Home made swingweight machine emulating Babolat RDC/Prince PTC - a fully working one. Total cost roughly $10...

[jmnk]

So that whole pandemic lock-down, free time, and curiosity made me think about building a swingweight machine. Originally I just wanted to emulate RDC frame stiffness measurement - but once that was done I was sort of unsatisfied on multiple levels. First - it was too easy to make . Second - since Babolat does not say what the stiffness number mean, and trying to get empirical data from folks owning such a machine gave inconclusive results, it was hard to tell if it 'works'. I mean it surely measures the stiffness - just it is hard to tell how it correlates with Babolat RA number.

Anyway, onto the swingweight measuring machine. Few disclaimers. I'm an avid user of an excellent SwingTool app by Sten Kaiser (@stoneage) That tool is absolutely great, gives very accurate results, no complains whatsoever. The only thing is that it is somewhat cumbersome to use: you need to accurately measure the weight, the balance, the distances - and each of those can introduce an error. Then you have to put in the numbers in the app, possibly different numbers for each racket. It is still easy enough to use if you want to measure a racket or two. But if you have many rackets you want to measure it becomes a bit cumbersome. Still, great tool.

My machine is by no means 'better' than that tool, just easier to use.

The idea came from watching how Prince PTC works, and few research papers that confirmed that Babolat RDC works pretty much the exactly same way. After several hours in the garage, plus a semi-working prototype, the second creation came out fairly nicely. It is as accurate as RDC.

As the video shows it still uses that excellent SwingTool app to give me the result. Originally I've used it only as a means to measure the oscillation period after which I had to do some math calculations - but a bit of thinking made me realize that I can make it so that app will tell me swingweight outright. (so technically speaking it is about $10 plus the cost of an used old iPhone)

I'll describe some details and physics behind it later.

 

[jmnk]

Parts:
A disclaimer: it was supposed to be a second prototype so I did not exactly pre-planned all the parts. Rather it was 'hmm, that thing in one of the bins in the garage looks like it could be used, let's try that'. But that prototype worked so well that I decided just F**k it, that's all it is going to be.

1. Base - a piece of wood. I went overboard and also added four rubber legs underneath. You know, expensive touch.
2. Spring holder - that is I think light fixture crossbar, something along this part https://images.homedepot-static.com...electric-ceiling-light-parts-81775-64_400.jpg It's just a piece of metal with two sturdy studs about 4-5 inches apart.
3. Metal electric box to serve as the main housing. Anything sturdy will work. Something along this https://images.homedepot-static.com...0b2b4f53e/svn/boxes-brackets-8660-64_1000.jpg
4. a bolt holding an old rollerblade wheel. Just the proper size so it can go through but fit tightly in the rolleblade wheel bearing.
5. The rollerblade wheel with bearing is a crucial part. The whole apparatus must oscillate freely so you need to avoid any friction. These wheels have usually two bearings - make sure it all spins very, very well.
6. Metal bracket so I can attach the rest of the apparatus to the wheel. Some random piece of metal I've shaped to fit over the wheel.
7. The wheel + bracket rotates freely around the bolt.
8. The thingy that will hold the racket. Another piece of random wood. With drilled holes to fit the rollerblade wheel+bracket. The bigger hole in the middle is there so it can rotate around the bolt.
9. The backtop. A random L shaped piece of metal.
10. Whatever you can think that will hold the racket tightly. I've started with velcro but it was not rigid enough. So constructed this thingy with the screw on top - it will press the racket down and hold it nicely.
11. Springs - another very crucial element. That was very much trial and error. You need two identical ones. I had some laying around, tried various ones used for screen doors. It turned out that the springs used in these work lamps are the best - like this https://www.ikea.com/us/en/images/p...th-light-bulb__0609306_PE684440_S5.JPG?f=xxxl . These springs need to be just right so the whole thing, with the racket attached, will oscillate ~15 times at least.
12. cover - that is an old watering can. It has cutouts made so yo can't swing the racket too much.

I think that's pretty much it.

 

[jmnk]

Construction:
Start with a base, probably around 12inches x 6inches. Drill the whole through the electrical box and attach the bolt - that needs to be super solid and rigid. Screw the electrical box solid into the base roughly in the center of the base.

The rollerblade wheel with bearings goes onto the bolt. I had some rolleblade spacer added so the wheel stays above the box as seen in the picture. Again, super important that it spins around the bolt very freely. I put three smaller bolts through the wheel - those plus the metal bracket on top of the wheel will hold the piece of wood that holds the racket.
In addition there are also bolts protruding sideways from the bracket - that's where the springs are attached.

The top part needs to be rigidly secured to the wheel/bracket . The backstop is exactly 10cm (~4inches) from the pivot point - because we want to measure the swingweight around an axis 10cm from the end of the racket (I mean it could be any other distance too - but it would make calibration/calculations a bit more complicated).

The distance of spring-holding studs to the main part is trial and error, it depends on the springs you have. I made it adjustable. The goal is to have the apparatus to oscillate roughly 15-17 times at least because that is what SwingTool app needs.

Cover goes over the main box+wheel. I made cutouts in that cover such that those protruding bolts would prevent the swing to be too big.

Then you need something holding an iPhone running SwingTool. I've used camera tripod. The eye of the camera is exactly over the edge of the frame so the app can easily detect the oscillation.
That's all as far as constructions.

Again, and I can't stress it enough, there are two things that really matter:

1. Very good bearings to eliminate as much friction as possible.
2. Springs that are just right force-wise that the whole thing will oscillate nicely. I was tinkering with concentric spring, like the ones used in old big pendulum clocks, it seemed better suited to provide consistent force - but since both Prince PTC and Babolat RDC just use plain compression springs I figured it must work too. And it does.

Next part - calibration and the physics behind the whole thing. That is actually fun too.
Math and Physics Part 1. Admittedly not for the faint of heart:

 

[First Serve]

From an engineering standpoint impressive.

But to a layman coming into a shop to buy a racquet what does this info tell me.

For instance when I size a friend for a new racquet, I usually advise them on total weight in grams, Head light rating, head size and number of mains and crosses for control and topspin.

 

[Irvin]

How did you make the pivot or racket holder?

 

[Crozzer95]

Following this!! Seems interesting

 

[Irvin]

@jmnk I use SwingTool also. I had trouble getting ST to focus on the racket with an object close behind it. How do you get away from that with the setup you have? Your setup also does not appear to having the racket oscillate by gravity because it looks like it’s on a horizontal plain. How do you get ST to account for a different force oscillating the racket?

 

[zipplock]

So that whole pandemic lock-down, free time, and curiosity made me think about building a swingweight machine. Originally I just wanted to emulate RDC frame stiffness measurement - but once that was done I was sort of unsatisfied on multiple levels. First - it was too easy to make . Second - since Babolat does not say what the stiffness number mean, and trying to get empirical data from folks owning such a machine gave inconclusive results, it was hard to tell if it 'works'. I mean it surely measures the stiffness - just it is hard to tell how it correlates with Babolat RA number.

Anyway, onto the swingweight measuring machine. Few disclaimers. I'm an avid user of an excellent SwingTool app by Sten Kaiser (@stoneage) That tool is absolutely great, gives very accurate results, no complains whatsoever. The only thing is that it is somewhat cumbersome to use: you need to accurately measure the weight, the balance, the distances - and each of those can introduce an error. Then you have to put in the numbers in the app, possibly different numbers for each racket. It is still easy enough to use if you want to measure a racket or two. But if you have many rackets you want to measure it becomes a bit cumbersome. Still, great tool.

My machine is by no means 'better' than that tool, just easier to use.

The idea came from watching how Prince PTC works, and few research papers that confirmed that Babolat RDC works pretty much the exactly same way. After several hours in the garage, plus a semi-working prototype, the second creation came out fairly nicely. It is as accurate as RDC.

As the video shows it still uses that excellent SwingTool app to give me the result. Originally I've used it only as a means to measure the oscillation period after which I had to do some math calculations - but a bit of thinking made me realize that I can make it so that app will tell me swingweight outright. (so technically speaking it is about $10 plus the cost of an used old iPhone)

Home Made Swingweight Machine - photos

I'll describe some details and physics behind it later.

Watching for a "how to" on materials and assembly ...

 

[Tregix]

It looks like the COVID lockdown gave the same idea to a couple of TT members: a DIY SW machine.

The idea is simple, put the racquet in rotation horizontally with a spring and capture the period of oscillation using some kind of angular sensor. The theory tells you that once you measure the period of oscillation T you can get the SW using the following relation:

(SW_racquet + SW_machine) = k x T^2 <===> SW_racquet = k x T^2 - SW_machine

where SW_racquet is the SW of the racquet, SW_machine the SW of the racquet holder the axis and all the moving parts of the machine. k is a parameter linked to the spring stiffness.

There is a very important point here. In order to measure directly the SW, the axis of rotation has to be exactly at 10cm from the end of the racquet handle otherwise you have to make use of the parallel axis theorem to transform the inertia you are measuring into SW and that makes things very complicated.

I’m using an Hall effect angular sensor and a simple Arduino Uno for the data acquisition and processing.

Anyway, here are the pictures of my SW machine:

A crucial step is to calibrate the machine. The calibration allows you to determine precisly the two coefficients SW_machine and k.

For that you need calibration rods of precisely known SW. I use simple aluminum tubes (there are formulae which give you the inertia from the mass, the length and the diameter of the tube). I mesure the period of oscillation and plot in Excel a graph SW_tube vs T^2

This picture shows you the results of the calibration. The X axis is the measured oscillation period squared (T^2) while the Y axis is the SW of the calibration rods. Here I used 4 different calibration rods.

For determining the two parameters SW_machine and k, the easiest thing is to perform a linear regression in Excel. The first parameter in the equation is k and is proportional to the spring stiffness and the second one is the SW of the machine (SW_machine). In my case the k = 291.61 and SW_machine = 5.58 kg.cm2.

From that you can determine the SW of any racquet, you just have measure the period of oscillation T and replace it in the equation SW_racquet = k x T^2 - SW_machine which is in the case above SW_racquet = 291.61 x T^2 - 5.58

It is actually not that simple to get a very precise measurement of the SW (I mean less than 1 kg.cm2) as you need to measure the period of oscillation T with a very high accuracy. In the case shown here, an error of 1ms in the measurement of T induces an error of 0.6 kg.cm2 in SW. There is also the issue that the period of oscillation usually depends slightly on the amplitude.

------------------
EDIT 2020/11/20: Since this thread is now a sticky, I edited the post to provide more information to the interested viewers.

 

[esm]

Home Made Swingweight Machine - photos

I'll describe some details and physics behind it later.

wow - this is amazing . i have actually been thinking about if a home made version can be done.

when i get some more time, i'd love to take a good look at it again (hopefully you'd given us more details) and i'd love to give it a go.

my immediate question was around the build of the holder and the spring rate required to give enough swing for the durartion of the SW app calculation.

quick q - in your setup, before the start of the SW calculation, which part of the racquet head do you focus with the yellow box on the SW app?

 

[jmnk]

added description of parts - see second post.
added description of assembly - see third post.

 

[Tregix]

The idea came from watching how Prince PTC works, and few research papers that confirmed that Babolat RDC works pretty much the exactly same way. After several hours in the garage, plus a semi-working prototype, the second creation came out fairly nicely. It is as accurate as RDC.

Could you share the info on how the Prince works and also the research papiers you are mentioning. I'm curious.

For my machine, I actually avoided, on purpose, doing bibliography research as my personal challenge was to built one on my own without being influenced by the way Prince, Babolat or Head had done it. But I probably have missed some good ideas ;-).

But man, you are a true MacGyver. I'm impressed !

 

[TennisHunter]

Iam in the same path. I do some 3d printing.

 

[fritzhimself]

................

 

[esm]

Iam in the same path. I do some 3d printing.

Woo - please tell us more

 

[TennisHunter]

My idea is try to do somthing like Roman Prokes machine. I am looking for the best way to put the springs like @jmnk did.

 

[jmnk]

Could you share the info on how the Prince works and also the research papiers you are mentioning. I'm curious.

For my machine, I actually avoided, on purpose, doing bibliography research as my personal challenge was to built one on my own without being influenced by the way Prince, Babolat or Head had done it. But I probably have missed some good ideas ;-).

But man, you are a true MacGyver. I'm impressed !

thanks for kind words. Yes, I'll write it all up as soon as I find few hours and and easy way to write mathematical equations with subscripts and stuff.
I do love your Arduino based setup! And the way you solved racket handle mounting - I need to find such shaped metal piece somewhere.

 

[Tregix]

My idea is try to do somthing like Roman Prokes machine. I am looking for the best way to put the springs like @jmnk did.

I'm puzzled. Roman Prokes machine is not gravity diven? Why is there a need for a spring ? I'm missing something here.

Also It looks like the axis of rotation is not 10cm from the end of the racquet. It means that to get the SW you will have to use the parallel axis theorem, which is not a good idea as you will need the mass and the center of gravity of whole system, that is the racquet holder and the racquet itself... And then get the SW of the racquet itself which is not going to be that straightforward...

 

[jmnk]

My idea is try to do somthing like Roman Prokes machine. I am looking for the best way to put the springs like @jmnk did.

what is a "Roman Prokes machine"?

 

[Tregix]

And the way you solved racket handle mounting - I need to find such shaped metal piece somewhere.

I thought a loooooot about the racquet holder and I think I found a simple and very effective way of holding the racquet . It is actually just two pieces of aluminum glued together. One has a U shape and the other one a V shape. It works very well. And I could also easily set the axis of rotation at 10 cm from the end of the racquet holder with a precision of 0.25 to 0.5 mm. That was important as 1 mm translates roughly in an error in the SW of 0.1 kg.cm2.

 

[Irvin]

what is a "Roman Prokes machine"?

That’s just a thumbnail of his set up from a video. That’s where he is building the rackets for Novak. From the looks of it he just uses gravity to oscillate the racket I doubt there are springs in it.

 

[kkm]

That’s just a thumbnail of his set up from a video. That’s where he is building the rackets for Novak. From the looks of it he just uses gravity to oscillate the racket I doubt there are springs in it.

That machine is from the Jay Schweid era:

US6132326A - Sports implement customizing system - Google Patents

The weight, balance point and swing weight of a sports implement such as a tennis racket can be automatically duplicated using a measuring unit and a computer program that uses data supplied by the measuring unit and data prestored in a database. The measuring unit measures the total weight of a...

patents.google.com

 

[TennisHunter]

That machine is from the Jay Schweid era:

US6132326A - Sports implement customizing system - Google Patents

The weight, balance point and swing weight of a sports implement such as a tennis racket can be automatically duplicated using a measuring unit and a computer program that uses data supplied by the measuring unit and data prestored in a database. The measuring unit measures the total weight of a...

patents.google.com

Excellent information, very nice. Thanks.

 

[kkm]

Could you share the info on how the Prince works and also the research papiers you are mentioning. I'm curious.

For my machine, I actually avoided, on purpose, doing bibliography research as my personal challenge was to built one on my own without being influenced by the way Prince, Babolat or Head had done it. But I probably have missed some good ideas ;-).

But man, you are a true MacGyver. I'm impressed !

Measuring the Inertial Properties of a Tennis Racket

Simple and bifilar pendulum were used to measure the mass moments of inertia of three tennis rackets. The pendulum setups were filmed using an off-the…

www.sciencedirect.com

 

[jmnk]

added description of math + physics, Part 1, in post #3

@Tregix - as far as 'info how Prince PTC works'. I do not have that machine, nor any particular insight into inner parts of that machine - but I've seen videos of it. You can clearly see that they use two compression strings to provide oscillating motion. Then that very paper that @kkm cited, the 'Measuring the inertial properties of a tennis racket' (which I was very familiar with) indeed states that Babolat RDC uses the same principle - which was good to know since on RDC machine everything is hidden so I initially had no idea what it uses. I thought it may be using torsion spring. This paper https://www.3bscientific.com/PhysicsExperiments/UE1040201_EN.pdf also gave me some ideas.

 

[kmocho]

Baolat RDC use se two compression strings to provide oscillating motion too. On pictures on right: https://photos.google.com/share/AF1...?key=YzQ0VjI1a2lhZkpUakkxdG43MWUxYVhWcWNmOHN3

 

[Tregix]

as far as 'info how Prince PTC works'. I do not have that machine, nor any particular insight into inner parts of that machine - but I've seen videos of it. You can clearly see that they use two compression strings to provide oscillating motion.

Baolat RDC use se two compression strings to provide oscillating motion too.

Thanks for the information and the picture . I'm actually testing a single spring and a two springs design. Both work pretty well. I started with the one spring design as I find it simpler but I now have the feeling that the two spring design has some advantages in terms non linearties of the equation (I mean that it is "less" non-linear for large angle, but have to do the math untill the end to be certain...). For the curious, see that paper for the effect of monlinearities on the pendulum period for lagre angle http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/mechan/Pendulo2.pdf

 

[Schrodinger]

It looks like the COVID lockdown gave the same idea to a couple of TT members: a DIY SW machine.

The idea is simple, put the racquet in rotation horizontally with a spring and capture the period of oscillation using an angular sensor. The theory tells you that once you measure the period of oscillation T you can get the SW. I’m using a simple Arduino Uno for the data acquisition and processing.

Anyway, here are the pictures of my SW machine:

A crucial step is to calibrate the machine. For that you need calibration rods of precisely known SW. I use simple aluminum tubes.

This picture shows you the results of the calibration. The X axis is the measured oscillation period squared (T^2) while the Y axis is the SW of the calibration rods. Here I used 4 different calibration rods. The first parameter in the equation is proportional to the spring stiffness and the second one is the SW of the machine (precisly - SW0) without the rod. I.e. the SW of the machine alone is 5.58 kg.cm2 here.

From that you can determine the SW and TW of any racquet, you just have to replace X by T^2

It is actually not that simple to get a very precise measurement of the SW (I mean less than 1 kg.cm2). I have to read the angular sensor at a quite high frequency and probably need a 12 bit ADC (10 bit not good enough...).

Do you have a link to where I could buy the sensor you used?

 

[Tregix]

Do you have a link to where I could buy the sensor you used?

You can find it here:

Gravity: 360 Degree Hall Angle Sensor

This is a miniature non-contact angle sensor which works through hall electromagnetic induction.

www.dfrobot.com

I bought it from Amazon for 22 euros:

Nrpfell Capteur de DéPlacement Angulaire Industriel Sans Contact 0-360 DegréS de Capteur D'Angle une Effet Hall CC 5V : Amazon.fr: Commerce, Industrie et Science

Nrpfell Capteur de DéPlacement Angulaire Industriel Sans Contact 0-360 DegréS de Capteur D'Angle une Effet Hall CC 5V : Amazon.fr: Commerce, Industrie et Science

www.amazon.fr

It can also be found on a number of Chinese websites for even cheaper:

https://m.fr.aliexpress.com/item/32...IXYwzVxJZ61GOP1BovDRgjZAex9RLFaUaAhhGEALw_wcB

 

[esm]

You can find it here:

thanks for these - good option, as i was looking for something similar to "drive" the swing path.
with this Angle sensor - suppose it provides enough power/drive to swing a racquet?
(can we please see yours in action? )

 

[Tregix]

thanks for these - good option, as i was looking for something similar to "drive" the swing path.
with this Angle sensor - suppose it provides enough power/drive to swing a racquet?
(can we please see yours in action? )

It depends on the stiffness of your spring. That will set the period of oscillation. With my one-spring design, the spring is rather stiff (1.2 N/mm) and I have a period T of oscillation of 1.2s. With the two-spring design I use less stiff springs (but more stretchy) and I get an oscillation period of 1.6s.

Here is the machine in action

 

[jason n]

It depends on the stiffness of you spring. That will set the period of oscillation. With my one-spring design, the spring is rather stiff (1.2 N/mm) and I have a period T of oscillation of 1.2s. With the two-spring design I use less stiff springs (but more stretchy) and I get an oscillation period of 1.6s.

Here is the machine in action

Nice job! Are you taking preorders?!
You guys make it look so simple to manufacture, I always wondered why there are not available from the big tennis companies.

 

[jmnk]

For those interested in math and physics of it all - admittedly not the easiest read....

 

[Tregix]

Nice job! Are you taking preorders?!
You guys make it look so simple to manufacture

Thanks !

(...) I always wondered why there are not available from the big tennis companies.

Actually Head has a 3 in 1 SW machine but it costs 1800 euros...

Head 3-in-1 Swingweight Tuning Machine

Buy racquets, strings, bags, grips and accessories online at Racquet Depot UK. It is one of the largest internet resellers of brand name products for tennis, squash, badminton and injury supports.

www.racquetdepot.co.uk

Gamma had a SW machine and it was around 600 to 800 US dollars as far as I remember.

But I agree, I really wonder why Stringway for example @Stringway Official, which is making VERY good stringing machines, is not looking into this. For them it would be a peace of cake to manufacture a SW machine (it is much simpler than a stringing machine) and I think there is a market for that if the price stays reasonable.

 

[Tregix]

(...) That is, mind you a discrepancy of 0.5%. Now, let me tell you, if I ever got such a small error in high school or college for any physics experiment, I would be excused from, the class at lease till the end of the semester.

Lol.

I also realized that there are those super extra sensitive folks that can detect a single swingpoint of a difference between two rackets – so clearly the device is not good enough for them.

As far as I know, when the Babolat Performance Lab is preparing a set of 6 racquets for their profesionnal tennis players it is within 1g, 1mm in balance and 1 point in swingweight. So if it is good enough for them it should good enough for us .

Just a side comment: a 0.5% error on the SW translates into 1.5 kg.cm2 which means an error up to 3 kg.cm2 on the twistweight (TW) measurment. Since the TW varies from 12 to 17 kg.cm2 the TW error measurement would be 20% which is not great. But we usally don't pay much attention to the TW as the SW is a much more important parameter.

But then again nothing will ever be as there’s not even military grade measuring device that is accurate to a 1 kg.cm2 when measuring swingweight in 250-350 range.

You are exaggerating a tiny little bit here Commercial SW machines such as the Head 3 in 1 have an accuracy of 0.5 kg.cm2 which means 0.15%. With my machine I have an accuracy around 0.7 kg.cm2 @ 330 kg.cm2 which means 0.2% and I know how to improve. I'm sure that a true military grade SW machine would be better than 0.1 kg.cm2 (0.03%) .

The thing is that with the Swing Tool app you will never be able to get a better estimation of the SW than +-1.5 kg.cm2 (which is enough I agree). The reason is that the Swing Tool app is making the approximation that the period of oscillation is independante of the amplitute of the oscillation. And this is only true for very small amplitudes (basically when sin(X) = X to a very good precision).

For larger amplitutes you have to take into account corrections. Here is the measurement of the period of oscillations I made (in ms) with respect to the amplitude (in deg) of the oscillations. You see that the periode T increases slightly with the amplitude. Not by a lot but enough to stop you from being able to measure the SW within 0.5 kg.cm2 like a commercial SW machine.

 

[Trinity110]

For those interested in math and physics of it all - admittedly not the easiest read....

Yeah, that's what I thought. ;-)

 

[fritzhimself]

.............

 

[Tregix]

@Tregix
I do not want to disappoint you - the Head SW 3 in 1 can also measure on 0,1kg.cm2.
I also have a RDC - that is 3 points spread between both devices.

0.1 kg.cm2 is extremely good. It's possible but I am surprised as it is rated at an accuracy of 0.5 kg.cm2 here:

http://www.apolloleisure.co.uk/default.cfm/sect.2/manu.6

But if it is true I would have to work much harder on my own machine to get to the same level ;-)

Regarding your second comment, it does not surprise me. Did you calibrate your machines recently? Also, there is a calibration rod with the Head. Did you try to measure its SW with the RDC and the Head? I'm curious to know what are the results.

 

[fritzhimself]

..................

 

[fritzhimself]

....................

 

[jmnk]

Lol.


As far as I know, when the Babolat Performance Lab is preparing a set of 6 racquets for their profesionnal tennis players it is within 1g, 1mm in balance and 1 point in swingweight. So if it is good enough for them it should good enough for us .

Just a side comment: a 0.5% error on the SW translates into 1.5 kg.cm2 which means an error up to 3 kg.cm2 on the twistweight (TW) measurment. Since the TW varies from 12 to 17 kg.cm2 the TW error measurement would be 20% which is not great. But we usally don't pay much attention to the TW as the SW is a much more important parameter.


You are exaggerating a tiny little bit here Commercial SW machines such as the Head 3 in 1 have an accuracy of 0.5 kg.cm2 which means 0.15%. With my machine I have an accuracy around 0.7 kg.cm2 @ 330 kg.cm2 which means 0.2% and I know how to improve. I'm sure that a true military grade SW machine would be better than 0.1 kg.cm2 (0.03%) .

yeah, yes, just poking a little fun at those folks that can tell 1point of a swing-weight difference by just swinging a racket. Although if I were to believe the conclusions of this paper "Measuring the inertial properties of a tennis racket" the claims that these RDC/Head/PTC machines are as accurate as 0.5kg*cm^2 seem a bit too good to be true.

The thing is that with the Swing Tool app you will never be able to get a better estimation of the SW than +-1.5 kg.cm2 (which is enough I agree). The reason is that the Swing Tool app is making the approximation that the period of oscillation is independante of the amplitute of the oscillation. And this is only true for very small amplitudes (basically when sin(X) = X to a very good precision).

For larger amplitutes you have to take into account corrections. Here is the measurement of the period of oscillations I made (in ms) with respect to the amplitude (in deg) of the oscillations. You see that the periode T increases slightly with the amplitude. Not by a lot but enough to stop you from being able to measure the SW within 0.5 kg.cm2 like a commercial SW machine.

yes, absolutely correct for the SwingTool app. Nice graph! Which is why on my device I made it so you just can't physically swing the racket with large amplitude to make sure the error is as small as possible. I've always wondered if those commercial machines do indeed somehow take into account that period-vs-amplitude error. I kind of doubt they do.

In addition to an error due to high amplitude, there's also another phenomena at play here.

I thought a bit about it and maybe that is why RDC calibration is done with three rods. Because technically speaking what we have here is a dampening oscillation with light damping. The SwingTool, just like any tool that is derived based on a physical pendulum, assumes a non-dampening oscillation. Which is obviously impossible in practice. When you take a dampening effect into consideration the performance of the device is dependent on three variables - its own swingweight, the constant of the springs providing oscillating force, and the damping constant. So you need three equations to find those out - perhaps that's why RDC needs to be calibrated with three known rods? Because of the dampening effect the period of oscillation is a bit greater than it would have been in ideal non-damping case - which means the the resulting swingweight is a bit higher than the actual swingweight (at least for SwingTool app and my device). It would be interesting to know if RDC/Prince PTC/Head3-in-1 do account for that affect. It would be actually rather difficult to do that - because the damping constant depends on friction - which varies with the weight of an object being measured, and air resistance - which varies with each racket due to its shape, being strung or not, etc. So it is almost impossible in practice to find out exactly what the damping constant is since it essentially varies with each racket.
Great discussion!

 

[jmnk]

Yeah, that's what I thought. ;-)

But - did you read it ?

 

[Tregix]

When Rossignol brought the forefather of the SW machines onto the market a good 30 years ago, and a little later Babolat, it was necessary to say which machine was used for measuring.
They had a similar Delta.

I did not know about the Rossignol machine. Thanks. Found that patent from 1987 which explains how it works.

FR2611044A3 - Device for evaluating the dynamic equilibrium of a racket by a moment of inertia measurement - Google Patents

Device for measuring the moment of inertia of a tennis, squash, badminton or other racket. The racket 35 is fixed, with its handle 34 horizontal, at its gripping point 36, so as to be able to rotate about a vertical axis 32, creating, in combination with return springs 19, 20, a torsion...

patents.google.com

 

[Tregix]

Yes, it doesn't matter - not everything that the senders write is always correct

Totally true ;-)

You can make 3 settings. Set whole number or 0.5 or 0.1.

Yes but it does not mean that the accuracy is 0.1 kg.cm2 just because you can display at 0.1 precision !!

Actually, the more I think about it and experiment with my own machine the more I feel that an accuracy of 0.1 kg.cm2 is nearly impossible to reach. You have to do the measurement in vaccum with a laser to get that level of accuracy ! Even to get an accuracy of 0.5 kg.cm2 you have to work pretty hard...

 

[Irvin]

Although if I were to believe the conclusions of this paper "Measuring the inertial properties of a tennis racket" the claims that these RDC/Head/PTC machines are as accurate as 0.5kg*cm^2 seem a bit too good to be true.

What if you were to believe the conclusions? LOL I have a cheap micrometer that reads to 1/1000th of a mm. Just because the readout is x.xxx I’m not fooling myself into believing it Is that accurate. Take SwingTool for instance it reads the periods of oscillatins of a racket for 16 periods. The camera I use operates at 30 FPS so each frame is 0.0016 seconds. Therefore the best accuracy you can get with SwingTool is rounded to +/- 0.002 seconds. A 0.004 second difference is 2 whole SW points.

What I getting at is just because the Head has a readout of 1/2 or 1/10 of a second I seriously doubt it is accurate enough to measure it accurately.

 

[Tregix]

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Here is another picture where both machines can be seen.
Small example: If I take the calibration rod alone, the HEAD SW shows the ominous 100 points.
With the RDC it is enough to let the holder swing alone to display these 100 points.
With the HEAD there are two additional notches on the calibration rod for SW 200 and 300. With the holder alone the HEAD shows 26.4 points.

Very interesting. Thanks a lot.
The 203 reading on the RDC (instead of 200) does not surprise me that much as the calibration range of the RDC is between 252 and 389. But I think that it could be improved a little bit see below.

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On the RDC the rods are set to 252, 315 and 389. So there you have to work with calibrated rods.
I made these rods from an old racket and some lead. I know two people who also have an RDC - with one friend I had no difference and with the other colleague the value (I think minus?)1.
So assume that my rods are correct.
In the same way I assume that the head calibration rod is correct - but on a different curve. which meet at about 315 SW points.

A couple of additional questions . After making sure that the Head 3 in 1 is well calibrated using the Head calibrated rod (at 100, 200 and 300 kg.cm2), did you try to measure the SW of the 252, 315 (this one you did) and 389 kg.cm2 calibrated racquets using the Head 3 in 1 machine? What did you get?

I feel that you will not get 252 and 389 but something 1 or 2 points different. From that it would interesting to add or remove a little bit of lead on your calibrated racquets so that you get precisely 252, 315 and 389 kg.cm2 on the Head 3 in 1.

The last step would be to recalibrate the RDC (there is a procedure for that I believe) based on the new 252, 315 and 389 calibrated racquets. I am pretty sure that if you do it you will get very very close measurements from both machines in the range 250 – 390 kg.cm2. I mean, less than 1 kg.cm2 difference. And probably something closer to 200 on the RDC using the Head calibration rod.

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Now as an overprivileged person who owns two SW devices - I don't really care what the output is - if all raqucets are measured and adjusted with the same device, everything is fine.

Totally agree with that. What is really important is that the player is confortable with his racquets and that they are matched.

 

[jmnk]

I second the request to perform this test

A couple of additional questions . After making sure that the Head 3 in 1 is well calibrated using the Head calibrated rod (at 100, 200 and 300 kg.cm2), did you try to measure the SW of the 252, 315 (this one you did) and 389 kg.cm2 calibrated racquets using the Head 3 in 1 machine? What did you get?

 

[max]

Great stuff. Sometime back, I made an add-on to my Klippermate that lets me use it as a cheese press.

 

[Tregix]

(...)there's also another phenomena at play here.

I thought a bit about it and maybe that is why RDC calibration is done with three rods. Because technically speaking what we have here is a dampening oscillation with light damping. The SwingTool, just like any tool that is derived based on a physical pendulum, assumes a non-dampening oscillation. Which is obviously impossible in practice. When you take a dampening effect into consideration the performance of the device is dependent on three variables - its own swingweight, the constant of the springs providing oscillating force, and the damping constant. So you need three equations to find those out - perhaps that's why RDC needs to be calibrated with three known rods? Because of the dampening effect the period of oscillation is a bit greater than it would have been in ideal non-damping case - which means the the resulting swingweight is a bit higher than the actual swingweight (at least for SwingTool app and my device). It would be interesting to know if RDC/Prince PTC/Head3-in-1 do account for that affect.

I don't think that the 3 calibration rods has anything to do with that. The damping coefficient changes from racquet to racquet. It is not a constant of the system like the SW of the machine and the constant of the springs. This parameter has to be evaluated for each racquet individually as it depends on the air friction of the racquet.

Actually, you can very easily measure the damping coefficient by monitoring the amplitude as a function of time. The amplitude decreases exponentially with the number oscillations.

I also wonder if commercial SW machines take into account corrections coming from large angle oscillation and friction. If they do indeed reach a true 0.5 kg.cm2 accuracy, most probably yes.

(It would be actually rather difficult to do that - because the damping constant depends on friction - which varies with the weight of an object being measured, and air resistance - which varies with each racket due to its shape, being strung or not, etc. So it is almost impossible in practice to find out exactly what the damping constant is since it essentially varies with each racket.

Agree that the damping coefficent is depending on many parameters but it is a simple parameter to measure.

I just made the following experiment. I recorded the maximum amplitude with time of 3 different objects of very similar SW (around 340kg.cm2) and weight (340g) but of very different air resistance: a calibration rod of 25mm in diameter and 67cm long, a racquet with the head vertical (standard SW measurement) and the same racquet with the head horizontal (TW measurement). You can see that the dampening is quite different as the amplitude is decrasing with time at a different rate.

The results are making sense. The rod has the smallest air friction and the damping is the lowest of the three. The racquet with the head horizontal has also a smaller air friction than when the head is vertical which affects the damping.

Now I have to evaluate how much the damping affects the period of oscillation and therefore the SW. For a pendulum the therory says that the correction to the anglular period is sqrt(1-lambda^2) ...

 

[jmnk]

I don't think that the 3 calibration rods has anything to do with that. The damping coefficient changes from racquet to racquet. It is not a constant of the system like the SW of the machine and the constant of the springs. This parameter has to be evaluated for each racquet individually as it depends on the air friction of the racquet.

yes, agree, that's what I said as well

Actually, you can very easily measure the damping coefficient by monitoring the amplitude as a function of time. The amplitude decreases exponentially with the number oscillations.

I also wonder if commercial SW machines take into account corrections coming from large angle oscillation and friction. If they do indeed reach a true 0.5 kg.cm2 accuracy, most probably yes.

Agree that the damping coefficent is depending on many parameters but it is a simple parameter to measure.

true, as you say for a particular object.

I just made the following experiment. I recorded the maximum amplitude with time of 3 different objects of very similar SW (around 340kg.cm2) and weight (340g) but of very different air resistance: a calibration rod of 25mm in diameter and 67cm long, a racquet with the head vertical (standard SW measurement) and the same racquet with the head horizontal (TW measurement). You can see that the dampening is quite different as the amplitude is decrasing with time at a different rate.

The results are making sense. The rod has the smallest air friction and the damping is the lowest of the three. The racquet with the head horizontal has also a smaller air friction than when the head is vertical which affects the damping.

Now I have to evaluate how much the damping affects the period of oscillation and therefore the SW. For a pendulum the therory says that the correction to the anglular period is sqrt(1-lambda^2) ...

very nice!
If I may ask - how do you accurately measure the amplitude?

Now - as far as an error introduced by 'too large of an amplitude'. I think that does not actually apply for the devices like RD (or our home made devices) that rely on springs to provide oscillations. For a physical pendulum the amplitude error, as you noted earlier, is due to the fact that the assumption that sin(X) = X is correct for small angles only, and the larger the angle the less true it is. That in turn comes from how the gravitational force providing oscillation is derived - it is assumed that the force is proportional to the displacement from equilibrium - but it is actually not exactly so. But for the system that relies on springs, at least theoretically speaking, the force of the force of the spring _is_ only proportional to the displacement so whether the object is oscillating with (initial) large or small amplitude does not matter.

So on those RDC like devices the error comes from _not_ accounting for the dampening effect (I mean I assume they do not account for that) - but I think the initial amplitude does not matter?