How far could a square rigged ship heel before it capsized?

[Kentop]

Thanks to the USS Niagara, we have an answer:

http://dx.doi.org/10.1080/19942060.2009.11015255

[Nightmoss]

Thanks for the link. A tad over my head, but fascinating research just the same.

[Kentop]

Thanks for the link. A tad over my head, but fascinating research just the same.

Over my head too, but here is a bit from the report that you can take to the bank:

In addition to the general trends, the captain of Niagara is interested in two specific wind velocities—those which create heel angles of 10 and 30 degrees. Ten degrees is the “comfortable” limit of heel—due to the importance of safety, the captain does not want to exceed this heel angle as a matter of practice. At 30 degrees the ship will capsize and be lost, so the captain does not want to get even close to that limit.
An examination of Fig. 10 shows the wisdom of not wanting to exceed 10 degrees of heel. For example, for configuration 1 the wind speed required to produce a heel angle of 10 degrees is approximately 25 knots, and the maximum wind speed for survivability of the vessel is 39 knots. In wind conditions with mean wind speeds of 25 knots it is not uncommon to have temporary gusts in excess of 40 knots. While it will take time for the ship to respond to a gust of short duration, the possibility that the ship will capsize must be avoided.
Wind speeds in excess of 60 knots are infrequent on the Great Lakes, so it is doubtful that the Captain would have to be concerned about configuration 4 while sailing in home waters. The only concern in this case would be if the ship were to be on an extended ocean voyage, which has not been attempted in her history. Configuration 4 can be considered safe for essentially any weather condition that the ship is likely to experience.
It was previously mentioned that configuration 3 was uncomfortable because it was under- canvassed in winds of 25 knots. Figure 10 shows that this configuration should produce a heel angle of approximately 4 degrees at 25 knots, and is better suited for wind speeds of 30–40 knots, thus supporting the Captain’s original observations.
Finally, the Captain has noted that the wind speeds that would capsize the ship are somewhat lower than what he expected. Niagara does not have a very deep draft due to the fact that it had to be moved over a sandbar to get from the harbor where it was built into Lake Erie. As a result of this low draft the ship does not have the same stability as other ships of that era with similar size and mission. The low relative stability of Niagara makes the results of this work even more important.

[Bligh]

Seems like a quite concise appraisal Ken.
As a landlubber, I think that even I can get the gist of this explanation.
Thank you.
Rob.

[7eat51]

Thanks for the .pdf link, Ken. This will make enjoyable reading this weekend.

I miss math. I had an extraordinary professor with whom I studied some calculus and differential equations. Problems like this would have been right up his alley. He always presented us with interesting scenarios from which we had to derive the corresponding equations. Unfortunately, I don't remember much, having never used math other than statistics in any subsequent job.

[Devsdoc]

Hi Ken
Thanks for the link. I will sit at some point and give it the time I think it needs to read properly. Thanks again.
Be safe
Rory

[7eat51]

I just read the article. The following is from the Results and Discussion section:

With the exception of configuration 2, the driving force for all cases is quite small compared to the side force. This is generally the desired effect, as the goal in heaving-to is to minimize forward motion.

I do not understand why this is the case. I would think that a large driving force relative to the side force would be desirable, and that the side force is the force of concern regarding capsizing. Can anyone explain this?

Am I correct, as well, in that the entire article is concerned with sailing into the wind? The reason I ask is that the AWA in each trial was 90-degrees or less. If this is the case, then would I be correct in assuming that sailing with the wind creates less concern regarding capsizing? One could still have a large AWA if measured from the stern, putting, I would think, significant side force on the ship. Again, I would relish any explanation.

This is fascinating stuff.

[DeRuyter]

I just read the article. The following is from the Results and Discussion section:

With the exception of configuration 2, the driving force for all cases is quite small compared to the side force. This is generally the desired effect, as the goal in heaving-to is to minimize forward motion.

I do not understand why this is the case. I would think that a large driving force relative to the side force would be desirable, and that the side force is the force of concern regarding capsizing. Can anyone explain this?

Am I correct, as well, in that the entire article is concerned with sailing into the wind? The reason I ask is that the AWA in each trial was 90-degrees or less. If this is the case, then would I be correct in assuming that sailing with the wind creates less concern regarding capsizing? One could still have a large AWA if measured from the stern, putting, I would think, significant side force on the ship. Again, I would relish any explanation.

This is fascinating stuff.

Well just going by sailing experience as I have not read the article (and I stay away from math!), you have much more heeling effect with the wind abeam and forward than with a following wind. Notice a fore and aft modern sailboat heels over whilst sailing close hauled but not whilst sailing downwind (running). I was just out yesterday in a catamaran, which obviously has different properties and a following wind can be dangerous because if you bury the bow of the leeward hull in the sea you could pitchpole (stern flips over the bow). But with the wind abeam or close hauled the effect is similar, you heel to leeward as you come up into the wind. In a cat you try and fly the windward hull but it is a fine line between that and capsizing!

I think Harland had a good section on the wind effect on sails.

[7eat51]

you have much more heeling effect with the wind abeam and forward than with a following wind

Eric, how much of this is due to the shape of the hull? As I try to picture wind hitting a ship, I can't help but think that there would be more resistance due to how the stern is shaped as opposed to the bow, and so running into the wind would accentuate any side force, whereas once the wind direction crosses the 90-degree line and the ship starts to sail with the wind, the shape of the bow would help transfer some of the side force to driving force, or at the least mitigate some of the side force.

This is new territory for me, so I apologize if I am asking something that is well-known or if I am completely off-target.

[Dobbs]

Something to bear in mind is that the more a boat heels, the less effect the wind has on its sails.

Also, running before the wind, the center of effort moves aft, and the boat experiences increased weather helm. In extreme situations this can lead to broaching. Even though a boat heels when going to windward, this is a much more stable point of sail.

[Dobbs]

Before they figured out how to make bob-stays, there where a number of ideas for moving the center of effort forward. The spritsail is a holdover. An idea that faded quickly once they were able to have the bobstay to pull against the headsails was the sprit topsail, common on late 17th century boats. In the 16th century, the foremast was raked forward to help with balance.

[Dobbs]

I just read the article. The following is from the Results and Discussion section:

With the exception of configuration 2, the driving force for all cases is quite small compared to the side force. This is generally the desired effect, as the goal in heaving-to is to minimize forward motion.

I do not understand why this is the case. I would think that a large driving force relative to the side force would be desirable, and that the side force is the force of concern regarding capsizing. Can anyone explain this?

Am I correct, as well, in that the entire article is concerned with sailing into the wind? The reason I ask is that the AWA in each trial was 90-degrees or less. If this is the case, then would I be correct in assuming that sailing with the wind creates less concern regarding capsizing? One could still have a large AWA if measured from the stern, putting, I would think, significant side force on the ship. Again, I would relish any explanation.

This is fascinating stuff.

Heaving-to is a special case situation for surviving in unreasonable conditions or trying to hold position without sagging off to leeward (trading mail or passengers). The idea is to minimize headway while making a slick on the windward side to break any incoming waves, thusly making a more comfortable situation.

[7eat51]

Dobbs, thanks for the replies. Having spent over five decades as a landlubber, I will need to work through these a bit to ensure I understand and envision what is occurring.

[DeRuyter]

Something to bear in mind is that the more a boat heels, the less effect the wind has on its sails.

Also, running before the wind, the center of effort moves aft, and the boat experiences increased weather helm. In extreme situations this can lead to broaching. Even though a boat heels when going to windward, this is a much more stable point of sail.

Hmm, when I was racing boats usually capsized when driving upwind or rounding the windward mark. True you do have more wind spilling off the sails but the more you heel the less room you have for error when that gust hits. Having said that I have broached whilst flying a spinnaker as well. But I would say that would be less likely on a broad reach then when on a beam reach, especially racing planning dinghy's.

[DeRuyter]

Dobbs, thanks for the replies. Having spent over five decades as a landlubber, I will need to work through these a bit to ensure I understand and envision what is occurring.

Eric you need to correct that situation, especially given your location! Take some Dramamine and get out on the lake, now would be a good time given the generally lighter winds.

I did some catamaran sailing last week which in some ways is similar to sailing on a square rigger in that catamarans don't point very well (sail close to the wind) and they generally tack like pigs. But the speed.....

[capncarp]

I strove manfully through the abstract until the math started to make my eyes cross.
My thought throughout was how the engineers and shipwrights of the day, unencumbered by wind tunnels and computer models, used their "mind's eye" for shaping and growing a ship and its upperworks. And I would assume a lot of capsized hulls would provide plenty of prior bad examples of practices to shy away from.