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10022014, 12:30 PM  #1 
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

DIY  Matching rackets
I have made a jig I use for matching racket using Sten Kaiser’s SwingTool app on my iPad. Before I show the jig and how it is used I would like to discuss a few key basic terms. The items you will need to make the jig are:
1  1”x4” board about 24” long 2 – 1”x4” board about 7.5” long (Optional) 1  5 gallon paint paddle 1  3/8” dowel about 12” long 2  cup hooks for SW 2  cup hooks or nails for TW (optional) Wood glue SwingTool app or a stop watch Center of Mass / Balance Point The Center of Mass (also referred to as the balance point) is a unique point where the weighted relative position of the distributed mass sums to zero. The weight on each side does not have to be the same on both sides of the balance point. Imagine two children on a seesaw if the heavier child is closer to the pivot point the seesaw will balance and each child can push the seesaw up and down. The center of mass in a rigid body (like a tennis racket) does not have to be in the center of the racket. If one side weight more than the other the center of mass will be closer to that side. Often times tennis rackets will be Head Light (HL) indicating the lower portion of the racket has more mass than the upper portion. If the greater amount of mass is located in the head of the racket the racket will be Head Heavy (HH.) Often a racket’s balance point is said to be a center number of point HL or HH. Each point is 1/8” so if a 27” racket is 5 pts HL and the center of the racket is 13.5”, the center of mass will be 12.875” from the butt end (13.5” – 5/8” = 12.875”. To use the SwingTool app the balance point is measured in either inches or cm from the butt end of the racket. I prefer to use cm so a 27” racket 5 pts HL would have a balance point of 32.7 cm. I don’t use any conversions I just measure it with the jig and a tape measure capable of measuring in cm. You could also use a scale to calculate the balance point that that takes a little long in my opinion and may not be as accurate. Once I find the balance point or Center of Mass if I add the same mass at the same distance from the balance point the balance point does not change. Or if the products of the mass and distance of the weight from the balance point are the same the balance point does not change. For instance, If I add 5 grams of mass on each side of the balance point the balance point does not change. If I add 10 grams of mass 20 cm from the balance point on one side and 20 grams of mass 10 cm on the other side because the products are both 200 gcm the balance point does not change. Moment of Inertia The Moment of Inertia is the mass property of a rigid body (such as a tennis racket) that determines the torque needed for a desired angular acceleration about an axis of rotation. The moment of inertia is the sum of all the elemental point masses each multiplied by the square of its perpendicular distance to an axis. A larger moment of inertia around a given axis requires more torque to increase the rotation, or to stop the rotation, of a body like a tennis racket about that axis. NOTE: A geometric (0dimensional) point that may be assigned a finite mass. Since a point has zero volume, the density of a point mass having a finite mass is infinite, so point masses do not exist in reality. However, it is often a useful simplification in real problems to consider bodies point masses, especially when the dimensions of the bodies are much less than the distances among them. The Moment of Inertia is dependent upon the amount of mass and the distribution of that mass along the rigid body. The more the mass is distributed to the outer ends of the rigid and the higher the mass the higher the moment of inertia will be. The more the mass is distributed to the axis point and the lower the mass the lower the moment of inertia will be. To find the moment of inertia you must put the rigid body in motion so that it is rotating around the axis in question or around an axis parallel to the axis in question. For instance, If you want to find the swing weight of a tennis racket you should rotate the racket so the axis is parallel to the cross strings in the racket. If you want to find the twist weight of a tennis racket you should rotate the racket so the axis is parallel to the center line from the butt cap to the head of the racket. Because the mass in a tennis racket is farther from the center of mass with computing the swing weight than it is when computing the twist weight the swing weight of a tennis racket will always be higher than the twist weight. Parallel Axis Theorem The parallel axis theorem can be used to determine the mass moment of inertia of a rigid body about any axis. The mass moment of inertia is computed using the center of mass and is sometimes referred to as the first moment of inertia. In tennis specifications a more common term is the second moment of inertia commonly referred to as the swing weight. (Twist weight is actually calculated around the center line axis from the butt cap to the head of the racket.) To calculate a second moment of inertia you would use the formula: SW = mr2 + I Where SW = Swing Weight m = mass of the racket in Kg r = distance from SW axis to the center of mass I = moment of inertia If the SW, balance point, mass, and axis is known you may use the following equation to find the racket’s moment of inertia. I = SW – mr2 NOTE: I have measure the pivot point on a Babolat RDC machine and it was 9.8 cm not 10 cm. The RDC could use the parallel axis theorem to compute the SW at 10 cm though. Other machines or systems could use any pivot point for the SW some use 10 cm others 4”. Swing Weight Swing weight is a numerical indicator that identifies how much torque is required to rotate a racket around an axis. Often the axis is 10 cm and the measurement is Kgcm2. There is much debate on where the axis for SW should be measured. Personally I do not feel that it is possible to rotate a racket in a normal tennis stroke at 10 cm. Also the actual axis point for different players would be different dependent on their stroke and height. It is possible for the balance, weight, and SW for a two or more rackets to be identical for a given axis and the moment of inertia could be different. It is impossible for the balance, weight, and moment of inertia of two or more rackets to be identical and the SW is different. If you ever add the same masses at the same points on two or more rackets where the balance, weight, and moment of inertia were all the same everything will be the same after the addition of the masses. For these reasons I suggest never using swing weight to match up rackets but instead use the moment of inertia. The balance point and weight ensure the feel of the rackets are the same and the moment of inertia insures the distribution of weight is the same. Video for making measurements Here is an updated complete video  http://youtu.be/VfB8oy9CGMc There are some glaring errors in the video but they are so obvious I choose not to correct them because of the length of time it would take, sorry for that. Questions / Comments?
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 Last edited by Irvin : 10032014 at 04:56 PM. 
10022014, 12:39 PM  #2 
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

If you interested in the Swing Weight of those two rackets from the 10 cm axis point they would be 326 for the black handled racket in the video and 311 for the blue handled racket with no modifications. Just use the Parallel Axis Theorem (SW = I + (m*d*d.)
With both racket modified to the same 32.6 balance point and 335 g weight the SW would be 327.
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 Last edited by Irvin : 10022014 at 01:08 PM. 
10032014, 05:04 AM  #3 
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

It has been brought to my attention the video stops about 7 minutes short. I will do the videos over.
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 
10032014, 04:57 PM  #4 
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

Because the old video cut off at 15:00 minutes I had to fix the problem. Here is the updated video. The first 15 minutes are the same.
http://youtu.be/VfB8oy9CGMc
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 Last edited by Irvin : 10042014 at 05:10 AM. 
10032014, 10:30 PM  #5 
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Join Date: Jul 2014
Location: Wisconsin
Posts: 181

Thanks, Irvin!
A great instruction video as usual. Keep up the great work! 
davidhshon 
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10042014, 03:05 PM  #6 
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Join Date: Feb 2009
Posts: 14

Thank you
Thank you Irvin!!!

10302014, 01:04 PM  #7  
New User
Join Date: Oct 2014
Posts: 1

Quote:
I do have a question though about the statement above. Based on the parallel axis theorem, if SW1=SW2 and mr^2_1=mr^2_2, then I1 has to equal I2. Unless I am missing something, I don't see how the statement above can be true. 

10302014, 07:47 PM  #8  
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Join Date: Feb 2010
Posts: 629

Quote:
It's all amateur gibberish, IMO. If one wants to get good at customizing racquets, you need the right tools (RDC, Tuning Center, etc.) 

floydcouncil 
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10312014, 02:00 AM  #9  
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

Quote:
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 Last edited by Irvin : 10312014 at 02:42 AM. 

11292014, 08:01 AM  #10 
G.O.A.T.
Join Date: Mar 2007
Location: Marietta, Ga
Posts: 10,867

I made a mistake inputting info today in SwingTool and found out a new little trick. Instead of inputting a weight of 362 I fat fingered the keyboard and input 3622. Makes a big difference as the SW came out to be 3,544 on a stock RF97A. After correcting the weight problem the SW measured. So if you're a little on the OCD side you can get ST to measure the SW to .1 Kgcm^2 by inputting the weight x 10 as your SW will be 10 times as great though. I did not know ST would go that high.
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Everyone has the right to be stupid... it's just that some people abuse the privilege... Balance  31.0 cm, Weight  358 g, SW  346 Kgcm^2 

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