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Angle of pitch and heel for a boat snagged on the side wall

  1. Jan 16, 2017 #1

    sbg

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    Hi everyone, this is a real world problem following the sinking of a narrowboat in 2014. The boat caught on the side of the lock as the water level dropped, and the resultant combination of pitch and heel resulted in the boat taking on water at the stern and sinking - luckily with no loss of life or injury. Without giving too much away (as the owner has settled the case with the navigation authority) I can offer the following information:

    - boat length 60'
    - boat displacement 15 tons (steel construction)
    - The snag occurred on the port side, 10' from the bow
    - Narrowboats tend to sit lower at the stern than at the bow so the CoG is probably aft of the centrepoint (Assumption - is this true?)

    The boater stated that the water level dropped "a few inches" then later stated that the sinking actually occurred when the level had dropped by 2'. A few maths wizards have suggested that a 2' drop at the stern would equate to 2 degrees of pitch which seems a very small amount to me, and I'm pretty sure my boat (about the same size) rose by a couple of degrees at the bow just by having an empty water tank.... I also think that my boat going up the slipway took on more than a 2 degree pitch

    I'm not trying to make the boater look bad, and am in no way connected with the event or the owner (or the Authority) but am trying to make sense of the physics of such an event and what a 2' drop would look like in terms of the angle. Of course, there is the heel effect to consider due to the boat snagging on one side.

    Grateful for any help!
     
    Last edited: Jan 16, 2017
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  3. Jan 16, 2017 #2

    BvU

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    Hello sbg, :welcome:
    If they are any good they have told you (not just suggested). 2' on 60' or on 50' IS two degrees, yes. Do you want he formula ?
    You mean it bent ? Did the stern stay horizontal ? or did the whole boat (as a reasonably stiff object) pitch ?
    I suppose so: a 2 degree slipway would have to be very long to be useful !?!?!
    No physics so far !
     
  4. Jan 16, 2017 #3

    anorlunda

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    The COG is certainly behind the snag point, 1/6 hull length from the bow.

    The boat would experience both pitch and heel causing the stern corner away from the wall to dip most and be the point of entry of the water.


    You ask about calculating the pitch, but you also need the angle of heel and (most important) the free board at the stern quarter, to make a conclusion. Free board is the height of the hull above the water line when level. Free board in the stern is usually less than at the bow.

    I'm not familiar with the term narrowboat. Do you mean something like this?
    25643.jpg

    That type of construction would be highly likely to get swamped if it snagged on the lock wall while descending. I would not trust feet or angle estimates by eye witnesses, so calculations would be pointless.
     
  5. Jan 16, 2017 #4

    jim hardy

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    Stability depends on heights of centers of gravity and bouyancy., too
    CG is usually above CB so there is some angle beyond which the vessel will try to capsize.
    The upward force of snag makes a torque that opposes restoring moment , effectively moving center of bouyancy toward snag,
    and that greatly reduces the angle where you lose stability..
    so i expect it sank from excessive roll rather than pitch. Did it capsize ?

    http://www.learneasy.info/MDME/MEMmods/MEM23006A/fluid_mech/fluid_statics.html
    longboatsnag.jpg

    @anorlunda i'm no naval architect , but do remember basics of Statics course from 1965... is above plausible ?

    old jim
     
  6. Jan 16, 2017 #5

    anorlunda

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    Yes that's valid @jim hardy , but first you have to modify the numbers by taking on some tons of water first. Many boats capsize as they are sinking. In addition, assume that the front of the boat is snagged on the lock wall; the boat is not floating free. (By the way, the angle where you lose stability on my boat is 120 degrees. That is the effect of having a heavy keel low down. It is like a rolly-polly toy.).

    Here is a video of a ship capsizing because of stability. Start at 1:10.


    What I think happened in this case is more like in the following videos. Lifting the bow makes the stern go under water.

    Start this video at 3:07.


    And this video (only 39 seconds long)


    Most dramatic is the first 7 seconds of this video. (the next 50 seconds is another stability failure)
     
  7. Jan 16, 2017 #6

    Baluncore

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    Pitch and Heel can be treated separately here, as heel is not the major problem. The fundamental problem arises from several factors but the most significant is that the snag or hang-up is not at the end of the boat but at 10' along the 60' hull. That is only 20' from the mid-point of the hull.
    The centre of mass of the hull is effectively a fulcrum. The point that is lifted by 2' is 20' from that fulcrum, but the stern is 30' beyond the fulcrum. So freeboard at the stern will actually be reduced by about 3'. That was more than sufficient to cause the flooding.
    The pitch angle was then close to Pa = Asin( 2' / 20' ) = 5.7°

    I have ignored the issue that lifting one point on the hull reduces the buoyancy required to support the hull. It is important in the detail but not in the understanding of the lever and fulcrum model.

    The situation is aggravated when;
    1. Most of the buoyancy of a hull is in the middle of the vessel. The ends of the hull are tapered underwater to reduce drag. This significantly reduces buoyancy at the end corners of the hull. It is more pronounced at the pointed stern than at the more rounded bow.
    2. The closer the hang-up point is to the centre of mass the greater will be the loss of freeboard at the far end of the other side of the hull.
    3. The direction of water flow in the canal is from the low end of the hull. A “bow” wave reduces freeboard. Also, flow along the rising bottom of the hull draws the hull downwards.
     
  8. Jan 17, 2017 #7

    sbg

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    Thanks for the replies so far folks - I appreciate it. Apologies if the initial statement was a little vague - I now have more information from the owner.

    Anorlunda - yes, that is the correct type of boat. 60' long, 6'10" wide and (mostly) flat bottomed. It 's a common inland waterways vessel in the UK and although most have no keel, the baseplates are usually 10mm steel and they are remarkably stable. A few intrepid people have even motored across the English Channel - properly prepared and accompanied by a pilot of course!

    The boat sank at the stern rather than capsizing; according to the owner the induced heel was a factor but the greater issue was the change in pitch i.e as the bow stayed snagged and the water dropped, the stern was swamped.

    BvU - thanks for the welcome. I understand that 2' on a 60' length rotating about a single end pivot point would be 2 degrees, but I think this is more complex. I think Baluncore has hit the nail on the head as the snag was 20' from the boat centre of mass, and the fulcrum effect would be to drop the stern by 3' However, would there not be a further complicating factor in that the vessel continued to have buoyancy, albeit reduced? It seems to me that with the bow lifting out of the water, the apparent centre of buoyancy (is this the metacentre Jim?) would move rearwards but would continue to keep the boat afloat until the water came over the cant. In answer to your other questions, our water tank was in the bow, and when empty, caused the bow to rise noticeably from the fully loaded mark - the whole boat pitched. As our boat was constructed in the same fashion (all steel) as the narrowboat pictured, there was no bending involved! However, on reflection, this could have been no more than a couple of inches... so I am incorrect in stating two degrees here.

    I'm trying to understand the forces in action in this case and the maths involved - I've completed a diploma in marine survey and although we dealt with stability, the metacentre calculations focused on loading and jib effect with cranes. I suspect a similar set of equations are appropriate but am struggling to figure out various rotational effects, countered by the buoyancy.

    Edited to add that the owner now states that the freeboard at the stern was 16" but - frustratingly - the water level changes stated was "a few inches". I have no idea why the water level drop quoted has been changed but there you are.
     
  9. Jan 17, 2017 #8

    jim hardy

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    Roll, pitch, or both ? An eyewitness or cellphone video would sure be nice.

    Lifting bow moves CB aft

    water into stern moves CG aft,
    water goes to low side of vessel moving CG that way

    did water first come over stern at a corner or clear across it ?

    Look at your boat and work it in your head.
     
  10. Jan 17, 2017 #9

    Baluncore

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    There are several complicating factors that slightly reduce loss of freeboard, but not enough to prevent the sinking. The mass that must be supported by hull buoyancy is less because the snag is supporting the forward 33% of the boat mass. But the remaining 66% centre of mass has moved aft from the 30' section to the 40' section. The buoyancy needed to support the remaining mass is slightly less because of the lever length as the centre of buoyancy moves towards the stern. But the boat had a motor and propeller, so would have had a more tapered hull at the stern. The reduced stern buoyancy limits how far the centre of buoyancy can migrate aft as the pitch increases.

    But the overriding effect is the great length of the rectangular section hull and the immediate loss of a significant part of the normal buoyancy when one end of the hull is slightly raised. That effect is magnified for a long hull with a flat bottom and shallow draft.
     
  11. Jan 17, 2017 #10

    anorlunda

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    The ratio of length to stern freeboard is 45:1. That same ratio on my boat is 8:1. That is why I say the narrowboat type of construction is very vulnerable to this sinking by the stern problem. @Baluncore said the same thing in different words.

    But it seems that nobody else saw the connection between that ratio and the three videos in #5 showing boats sinking at the stern at boat ramps. Backing a boat down the ramp is very analogous to this case of the boat getting snagged on the lock wall, simply because the bow is lifted relative to the stern.

    A boat with 45:1 or higher ratio can not be backed down a ramp into the water without sinking the stern, whereas a boat with 8:1 ratio can do that successfully. Of course ramp angle also plays a role, but it does not change the principle. Most boats snagged on the lock wall will not sink, but this one did. The different outcome is dictated by the dimensions.
     
  12. Jan 18, 2017 #11

    CWatters

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    I've also experienced a hang up as described in the OP. Can confirm that the roll was much more of a concern than the pitch. Fortunately the rope causing the hang up broke before we took on water.
     
  13. Jan 18, 2017 #12

    sbg

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    No videos available and the only pictures are after the event and the subsequent draining of the lock - not helpful in this case.
    The water came over the starboard stern cant, primarily due to the induced pitch / lowering of the stern but exacerbated by the roll.
     
  14. Jan 18, 2017 #13

    sbg

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    Was the boat roped to the centreline t-stud, forward or stern points?
     
  15. Jan 18, 2017 #14

    CWatters

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    In our case it was one side of the transom/stern. We were in a lock and the person on the bank put a full turn around a post. As the lock emptied they found the rope had jammed and they were unable to pay out rope.
     
  16. Jan 19, 2017 #15

    sbg

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    Ah, that makes sense.
     
  17. Jan 19, 2017 #16

    Baluncore

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    It seems rare that a boat might snag on one side of the lock, so I wonder if the report has become confused in the telling. It seems much more likely for such a hang-up to occur on the cill. A leaking gate during low water levels can catch a narrow boat on the cill, 10' from the bow.
    https://en.wikipedia.org/wiki/Lock_(water_navigation)#Cill

    I googled images 'narrowboat sinks in lock' and got plenty of hits.
    http://l7.alamy.com/zooms/a9d3f840f...ign-on-a-lock-gate-warning-of-cill-bwmwy7.jpg
    http://waterwaynews.blogspot.com.au/2013/08/photograph-of-latest-huddersfield.html
    http://www.dailymail.co.uk/news/art...rowboat-started-sink-getting-wedged-lock.html
    http://www.alamy.com/stock-photo-ba...ow-boat-stuck-on-the-stone-cill-67798693.html
     
  18. Jan 19, 2017 #17

    CWatters

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    Yes hang ups on the Cill are a well known problem. Many locks have a warning sign in addition to the white line. That could well have been the cause.

    Now that I think about it I've also a small cabin cruiser hang up on the edge of a lock. The cruiser was made from two fibre glass mouldings (a top and a bottom). and where the two parts join there was quite a large inverted lip fitted with a rubbing strip. However most canal boats don't normally have such a wide rubbing strips.
     
  19. Jan 20, 2017 #18

    sbg

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    No - this was not a cilling event although you are right in that the majority of lock sinkings are down to the boat either being on the cill (usually at the stern) or a bow / stern fender becoming wedged in the gates and hanging up. I am an experienced boater and want to understand more of what happened as by all accounts this sinking occurred very quickly.
    The lock in question has stone sides and has a bulge below the high water line - this is the subject of a legal challenge as the owners of the boat have settled out of court but still believe there is a Health and Safety issue i.e. the Canal and River Trust have not maintained the lock to the minimum safety standards. I'll try to upload the pictures from the original website.

    Most modern narrowboats have a 10mm steel baseplate which usually protrudes a few mm beyond the junction with the hull sides. This chine protects the welded join from damage from underwater objects, canal pilings, lock sides etc but the downside is that the protrusion along the length of the hull increases the possibility of being hung up. There were two boats in the wide lock and the pictures from the event clearly show the witness marks on the lock side bulge where the boat was snagged, eventually slipping off as the boat took on water.

    I'm trying to stay away from the legal stuff to focus on the events and dynamics of the boat becoming swamped and sinking.

    Edited for typos.
     
  20. Jan 20, 2017 #19

    sbg

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    Here's what I think happened:

    Under normal circumstances the boat has a single centre of gravity, with a centre of buoyancy. The hangup creates a second point, carrying some of the weight (apparently up to 33% if the bow is completely lifted out and the snag is 10' back on a 60' boat), with the buoyancy point (I think this is the metacentre) taking up the rest. As the water level drops, the metacentre moves rearwards but remains the fulcrum around which the boat rotates in pitch. Buoyancy is reduced as a greater proportion of the hull remaining in the water is taken up by the swim, but this is balanced (maybe (probably?) not entirely) by the amount of weight being carried by the snag.

    If I have this right, the lever length is from the snag to the metacentre, and the stern will drop by a corresponding ratio dependant upon the lever length from the metacentre to the stern. The heel effect will also be apparent as the hull will rotate to the right, hence the water coming in over the starboard cant. I think the formulae and maths are actually pretty complicated and I'm trying to correlate the calculations needed against the owner's observations of the event i.e. a snag 10' from the bow combined with a water level drop of a few inches conspired to swamp the starboard stern cant. Still too many unknown factors to try to make sense of it though - at least to this bear of little brain. I think the key is how much the metacentre moves.
     
  21. Jan 20, 2017 #20

    Baluncore

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    Thank you sbg for confirming the situation.
    It would not take much heel for the 10mm plate to slide off the snag. There must have been something preventing the hull from moving away from the wall, maybe the other hull in the lock?

    The heel required would be the arctangent of the coefficient of friction of hull against lock. Likewise a hull would not slide lengthways off a snag (or a cill) until the pitch angle exceeded the arctangent of the coefficient of friction of hull on lock.

    What was the beam of the boat in question ?
     
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