DIY - Matching rackets

Irvin

Irvin

Talk Tennis Guru
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 (0-dimensional) 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 impossible 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 -

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?
 
Last edited:
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.
 
Last edited:
It has been brought to my attention the video stops about 7 minutes short. I will do the videos over.
 
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.
Click to expand...

First, I would like to say that this write up and video are very good.

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.
 
WHS1983 said:
First, I would like to say that this write up and video are very good.

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.
Click to expand...

He's throwing crap against the wall and seeing what sticks.

It's all amateur gibberish, IMO.

If one wants to get good at customizing racquets, you need the right tools (RDC, Tuning Center, etc.)
 
WHS1983 said:
First, I would like to say that this write up and video are very good.

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.
Click to expand...

You are correct assuming the length of the two rackets are the same and that's should be a given anyway. If the lengths are slightly off or the point you're using for the axis are rounded up/down to the same SW, the SW may be farther off at a different length. Assume racket 1 rounds down to a MMOI of 170 and racket two rounds up to 170. When you calculate the MOI from another axis say the 10 cm point there could be a greater difference. If you're trying to match rackets it should not matter which point you use for the axis of rotation. It could be the balance point, 10 cm, 4 inches, or the end of the butt cap. A difference of a few grams in weight, or Kgcm^2 in SW, or a mm in balance isn't going to be noticeable anyway. Whatever the statement I made was wrong.
 
Last edited:
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.
 
I know this thread is old but Im sure people could still get use out of it (Unless there is a newer better thread i do not know of) But anyways, @Irvin do you know if there are any android apps I could use in place of swingtool? It is not available for android
 
Sorry I don't think there is one. Sten tried to make one but there was not enough interest in it so he dropped it.
 
mfpeden said:
Tennis warehouse has a swingweight calculator, you swing your racket in the same way as the apps, but clock the time manually with a stopwatch.

Sent from my Nexus 5X using Tapatalk
Click to expand...
Alright thanks! Ill check it out! If not, will the swingweight not be similar if the balance and weights are the same?
 
WisconsinPlayer said:
what would you advise then? Should i just use my balance board and scale to match the balance and weight?
Click to expand...
That is a good option but matching the SW / Inertia is a better option. Use the TW SW calculator and measure the periods of the rackets swinging from the top string with the stop watch on your phone.
 
Irvin said:
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 (0-dimensional) 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 -

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?
Click to expand...

Irvin said:
You are correct assuming the length of the two rackets are the same and that's should be a given anyway. If the lengths are slightly off or the point you're using for the axis are rounded up/down to the same SW, the SW may be farther off at a different length. Assume racket 1 rounds down to a MMOI of 170 and racket two rounds up to 170. When you calculate the MOI from another axis say the 10 cm point there could be a greater difference. If you're trying to match rackets it should not matter which point you use for the axis of rotation. It could be the balance point, 10 cm, 4 inches, or the end of the butt cap. A difference of a few grams in weight, or Kgcm^2 in SW, or a mm in balance isn't going to be noticeable anyway. Whatever the statement I made was wrong.
Click to expand...

Since this got resurrected, might as well update that.

Didn't really notice the errors you made in the video since I wasn't fully focused on it (just glanced at the equipment to you used and what accuracy you measure to), but you could probably lay our the mistakes in another section for those new to racket modding.
 
xFullCourtTenniSx said:
Since this got resurrected, might as well update that.

Didn't really notice the errors you made in the video since I wasn't fully focused on it (just glanced at the equipment to you used and what accuracy you measure to), but you could probably lay our the mistakes in another section for those new to racket modding.
Click to expand...
Rather than me reading all that again why don't you just tell me what you think is wrong.
 
Irvin said:
Rather than me reading all that again why don't you just tell me what you think is wrong.
Click to expand...

Bolded the section for you in the first quote.

"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."
 
xFullCourtTenniSx said:
Bolded the section for you in the first quote.

"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."
Click to expand...
You are correct that's impossible and I corrected that. Good catch. I changed possible to impossible. Assuming we are not talking about small errors introduced when rounding off.
 
Irvin said:
You are correct that's impossible and I corrected that. Good catch. I changed possible to impossible. Assuming we are not talking about small errors introduced when rounding off.
Click to expand...

Someone else technically noticed it before I did. But when I read it my mind blew up a bit and I was checking my math and looking at the parallel axis theorem and trying to mathematically break it. Then I looked down and saw someone else noticed the same thing and breathed a sigh of relief.

And of course, there will always be error because there will always be a level of error in the measurements (and therefore any calculations done with them, including inertia calculations). All you can really do is do your best to keep the errors to a minimum and be mindful of how large the errors are and try to keep them in an acceptable range. No two objects will ever be perfect clones, but we can do our best to make to make them seem like they are.
 
No two objects will ever be perfect clones? Maybe not but with a $10 scale you should be able to get the weight within +/-0.1 g, with a $2 app you can measure the period to within +/-0.002 seconds, and with a homemade balance board you can easily get the balance within +/-0.5 mm.
 
@Irvin apologies if this has been covered before, how does the kg cm2 figure relate to the simple swingweight number provided by manufacturers and how can you convert kg cm2 to this number? Thanks.
 
irish-phil said:
@Irvin apologies if this has been covered before, how does the kg cm2 figure relate to the simple swingweight number provided by manufacturers and how can you convert kg cm2 to this number? Thanks.
Click to expand...
I'm not really sure I understand you question so let me just explain inertia. Inertia is property of matter where it wants to stay in it present state. Does no matter if the matter is at rest or in motion. If the matter is at rest it takes some force to move it and if it is in motion it take some force to stop it. In then is we measure that for in kgcm^2 units. In other arena the SI units are Kgm^2 but that's too large for our 300+ g rackets with lengths in cm we use.

The inertia (at center of mass aka Icm) of a racket (physical pendulum) is the sum of the mass points tines the square of the distance from the COM of each point mass. But we can't pivot a physical pendulum from the COM because that's the point of equilibrium when systemded from the COM it won't move. So we have to suspend it from some other point. If you have an RDC the racket is suspended from the handle. If you use the TW calculator the racket is suspended from a cross string. At rest the COM will always be below the support or pivot.

One you support the racket and get it oscillating you can measure the period of oscillations. The period is dependent on the distance between the COM and pivot and the inertia around the pivot. So the formulas we use allow to measure inertia. In tennis inertia is also call swing weight. So let's assume we measure the inertia from the top cross string and that string is 32 cm from the COM, the racket weight is 333 g, and the SW is 500 kgcm^2. We can use a parallel axis theorem to determine the Icm. We know the pivot is 32 cm above the COM and the racket weighs .333 kg. I'm using SWp as the SW at the pivot. Icm = SWp - mdd = 500 - (0.333*32*32 = 159. Now that we have the Icm we can easily determine the SW at any other point. Let determine the SW for this racket at 10 cm which is the industry standard. SW @ 10 cm = Icm + mdd = 159 + (.333*22*22) = 320.

So now all the mumbo jumbo means is the SW is the mass in kg time the square of the distance from the axis to COM plus the Inertia at the COM. I hope that's not too confusing.
 
Irvin said:
I'm not really sure I understand you question so let me just explain inertia. Inertia is property of matter where it wants to stay in it present state. Does no matter if the matter is at rest or in motion. If the matter is at rest it takes some force to move it and if it is in motion it take some force to stop it. In then is we measure that for in kgcm^2 units. In other arena the SI units are Kgm^2 but that's too large for our 300+ g rackets with lengths in cm we use.

The inertia (at center of mass aka Icm) of a racket (physical pendulum) is the sum of the mass points tines the square of the distance from the COM of each point mass. But we can't pivot a physical pendulum from the COM because that's the point of equilibrium when systemded from the COM it won't move. So we have to suspend it from some other point. If you have an RDC the racket is suspended from the handle. If you use the TW calculator the racket is suspended from a cross string. At rest the COM will always be below the support or pivot.

One you support the racket and get it oscillating you can measure the period of oscillations. The period is dependent on the distance between the COM and pivot and the inertia around the pivot. So the formulas we use allow to measure inertia. In tennis inertia is also call swing weight. So let's assume we measure the inertia from the top cross string and that string is 32 cm from the COM, the racket weight is 333 g, and the SW is 500 kgcm^2. We can use a parallel axis theorem to determine the Icm. We know the pivot is 32 cm above the COM and the racket weighs .333 kg. I'm using SWp as the SW at the pivot. Icm = SWp - mdd = 500 - (0.333*32*32 = 159. Now that we have the Icm we can easily determine the SW at any other point. Let determine the SW for this racket at 10 cm which is the industry standard. SW @ 10 cm = Icm + mdd = 159 + (.333*22*22) = 320.

So now all the mumbo jumbo means is the SW is the mass in kg time the square of the distance from the axis to COM plus the Inertia at the COM. I hope that's not too confusing.
Click to expand...

Thanks for explaining that. So in effect, using something like the stringway calculator

https://www.stringwaynederland.nl/SW-TA-online/SwingCalc/index-en.php

where you input length, balance point and weight and get a figure in kg cm2 can't be used to then determine swingweight without some additional info, is that correct?
 
Hi Irvin, I tried this method on the attempt to match 2 Head Graphene Prestige MP rackets, I stringed only 3 horizontal strings at a really low tension on both rackets trying to be as close to unstrung specs as possible only adding 1,4 grams to the rackets, I ended up having both rackets with this specs: 1) 329,1g - 30,7cm - 161 (moment of inertia) 2) 329,0g - 30,7cm - 162. Do you think the job is done or is it worth trying to match the moment of inertia to the exactly same value? btw sorry for bringing the thread back to life, I'll post photos of the lead placement later just for those who are interested on the whole racket matching thing
 
That’s probably close enough @Dufur719. Next time put an @ symbol in front of my name so I’ll be notified because I don’t watch this forum much. Or PM me.
 
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