Weight Distribution In A Small Boat

Discussion in 'Sailboats' started by SuperPiper, Jan 26, 2014.

  1. Skyak
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    Skyak Senior Member

    All true and good advice generally -moving mass toward the center is best for trim and minimizes rotational inertia. This is the right thing to do for fixed weights because there are some conditions and failure modes that are sensitive to large rotational moment of inertia -a heavy boat surfing down wind down a large swell in the ocean wants the absolute minimum rotational inertia to not stuff it's bow and broach.

    The OP has a specific problem -hobby hoarse motion, in sharp chop around the size of his freeboard, wavelength near his waterline length and (I would bet based on his problem) he is heading upwind against the waves -high frequency incidence. In this condition and for this problem minimizing rotational inertia is only the solution to hobby hoarse motion IF you can't lower the rotational natural frequency of the boat well below the driving frequency of the waves. If he can then he would would be better off doing so and driving through the waves. His sail will be more effective and the increase in speed will further separate boat Fn from wave natural frequency -until he reaches a harmonic.

    I don't know the frequencies but I do know the area and conditions. The ability to raise rotational inertia might be very effective. Just be sure to get the weight out of the bow when you turn downwind.
     
  2. SuperPiper
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    SuperPiper Men With Little Boats . .

    I'm getting confused now.

    I thought that moving the weight to the ends of the boat would INCREASE the angular momentum and that was a BAD thing. Putting the weight in a bulb is also bad?

    I'm getting lost in the physics. Can someone brief me on angular momentum and also gyradius? Are larger numbers better or worse?
     
  3. Baltic Bandit

    Baltic Bandit Previous Member

    Physics def of Gyradius is
    so on a boat that is hobby horsing, the max gyradius will be from the point of rotation to the mast tip. Not really meaningful here.

    But in terms of mechanics the Radius of Gyration is give as

    RG = SQRT( MassMomentofInertia / mass )

    where MassMomentOfInertia = the amount of torque needed for a desired change in angular velocity about an axis of rotation, given in units of KgM2

    Normally you do want to reduce the weight in the ends, as that reduces the amplitude of the oscillations that each wave geerates. BUT moving weight to the keel does a couple of things to the dynamics of the system

    • it does increase the Mass Moment of Inertia. which makes the boats movement have more amplitude once it starts moving, but it also dramatically drops the resonant frequency of the system. which is part of what is causing the hobby-horsing in the chop - the resonant frequency of the boat is too close to that of the waves so it is an amplifying feedback loop
    • It drops the axis of rotation for the Gyradius deeper down below waterline. This has the effect of increasing the amount of torque that the waves have to generate to move the bow of the boat. Here's why. The buoyance vector is normal to the surface of the water. And when the Axis of rotation is at the surface of the water (which it basically is with the weight in the shallow bilges) the torque vector and the buoyancy vector are aligned

      but if you drop the Axis of Gyration below the waterline (900ft# on a 1700# boat is significant, it would move the Axis to halfway down the CB) the torque radius is now a diagonal from the WL at the bow, down to the center of the CB. That means that the Torque vector which is normal to that radius, is no longer aligned with the Bouyancy vector.

      That means that less of the buoyance force contributes to the torque lifting the bow. So the Bow hobbyhorses less. On your boat that would work out to about a 5% reduction in the rotational torque force.
     
  4. Mike Graham
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    Mike Graham Junior Member

    The gyradius (also called the radius of gyration) and the moment of inertia I are two ways of representing the same information. Let me talk about the moment of inertia for just a moment, but understand that a high moment of inertia and a high gyradius are the same thing.

    The moment of inertia is to rotation what mass is to translation.

    Let's look at translation. If you have a linear acceleration a, then the inertial force generated is m × a, where m is the mass of the object. This is just Newton's second law.

    The same thing happens with rotation. If you have a rotational acceleration α (in units like radians per second per second), then the inertial torque τ (in units like ft-lb) is just τ = I α.

    Similarly, the rotational momentum L (which isn't quite as important) is just L = I × ω, for the rotational velocity ω (which is in units like rpm).

    Having more weight forward and aft gives you a higher moment of inertia in pitch. Having more near your center of flotation gives you a lower moment of inertia.

    If you have a high moment of inertia:

    • You have lesser motions in waves.
    • Your tendency to hobbyhorse changes, getting slightly worse in general, but specific cases vary. (This is because the natural frequency of the resonance is inversely proportional to the square root of the moment of inertia freq ∝ 1/sqrt(I). That is to say, higher moment of inertia means lower natural frequency. Lower natural frequencies are more excitable.)
    • You have higher hull girder stresses (you require more hull girder strength).


    The gyradius r is just a way of normalizing the moment of inerita to the mass. I = m × r² or r = sqrt(I/m). This makes it a lot easier to compare expectations, as you can think about the gyradius in terms of the geometry of the ship. It makes it much easier to spot crazy values.
     
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  5. Baltic Bandit

    Baltic Bandit Previous Member

    Depends on which Gyradius you are taling about. In the Dynamics case, you have to identify the axis based on the weighted aveages of the mass in roation
     
  6. SuperPiper
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    SuperPiper Men With Little Boats . .


    Mike has made a comment that I had never heard before. Rather than place gear and additional weight near the keel, he suggested that additional mass should be located near the centre of flotation. These 2 positions may typically be very close to each other, but in a boat full of compromises, there may be enough separation to warrant a 2nd look.

    As the cockpit and the lazarette get loaded and the boat trims stern-down, the centre of flotation may shift aft away from the keel.

    What is the usual relationship between the keel location and the centre of flotation?
     
  7. Baltic Bandit

    Baltic Bandit Previous Member

    Superpiper's point is important. Part of why you move weight in the boat towards the keel is that this is typically where the intended CoF is. and the goal is to connect the two
     
  8. Mike Graham
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    Mike Graham Junior Member

    To the precision that the advice is given, the keel and the center of flotation are probably similar enough. Even "at midship" would probably be precise enough. (Indeed, although saying that the boat pitches about the LCF is popular, the LCF is actually the location at which adding weight above it doesn't cause any trim--it's not quite the axis about which the vessel trims at constant displacement.) I think the message is just "keep weight low and to the middle", but I could be misjudging the intent.

    If your boat is trimming so far to stern your LCF has moved appreciably, you might have bigger problems than hobbyhorsing.
     
  9. Skyak
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    Skyak Senior Member

    I would like to thank Mike and BB for explaining moments of inertia. Great job! That said I suspect the OP and many others are still confused. They have lots of new terms and concepts to look up and even when they understand them they still have to wrap their brain around the driving forces of hydrodynamics and the idea that the boat is rotating in each axis about points that are moving with the water contact on the hull. For anyone who enjoys boat design math and physics -have at it!

    One point I would like to make is that while 'increasing moment of inertia always increases natural frequency' is always true, the following statement 'Lower natural frequencies are more excitable' might be technically true but that would be to assume that the universe is providing all frequencies of excitation in equal amount. The reality is that the universe offers limited sets of frequencies at different times and conditions. Often the best solution is lowering the natural frequency of the craft below the excitation freq. of the environment. Another example is that increased damping also lowers resonant frequency but lowers excitation.

    For those who are looking to dedicate LESS of their brain to the subject but still get any benefit of cheap easy performance I offer the following.

    -the 'rule' that weight should be placed as close to the center of mass is still good for large fixed weights and on traditional boats to be prepared for most conditions. The driving concern associated with this 'rule' is "I always want to go over waves. If the bow always followed a fixed height over the surface that would be best"


    -less traditional boats can move masses away from the center to improve performance in some ways and some conditions. The simplest way to think about this opportunity is frequency response. The driving concern associated with this 'rule' would be " I don't want my boat to always go over waves, I want to increase performance or comfort by going through the waves"

    When can increasing moment of inertia improve performance? When wave frequency of incidence is high (on the heading you want count the wave tops passing by -is the number high?) and the wave height is acceptably low relative to freeboard.
     
  10. SuperPiper
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    SuperPiper Men With Little Boats . .

    A T-foil rudder would help to damp hobby-horsing. Would that relax the rules about where to stow gear? If the T-foil applied a little bit of lift too, it could help to correct the trim issue.
     
  11. Baltic Bandit

    Baltic Bandit Previous Member

    I don't think a T foil rudder would have a whole lot of effect on dampning hobby horsing. On the I-14 that I sailed with a T-foil it had no effect on jumping waves. What it did do is let me control the Angle of the hull WRT the bow wave.

    Now done right, the T foil provides some amount of lift at the stern. the amount of lift being related to the section used, the area of the horizontal surface and the speed of the hull through water

    And it is this last that's going to get you. you are going to need a fairly significant surface area to have much effect at the low speeds a boat this short is limited to.
     

  12. SuperPiper
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    SuperPiper Men With Little Boats . .

    Related to hobby-horsing: I just read that Chinese junks had bow and/or stern compartments that were open to the sea. Seawater flooded or drained through holes in the hull. The restricted filling and draining action in waves damped the pitching.

    Can someone confirm this concept?
     
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