the frequency is higher, the damping cause the angular displacement to be limited to 3 degrees.
Attached Thumbnails

Last edited by BryceGTX; 03-01-2012 at 10:14 PM.
BryceGTX is offline
Old 03-01-2012
Senior Member

Join Date: Sep 2011
Location: Michigan
Posts: 319
Thanks: 0
Thanked 0 Times in 0 Posts
Rep Power: 6

Even though the heeling angle is reduced without the mast, you may be more sensitive to the accelerations. In that case, without the mast, the accelerations are about three times higher than with the mast.

And since these accelerations are such low frequency, the higher accelerations may actually be more uncomfortable. And since the heeling angle is only slightly reduced, but a higher frequency, we may also find this more uncomfortable.
Attached Thumbnails

Last edited by BryceGTX; 03-01-2012 at 10:43 PM.
BryceGTX is offline

Message:
Options

By choosing to post the reply above you agree to the rules you agreed to when joining Sailnet.

## Register Now

In order to be able to post messages on the SailNet Community forums, you must first register.
Please note: After entering 3 characters a list of Usernames already in use will appear and the list will disappear once a valid Username is entered.

User Name:
OR

## Log-in

Human Verification

In order to verify that you are a human and not a spam bot, please enter the answer into the following box below based on the instructions contained in the graphic.

 Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)