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Moment of Inertia of grand action parts.

  • 1.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 13:29
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Inertia Heads,
    
    The next step toward understanding how the action works when actually 
    played is to find the total MOI as measured at the front of the key. 
    First we need to find the MOI of the key, wippen and shank. I thought it 
    would be useful to find ways to estimate this. The drawing shows a way 
    to estimate the MOI of the key. I have ways to estimate the MOI of the 
    wip and the hammer/shank as well but first I wanted to se if anyone else 
    had ideas on how to do this.
    
    We could use a variety of methods to measure the MOI directly like using 
    a torsion table or torsion pendulum. But these are difficult to build 
    and calibrate, more useful for demonstrating the principles of inertia 
    than for getting accurate measurement. Professional measuring equipment 
    is beyond my reach so for now the estimated MOI will have to do.
    
    After finding the MOI of the three parts the total MOI can be figured 
    with an equation.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 2.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 14:17
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Hi John:
    
    That formula you are using won't even get you anywhere close to the total
    moment of inertia.  The second part is probably all right.  You're assuming
    that the leads are small enough that they will perform like point masses,
    which will probably get you pretty close.  But the first part (1/2ML^2) is
    wayyyy off.
    
    The formula you should use for a rectangular shaft that pivots at its center
    is
    
    I = 1/12 * m * (h^2 + L^2)
    
    where h is the height of the key, bottom to top.
    
    Good luck!
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    


  • 3.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 14:53
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Don A. Gilmore wrote:
    > Hi John:
    > 
    > That formula you are using won't even get you anywhere close to the total
    > moment of inertia.  The second part is probably all right.  You're assuming
    > that the leads are small enough that they will perform like point masses,
    > which will probably get you pretty close.  But the first part (1/2ML^2) is
    > wayyyy off.
    > 
    > The formula you should use for a rectangular shaft that pivots at its center
    > is
    > 
    > I = 1/12 * m * (h^2 + L^2)
    > 
    > where h is the height of the key, bottom to top.
    
    Thanks,
    
    I meant it to read 1/12ML^2. I forgot the 1 in the denominator. I 
    changed the drawing to reflect your suggestion to include the height.
    
    It's good to have someone on the list to help with this stuff. I sent 
    two other drawings with simple equations. Did you have a chance to view 
    them? If there is something wrong with them it would be good to clear it 
    up now before moving on.
    
    Thanks for taking the time to help.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 4.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 15:07
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Sorry Don,
    
    I left out a bracket from the last drawing. Here it is again with the 
    little more clarification.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 5.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 16:09
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    This one looks great, John.  Can you send me the other ones you mentioned?
    
    eromlignod@kc.rr.com
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    


  • 6.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 17:41
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Don A. Gilmore wrote:
    > This one looks great, John.  Can you send me the other ones you mentioned?
    
    
    O.K. Ron,
    
    I will send one at a time since the list seems to reject attachments 
    over 30 k.
    
    So here is the first one.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 7.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 20:20
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Hi John:
    
    Well, you did the math right and got the correct answer, but there are a few
    minor discrepancies in your formulas in step 2.  Step 1 looks great.
    
    You state the formula for angular acceleration correctly, but you have shown
    angular acceleration as w^2.  I'm assuming that this denotes angular
    velocity squared (I have been using w for angular velocity in my posts, but
    it's usually denoted by a small omega, which looks like a roundish w).
    Angular acceleration is not the square of angular velocity.  If it were it
    would have the units "square meters per second squared".  Angular
    acceleration is usually denoted with a small alpha.  Also, you call the
    downward force F in the diagram, but N in the formula...just a typo.
    
    Otherwise it looks good.  I'm glad to see you convert newtons to kg-m/s^2 as
    this makes the units more understandable.
    
    Good job.
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    
    


  • 8.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 20:50
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Oops.  I meant to write that w^2 would have units of radians^2/s^2, not
    meters.  Sorry.
    
    


  • 9.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 17:46
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Don A. Gilmore wrote:
    > This one looks great, John.  Can you send me the other ones you mentioned?
    
    Don,
    
    Here's number 2.
    
    Anyone bothered by this? Don and I could go off-line if the attachments 
    are too much.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 10.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 20:45
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Hi John:
    
    I was following this one until I got to the algebra at the bottom.  In the
    next-to-last line you seem to have factored out a 1/R^2, which I don't think
    you can get away with since only one term has R^2 in it.  You can, however,
    factor out V^2/2 to get
    
    mgh = v^2/2 * (m + I/R^2)
    
    This would solve to
    
    v = sqrt [2mgh/(m + I/R^2)]
    
    Hope this helps!
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    


  • 11.  Moment of Inertia of grand action parts.

    Posted 12-27-2003 20:30
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    John Hartman wrote:
    
    >I have ways to estimate the MOI of the wip
    >and the hammer/shank as well but first I
    >wanted to se if anyone else had ideas on
    >how to do this.
    
    For hammer & shank I have estimated as follows:
    
    I think Stanwood gives 1.8g as typical SW of shank.  So for purposes of
    estimating MOI you can use 2 x 1.8 as the total mass of the shank.  This
    helps to correct for the fact that the shank is fatter near the center pin,
    but most of the MOI is at the skinny end.  So 3.6g for mass.  Length is the
    length from center pin to end of shank, not to center of hammer molding.
    Then you can use m*L^2/3 for moment of inertia (stick rotating around one
    end).  For hammer, use SW-1.8 grams for mass and for radius measure from
    center pin to center of molding 1/2" above shank.  Treat as point mass for
    estimating. Add shank and hammer MOIs to get total.
    
    Wippen is harder.
    
    Fortunately due to modest mass and small motion it is less significant in
    the end so errors are not as important.  I have used m*L^2/3 for wippen
    (same as formula for stick rotating around endpoint), taking the total mass
    as m and distance from center pin to jack center as L.  Crude, but puts you
    in the ballpark.
    
    Your revised key estimate looks good.  Certainly the key inertia is no
    smaller than that.
    
    I made an attempt to relate hammer, wippen and key inertia to total
    reflected inertia here:
    
    http://www.ptg.org/pipermail/pianotech/2003-August/140901.html
    
    
    -Mark
    


  • 12.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 07:21
    From John Hartman <pianos@hartmanstudios.net>
    
    Mark Davidson wrote:
    
    
    > I made an attempt to relate hammer, wippen and key inertia to total
    > reflected inertia here:
    > 
    > http://www.ptg.org/pipermail/pianotech/2003-August/140901.html
    > 
    
    
    Mark,
    
    Thanks for sharing this with me. Just yesterday I came to exactly the 
    same conclusion. I am doing a drawing to show the acceleration ratios of 
    the wip and shank in relation to the key. The fact that we both came up 
    with the same formula is encouraging but to be sure we need to have Don 
    go over it.
    
    Have you plugged in the MOIs? It looks like the shank and hammer 
    contribute about 12 times or more of the total I as felt at the key. If 
    the formula is right it shows how unimportant changes to the key MOI is 
    in relation to overall efficiency. Also, if there is any benefit to 
    pattern leading it is not to make the action feel even from note to 
    note. Adding lead to the key is not the big evil commonly thought unless 
    it has some effect on repetition.
    
    I think we are going to find that the biggest problem with increasing 
    the mass of the action parts is the losses due to bending and compliance.
    
    I still need to complete the kinetic model of the action but I can see 
    ahead to the next step. Maybe you are already there. Is there a way to 
    convert the kinetic forces developed at different levels of play into 
    static loads. Then we can see how these loads bend the shank and key. It 
    would be great if this could lead to a formula for finding the terminal 
    velocity of the hammer.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 13.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 08:15
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    John Hartman wrote:
    
    > Have you plugged in the MOIs? It looks like the shank and hammer
    > contribute about 12 times or more of the total I as felt at the key. If
    > the formula is right it shows how unimportant changes to the key MOI is
    > in relation to overall efficiency. Also, if there is any benefit to
    > pattern leading it is not to make the action feel even from note to
    > note. Adding lead to the key is not the big evil commonly thought unless
    > it has some effect on repetition.
    >
    > I think we are going to find that the biggest problem with increasing
    > the mass of the action parts is the losses due to bending and compliance.
    
    Obviously depends on your assumptions about hammer weight and SWR, but I
    have come up with about 87-81% of the reflected inertia in the hammer/shank,
    12-16% in the key, 1-3% in the wippen (range from bass-treble).
    
    Pretty much the same conclusions about leading, except... there seems to be
    a lot of anecdotal evidence to suggest a noticeable difference in feel
    between a more-leaded action versus a wippen assisted action (with same SW,
    SWRs, BW).  Haven't quite worked that out to my satisfaction.  Too many
    people out there with lots of rebuilding experience saying there's a
    difference. Probably has to do with how each part starts moving/flexes as
    things compress at the start of the keystroke.
    
    > I still need to complete the kinetic model of the action but I can see
    > ahead to the next step. Maybe you are already there. Is there a way to
    > convert the kinetic forces developed at different levels of play into
    > static loads. Then we can see how these loads bend the shank and key. It
    > would be great if this could lead to a formula for finding the terminal
    > velocity of the hammer.
    
    I think I see what you're asking.  The upward force at the capstan on the
    wippen heel would the torque on the key (key front radius * (finger - BW -
    friction) divided by the capstan radius.  This force is the input on the
    wippen.  The torque on the wippen is this force * wippen heel radius.  See
    where this is going?
    
    -Mark
    


  • 14.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 09:21
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Gentlemen:
    
    Up to now I have just been trying to straighten out the proper use of
    formulas.  Ironically, I wasn't even sure what the final goal was.  If you
    want ro relate the force applied to a key to what velocity will be produced
    in the hammer when it is released, it may be easier than you think.
    
    If we first consider the simplified case of a constant force on the key then
    I think the concept of impulse/momentum might be useful.  A constant force
    on the key would be the case if you laid a weight on it.  The force would be
    constant throughout the stroke.  The "impulse" given to the mechanism would
    be the weight (force) multiplied by the time in seconds it takes to strike
    the stop at the bottom (forgive me if I don't know all the terms you guys
    use for these things).  The impulse at the key is equal to the change in
    momentum of the system.
    
    The interesting thing is that momentum is conserved regardless of the masses
    of individual mechanism parts or friction.  You could have any Rube Goldberg
    contraption between the key and the hammer and the relation between impulse
    and momentum would be the same.
    
    Now that I have everyone excited, how easy is this to do?  You need to be
    able to accurately time the fall of the weight.  You also have to have a way
    to determine the velocity of the weight just before it hits bottom, though
    we might be able to get away with assuming that the acceleration is constant
    and approximate a final velocity.  And you need to know the m.o.i. of the
    hammer, as usual.
    
    Here's how it might go.  We put a 5 lb weight on the key and time how long
    it takes to bottom out.  We determine the impulse by multiplying this time
    by the weight, W
    
    Implulse = Wt
    
    Then if we assume constant acceleration we can get the terminal velocity by
    
    v = 2h / t
    
    where h is the vertical distance we travel.  From this we can calculate the
    momentum of the weight.
    
    momentum = mv = Wv / g
    
    where g is the acceleration of gravity (we're just converting pounds to
    slugs).
    
    OK, we know that impulse is equal to the change in momentum and the momentum
    was zero before we started, so whatever Ft comes out to be will be equal to
    the momentum of the weight *and* the angular momentum of the hammer added
    together.  Now that we know the weight momentum we can subtract it from the
    total (Ft) and what's left over should be the momentum of the hammer.
    
    Now we just need the velocity of the hammer.  Angular momentum is
    
    angular momentum = Iw
    
    or moment of inertia times angular velocity.  If we rearrange this equation
    we have
    
    w = a.m. / I
    
    So if we divide the leftover momentum by the moment of inertia of the
    hammer, we should get its angular velocity at release.
    
    If you wanted to really get fancy, we could also do this if the force is not
    constant.  If we had a way to graph the force against time (time along the x
    axis and force on the y axis), the total impulse would be the area under the
    curve.
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    


  • 15.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 09:50
    From "Don A. Gilmore" <eromlignod@kc.rr.com>
    
    Oops.  I just realized a major flaw in my reasoning.  Other components of
    the action are also moving right before the key bottoms out.  They would add
    to the total momentum of the system as well.  So much for simple.
    
    Let me give this more than two seconds of thought and I'll see what I can
    come up with.  Sorry for the false alarm.
    
    Don A. Gilmore
    Mechanical Engineer
    Kansas City
    
    


  • 16.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 11:18
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    > Oops.  I just realized a major flaw in my reasoning.  Other components of
    > the action are also moving right before the key bottoms out.  They would
    add
    > to the total momentum of the system as well.  So much for simple.
    >
    > Let me give this more than two seconds of thought and I'll see what I can
    > come up with.  Sorry for the false alarm.
    >
    > Don A. Gilmore
    
    Yup.  Key, wippen and hammer all move.  And all have different m.o.i.  And
    all have different angular accelerations  that depend on the lengths of the
    various lever arms.
    
    [Also, the jack trips out from under the knuckle just before the key hits
    bottom  :).  Oh yeah, there are dampers too, but they don't start moving
    until the key is halfway down.]
    
    I think the goal here is to develop a model for predicting when an action
    when feel light, medium, heavy, etc.  The presumption is that the moment of
    inertia is a big part of this model.  But it needs to be the total moment of
    inertia of key, wippen and hammer, as felt at the key, and not just the
    key's m.o.i..  Also useful is knowing which of the various components is
    most significant, allowing one to focus on the areas that will give the most
    bang for the buck (i.e. how much time should one spend finding the perfect
    keylead position).
    
    Once you know the total reflected m.o.i. and front key radius it is possible
    to figure the speed the key will accelerate for a given force which I would
    expect goes a long way toward the goal.
    
    ...none of which takes into account "compliance" issues - flexing of wood,
    compression of felt/leather, etc.
    
    If you want to figure hammer velocity, it's probably more useful to do it in
    terms of force on key and key dip, rather than keystroke time.  Key dip is
    easily measured to .01", whereas keystroke time is considerably more
    difficult.
    
    -Mark
    


  • 17.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 12:28
    From John Hartman <pianos@hartmanstudios.net>
    
    Mark Davidson wrote:
    
    > Yup.  Key, wippen and hammer all move.  And all have different m.o.i.  And
    > all have different angular accelerations  that depend on the lengths of the
    > various lever arms.
    > 
    > [Also, the jack trips out from under the knuckle just before the key hits
    > bottom  :).  Oh yeah, there are dampers too, but they don't start moving
    > until the key is halfway down.]
    
    Mark, let's leave out the dampers for now, this is going to be hard enough.
    
    
    > I think the goal here is to develop a model for predicting when an action
    > when feel light, medium, heavy, etc.  The presumption is that the moment of
    > inertia is a big part of this model.  But it needs to be the total moment of
    > inertia of key, wippen and hammer, as felt at the key, and not just the
    > key's m.o.i..  Also useful is knowing which of the various components is
    > most significant, allowing one to focus on the areas that will give the most
    > bang for the buck (i.e. how much time should one spend finding the perfect
    > keylead position).
    
    exactly! Sarah made the observation that the kinetic energy in the key 
    would not go into the final product but be wasted. It was suggested that 
    we could improve the action's efficiency by reducing the MOI of the key. 
    Yes that does work but we now see that the improvement to efficiency is 
    very little even if remove all the lead from the key.
    
    > Once you know the total reflected m.o.i. and front key radius it is possible
    > to figure the speed the key will accelerate for a given force which I would
    > expect goes a long way toward the goal.
    
    With a little more work (getting the equation for velocity right for 
    one) we can do just that.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 18.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 12:53
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    Let's look at it a little more.
    Forces on key are:
     
    FF: finger force
    F: friction
    G: gravity
    S: spring
     
    FF is self-explanatory
    G: is basically the same magnitude as BW, but pushes UP.  
     It is the net force measured at the key front, due to all 
     the gravitational forces and leverage of the action.
    F: friction is always opposite the direction of motion.  If
     we define down as positive direction, then F is negative when
     key is going down and positive when key is going up.
    S: any spring/magnet forces, as measured at the key front.
     These normally help push the key down, so are positive.
    
    also:
    AA: angular acceleration
    KFA: key front acceleration
    L: radius of key front
     
    Total force is FF + S - G - F.  Note that 
    DW + S - G - F = 0, or
    DW = -(S - G - F), so 
    total force is FF-DW.
     
    Torque T is force * L (key front length)
    T = (FF-DW) * L.
    
    key front acceleration KFA:
     
    KFA = AA * key radius = (T / I) * key radius 
     
    gives
     
    KFA = (T / I) * L, which in turn gives
     
    *** KFA = (FF-DW)*L^2/I ***
     
    This gives us the vertical key front acceleration,
    as a function of the force on the key, total reflected inertia
    and key front radius.
    
    What it says is that if I is small, then
    KFA will be big, and vice versa.  (L^2/I) 
    is basically the quantity we've been looking 
    for, that lets you compare how easy or difficult 
    it is to accelerate a key for a given amount 
    of force.  Comparing I alone between two pianos 
    doesn't tell you much.  We need to compare
    L^2/I to make comparisons of key acceleration, or 
    I/(L^2) to make meaningful comparisons of
    inertia.
     
    The analogy is you have two rocks, with mass M1 and M2.
    And two levers, L1 and L2.  And I ask you which lever
    is easier to push down, by only looking at M1 and M2.
    Well, you have to look at the lever lengths also.  
    Same thing in piano action. We have I, but 
    without L, it doesn't tell us much.
      
    -Mark
    


  • 19.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 12:18
    From John Hartman <pianos@hartmanstudios.net>
    
    Don A. Gilmore wrote:
    > Oops.  I just realized a major flaw in my reasoning.  Other components of
    > the action are also moving right before the key bottoms out.  They would add
    > to the total momentum of the system as well.  So much for simple.
    > 
    > Let me give this more than two seconds of thought and I'll see what I can
    > come up with.  Sorry for the false alarm.
    
    
    That's all right don,
    
    I didn't have time to think through your last post (looks a bit over my 
    head anyway) since I am working to get my equations right first. Thanks 
    for the help on this just let me catch up before moving to a higher plateau.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 20.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 12:32
    From Ron Nossaman <RNossaman@cox.net>
    
    >Now we just need the velocity of the hammer.
    
    Except it doesn't work that way in a real action. The peak velocity of a 
    hammer in a real action is limited by the compliance of the parts, not the 
    input impulse. That is primarily, but not entirely, key flex. So beyond a 
    certain level of input impulse, hammer velocity won't increase no matter 
    how hard the key bottoms out on the punching. Action saturation, and hence 
    maximum hammer velocity, depends on cumulative and interactive effects of 
    the mass, stiffness, moment arms, compressibility of felt and leather, of 
    every affected part for each hammer. Factors influencing saturation point 
    of any given  position in the scale include the hammer mass, shank length, 
    mass and flexibility, knuckle placement and compressibility, hammer rail 
    stiffness, wippen mass, beam stiffness, capstan pad compressibility, angle 
    and positioning, wippen rail stiffness, key mass, stiffness,  and moment 
    arms, balance rail punching compressibility, and balance rail stiffness. 
    Key bed flex is also present, but it's usually way down on the list. All 
    mass measurements include considering MOI, naturally, and I probably missed 
    some things, but the point is that this isn't something you are going to 
    casually calculate to any degree of accuracy beyond a very rough estimate.
    
    This is the way I see it, for whatever that might be worth, with more than 
    a few decimal points lopped off. Once the basic geometry is established and 
    the friction is under control, the hammer weights are the priority. High 
    hammer weights need more key lead to get static weights in the ball park of 
    usability. The excess key leads are perceived as being the cause of the 
    inertia problem, when they are only there because the hammers are already 
    too heavy. Moving the leads back toward the center of the key and adding 
    more does change the inertial effects of the key leading. It also increases 
    the flexibility of the key making it somewhat easier to bottom the key 
    before the hammer moves significantly, giving the impression of playing 
    easier as the more flexible key lowers the saturation point and limits 
    hammer velocity. It isn't the Moonlight Sonata crowd that notices the 
    difference. It's the aggressive pianist.
    
    Adding a wippen assist spring does a number of things. It provides static 
    balance compensation for excess hammer weight, which allows lead removal 
    from the keys, which lowers the overall inertia of the action. The spring 
    obviously has no direct affect on the inertia of anything in the action. 
    When we set repetition springs on the bench, we typically use hammer rise 
    as an indication of spring strength. In play, the hammer doesn't rise for 
    the jack to reset. The key does, lifted by that little rep spring. With no 
    wippen assist spring, there is somewhat of a correlation between hammer 
    weight and key weight as seen by the rep spring, but the addition of a 
    wippen assist spring changes that relationship considerably. So less key 
    mass means faster jack reset and higher repetition rates even if the 
    hammers ARE still too heavy. Less key mass will translate to slightly 
    higher key down velocities for a given input even though the hammers still 
    contribute most of the overall inertia. Fewer leads mean fewer holes, 
    therefor stiffer keys, making terminal hammer velocity more a function of 
    input, and less of action compliance. It raises the saturation point. In 
    some instances, this will mean that the pianist needn't pound the keys as 
    hard to get the high end, and should get better control over a wider range.
    
    I don't know if the rep spring will lift a center weighted key easier and 
    quicker than an end weighted key, but I suspect so, even if it is only that 
    the key flex means that weights toward the ends of the keys travel 
    proportionately farther than weights placed toward the center, and so have 
    to be moved proportionally farther to reset the jack. Again, this is a real 
    concern only with high amplitude, quick repetition playing, but that's 
    where this stuff is noticed, so I think it's a factor.
    
    As long as I'm already here and have some on me, I'd also like to comment 
    on the idea that key lead inertia doesn't happen until the downward 
    acceleration exceeds gravitational acceleration. I disagree. The system is 
    counterweighted. The key weights are not in free fall, so for mass being 
    pushed down, mass is being levered up. Gravity only counts in static 
    balance measurements.
    
    No math, no minutia, just my attempt to step back for an overview of my 
    own. There are a whole lot of minute details being discussed here, all of 
    which are worth defining and clarifying to the degree that it's possible, 
    but the original questions of how these things fit together in an action 
    are of more general interest and use, and that still isn't being addressed. 
    The problems we deal with, and the confusion that remains is still how all 
    this stuff mechanically interacts in a piano action.
    
    Ron N
    


  • 21.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 14:05
    From Ron Nossaman <RNossaman@cox.net>
    
    >Is it so that this basic geometry is relatively the same for any action
    >(grands) of the same size piano? Or possibly of all (grand) pianos?
    >
    >Paul Chick.
    
    Hi Paul,
    Relatively, in principal. The same sort of juggling of ratios and weights 
    to find something that meets your requirements from what you have to work 
    with and available parts applies to everything, and everyone seems to have 
    a slightly different set of priorities and approaches. It's like scaling or 
    anything else. You find the particular set of cumulative compromises that 
    seem to you to be the best alternative under the circumstances. Or you can 
    design and build a whole new action for each piano with a different set of 
    cumulative compromises that seem to you to be the best alternative under 
    the circumstances. We try to get far enough into the realm of diminishing 
    returns that humans can't tell the difference between our intentions, and 
    our results. Defining our intentions to meet all user requirements is the 
    impossible part. The rest is just mechanics.
    
    Ron N
    


  • 22.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 15:52
    From Ron Nossaman <RNossaman@cox.net>
    
    >Hello Ron,
    >
    >Thanks for the reply.  I was talking about this subject with my father
    >yesterday and we talked about pretty much the same thing that you wrote in
    >your post.  Is it possible to go through Stanwood's Touchweight
    >calculations, come up with good numbers and still have an action with high
    >inertia?
    
    I presume so, if you start with heavy enough hammers. We have a couple of 
    Davids on list, Stanwood and Love, who could do the details better than I.
    
    
    >  And, is it true that an action with high inertia will still
    >function correctly (the pianist just has amazing, like Popeye, strength)?
    
    The definition of "function correctly" is part of the problem. Again, the 
    Moonlight Sonata players probably won't have a problem, but the Art Tatum 
    fans are going to have touch weight and repetition troubles even with UW 
    and DW in perfectly acceptable ranges.
    
    Ron N
    


  • 23.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 18:15
    From Richard Brekne <Richard.Brekne@grieg.uib.no>
    
    Stanwoods favourite solution for the time being is generally a heavy
    hammer, usually half top on his scale, a low ratio (5.5 or less Strike
    Weight Ratio) and assist springs to do significant portions of the
    counterbalancing, leads to do the rest. This is going to generally end
    up being an action with lots of top action inertia and not so much key
    inertia.
    
    To date there is no study that can show what levels of action inertia on
    average are most preferable amoung pianists. Stannwoods method allows
    for such a study however, even if in general terms. One thing that
    Stanwoods method does not take into consideration whatsover is action
    complaince. As such it is at present not possible to use Stanwoods
    balancing system to manipulate overall action efficiency. One is only
    able to precisely balance SWs, and Counterbalances for a given ratio.
    
    Cheers
    RicB
    
    Ron Nossaman wrote:
    > 
    > >Hello Ron,
    > >
    > >Thanks for the reply.  I was talking about this subject with my father
    > >yesterday and we talked about pretty much the same thing that you wrote in
    > >your post.  Is it possible to go through Stanwood's Touchweight
    > >calculations, come up with good numbers and still have an action with high
    > >inertia?
    > 
    > I presume so, if you start with heavy enough hammers. We have a couple of
    > Davids on list, Stanwood and Love, who could do the details better than I.
    > 
    > >  And, is it true that an action with high inertia will still
    > >function correctly (the pianist just has amazing, like Popeye, strength)?
    > 
    > The definition of "function correctly" is part of the problem. Again, the
    > Moonlight Sonata players probably won't have a problem, but the Art Tatum
    > fans are going to have touch weight and repetition troubles even with UW
    > and DW in perfectly acceptable ranges.
    > 
    > Ron N
    > 
    >   ------------------------------------------------------------------------
    > 
    > ---
    > 
    > Checked by AVG anti-virus system (http://www.grisoft.com).
    > Version: 6.0.551 / Virus Database: 343 - Release Date: 12/11/2003
    > 
    >   ------------------------------------------------------------------------
    > _______________________________________________
    > pianotech list info: http://www.ptg.org/mailman/listinfo/pianotech
    


  • 24.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 15:34
    From Ron Nossaman <RNossaman@cox.net>
    
    >Can you give a definition of action saturation ? I am unsure if it is
    >the fact that the move of the key at a certain moment can't accelerate
    >more the hammer and is it for limit in flexibility or because the key
    >bottoms.
    
    The hammer is always driven by the key (key bed, action rail, key frame, 
    etc) stiffness, whether you're playing hard or soft. When the key bottoms 
    before the hammer moves, that is the limit of the power available to the 
    hammer - saturation. No matter how hard you hit the key beyond the action 
    saturation point, the hammer won't hit the strings any harder than it will 
    at saturation.
    
    
    >  is it only
    >tone saturation ?
    
    No. Tone is another concern, with different cause and effect relationships. 
    Tone happens after the action has cycled and the hammer hits the string. 
    Action saturation happens during the action cycle before the hammer hits 
    the string.
    
    
    >I like to see that like 2 different aspects.
    
    They are.
    
    
    >BTW, the piano hammer is may be tone of the fastest accelerated
    >actions on earth, 0 to 40 miles/hour in 1/400 sec is faster than my
    >motorcycle (that accelerates fast enough yet!)
    >
    >Greetings.
    >
    >Isaac OLEG
    
    Ah, but what kind of tone can you get driving your motorcycle into a strung 
    piano? Be mindful of the strike point.
    
    Ron N
    


  • 25.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 17:59
    From Richard Brekne <Richard.Brekne@grieg.uib.no>
    
    > 
    > >Now we just need the velocity of the hammer.
    > 
    > Except it doesn't work that way in a real action. The peak velocity of a
    > hammer in a real action is limited by the compliance of the parts, not the
    > input impulse. 
    
    
    Yes... thats true enough. But one thing at a time as it were. It seems
    reasonable to first figure the velocity of the hammer for key velocity
    as if it were in total compliance, then figure a compliance value, then
    find that combination of inertia, mass, leverage, whathaveyou that sees
    the maximum amount of hammer velocity for key velocity coincide best
    with the saturation point of the action. Yes ?
    
    RicB
    


  • 26.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 20:45
    From Bill Ballard <yardbird@vermontel.net>
    
    At 1:58 AM +0100 12/29/03, Richard Brekne wrote:
    >Yes... thats true enough. But one thing at a time as it were. It seems
    >reasonable to first figure the velocity of the hammer for key velocity
    >as if it were in total compliance, then figure a compliance value, then
    >find that combination of inertia, mass, leverage, whathaveyou that sees
    >the maximum amount of hammer velocity for key velocity coincide best
    >with the saturation point of the action. Yes ?
    
    Clearly there's no sense in pouring further energy into the action 
    after you've overcome its ability to absorb your energy. It sounds as 
    though we're going to tune action leverage, so as to carry the weight 
    hammer we want without either counterbalancing the action so much as 
    to slow it up, or so badly unbalanced that the force of our attack 
    will allow the flexibility of parts to waylay energy.
    
    If we're worrying about lowering the maximum amount of energy the 
    action can absorb due to the leveraged weight of parts and consequent 
    counterbalancing, there's another point where energy is transferred 
    from one system to another, and where saturation is also to be 
    avoided. That's between the hammer and the string. The last thing we 
    need here is for energy to be wasted during the transfer of energy at 
    the collision of hammer and string. (Yes, heavy and hard hammers do 
    block the strings in high force situations.)
    
    It would be nice if the weight of the hammer could be mated to the 
    strings' ability to absorb its impact. Then success at mating the 
    action leverage, weight and counterbalancing could occur in 
    conjunction with it. That would be a well designed piano.
    
    Bill Ballard RPT
    NH Chapter, P.T.G.
    
    "No one builds the *perfect* piano, you can only remove the obstacles 
    to that perfection during the building."
         ...........LaRoy Edwards, Yamaha International Corp
    +++++++++++++++++++++
    


  • 27.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 21:18
    From John Hartman <pianos@hartmanstudios.net>
    
    Bill Ballard wrote:
    
    > The last thing we need here is 
    > for energy to be wasted during the transfer of energy at the collision 
    > of hammer and string. 
    
    You made some good points Bill, But I would have to disagree with this 
    statement. It seams to me that wasting energy is just what we want the 
    hammer to do at all levels of play. At soft levels of play we want it to 
    waist a lot of energy to make soft playing more assessable. At very laud 
    playing levels we what it to waist much less in order to expand the 
    dynamic level. This is achieved by the hammer's non linear compliance. 
     From a tonal point of view we also don't want the hammer to deliver all 
    of its energy to the string. It has to have enough energy left to 
    rebound from the string.
    
    But I agree with you on the possibility that there may be a relationship 
    between the string scale / strike point design and the mass of the hammer.
    
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 28.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 21:42
    From Bill Ballard <yardbird@vermontel.net>
    
    Hi, John.
    
    At 11:17 PM -0500 12/28/03, John Hartman wrote:
    >From a tonal point of view we also don't want the hammer to deliver 
    >all of its energy to the string. It has to have enough energy left 
    >to rebound from the string.
    
    It'll will have enough energy to rebound, alright. The energy for 
    that rebound is absorbed during the moment of impact in the elastic 
    deformation of both the hammer and the string. Each of these are 
    springs. The hammer crown squashes and the string gets stretched out 
    of the way.
    
    >But I agree with you on the possibility that there may be a 
    >relationship between the string scale / strike point design and the 
    >mass of the hammer.
    
    I've long felt that the best combination of hammer and string is one 
    where both are a well-matched set of springs. For optimal energy 
    transfer, each should reach its maximum displacement at the same 
    moment. Where the string scale enters in is in the stiffness with 
    which the stings greet the hammers' impact. With a hammer too hard, 
    it may not still be stopped by the time the string has reached its 
    maximum displacement. With a hammer too soft, the string will never 
    get properly displaced. With the hammer properly selected (and here, 
    weight and hardness can be independent yet complementary factors), 
    the action can be set-up (hung as 'twere) so that energy loss inside 
    the action due to action saturation can be avoided. (Energy loss due 
    to frictional, gravitational and inertial resistance however comes 
    with the territory.) In a nutshell, the action set-up starts in the 
    string scale AND the board design.
    
    Bill Ballard RPT
    NH Chapter, P.T.G.
    
    "No, Please wait, you're all individuals" Brain Cohen, exasperated
    "Yes, we're all individuals"  the throng assembled in the street          
                     below his window, in unison
    "I'm not..."  Lone dissenter.
         ...........Monty Python's "Life of Brian"
    +++++++++++++++++++++
    


  • 29.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 22:12
    From Ron Nossaman <RNossaman@cox.net>
    
    >  In a nutshell, the action set-up starts in the string scale AND the 
    > board design.
    >
    >Bill Ballard RPT
    
    No... ya think???
    
    Ron N
    


  • 30.  Moment of Inertia of grand action parts.

    Posted 12-29-2003 18:05
    From Bill Ballard <yardbird@vermontel.net>
    
    At 11:11 PM -0600 12/28/03, Ron Nossaman wrote:
    >No... ya think???
    
    Nah, just repeating what's been said on this list before.
    
    >I wasn't aware that I had a choice as to whether or not the hammer 
    >rebounded off of the string. Where might I buy a hammer that doesn't?
    
    Actually John Hartman was the one who wanted to make sure that we got 
    the kind which did.
    
    At 11:17 PM -0500 12/28/03, John Hartman wrote:
    >From a tonal point of view we also don't want the hammer to deliver 
    >all of its energy to the string. It has to have enough energy left 
    >to rebound from the string.
    
    What I can do for you, Ron, is to sell you a set of hammershanks 
    which will keep the hammers up at the string. Vintage Steinway shanks 
    from the classic era (when Steinways were Steinways). Some sort of 
    weird grease in the bushings.
    
    Mr. Bill
    
    "If ducks were smart enough and well-built enough, they'd be shooting 
    at us. It's not my fault they can't aim and shoot."
         ...........Talk Show host Rush Lamebaugh, explaining why duck 
    hunting is a sport, 1/12/98
    +++++++++++++++++++++
    


  • 31.  Moment of Inertia of grand action parts.

    Posted 12-29-2003 23:32
    From Ron Nossaman <RNossaman@cox.net>
    
    >>No... ya think???
    >
    >Nah, just repeating what's been said on this list before.
    
    Oh... then never mind.
    
    
    >>I wasn't aware that I had a choice as to whether or not the hammer 
    >>rebounded off of the string. Where might I buy a hammer that doesn't?
    >
    >Actually John Hartman was the one who wanted to make sure that we got the 
    >kind which did.
    
    Yea, I know. It just struck me as a firm grasp of the obvious sort of 
    thing, as well as unavoidable. As a matter of degree though, rather than an 
    absolute, the rate at which a hammer rebounds from the string is both of 
    considerable importance, and not easily defined or specified. I expect 
    that's more like what John meant.
    
    
    > From a tonal point of view we also don't want the hammer to deliver
    >>all of its energy to the string. It has to have enough energy left to 
    >>rebound from the string.
    >
    >What I can do for you, Ron, is to sell you a set of hammershanks which 
    >will keep the hammers up at the string. Vintage Steinway shanks from the 
    >classic era (when Steinways were Steinways). Some sort of weird grease in 
    >the bushings.
    >
    >Mr. Bill
    
    But then that's not the hammers' fault, is it? Assigning the appropriate 
    credit or blame to the proper parts is what I took this discussion to be 
    about. If not, I'll just blame everything on the casters and be done with 
    it. I won't even ask why you saved a set of goo-frozen take-out shanks and 
    flanges from Steinway's "golden" era - whenever that was presumed or 
    proclaimed to be.
    
    Ron N
    


  • 32.  Moment of Inertia of grand action parts.

    Posted 12-30-2003 10:04
    From "Barbara Richmond" <piano57@flash.net>
    
    > >
    > >What I can do for you, Ron, is to sell you a set of hammershanks which
    > >will keep the hammers up at the string. Vintage Steinway shanks from the
    > >classic era (when Steinways were Steinways). Some sort of weird grease in
    > >the bushings.
    > >
    > >Mr. Bill
    >
    > I won't even ask why you saved a set of goo-frozen take-out shanks and
    > flanges from Steinway's "golden" era - whenever that was presumed or
    > proclaimed to be.
    >
    > Ron N
    
    
    It's art, man.
    
    Besides, one must always be prepared.  You know how it is, you point out a
    problem to the customer and then they say, "But I like it that way."  Mr.
    Bill is just waiting for one of those folks to come along--specifically, the
    ones who claim to like a piano with now and then repetition.  :-)
    
    
    Barbara Richmond, RPT
    somewhere near Peoria, IL
    
    
    
    
    
    
    > _______________________________________________
    > pianotech list info: http://www.ptg.org/mailman/listinfo/pianotech
    >
    


  • 33.  OT Re: Moment of Inertia of grand action parts.

    Posted 12-30-2003 18:01
    From Bill Ballard <yardbird@vermontel.net>
    
    At 12:32 AM -0600 12/30/03, Ron Nossaman wrote:
    >As a matter of degree though, rather than an absolute, the rate at 
    >which a hammer rebounds from the string is both of considerable 
    >importance, and not easily defined or specified. I expect that's 
    >more like what John meant.
    
    Three things make the hammer rebound: 1.) the fact that it's 
    nose-to-nose with the string which about to restore itself to a 
    nominally straight line, 2.) the fact that it's own nose has been 
    squashed and is eager to restore itself, and finally, 3.) gravity. 
    Only one of them has to do with the hammer. And the poor thing does 
    indeed cough up its last nanojoule of kinetic energy in coming to a 
    dead stop at the string.
    
    >If not, I'll just blame everything on the casters and be done with 
    >it. I won't even ask why you saved a set of goo-frozen take-out 
    >shanks and flanges from Steinway's "golden" era - whenever that was 
    >presumed or proclaimed to be.
    
    Quit hemming and hawing, Ron. You've got first option on this vintage 
    set of shanks before I post them on eBay, but only for another 12 
    hours.
    
    Mr. Bill
    
    "Garth, Take me!"
    "Where? I'm low on gas and you need a jacket"
         ...........Kim Bassinger and Dana Carvey in "Wayne's World 2"
    +++++++++++++++++++++
    


  • 34.  Moment of Inertia of grand action parts.

    Posted 12-30-2003 23:55
    From Ron Nossaman <RNossaman@cox.net>
    
    >It's art, man.
    >
    >Besides, one must always be prepared.  You know how it is, you point out a
    >problem to the customer and then they say, "But I like it that way."  Mr.
    >Bill is just waiting for one of those folks to come along--specifically, the
    >ones who claim to like a piano with now and then repetition.  :-)
    >
    >
    >Barbara Richmond, RPT
    
    I get it. Then he must have a set of Brambach wippens on the shelf too, right?
    
    Ron N
    


  • 35.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 22:26
    From Ron Nossaman <RNossaman@cox.net>
    
    >You made some good points Bill, But I would have to disagree with this 
    >statement. It seams to me that wasting energy is just what we want the 
    >hammer to do at all levels of play. At soft levels of play we want it to 
    >waist a lot of energy to make soft playing more assessable. At very laud 
    >playing levels we what it to waist much less in order to expand the 
    >dynamic level. This is achieved by the hammer's non linear compliance. 
    > From a tonal point of view we also don't want the hammer to deliver all 
    >of its energy to the string. It has to have enough energy left to rebound 
    >from the string.
    
    I wasn't aware that I had a choice as to whether or not the hammer 
    rebounded off of the string. Where might I buy a hammer that doesn't?
    
    
    >But I agree with you on the possibility that there may be a relationship 
    >between the string scale / strike point design and the mass of the hammer.
    >John Hartman RPT
    
    There may indeed, and just possibly the soundboard design as well.
    
    Ron N
    


  • 36.  Moment of Inertia of grand action parts.

    Posted 12-29-2003 19:54
    From John Hartman <pianos@hartmanstudios.net>
    
    Richard Brekne wrote:
    
    > Yes... thats true enough. But one thing at a time as it were. It seems
    > reasonable to first figure the velocity of the hammer for key velocity
    > as if it were in total compliance, then figure a compliance value, then
    > find that combination of inertia, mass, leverage, whathaveyou that sees
    > the maximum amount of hammer velocity for key velocity coincide best
    > with the saturation point of the action. Yes ?
    
    
    Richard,
    
    Your right about the primacy of finding the relationship between 
    acceleration, velocity and inertia in the action. Especially if one 
    wants to graduate from the simple problems of action statics, that only 
    address the action at rest,  to the difficult but more promising study 
    of the action in motion.  In fact there is no other way to study the 
    forces that develop in the action except by finding the MOI first. It 
    stands to reason that without knowing the forces you can't begin to 
    understand the various reactions such as bending and compression that 
    rob the action of power.
    
    For example, it is not enough to simply know the force applied at the 
    key to figure out how much force is applied to bend the key.  Let's say 
    you drop a weight on the key of an action from a certain height. The 
    force bending the key can not be know from this information alone. If 
    the same weight is dropped on the note with little MOI in the action 
    chain the key will bend less than if it were dropped on a note with 
    large amounts. The forces available to bend the key are directly 
    proportional to the MOI of the action chain.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 37.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 16:13
      |   view attached
    From John Hartman <pianos@hartmanstudios.net>
    
    Inertia Heads,
    
    Here is what I came up with for figuring the total MOI of the action. 
    Pretty much the same thing Mark D. came up with. If you plug in some 
    numbers you will see that the hammer and shank contribute most of the 
    MOI as felt at the key.
    
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 38.  Moment of Inertia of grand action parts.

    Registered Piano Technician
    Posted 12-30-2003 03:02
    From Robin Hufford <hufford1@airmail.net>
    
    Hello John,
        Just a short commentary on this drawing - later this week I will post a
    better description of the altered MOI formula I suggested the use of the
    yesterday.    I do think it is important, at least at the moment.   It was
    done in a real hurry as is this post and the one yesterday, unfortunately, is
    not very clear.
         Your proposed analysis of the moment arms of the action is, I think,
    essentially on the mark.  Very similar approaches are taken by Pfeiffer in
    analyzing an upright action which he lays out in his book.   I think these
    kinds of analyses are, unfortunately, very poorly known in the US even though
    they were done, repeatedly I think,  in Germany, the land of mechanical
    analysis,  along with other very extensive studies of bearing pressure and
    friction and  wear at contact points,  as far back as the 1860's or 70's, if
    not earlier.
         In my opinion, it would be better to consider the whippen output to be
    the line from the center of the whippen center to that of the jack center.
    This is the point where, for much the greater part,  the load of the hammer
    assembly is first reacted, for lack of a better word.   I don't think this
    factor can be ignored without real penalty to the analysis.  The shank input
    and output you suggest is the same as I conceive of.  However, the interaction
    of the jack and the knuckle needs work which I will have to give more thought
    to.
         I will come back later with more on this subject, and agree
    wholeheartedly with your other post as to why this is important and why a
    dynamic study of the action is, at least equally, if not more so, important
    than the conventional, static approach, which, rightfully, gets big play here
    but can benefit in a complementary way from such a study.   Some may find this
    approach to be tediously mechanical but, to me, using conventional mechanical
    concepts inspite of the work this may require is the only way to get a real
    handle on what actually goes on in an action.   This may,  actually, render
    objective, many of the rather subjective comments on this subject which are
    regularly encountered here.  I do not exclude my comments from this criticism
    by any means, nor do I mean to disparage the comments made in any way.
         Calculating the mass moments of inertia of the parts about the axial
    points in an action is, as you say, a first necessary step.  This, however, is
    a formidable and highly repetitious task to do accurately, even for the
    keyset, much less the entire action train.   Although I am not sure of its
    significance, obviously, every key will have a different value.  Along this
    line I had a brief discussion with a nephew in town for the holidays who is a
    mechanical engineer as it had occurred to me that surely, there are programs
    which can be had which will do this upon data supplied to them.  Something
    intervened and I did not get an answer at the time but I think such surely
    exists.   Are you aware of such a program?  This,  I think,  this would make
    the entire task much more tractable.
    Regards, Robin Hufford
    John Hartman wrote:
    
    > Inertia Heads,
    >
    > Here is what I came up with for figuring the total MOI of the action.
    > Pretty much the same thing Mark D. came up with. If you plug in some
    > numbers you will see that the hammer and shank contribute most of the
    > MOI as felt at the key.
    >
    > John Hartman RPT
    >
    > John Hartman Pianos
    > www.pianos.hartmanstudios.net
    > Rebuilding Steinway and Mason & Hamlin
    > Grand Pianos Since 1979
    >
    > Piano Technicians Journal
    > Journal Illustrator/Contributing Editor
    > www.journal.hartmanstudios.net
    >
    >   ------------------------------------------------------------------------
    >                       Name: Speed-Ratio.jpg
    >    Speed-Ratio.jpg    Type: JPEG Image (image/jpeg)
    >                   Encoding: base64
    >
    >    Part 1.3    Type: Plain Text (text/plain)
    >            Encoding: 7bit
    


  • 39.  Moment of Inertia of grand action parts.

    Posted 12-30-2003 09:43
    From John Hartman <pianos@hartmanstudios.net>
    
    Robin Hufford wrote:
    > 
    >      In my opinion, it would be better to consider the whippen output to be
    > the line from the center of the whippen center to that of the jack center.
    > This is the point where, for much the greater part,  the load of the hammer
    > assembly is first reacted, for lack of a better word.   I don't think this
    > factor can be ignored without real penalty to the analysis.  The shank input
    > and output you suggest is the same as I conceive of.  However, the interaction
    > of the jack and the knuckle needs work which I will have to give more thought
    > to.
    >
    
    
    Robin,
    
    You are right, the interaction of the jack and knuckle is a little more 
    involved than just simply measuring the parts. Here is a drawing I use 
    to show how to measure the output of the wip and the input of the shank. 
    The action is at half stroke for an average measurement. The pitch point 
    movers along the line of centers as the key is depressed. A similar 
    situation happens at the capstan/wip connection.
    
    I don't think this degree of accuracy is going to be needed for our 
    initial forays into action kinematics.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 40.  Moment of Inertia of grand action parts.

    Posted 01-01-2004 19:06
    From John Hartman <pianos@hartmanstudios.net>
    
    Inertia Heads,
    
    I have a little more to report on measuring the MOI of the action parts. 
    A friend brought this method to my attention and I am very grateful for 
    his help. A method based on the principles of a physical pendulum can be 
    use to measure the MOI of odd shaped parts.
    
    I have been trying this out on some grand keys. I think it may be more 
    accurate than the estimating method I proposed before. I compared using 
    the estimate with the pendulum method and found a discrepancy of 8.5%. 
    So our estimate is not too bad after all.
    
    Note C40 M&H BB with two leads in the key.
    
    Estimated MOI = 25077gmcm^2
    Measure MOI = 27389gmcm^2
    
    More on this later.
    
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 41.  Moment of Inertia of grand action parts.

    Registered Piano Technician
    Posted 01-05-2004 04:59
    From Robin Hufford <hufford1@airmail.net>
    
    Hello John,
         It is interesting to me to see that your experimental results are as
    close as they are to the calculated result.  A #40 keystick will probably
    have a minimal level of flaring compared to others further away from the
    central part of the keyboard in both directions and hence may be more
    closely approximated by the formula for I(g) for a symmetric rod than may be
    the case with many other keys.
         Still, I think it would be even more of a job using the torsional
    pendulum, which I think you used in your experimental determination of
    this,   than calculating these values, so I am looking for a program to do
    this.   I know you are aware of this but to those technicians that are still
    trying to understand the importance of  I  in the question of action
    behavior I am going to offer my own repetition of definitions learned
    elsewhere on this subject.
         In the rather heated discussion of inertia a week or two ago on this
    subject the point was made that inertia is not exactly an engineering
    quantity and lacks units per se which is precisely right.  As was said by
    several, the term and concept of inertia is merely a way to indicate the
    tendancy of a body to resist acceleration.
         As far as I understand the nature of motion determines how this
    inertial tendancy will be quantified and expressed.  In translatory motion
    where the particles comprising a body move in parallel paths the effects of
    inertia working to resist a change in direction or velocity, that is
    acceleration, can be quantified and referred to as the mass of the body.
    This mass is a measure of the amount of matter in the body itself.  It
    correlates in a gravity field with the weight of a body but exists
    independantly of gravity.   Most people are aware of this and of the F = MA
    equation which relates force, mass and acceleration.
         Where rotation about a fixed axis is concerned such as approximately
    occurs in a piano action,  the collective effects of the mass of the parts
    and its distribution  about the axis of rotation must be given due account.
    As the particles may be closer or further to the axis of rotation their
    inertial effects differ.  Collectively, the measure of these effects  is
    termed the moment of inertia.  One must arbitrarily impose an axis of
    rotation.  The concept has no meaning without one.  Also,  this axis must be
    fixed and perpendicular to the plane of rotation.
         This is precisely the analogue of the term mass used  in the case of
    translatory motion  where you had f = ma.  Now, however, a new but similar
    set of terms is used to decribe these events in rotary motion about a fixed
    axis.  Where force was equal to mass times acceleration,  the rotational
    analogue of force, torque,  is equal to the moment of inertia times angular
    acceleration and f=ma becomes (here the keyboard I am using lacks  the
    correct characters) alpha (torque) equals I(moment of inertia) times angular
    acceleration(omega).
         Despite the similarity of the two expressions, there are, however, some
    important differences. When conceiving of the moment of inertia of an object
    one must actively impose an axis of rotation which will then imply an I.
    Taking a different axis will result in a different value for the same
    object.  These axes may be represent by a subscript following the symbol I.
    One frequently encounters I(g) which is an axis through the center of
    gravity, also, I(x), I(y) or I(z).   Mass, on the other hand, is constant at
    ordinary speeds.  So, we have the possiblity of one and the same rigid body
    having differing values emanating from inertial effects which depend upon
    the nature of the motion and the nature of the axes chosen.
    Regards, Robin Hufford
    
    > Inertia Heads,
    >
    > I have a little more to report on measuring the MOI of the action parts.
    > A friend brought this method to my attention and I am very grateful for
    > his help. A method based on the principles of a physical pendulum can be
    > use to measure the MOI of odd shaped parts.
    >
    > I have been trying this out on some grand keys. I think it may be more
    > accurate than the estimating method I proposed before. I compared using
    > the estimate with the pendulum method and found a discrepancy of 8.5%.
    > So our estimate is not too bad after all.
    >
    > Note C40 M&H BB with two leads in the key.
    >
    > Estimated MOI = 25077gmcm^2
    > Measure MOI = 27389gmcm^2
    >
    > More on this later.
    >
    > John Hartman RPT
    >
    > John Hartman Pianos
    > www.pianos.hartmanstudios.net
    > Rebuilding Steinway and Mason & Hamlin
    > Grand Pianos Since 1979
    >
    > Piano Technicians Journal
    > Journal Illustrator/Contributing Editor
    > www.journal.hartmanstudios.net
    >
    > _______________________________________________
    > pianotech list info: http://www.ptg.org/mailman/listinfo/pianotech
    


  • 42.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 13:37
    From "Paul Chick" <paulchick@myclearwave.net>
    
    Ron,
    
    Ron Wrote-
    This is the way I see it, for whatever that might be worth, with more than
    a few decimal points lopped off. Once the basic geometry is established and
    the friction is under control, the hammer weights are the priority.
    
    
    Is it so that this basic geometry is relatively the same for any action
    (grands) of the same size piano? Or possibly of all (grand) pianos?
    
    Paul Chick.
    


  • 43.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 14:31
    From "Isaac sur Noos" <oleg-i@noos.fr>
    
    Ron,
    
    Thanks for that resumed point of view, seem to meet what I suspect.
    
    Can you give a definition of action saturation ? I am unsure if it is
    the fact that the move of the key at a certain moment can't accelerate
    more the hammer and is it for limit in flexibility or because the key
    bottoms.
    if I believe the fact that the key can be made bottoming before the
    hammer have even start to move on certain actions (may be due also to
    lack of stiffness under the keybed), the hammer will still be driven
    by the key un flexing so when is the saturation occurring ? is it only
    tone saturation ? I like to see that like 2 different aspects.
    
    BTW, the piano hammer is may be tone of the fastest accelerated
    actions on earth, 0 to 40 miles/hour in 1/400 sec is faster than my
    motorcycle (that accelerates fast enough yet!)
    
    Greetings.
    
    Isaac OLEG
    
    
    ------------------------------------
    Isaac OLEG
    accordeur - reparateur - concert
    oleg-i@noos.fr
    19 rue Jules Ferry
    94400 VITRY sur SEINE
    tel: 033 01 47 18 06 98
    fax: 33 01 47 18 06 90
    mobile: 033 06 60 42 58 77
    ------------------------------------
    
    
    > -----Message d'origine-----
    > De : pianotech-bounces@ptg.org
    > [mailto:pianotech-bounces@ptg.org]De la
    >
    


  • 44.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 14:35
    From "Isaac sur Noos" <oleg-i@noos.fr>
    
    Is not the leverage very short (high ratio) for a very little moment
    on the last moment before real letoff , and that more on some action
    than others ?
    
    
    
    ------------------------------------
    Isaac OLEG
    accordeur - reparateur - concert
    oleg-i@noos.fr
    19 rue Jules Ferry
    94400 VITRY sur SEINE
    tel: 033 01 47 18 06 98
    fax: 33 01 47 18 06 90
    mobile: 033 06 60 42 58 77
    ------------------------------------
    
    >
    


  • 45.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 15:03
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    Ron N wrote:
    
    >Except it doesn't work that way in a real action. The peak velocity of a
    >hammer in a real action is limited by the compliance of the parts, not the
    >input impulse. That is primarily, but not entirely, key flex.
    
    Not disagreeing with this, but I don't think we've necessarily been talking
    about "peak" velocity, just velocity in general.  Somewhere between ppp,
    where BW and friction are the main issues, and fff, where action saturation
    occurs, is a whole range of other dynamics that are very much affected by
    these discussions of inertia.  And that's the range where people do most of
    their playing.
    
    >Gravity only counts in static balance measurements.
    
    Gravity is a constant force, whether you're moving or not.  And the force
    between two objects does change when there is vertical acceleration, like
    standing in an elevator when it starts to go down, or starts going up.  If
    the elevator were to fall at the rate of gravitational acceleration you will
    cease to exert a force on the floor of the elevator.  If it falls faster
    than the rate of gravitational acceleration due to some other force on the
    elevator, then the top of the elevator will start to push on you.
    
    Now key leads are in a rotational system, which isn't as simple as an
    elevator.  There are horizontal and rotational forces as well as vertical.
    However there is still some rate of angular acceleration of the key at which
    the same finger force on the key will produce the same angular acceleration.
    
    We can solve for that force as follows.
    
    Using the formula I recently posted, we have
    
    (1) KFA = (FF-DW) * L^2 / I
    
    KFA = key front acceleration
    FF = finger force
    DW = downweight
    L = front key radius
    I = moment of inertia
    
    If we add a lead with mass M at radius L this changes to
    
    (2) KFA = (FF-DW+M) * L^2 / (I + M*L^2)
    
    We want the same key front acceleration, (KFA same), so set (1) equal to
    (2):
    
    (FF-DW) * L^2 / I = (FF-DW+M) * L^2 / (I + M*L^2)
    
    With a bit of algebra, you can solve for FF, the force that gives the same
    acceleration with and without keylead of mass M at radius L.
    
    FF = DW + I / L^2
    
    Not sure how useful that is, but maybe we can put the question to bed.
    
    Conceptually, adding a lead decreases BW but increases inertia.  So it makes
    sense that you can get the key moving with less force, but at some point you
    will have to exert more force for the same acceleration.  The crossover
    point is what I just solved for.
    
    -Mark
    


  • 46.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 15:36
    From "Paul Chick" <paulchick@myclearwave.net>
    
    Hello Ron,
    
    Thanks for the reply.  I was talking about this subject with my father
    yesterday and we talked about pretty much the same thing that you wrote in
    your post.  Is it possible to go through Stanwood's Touchweight
    calculations, come up with good numbers and still have an action with high
    inertia?  And, is it true that an action with high inertia will still
    function correctly (the pianist just has amazing, like Popeye, strength)?
    
    >Is it so that this basic geometry is relatively the same for any action
    >(grands) of the same size piano? Or possibly of all (grand) pianos?
    >
    >Paul Chick.
    
    Hi Paul,
    Relatively, in principal. The same sort of juggling of ratios and weights
    to find something that meets your requirements from what you have to work
    with and available parts applies to everything, and everyone seems to have
    a slightly different set of priorities and approaches. It's like scaling or
    anything else. You find the particular set of cumulative compromises that
    seem to you to be the best alternative under the circumstances. Or you can
    design and build a whole new action for each piano with a different set of
    cumulative compromises that seem to you to be the best alternative under
    the circumstances. We try to get far enough into the realm of diminishing
    returns that humans can't tell the difference between our intentions, and
    our results. Defining our intentions to meet all user requirements is the
    impossible part. The rest is just mechanics.
    
    Ron N
    


  • 47.  Moment of Inertia of grand action parts.

    Registered Piano Technician
    Posted 12-28-2003 16:33
    From Robin Hufford <hufford1@airmail.net>
    
    John,
         I know you attempt to approximate I here for the keystick and the result
    you arrive at here may be adequate for this yet I would suggest a fairly
    better measure for the mass moment of inertia for the keystick itself can be
    arrived at relatively easily with a little more effort.
         I(g) = 1/12ml^2 is the moment of inertia about an axis perpendicular to
    the plane of rotation and passing through the center of gravity of a straight,
    symmetric rod which of course of the key, due to flare, particularly,  and
    other things is not.  For the moment though, ignoring these complications and
    taking the the keystick to be essentially symmetric the formula you suggest is
    for determing I can be improved by taking into account the fact that the axis
    of rotation of the keystick does not pass through the center of gravity.
         I(g), (correct me here please Don, if I am wrong,) is suitable where the
    axis of rotation passes through the center of gravity.  which is not
    generally  the case with a piano keystick.   Where such is not the case it is
    necessary to use a formulation called the Parallel-Axis Theorem which
    basically says that the moment of inertia of an object about an axis different
    than one through the center of gravity but parallel to it,  can be calculated
    by adding to I(g) = 1/12ml^2 the moment of the distance to the axis along the
    body.  The formula becomes(using I(est)) to indicate rotation at the balance
    rail, I(est) = 1/12ml^2 + md^2.
         I want to add my thanks to those of others to Don Gilmore for kindly
    sharing his expertise with us on these questions
    Regards, Robin Hufford
    
    John Hartman wrote:
    
    > Inertia Heads,
    >
    > The next step toward understanding how the action works when actually
    > played is to find the total MOI as measured at the front of the key.
    > First we need to find the MOI of the key, wippen and shank. I thought it
    > would be useful to find ways to estimate this. The drawing shows a way
    > to estimate the MOI of the key. I have ways to estimate the MOI of the
    > wip and the hammer/shank as well but first I wanted to se if anyone else
    > had ideas on how to do this.
    >
    > We could use a variety of methods to measure the MOI directly like using
    > a torsion table or torsion pendulum. But these are difficult to build
    > and calibrate, more useful for demonstrating the principles of inertia
    > than for getting accurate measurement. Professional measuring equipment
    > is beyond my reach so for now the estimated MOI will have to do.
    >
    > After finding the MOI of the three parts the total MOI can be figured
    > with an equation.
    >
    > John Hartman RPT
    >
    > John Hartman Pianos
    > www.pianos.hartmanstudios.net
    > Rebuilding Steinway and Mason & Hamlin
    > Grand Pianos Since 1979
    >
    > Piano Technicians Journal
    > Journal Illustrator/Contributing Editor
    > www.journal.hartmanstudios.net
    >
    >   ------------------------------------------------------------------------
    >                      Name: MOI-of-key.jpg
    >    MOI-of-key.jpg    Type: JPEG Image (image/jpeg)
    >                  Encoding: base64
    >
    >    Part 1.3    Type: Plain Text (text/plain)
    >            Encoding: 7bit
    


  • 48.  Moment of Inertia of grand action parts.

    Posted 12-28-2003 15:40
    From John Hartman <pianos@hartmanstudios.net>
    
    Robin Hufford wrote:
    > John,
    >      I know you attempt to approximate I here for the keystick and the result
    > you arrive at here may be adequate for this yet I would suggest a fairly
    > better measure for the mass moment of inertia for the keystick itself can be
    > arrived at relatively easily with a little more effort.
    
    
    Thanks Robin,
    
    A drawing of this would be helpful. For now I am going to save your post 
    for future reference. To use this method would we have to remove any key 
    leads first? General speaking the center of balance of an un-leaded key 
    is close to the balance hole, at least on natural keys of a grand piano.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 49.  Moment of Inertia of grand action parts.

    Posted 12-29-2003 13:12
    From David Andersen <bigda@gte.net>
    
    on 12/28/03 12:32 PM, Ron Nossaman at RNossaman@cox.net wrote:
    
    > No math, no minutia, just my attempt to step back for an overview of my
    > own. There are a whole lot of minute details being discussed here, all of
    > which are worth defining and clarifying to the degree that it's possible,
    > but the original questions of how these things fit together in an action
    > are of more general interest and use, and that still isn't being addressed.
    > The problems we deal with, and the confusion that remains is still how all
    > this stuff mechanically interacts in a piano action.
    > 
    > Ron N
    
    Thank you, thank you, thank you---this post is brilliant, and an incredible
    breath of fresh air into an increasingly wonky discussion.
    Please: letus not forget the bottom line: how does it sound, and how does it
    feel, and how do ALL the factors of construction, mass, movement, and
    position in a piano action affect the "spielart" of the instrument.
    
    This is truly a deep and majestic craft, ladies and gentleman.
    Ron, my gratitude for this post.  Great job.
    
    David Andersen
    Malibu, CA
    


  • 50.  Moment of Inertia of grand action parts.

    Posted 12-30-2003 04:23
    From "Mark Davidson" <mark.davidson@mindspring.com>
    
    Robin Hufford wrote:
    
    >The formula becomes(using I(est)) to indicate
    >rotation at the balance rail,
    >I(est) = 1/12ml^2 + md^2
    
    If I understand you correctly, d is basically half the height of the key.
    I.e., you're rotating the key not around its center top-to-bottom, but
    around its bottom, so the center is displaced by the distance of half the
    key height.  If so, for a 20 inch key that is 1 inch high this represents
    only a 0.75% difference from using (1/12 ml^2) alone.  In the land of rough
    estimates, I would probably not make too much of this.
    
    -Mark
    


  • 51.  Moment of Inertia of grand action parts.

    Posted 01-01-2004 21:11
    From Erwinspiano@aol.com
    
    Ron 
      I just wanted to say publicly--Thanks . This is a great clarifying summary. 
    Clarification is always enlightening. Your post also points out that "the 
    confusion that remains is still how all this stuff mechanically relates" which is 
    true. At the end of the day we have to put all this into a useful sytematic 
    practice in rebuilding the actions we all work on.These discussion  increase 
    our confidence secure better results for us & perfromance benifits for our 
    clients.
       The idea of rebuilding a grand action with the refinements in design , 
    parts selection & geometry we're discussing on this list today wasn't even born 
    30 years ago. If it was I didn't know about it. We've come along way.
      I've followed this discussion with interest.  Thanks to all contributors.  
    What alot of work.
      Dale
    
    
    No math, no minutia, just my attempt to step back for an overview of my 
    own. There are a whole lot of minute details being discussed here, all of 
    which are worth defining and clarifying to the degree that it's possible, 
    but the original questions of how these things fit together in an action 
    are of more general interest and use, and that still isn't being addressed. 
    The problems we deal with, and the confusion that remains is still how all 
    this stuff mechanically interacts in a piano action.
    
    Ron N
    


  • 52.  Moment of Inertia of grand action parts.

    Posted 01-02-2004 15:46
    From John Hartman <pianos@hartmanstudios.net>
    
    Dale wrote:
    >  Ron
    >   I just wanted to say publicly--Thanks . This is a great clarifying 
    > summary. Clarification is always enlightening. Your post also points out 
    > that "the confusion that remains is still how all this stuff 
    > mechanically relates" which is true. At the end of the day we have to 
    > put all this into a useful sytematic practice in rebuilding the actions 
    > we all work on.These discussion  increase our confidence secure better 
    > results for us & perfromance benifits for our clients.
    
    
    Dale,
    
    Several people have complained that this material has just brought more 
      confusion to our understanding of the grand action. That's 
    understandable since the study of the dynamic action is at least ten 
    time more involved that studying the static action. It took many years 
    for the simple static principles Stanwood has developed to be accepted 
    and understood. I would expect these dynamic principles to take a lot 
    longer. The task is especially daunting since getting a mental grasp of 
    how it works requires familiarity with math and physics. I expect that 
    most piano technician's would need to bone up on high school level 
    algebra and physics to gain access to this knowledge.
    
    Even though this is going to be a lot of work, as you said, it can be 
    accomplished one step at a time. The first step is getting the notion of 
    moment of inertia clear in ones mind. Envision a cylinder attached to an 
    axle with a rope wrapped around it. We pull on the rope and the cylinder 
    rotates around its axle. If the cylinder is made from a light material 
    like wood, it is easy to pull the rope. If it is made from a heavy 
    material like steal, it will be hard to pull the rope. The moment of 
    inertia describes how hard it is to pull the rope and get the cylinder 
    to move. Knowing the MOI of the cylinder and the radius we can predict 
    how hard it is to move. We can also know how much tension there is in 
    the rope. With a high MOI the tension is high and with a low MOI the 
    tension is low.
    
    "What the heck does this have to do with pianos John?". Well, if the MOI 
    of the action is high it will feel harder to play. I am not sure if the 
    player could feel this with playing cords slowly at various dynamic 
    levels but it will certainly feel hard to play scales and fast passages. 
    Let's imagine a room full of our cylinders each with a rope attached. 
    Your job is to pull each of these ropes in fast order. It will be a lot 
    easier if they are made of wood rather than steel.
    
    But what about balance weight? Use the cylinder again, but this time 
    wrap another rope around the back side and attach a weight. have a shelf 
    for the weight to rest on. Now when you pull the rope you have a weight 
    to lift along with the inertia of the cylinder. The cylinder doesn't 
    move until the weight is lifted. Go back to the room of cylinders. Would 
    you like to have the wood cylinders with a heavy weight attached or the 
    steel ones with lighter weights?
    
    One of the things learned from studying MOI is just what Balance weight 
    does. It determines (along with friction and let off resistants) the 
    minimum force to move the action. The total force after that is 
    determined by the force required to accelerated the action minus the 
    force of the BW. At very soft levels of playing the BW will be a 
    significant part of the total force while at forceful levels the balance 
    weight is insignificant. Through the dynamic range of playing the force 
    needed to accelerate the action increases while force to overcome the BW 
    stays the same.
    
    Hope this attempt at a non math explanation helps.
    
    
    John Hartman RPT
    
    
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 53.  Moment of Inertia of grand action parts.

    Posted 01-02-2004 16:45
    From Richard Brekne <Richard.Brekne@grieg.uib.no>
    
    John
    
    Another nice post from one who probably will be amoung those who will
    lead us beyond where Stanwood left us er.. balanced as it were. A couple
    comments below.
    
    John Hartman wrote:
    > 
    > 
    > Several people have complained that this material has just brought more
    > confusion to our understanding of the grand action. That's
    > understandable since the study of the dynamic action is at least ten
    > time more involved that studying the static action. It took many years
    > for the simple static principles Stanwood has developed to be accepted
    > and understood. I would expect these dynamic principles to take a lot
    > longer. The task is especially daunting since getting a mental grasp of
    > how it works requires familiarity with math and physics. I expect that
    > most piano technician's would need to bone up on high school level
    > algebra and physics to gain access to this knowledge.
    
    One of the things we are going to end up needing is a very clear and
    simple way of measuring action MOI, comparing to a reference base ala
    Stanwoods Smart Chart... or something in the same spirit, and choose
    what hammer weights, ratio, and key leading will give us the particular
    performance characteristics we are after at any given time. This is one
    of the huge plusses with Stanwoods system, as far as that goes. It is
    very easy to understand, very easy to implement, and accomplishes
    exactly what it sets out to do, and not really a lot more. And, as with
    his system, you can sit down as I and a few others have, and figure out
    exactly what his formula is and how he arrived at it, or you can simply
    follow Stanwoods  <<yellow brick road>> as it were and pay for
    consultant services.  Either way, any system for balancing the action
    will have to be just as easy to implement. 
    
    
    > One of the things learned from studying MOI is just what Balance weight
    > does. It determines (along with friction and let off resistants) the
    > minimum force to move the action. The total force after that is
    > determined by the force required to accelerated the action minus the
    > force of the BW. At very soft levels of playing the BW will be a
    > significant part of the total force while at forceful levels the balance
    > weight is insignificant. Through the dynamic range of playing the force
    > needed to accelerate the action increases while force to overcome the BW
    > stays the same.
    
    An interesting comment and perspective on Balance Weight, and what
    follows. I havent had time to really look at your last diagrams, and
    posts which address a few of the questions I had about how leverage
    works into this equation, but I will get to it. Thanks again for your
    many thoughts and perspectives John.
    > 
    > 
    > John Hartman RPT
    > 
    Cheers
    RicB
    


  • 54.  Moment of Inertia of grand action parts.

    Posted 01-02-2004 21:34
    From John Hartman <pianos@hartmanstudios.net>
    
    Richard Brekne wrote:
    
    > 
    > One of the things we are going to end up needing is a very clear and
    > simple way of measuring action MOI, comparing to a reference base ala
    > Stanwoods Smart Chart... or something in the same spirit, and choose
    > what hammer weights, ratio, and key leading will give us the particular
    > performance characteristics we are after at any given time. 
    
    Well Richard,
    
    That would be nice but I don't think any simple process will come out of 
    this adventure. I think getting the action reasonably accurate in terms 
    of static balance is useful. It helps to make the action feel even at 
    soft levels of play. Once the action is played with more force many more 
    variables come into play and things become rather messy. To get the 
    action to play from note to note perfectly evenly at loader levels we 
    need to control things like the differences in key stiffness. Looking at 
    the difference between the naturals and sharps I don't think that is 
    going to be practical. I think the benefit to learning this stuff is in 
    guidance with the relative importance of some of the thinks we do to 
    actions. It will help to tell us what to pay attention to and what to 
    leave alone.
    
    John Hartman RPT
    
    John Hartman Pianos
    www.pianos.hartmanstudios.net
    Rebuilding Steinway and Mason & Hamlin
    Grand Pianos Since 1979
    
    Piano Technicians Journal
    Journal Illustrator/Contributing Editor
    www.journal.hartmanstudios.net
    


  • 55.  Moment of Inertia of grand action parts.

    Posted 01-03-2004 03:40
    From Richard Brekne <Richard.Brekne@grieg.uib.no>
    
    Hmm... 
    
    I dont really see why some useful and easy to implement method should be
    too awfully difficult to work out John, tho to be sure it depends on
    just what you are trying to do. That said there have been quite a few
    points drawn out that allow themselves to be rather easily quantified or
    measured. When thats doable, arranging these same on a scale gives a
    reference from which purposeful planning can be drawn. 
    
    That is essentially what Stanwoods system did. His so called equation of
    Balance is simply a set of measurable parameters that fit into an
    equation. Quantities such as Strike Weight and Front Weight have been
    scaled on graphical charts in reference to that same equation. It all
    adds up to a set of guidelines about static balance weight where a few
    cause/effect relationships are clearly shown. There is little or nothing
    in his formula per se that points to what SHOULD be. That depends
    largely on what one is after to begin with. It DOES show you how to get
    there once you've decided. Unfortunantly, it leaves out relevant
    information and guidlines as to the subject of action inertia,
    compliance, and other relavant overall ratios.
    
    In anycase, I would not be a bit suprised to see a <<next step>> system
    appear in the not to distant future.
    
    Cheers
    RicB
    
    
    
    John Hartman wrote:
    > 
    > Richard Brekne wrote:
    > 
    > >
    > > One of the things we are going to end up needing is a very clear and
    > > simple way of measuring action MOI, comparing to a reference base ala
    > > Stanwoods Smart Chart... or something in the same spirit, and choose
    > > what hammer weights, ratio, and key leading will give us the particular
    > > performance characteristics we are after at any given time.
    > 
    > Well Richard,
    > 
    > That would be nice but I don't think any simple process will come out of
    > this adventure. I think getting the action reasonably accurate in terms
    > of static balance is useful. It helps to make the action feel even at
    > soft levels of play. Once the action is played with more force many more
    > variables come into play and things become rather messy. To get the
    > action to play from note to note perfectly evenly at loader levels we
    > need to control things like the differences in key stiffness. Looking at
    > the difference between the naturals and sharps I don't think that is
    > going to be practical. I think the benefit to learning this stuff is in
    > guidance with the relative importance of some of the thinks we do to
    > actions. It will help to tell us what to pay attention to and what to
    > leave alone.
    > 
    > John Hartman RPT
    > 
    > John Hartman Pianos
    > www.pianos.hartmanstudios.net
    > Rebuilding Steinway and Mason & Hamlin
    > Grand Pianos Since 1979
    > 
    > Piano Technicians Journal
    > Journal Illustrator/Contributing Editor
    > www.journal.hartmanstudios.net
    > 
    > _______________________________________________
    > pianotech list info: http://www.ptg.org/mailman/listinfo/pianotech
    


  • 56.  Moment of Inertia of grand action parts.

    Posted 01-02-2004 23:18
    From Ron Nossaman <RNossaman@cox.net>
    
    >I think the benefit to learning this stuff is in guidance with the 
    >relative importance of some of the thinks we do to actions. It will help 
    >to tell us what to pay attention to and what to leave alone.
    >
    >John Hartman RPT
    
    
    Absolutely.
    
    Ron N