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Thread: Where is most of the stress taken - mast thwart or mast step ?

  1. #1
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    Unhappy Where is most of the stress taken - mast thwart or mast step ?

    Almost finished and ready for seatrials........ , but having put up the mast my mast thwart and step are looking a little under engineered. Where is most of the stress exerted thwart or step ? Any way I am strengthening the thwart but not sure by how much ?

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    Quote Originally Posted by seabeggar View Post
    Almost finished and ready for seatrials........ , but having put up the mast my mast thwart and step are looking a little under engineered. Where is most of the stress exerted thwart or step ? Any way I am strengthening the thwart but not sure by how much ?
    The stresses are equal!

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    Can you show us some pics to get a better idea of what you've done?

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    For an unstayed mast the lateral loads are slightly higher at the partners (thwart) than the step

    There can be significant compression loads in both stayed masted and those where the halyards run through turning blocks.

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    surely the force is greatest at the mast step? Is it not the case that the thwart acts as a fulcrum with wind force on a long lever above thwart acting on a short lever below thwart?
    ___________________________________

    Fredster, also known as The Commodore.

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    Quote Originally Posted by fredster View Post
    surely the force is greatest at the mast step? Is it not the case that the thwart acts as a fulcrum with wind force on a long lever above thwart acting on a short lever below thwart?


    OK - Levers and forces 101

    Just for fun we'll do this in Feet and Pounds

    Imagine an unstayed mast with the centre of effort for the sail some 10 feet above the step
    The thwart is 1 foot above the step

    We are on port track and the wind is exerting a force of 200 Lbs on the sail.

    What are the (minimum) forces on the mast stap and on the thwart?

    Method 1 The step is considered as the fulcrum i.e. a second order lever
    Moment is 200 lbs x 10 feet - 2,000 ft lbs
    This must be balanced by the moment from the force on the thwart
    2000/1 = 2000 pounds

    Now the force on the sail is from the left (port tack) so the force from the thwart is from the right.

    And as the rig is going nowhere the forces must add up to zero

    0 = Fthwart - Fsail - Fstep

    and the force on the Step is the difference between the two so
    Fstep = Fthwart - FSail
    Fstep = 2000 - 200
    Fstep = 1800.

    -------------------------------------------------------------
    Method two - Consider the thwart as the fulcrum first order lever.

    Fstep = (Fsail x Height above thwart)/height from step to thwart
    Fstep = (200 x 9)/1
    Fstep = 1800

    Since the thwart must resist both the Mast and step forces
    Fthwart = 1,800 + 200 = 2,000lbs.


    ----------------------------------------------------
    Both methods give the same answer!

  7. #7
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    The calculations for this should be torque calculations, not levers. (Twisting loads about two points)

    I accept that if the lever was horizontal as in a class 1 lever, then the fulcrum would need to take the weight of the beam plus the loads at both ends so the fulcrum would have greater loadings, plus the beam would rotate at the fulcrum, but with a vertical lever, gravity plays no part in it and our canoes are not rotating around the mast thwart.

    The loads are opposed equally between the mast foot and mast thwart. The exact mid point between the mast foot and the mast thwart has no sideways forces as this is the torque turning point. The forces then increase identically as you move up to the mast thwart in one direction as they move down to the mast foot in the other direction.

    In a normal class 1 lever (Like a seesaw) the turning point is in the middle of the hinge (Or fulcrum), but our canoes are not rotating at the fulcrum (Suggested to be the mast thwart), they are twisting half way between the mast thwart and the mast foot.

    Try not to think of it like this, a big lever pulling the canoe over:



    Think of it like this, forces opposing each other around a central point:

    Last edited by Steamerpoint; 31st-May-2012 at 12:43 AM.

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    Quote Originally Posted by Steamerpoint View Post
    The loads are opposed equally between the mast foot and mast thwart. The exact mid point between the mast foot and the mast thwart has no sideways forces as this is the torque turning point.
    My engineering mathematics dates to the 1980s... and hasn't been used since ~1989... but I'm not convinced on this one, Chris.

    When the canoe distorts to a new, stable shape, the forces from the mast step and the thwart must balance in some way, shape or form (or else further distortion would occur)... but that's surely possible with unequal forces on those two points. Taking DougR's example, with 1800 lbs (mast step end) and 2000lbs (thwart end)... the equilibrium would surely just be about a point along the mast that's not quite half way between the two forces.

    IIRC, we're looking at force x lever-arm calculations... which would mean (if I've got this right, and leaving aside the other sources of distortion, including whoever's hiked out to balance the boat, and the force being exerted by the leeboard, etc.) that the point about which mast-generated distortion is occurring is about 5/16" higher than the dot in your drawing.
    .
    Last edited by GregandGinaS; 31st-May-2012 at 09:35 AM.

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    I'm not going to try to provide any detailed description of the forces involved. I'm just thinking that there are only two points restraining the mast and a force someway further along. One of the two points is a fulcrum and the other is providing a resistance. I cannot see anyway in which the forces on these points will be different.

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    With a long mast and a short distance between mast foot and thwart, what we can definitely say is that the forces on the mast thwart and foot will be much larger than the force of the wind on the sail. Whether one is larger than the other is not obvious as they are of the same order. Doug is right though, that the force on the thwart is larger than the mast foot (slightly). This is easier to see if you imagine that the centre of effort of the sail is 1 ft above the thwart and the mast foot is 10ft away from the thwart. In this scenario it is obvious to me that the wind in the sail would be pushing on the mast thwart with a lot more force than will be transmitted to the mast foot.
    With a SD 44sq ft bermudan the centre of effort of the sail is around 7ft up the mast. Sitting right out on the gunwale my 170lbs of weight can just about hold up this sail close hauled in the top of a force 4. Top of a force 4 has a wind force of 1lb /sqft so the force on the sail is around 44lbs.
    With this force acting 7ft up the mast, and the thwart about 1ft above the mast foot, the force on the mast thwart will be around 310lbs. The force on the mast foot will be around 265lbs.
    Although not as high as Doug's example of 2000lbs, (which would equate to a large powerful dinghy), the forces on a canoe mast thwart and foot are still significant. This is why we prefer to also bolt or screw our mast feet into a plastic canoe rather than just relying on the epoxy glue joint.
    Sailing with outriggers can easily double these forces when sailing in the top of a force 5,as the force in the wind will then be 2lbs / sqft

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    Gosh this is such an interesting thread! Well to some people anyway...

    My take on it all is that it all needs to be rather strongly built as the forces involved with any decent/useful size of sail are surprisingly high.

    Another occasion when I have noticed very high peak loads on both mast and leeboard fittings has been when crossing eddy lines in tidal waters, passing from virtually no current into water going at 4 or 5 knots in the space of less than a metre. My substantially built fittings were flexing like I have never seen in any other circumstances. This stuff must not break in normal use including strong winds, large/steep waves and strong currents.

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    Thanks Dave & Keith... and I rest my case, as put in the SoTP Jubilee Honours thread

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