MgR/I is useless!

Discussion in 'Racquets' started by stoneage, Oct 9, 2010.

  1. stoneage

    stoneage Rookie

    Apr 8, 2010
    Stockholm, Sweden
    Sorry for starting another thread and sorry for the harsh title. But as I will hopefully show below, well founded. The relation MgR/I has has been kicked around as a supposedly good help to customize a racquet. I didn't find any information about why this would work, so I decided to dig a little deeper into equation. Unfortunately it turns out that it gives an infinite number of racquet configurations, most of them useless.

    First a general observation: The laws of mechanics have been used fairly successfully for a couple of hundred years to describe more advanced objects than a swinging tennis racquet. The parameters you need to describe how a racquet behaves when a force is applied to it, is mass, center of mass and MOI (moment of inertia/swing weight). If you take two of these parameters and divide by the third, you don't gain any information, but you loose a lot!

    If you assume that you want to keep MgR/I constant (e.g. =21) and we are playing on earth so g is constant we end up with MR/I = c where c is a constant (for example c=21/981= 0.214 if we talk kg and cm).

    Further assume that we have a racquet with mass m0, center of gravity r0 and MOI I0 to which we ad a number N of point weights mi at a distance ri. We then get (MOI for a point weight is m*r^2):


    Here we already see a scary thing. Any weight added at r=0 doesn't contribute to the total MR/I at all, which means that the idea of MR/I being a description of mass distribution falls apart. And anyone who thinks that adding a 1 kg lump to the handle of a racquet doesn't affect the playability raise a hand.

    Further, since we want to keep c constant while adding weights we can simplify the above expression to:


    This is the relation that added weights should fulfill to keep MR/I constant. Let us look at some practical cases.

    1. Adding one weight means that the relation is m*r=c*mr^2
    This has two solutions one is r=0 (as said before) the other is r=1/c. This means that you can add any weight you want at r=0 or r= 46.7 cm but nowhere else!

    2. Two weights. The idea behind the concept is to add a weight to increase swingweight, then tweak it a little to achieve the right MgR/I. So lets add a first weight of 30g at the top of the racquet, say at 70 cm. You then end up with a relation for the second weight to fulfill:
    0.03*70+m*r=c*(0.03*70*70+m*r^2) which can be simplified to
    If you plot the relation between m and r for the second weight you get:


    This means that you have have an infinite number of solutions for r<46.7 giving very varying combination of m and r. Which in its turn leads to huge differences in mass and swingweight of racquets that fulfills MgR/I=21

    The conclusion is thus:

    1. MgR/I does not describe any mechanical behavior of the racquet (apart from being proportional to swing time of if you hold the racquet at the but and let it swing like a pendulum)

    2. MgR/I does not describe the mass distribution

    3. Using MgR/I=const leads to an infinite number of very varying solutions making it impossible to use as a design criterion.


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  2. travlerajm

    travlerajm Hall of Fame

    Mar 14, 2006
    Actually, I use the fact that MgR/I stays constant when I add mass to the buttcap to my advantage. Once I have MgR/I tuned for my forehand by adding weight to the top of the handle, I can subsequently tune the MgR/I value for my 2hb by adding additonal mass to the end of the buttcap (assuming the 2hb MgR/I needs to be reduced) without disturbing the tuned MgR/I value for forehand. This method allows me to tune a racquet for both wings when I don't have the luxury of a scale or yardstick.

    Of course adding 1kg to the butt will affect playability, but we're only dealing with weights and balances within the very narrow range that is practical for a tennis racquet. And within that range, there exists an optimal MgR/I value for each of your groundstrokes.
  3. cellofaan

    cellofaan Semi-Pro

    Jul 13, 2009
    1. I thought that pendulum swing property was the whole point of the formula. Adjusting its natural (pendulum)swing to somehow match or cooperate with your personal tennis swing.

    3. It does lead to an infinite number of solutions, but it also excludes a lot of other combinations.

    So, what I'm trying to say is, while all your statements and eamples are true, I don't agree that it is completely useless, as it does provide information.
    Your opinion is that the relation between swing time for a pendulum and a tennis swing have no relation what so ever and changing the first does not affect the other, but the whole theory as far as I understand it, is based on the assumption that it does.
    When that assumption has been made, it is usefull as it excludes a lot of configurations, and in practice, there is a relatively limited number of reaching 21 (though the actual value is supposed to be different for different people) without adding large amounts of weight.
  4. Big Boris

    Big Boris Rookie

    Nov 2, 2006
    MgR/I works!! (but might need some fine tuning)

    I had a frame I really liked. It looped kind of by itself through the swing giving me spin and ability to get my racket fast to rapid incoming balls. But I thought it lacked power and stability. So I brought it up some 10 SW points using an Excel calculator from these forums combined with your MgR/I equations to keep the MgR/I exactly constant. First time I played after that modification was great. Almost no problems adjusting and massive power and stability. But continuing to play with that frame my strokes have lost some quality in comparison to the first. Maybe this is because my new set up does not force or steer my strokes into the same loops. I tend more to hit straight through the ball and have some trouble getting spin on my drives. I tend to hit too much straight back and forward instead of getting a natural high backswing then drop and up and around. So my new frame performs well but is maybe no good practice tool so to say.

    Could this be adjustable via lead in the but or other adjustments like bringing the MgR/I down a bit to "feel" the racquet head better?

    Also I have noticed my main problems are on forehands whereas my 1HB has stayed rather good I think. Could there be different optimal MgR/Is also for 1HB and FH?
  5. courtking

    courtking Semi-Pro

    Jan 31, 2010
    woow.. I thought i was reading the calculus forum or wrong thread.. this is some serious math..
  6. callmethedoctor

    callmethedoctor Banned

    Jan 14, 2010
    Wait, what's the formula for anyways? (algebra 2/geom/trig student here)
  7. sureshs

    sureshs Bionic Poster

    Oct 1, 2005
    I am not sure why someone is surprised that adding weight at r = 0 is counter intuitive. It depends on how you look at it. If a thin guy vs a fat guy sits exactly in the middle of a seesaw, it does not affect its behavior. Of course, if you try to move the see saw by shifting it, it will make a difference. That does not mean moments and torque and center of mass are meaningless.

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