Basic swing weight question

[Irvin]

The square of the distances is used in the calculation of the Swingweight.
The measurement error is therefore also taken in the square.

If that were true SW machines would not work because machines like the RDC, PTC, Head SW machine, Alpha Accuswing, etc do not measure distance only the period.

head, i though the balance point would be different for when the swing location is different, as the object "may" swing different.... hence the quick/experimental measurement. that was no way VERY accurate to achieve a desired outcome....

Unless you are pivoting a racket 10 cm from the butt you must first determine the inertia around the pivot point. That is determined by the period. From that point you must calculate the inertia at the center of mass and then you can calculate the SW. The fewer calculations that must be preformed the more accurate you results will be.

if you would like to try an experiment measure the SW from the top 5 strings on a tennis racket. I’d wager none of the results will be the same. How do you know which if any are accurate?

 

[chrisb]

Sorry I must be total old school. I judge rackets entirely how they feel in my hand

 

[shadow01]

in the normal circumstance, yes, i agree the measurement must be accurate... however, my "experiment" was to explain/make a point of the different balance measurement maybe required for the swing weight app for either hanging/swing from towards the top of the hoop or the towards end of the handle (or the 10cm location).
i my simple head, i thought the balance point would be different for when the swing location is different, as the object "may" swing differently.... hence the quick/experimental measurement. that was no way VERY accurate to achieve a desired outcome....

Yeah - I would still like to understand this better as well. I feel like I need to read up on the physics of it when I have time. However, what gets me over the hump for now that the measurement is from the butt and not the head regardless of the swing point being at the head or butt is that the apps arrows are showing that. And also if you take the balance measurement from the head but other measurements from the butt - the app won’t know where it is. (I am probably not articulating my point very well at all).

It is of major importance to measure all distances VERY accurately.

agreed!

 

[Irvin]

There are two numerical measures of the inertia of a body: its mass, which governs its resistance to the action of a force, and its moment of inertia about a specified axis, which measures its resistance to the action of a torque about the same axis. Swing Weight is a measure of the moment of inertia. When Swing Weight is measured a racket is put in motion around an axis with a known force. From the timing of the period the inertia or SW around that axis can be determined.

 

[Stringway Official]

The square of the distances is used in the calculation of the Swingweight.
The measurement error is therefore also taken in the square.

If that were true SW machines would not work because machines like the RDC, PTC, Head SW machine, Alpha Accuswing, etc do not measure distance only the period.

@ irvine
I think you are missing the point.
When a system calculates the SW based on entered distances this system uses the same formulas as we do in the SW advisor for the Moment of innertia.
https://en.wikipedia.org/wiki/Moment_of_inertia

If you enter the distances inaccurate the result will be even more inaccurate because of the square.

That SW machines measure the swing time (period) has nothing to do with this.

 

[Irvin]

@ irvine
I think you are missing the point.
When a system calculates the SW based on entered distances this system uses the same formulas as we do in the SW advisor for the Moment of innertia.
https://en.wikipedia.org/wiki/Moment_of_inertia

If you enter the distances inaccurate the result will be even more inaccurate because of the square.

That SW machines measure the swing time (period) has nothing to do with this.

I agree somewhat. If you pivot a racket from a 10 cm axis why would you have to calculate the inertia? You know the total inertia (resistance to acceleration) of the assembly and racket directly from the period, subtract the assembly inertia and you're done. It is impossible to accurately calculate SW from static measurements of weight and balance.

The problem with SwingTool is in its design. SwingToll assumes the pivot is not at a 10 cm point, but it does make allowances if it is. SwingTool measures the period at the pivot, then calculates the SW from data supplied to it assuming the pivot is or is not the SW axis. If your balance or weight is inaccurate errors are introduced. OTOH the period readout from SW is very accurate Usually +/- 0.002 seconds, If the pivot is at 10 cm and you know the period you have all you need.

 

[Stringway Official]

@irvine
I think we are talking different things.
When the moment of inertia (= SW) is calculated from the period time, when the racquet swings around the first cross string at the head the SW around the pivot point is calculated with the displacement formula:
Which is Mass * Distplacement ^2 (=58 in the example)

So if you measure the displacement unaccurate your result will be the square of the unaccuracy.

That is the only thing I try to say/

 

[Tregix]

I see a lot of confusion regarding SW and how to calculate it. I would like to clarify that a little bit.

Rotational Inertia or Moment of Inertia, or Inertia, or SW is a physical property of a rigid body which tells you how difficult it is to put an object, let say a racquet, into rotation around a particular axis. It is somehow similar to the mass of the racquet, but the mass tells how hard it is to put the racquet into translation. The Inertia deals with rotation.

It is important to understand that the Inertia of a racquet depends on the position of the axis of rotation with regards to the racquet. Just imagine a hammer. If you hold it by the handle, it is hard to put the hammer into rotation which means that its inertia is very high. And it is also very powerful. If you hold the hammer by the head, it is very easy to put it into rotation, which means that its inertia is very small, but also not so effective on a nail… Actually, the formulae to calculate the inertia involves the distance to the axis squared times the mass.

The SwingWeight (SW) of a racquet is by definition the Inertia of the racquet around an axis located 10 cm from the end of the handle with the head of the racquet being vertical (that is, the strings are not facing upward).

An important thing to know is that the Inertia of a racquet is closely related to the pendulum period of oscillation of the racquet around that axis of rotation. Basically, if you know the period of oscillation of the racquet you know the Inertia of the racquet around that particular axis.

 

[Tregix]

How is that related to the Tennis Warehouse Method or to the SwingTool App to calculate the SW?

First, we should note that it is the gravity that puts the racquet into rotation (which is not the case for an RDC).

When the racquet is oscillating around a particular string we can measure the period of oscillation which in turn gives us a measurement of the Inertia of the racquet around that string.

But this not the measurement of SW because the axis of rotation is not at the “right” place. For the SW, the axis should be at 10cm from the end of the handle.

Here comes an important property, the so-called parallel axis theorem (https://en.wikipedia.org/wiki/Parallel_axis_theorem). This theorem tells you that if you know the inertia of the racquet around a particular axis, if you know the location of the balance point and the mass of the racquet you can calculate the inertia of the racquet around its balance point.

Inertia around axis A = Inertia around the balance point + m * (X of axis A - X of balance point )^2.

And this is very useful because if you know the Inertia of the racquet around the balance point you can get the SW by applying the parallel axis theorem a second time:

SW = Inertia around the balance point + m * (10cm - X of balance point)^2.

Which means that:

SW = Inertia around axis A - m * (X of axis A - X of balance point )^2 + m * (10cm - X of balance point )^2

To say that differently, what the Tennis Warehouse Method or to the SwingTool App are doing is to measure the period of oscillation of the racquet around the hang string axis. This gives them the Inertia of the racquet around that axis. Then they apply the parallel axis theorem twice to get the SW. But for that they need to know the mass of the racquet, the location of the hang point as well as the location of the balance point as accurately as possible as these distances are squared in the calculations… This means that a small error in the measurement of the balance of the racquet translates into a much larger error in the calculation of the SW.

You also see that you can choose any string you like to hang the racquet as long as you know its location accurately.

 

[Tregix]

The Babolat RDC or the Head 3 in 1 machine are using a different and I would say much simpler way to get the SW.

First the racquet is oscillating horizontally and not vertically. It is a pair of springs that create the forces for the oscillations and not the gravity.

Second, the axis of rotation is precisely set at 10cm from the end of the handle of the racquet. This means that when they measure the period of oscillation, they directly get an evaluation of the SW. No need to apply the parallel axis theorem. No need to know the mass nor the balance point of the racquet.

Direct SW measurement!

 

[Tregix]

 

[Tregix]

I would like to emphasis that, knowing the balance of a racquet and its mass, there is absolutely NO way to get an exact value of the SW. It is physically impossible.

Actually, I can easily show you two different objects that have exactly the same length, exactly the same mass and the same balance but that have VERY different SW.

However, knowing the mass and the balance of a racquet one can get a more or less accurate estimation of the SW. And this is what the Stringway “Swingweight Advisor” tool does.

It works rather well because all racquets have somehow a similar mass distribution. But there is no physics involved. It is just am estimation of the SW.

If you apply the Stringway “Swingweight Advisor” tool on an aluminum cylinder that is used for the calibration of RDCs it does not work so well because the mass distribution is very different from a racquet. But that is not the goal of the tool.

 

[Irvin]

Here comes an important property, the so-called parallel axis theorem (https://en.wikipedia.org/wiki/Parallel_axis_theorem). This theorem tells you that if you know the inertia of the racquet around a particular axis, if you know the location of the balance point and the mass of the racquet you can calculate the inertia of the racquet around its balance point.

I agree with most of what you saying except for this. The Parallel Axis Theorem only works if the rigid object (racket) is uniform. Small error yes but it will be noticeable.

I believe you’re better off calibration your device and using the period to determine SW about the axis of rotation.

 

[shadow01]

This thread turned into an educational explanation (and debate) of swing weight: what it is, the physics of it, how to measure it, approximation methods.

one thing @Tregix - for swing tool - if hang point and swing point are the same (10 cm) - isn’t parallel axis theorem not used since the distance is 0 - thus measuring swing weight directly like the RDC does? I will have to try it, but then theoretically- it wouldn’t matter what we put for the balance and weight inputs in the app?

 

[Irvin]

This thread turned into an educational explanation (and debate) of swing weight: what it is, the physics of it, how to measure it, approximation methods.

one thing @Tregix - for swing tool - if hang point and swing point are the same (10 cm) - isn’t parallel axis theorem not used since the distance is 0 - thus measuring swing weight directly like the RDC does? I will have to try it, but then theoretically- it wouldn’t matter what we put for the balance and weight inputs in the app?

If you’re using SwingTool or TWU calculator the parallel axis theorem is used because that’s how it was designed I believe.

@Tregix here is a video I found again today. I’ve seen it before but never noticed him talking about the axis of rotation and the rigid system must be uniform or the theorem does not work.

 

[shadow01]

If you’re using SwingTool or TWU calculator the parallel axis theorem is used because that’s how it was designed I believe.

@Tregix here is a video I found again today. I’ve seen it before but never noticed him talking about the axis of rotation and the rigid system must be uniform or the theorem does not work.

Great vid - and I think this supports my theory that if the hang point and swing point are the same then balance and mass are irrelevant in swing tool. because at around 4:00 in the video it shows the math for the parallel axis theorem:
Measured inertia + mass of the system(I.e. total weight of racquet)*displacement distance squared.

well - displacement distance is 0 (because the swing point and hang point are the same) thus the answer is the measured inertia.

what am I missing?

 

[Tregix]

one thing @Tregix - for swing tool - if hang point and swing point are the same (10 cm) - isn’t parallel axis theorem not used since the distance is 0 -
thus measuring swing weight directly like the RDC does ?

Correct, you don't need to apply the parallel axis theorem and you are indeed measuring the SW more directly. But there is a fundamental difference with an RDC and it has to do with the gravity. See below .

but then theoretically- it wouldn’t matter what we put for the balance and weight inputs in the app?

Here you are forgetting that the force which sets the oscillations is the gravity and the moment of that force involved both the mass of the object and location of the center of mass. No way to get around that.

It means that to get the SW from the measured periode of oscillation you need to know the mass of the racquet and it's balance to calculate the torque. Even if you don't need to use the parallel axis theorem.

RDC work differently since it's a set of springs that induce the torque and not the gravity. With an RDC you don't need to know the mass of the racquet nor its balance. But RDCs need to be calibrated, which is not so easy.

 

[Tregix]

The Parallel Axis Theorem only works if the rigid object (racket) is uniform.

No, it's incorrect. The parallel axis theorem applies even if the mass density is dependant on x, y and z. Just look at the mathematical demonstration on the Wikipedia page to convince yourself.

Parallel axis theorem - Wikipedia

en.m.wikipedia.org

 

[Tregix]

The difference of 2,3 % between the RDC and the SW calculator is quite good compared to differences of SW test with different SW machines (as we did).

For information, I tried the Swingweight advisor tool on one if my son's Head Gravity Pro.

The racquet was measured at 316g, 31.0cm and SW 303 kg.cm2 unstrung by Tennis Waterhouse (matching service). I double checked and found the same values.

The tool gives a SW of 279 kg.cm2 which is off by 24 kg.cm2 which means 8%.

24 kg.cm2 is a very significant difference. 279 kg.cm2 is among the lowest SW on the market for an unstrung racquet, while 303 kg cm2 is among the highest SW on the market for an unstrung racquet.

It seems that the correlation you use does not work very well with head light racquet with high SW.

It does a better job with the latest edition of the Pro Staff. I measured one at 314g, 30.8cm and SW 284 kg.cm2 unstrung. Your tool gives 274 kg.cm2. which is 3.5% off.

 

[Irvin]

No, it's incorrect. The parallel axis theorem applies even if the mass density is dependant on x, y and z.

https://imgur.com/dIolABf

600 = 1,240? The PAT only works in a uniform system.

EDIT: The above calculations are incorrect see post #72

 

[Irvin]

I think SwingTool and the TWU use the measurements for hang point, center of mass, weight, period, and SW axis @ 10 cm to determine inertia. SwingTool is different the SW axis is variable and the timing is measured but each method uses calculations. First the inertia at the COM is calculated from the period. Then the inertia is Converted using the parallel axis theorem to the SW axis at 10 cm.

if you want more accurate inertia readings IMO it is best to measure the period while pivoting the racket from the SW axis, subtract any error introduced by the assembly used to pivot the racket and be done with it. Also small consistent displacements from the resting point are best. Anytime you use static measurements like weight and distance you’re asking for trouble.

 

[shadow01]

https://imgur.com/dIolABf

600 = 1,240? The PAT only works in a uniform system.

I think PAT is I(new) = I(cm) + m*d^2 where d is the displacement not the total length(r). In your example it would be 6 because that’s how far you moved the axis from the initial location. So 240 + 10*6*6 = 600

 

[Irvin]

I think PAT is I(new) = I(cm) + m*d^2 where d is the displacement not the total length(r). In your example it would be 6 because that’s how far you moved the axis from the initial location. So 240 + 10*6*6 = 600

You are correct but I cant change the picture. I’ll just leave it there, it makes people think.

 

[shadow01]

Correct, you don't need to apply the parallel axis theorem and you are indeed measuring the SW more directly. But there is a fundamental difference with an RDC and it has to do with the gravity. See below .



Here you are forgetting that the force which sets the oscillations is the gravity and the moment of that force involved both the mass of the object and location of the center of mass. No way to get around that.

It means that to get the SW from the measured periode of oscillation you need to know the mass of the racquet and it's balance to calculate the torque. Even if you don't need to use the parallel axis theorem.

RDC work differently since it's a set of springs that induce the torque and not the gravity. With an RDC you don't need to know the mass of the racquet nor its balance. But RDCs need to be calibrated, which is not so easy.

starting to get it... so an argument could be made that using gravity is better than RDC because gravity is constant and no calibration is needed. However RDC does not need measurements whereas gravity method needs precise weight and balance measurements. Still not clear why weight and balance would matter though - could you explain that a bit? Btw what’s your background if you don’t mind? Tennis enthusiast or more formal training in physics?

You are correct but I cant change the picture. I’ll just leave it there, it makes people think.

yeah. I’m getting a lot out of this discussion. Hope others do as well

 

[Irvin]

starting to get it... so an argument could be made that using gravity is better than RDC because gravity is constant and no calibration is needed. However RDC does not need measurements whereas gravity method needs precise weight and balance measurements. Still not clear why weight and balance would matter though - could you explain that a bit? Btw what’s your background if you don’t mind? Tennis enthusiast or more formal training in physics?

Why do you think a gravity system needs weight and distance measurements? Using SwingTool and the TWU calculator you need the weight and distance measurements because they are required fields.

Just because inertia at 10 cm is the same does not mean weight and balance will match. If you’re matching rackets you should match weight, balance and inertia.

 

[shadow01]

Why do you think a gravity system needs weight and distance measurements? If the period at 10 cm is 1.321 seconds the inertia at that point will always be the same. Using SwingTool and the TWU calculator you need the weight and distance measurements because they are required fields.

Just because inertia at 10 cm is the same does not mean weight and balance will match. If you’re matching rackets you should match weight, balance and inertia.

oh - I was asking a follow up question on @Tregix response to my question (post 67). I had compared the gravity system to RDC and theorized that weight and balance wouldn’t be needed. So asking a follow up around their response to my theory.

 

[Tregix]

well - displacement distance is 0 (because the swing point and hang point are the same) thus the answer is the measured inertia.

what am I missing?

starting to get it... so an argument could be made that using gravity is better than RDC because gravity is constant and no calibration is needed. However RDC does not need measurements whereas gravity method needs precise weight and balance measurements. Still not clear why weight and balance would matter though - could you explain that a bit?

Well what you are missing is that, if you set the axis of rotation at 10cm from the end of the handle (which means that you will not need to use the parallel axis theorem), the relation between the period of oscillation and the SW, for small angular amplitude, is the following:

SW = (mxgxLxT^2)/(4xPi^2)

where m is the mass of the racquet, g is the gravity and L is the distance between the axis of rotation and the center of mass of the racquet and T is the period of oscillation.

Why is the center of mass involved? Because the gravity applies at the center of mass. Why you need the distance between the axis of rotation and the center of mass of the racquet? Because this distance comes into play when you compute the torque .

As soon as you put the racquet vertical and measure the period of oscillations you will need the mass of the racquet and the balance point to get the SW. And that's why on RDCs, the racquet is horizontal.

 

[am1899]

“Basic swing weight question.”

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

 

[shadow01]

Well what you are missing is that, if you set the axis of rotation at 10cm from the end of the handle (which means that you will not need to use the parallel axis theorem), the relation between the period of oscillation and the SW, for small angular amplitude, is the following:

SW = (mxgxLxT^2)/(4xPi^2)

where m is the mass of the racquet, g is the gravity and L is the distance between the axis of rotation and the center of mass of the racquet and T is the period of oscillation.

Why is the center of mass involved? Because the gravity applies at the center of mass. Why you need the distance between the axis of rotation and the center of mass of the racquet? Because this distance comes into play when you compute the torque .

As soon as you put the racquet vertical and measure the period of oscillations you will need the mass of the racquet and the balance point to get the SW. And that's why on RDCs, the racquet is horizontal.

ok. I’m all the way there from a satisfied intellectual curiosity perspective of the following:
- what swing weight is and why it’s important
- how to estimate it with calculations of weight and balance point and the related risk factors using those calculations (“the calculations method”)
- why the period of oscillation method (swing tool and twu) are more accurate than using the “calculations method”
- how to calculate it with the period of oscillation method through swing tool and twu and how those 2 methods use the parallel axis theorem
- why balance and weight are important when using the period of oscillation method when measuring vertically

BUT - now I would like to know how RDC calculates swing weight. I understand there are springs of which the spring tension must be known and used in the calculation. I suppose it has to do with the period of oscillation and the known tension of the springs in a formula.

As an aside - this thread Is summarizing a lot of points that get discussed often. Perhaps a sticky if it answers all the questions on swing weight, how to measure it, and calculations behind the 3 methods: calculations estimation, vertical period of oscillation, horizontal period of oscillation (RDC). The first 2 are fairly complete imo.

 

[bfroxen]

For a torsion pendulum, the period of oscillation is described by:

T = 2 * pi * sqrt( I / k ),

where "I" is the moment of inertia of the pendulum and "k" is the spring constant. (http://www.physics.louisville.edu/cldavis/phys298/notes/torpend.html)

The RDC (and similar) is just a torsion pendulum. Solving for "I" gives the equation:

I = ( T^2 * k ) / ( 4 * pi^2 ).

Therefore, "I" is dependent only on "T" and "k". "T" is measured directly by the RDC. "k" is determine by calibration; by measuring "T" for an object of known "I" and solving for "k". Once "T" and "k" are known, "I" is calculated. However, "I" is not exactly equal to the swingweight (SW). It includes "SW" plus the moment of inertia of the device (Id):

"SW" = [( T^2 * k ) / ( 4 * pi^2 )] - "Id"

The calibration process is also used to determine "Id". By measuring the period of two different objects of known moment of inertia, "Id" can be calculated.

So, with calibration, an RDC can determine "SW" by measuring only the period of oscillation. There are many fewer measurements and sources of error compared to the gravity pendulum method, but they are still there:
- measurement of the period
- measurements of the calibration objects
- non-verticality of the oscillation axis (allows gravity to affect the pendulum and why the devices have a bubble level)
- non-linearity in the spring drive (linear springs driving angular motion)
- changes in spring constant due to temperature
- friction
- etc.

 

[Irvin]

@bfroxen what you said is accurate for a horizontal racket for a vertical racket the formula in it simplest for is:

for a horizontal racket replace mgl with k

 

[shadow01]

For a torsion pendulum, the period of oscillation is described by:

T = 2 * pi * sqrt( I / k ),

where "I" is the moment of inertia of the pendulum and "k" is the spring constant. (http://www.physics.louisville.edu/cldavis/phys298/notes/torpend.html)

The RDC (and similar) is just a torsion pendulum. Solving for "I" gives the equation:

I = ( T^2 * k ) / ( 4 * pi^2 ).

Therefore, "I" is dependent only on "T" and "k". "T" is measured directly by the RDC. "k" is determine by calibration; by measuring "T" for an object of known "I" and solving for "k". Once "T" and "k" are known, "I" is calculated. However, "I" is not exactly equal to the swingweight (SW). It includes "SW" plus the moment of inertia of the device (Id):

"SW" = [( T^2 * k ) / ( 4 * pi^2 )] - "Id"

The calibration process is also used to determine "Id". By measuring the period of two different objects of known moment of inertia, "Id" can be calculated.

So, with calibration, an RDC can determine "SW" by measuring only the period of oscillation. There are many fewer measurements and sources of error compared to the gravity pendulum method, but they are still there:
- measurement of the period
- measurements of the calibration objects
- non-verticality of the oscillation axis (allows gravity to affect the pendulum and why the devices have a bubble level)
- non-linearity in the spring drive (linear springs driving angular motion)
- changes in spring constant due to temperature
- friction
- etc.

Thanks for the explanation on RDC calcs and the related pros and cons!

Id is a good point and something @Irvin mentioned in one of his po. I suppose Id could be removed from a vertical system as well by the same method you describe (measuring 2 known swing weights) - no?

I also found this article: https://www.sciencedirect.com/scien...253052c&pid=1-s2.0-S1877705814006146-main.pdf

anyone else think this is worth a sticky?

@Polotechnics thanks for sparking the discussion which turned out to be not so basic

 

[bfroxen]

Id is a good point and something @Irvin mentioned in one of his po. I suppose Id could be removed from a vertical system as well by the same method you describe (measuring 2 known swing weights) - no?

Yes, it could be, but why? If pivoting on a string, it's zero. If using somethings else, it's probably easy enough to ensure it has a negligible moment of inertia. Here's an old post of how I used to measure balance and SW. I once calculated the moment of inertia of the rod and rubber bands, and it's definitely negligible.

Like Tregix, I've been developing my own SW machine, so I use that now.

 

[Stringway Official]

@Tregix

or information, I tried the Swingweight advisor tool on one if my son's Head Gravity Pro.

The racquet was measured at 316g, 31.0cm and SW 303 kg.cm2 unstrung by Tennis Waterhouse (matching service). I double checked and found the same values.

The tool gives a SW of 279 kg.cm2 which is off by 24 kg.cm2 which means 8%.

It seems that the correlation you use does not work very well with head light racquet with high SW.

Interesting

What if you use the head weight and throat weight system? This more accurate.

And very important: With the head of the racquet on 2 coins / washers!!

 

[Irvin]

@trexic

Interesting

What if you use the head weight and throat weight system? This more accurate.

If you're trying to get @Tregix's attention it would work better if your spelled his login correctly.

 

[Tregix]

@Tregix
Interesting

What if you use the head weight and throat weight system? This more accurate.

And very important: With the head of the racquet on 2 coins / washers!!

Here are the values with the strung racquet (Head gravity Pro, strung with a 1.25 monofilament with a vibration dampener and an over grip)

• Total weight: 343.4 g
• Balance: 31.9 cm
• SW (measured with my machine): 337.5 kg.cm2
• Head weight: 159.9 g, Bottom weight:183.05 g

Using the Swingweight calculator tool:

• if I enter the head and bottom weight I get a SW of 317.7 kg.cm2 and a balance of 31.94 cm, estimated total weight 342.95 g (pretty good compared to the 343.4 g measured total weight)
• if I enter the total weight and the balance I get a SW of 317.5 kg.cm2.

The difference is 20 kg.cm2 which means 6%. 6% might not look like a big difference but a 20 kg.cm2 difference in SW is very large. 317 kg.cm2 is a low SW racquet while 337 kg.cm2 is among the highest SW racquet on the market.

 

[Tregix]

Like Tregix, I've been developing my own SW machine, so I use that now.

Could you post a picture? I'm curious which engineering route you took . One-spring or two-spring system?

 

[Tregix]

BUT - now I would like to know how RDC calculates swing weight. I understand there are springs of which the spring tension must be known and used in the calculation. I suppose it has to do with the period of oscillation and the known tension of the springs in a formula.

I'll try to say it in a different way than bfroxen (I agree totally with what he said).

On a RDC, it is very important to set the axis of rotation at exactly at 10 cm from the end of the handle. This way there is no need to use the parallel axis theorem and you will get the SW almost directly by a measurment of the period of oscillation. The principle is the same as with the Tennis Warehouse method except that it is a pair of springs that create the oscilations and not the gravity.

A very important thing on an RDC is that you are measuring the SW of the racquet PLUS the SW of the machine (the racquet holder, the axis, etc)

Theory tells you, once again for small angular amplitude, that

(SW_racquet + SW_machine) = K x T^2

where T is the period of oscilation. It means that

SW_racquet = K x T^2 - SW_machine

In K there is all the physics of the springs (their stifness, their lengths etc) and the torque they create while SW_machine is the SW of the machine alone. But they are just 2 postitive numbers. These 2 numbers need to be determined and are different for every RDC. For that, what you do is to measure the period of oscillation T of two different objects of known SW, the so-called callabration rods.. From that you can evaluate the value of K and SW_machine (2 equations, 2 unknowns...).

In the image above I used 4 callibation rods and performed a linear regression to get K and SW_machine. In this example K = 291.61 USI and SW_machine = 5.58 kg.cm2

Once you know K and SW_machine you are done. You just need to measure the period of oscillation of a racquet, put its value in the relation SW_racquet = K x T^2 - SW_machine and you get the SW of the racquet. As simple as that.

Now you are ready to look at that thread, and make you own RDC : https://tt.tennis-warehouse.com/ind...lly-working-one-total-cost-roughly-10.675711/

 

[Tregix]

Thanks for the explanation on RDC calcs and the related pros and cons!
anyone else think this is worth a sticky?

Yes, we need a sticky: Everything you ever wanted to know about SW, what it is, how to calculate it, how to measure it

 

[bfroxen]

Could you post a picture? I'm curious which engineering route you took . One-spring or two-spring system?

@Tregix, I'm not ready to share any specifics publicly. I will say that it uses one spring, but it's not an extension spring.

 

[ClaudTT]

Don’t want to start a debate but the Stringway SW calculator (https://www.stringwaynederland.nl/SW-TA-online/SwingCalc/index-en.php) uses weight and balance only to determine SW. Using that calculator, if the weight and balance are the same the resulting SW is the same. How can you say one method is better than another?

EDIT: By the way I do not believe it is possible to determine SW from weight and balance alone. If SW, weight, and balance are all 3 matched it would be better than matching any 2 of the specs.

I found that the Stringway SW calculator is wrong... adding weight to my racket butt gives me LESS SW !!! it is against Physics... i.e. if I add weight at the butt the SW will be reduced drastically... ? Physics tells me something different, SW will keep increasing by the added weight times distance ^2.... not the opposite. As the Parallel axis Theorem states also... when considering a pivot outside CG.
Also I checked against TW measured SW and are OFF by ex:10 points... and not consistent either.

 

[am1899]

“Basic swing weight question.”

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

I said the above a bit in jest.

Seriously, this is fascinating stuff. Definitely worthy of a sticky.

 

[am1899]

I found that the Stringway SW calculator is wrong...

To me that’s not all that surprising. As preciously mentioned, it’s not possible to accurately calculate SW - with only weight and balance.

But don’t be shocked if someone (not me) suggests the Stringway tool is fine, and that you just don’t know how to use it.

 

[shadow01]

I'll try to say it in a different way than bfroxen (I agree totally with what he said).

On a RDC, it is very important to set the axis of rotation at exactly at 10 cm from the end of the handle. This way there is no need to use the parallel axis theorem and you will get the SW almost directly by a measurment of the period of oscillation. The principle is the same as with the Tennis Warehouse method except that it is a pair of springs that create the oscilations and not the gravity.

A very important thing on an RDC is that you are measuring the SW of the racquet PLUS the SW of the machine (the racquet holder, the axis, etc)

Theory tells you, once again for small angular amplitude, that

(SW_racquet + SW_machine) = K x T^2

where T is the period of oscilation. It means that

SW_racquet = K x T^2 - SW_machine

In K there is all the physics of the springs (their stifness, their lengths etc) and the torque they create while SW_machine is the SW of the machine alone. But they are just 2 postitive numbers. These 2 numbers need to be determined and are different for every RDC. For that, what you do is to measure the period of oscillation T of two different objects of known SW, the so-called callabration rods.. From that you can evaluate the value of K and SW_machine (2 equations, 2 unknowns...).

In the image above I used 4 callibation rods and performed a linear regression to get K and SW_machine. In this example K = 291.61 USI and SW_machine = 5.58 kg.cm2

Once you know K and SW_machine you are done. You just need to measure the period of oscillation of a racquet, put its value in the relation SW_racquet = K x T^2 - SW_machine and you get the SW of the racquet. As simple as that.

Now you are ready to look at that thread, and make you own RDC : https://tt.tennis-warehouse.com/ind...lly-working-one-total-cost-roughly-10.675711/

Nice setup. I would love to try to make one of those one day but time and handiness are rate limiting factors unfortunately. I am using a jig like the one @irwin described instead for now . This is using the vertical method. The horizontal method sounds like more elegant solution and eliminates a couple of steps - though those steps aren’t too difficult (weight and balance).

those calibration rods you are using - they look like pvc pipes correct? Since mass is uniform across the pipe you can calculate the swing weight and thus set that as a calibration rod?

 

[Stringway Official]

@Tregix

Nice piece of equipment.

I found that the Stringway SW calculator is wrong... adding weight to my racket butt gives me LESS SW !!! it is against Physics... i.e. if I add weight at the butt the SW will be reduced drastically... ? Physics tells me something different, SW will keep increasing by the added weight times distance ^2.... not the opposite. As the Parallel axis Theorem states also... when considering a pivot outside CG.
Also I checked against TW measured SW and are OFF by ex:10 points... and not consistent either.

@CloudTT
I certainly agree that this is true.

BUT that is not the way the calculator is meant to be used:

The intention is:
- To calculate the SW of a racquet without extra weight.
- To calculate how much weight must be added to raise the SW to a certain value.

When you add weight in one position and enter head and throat weight, the calculation assumes that this is a racquet without extra weight. So the extra weight is equally divided over the hole racquet.

So if you add weight at 5 cm in the butt, the system calculates a smaller balance point distance so the SW goes down.

But if you ask how much weight you must add at 5 cm in the butt to obtain 10 kgcm^2 more SW the system says 692.52 gram.

OFcourse adding weight in the butt so close to the pivot point is very ineffective to raise the SW.

 

[Stringway Official]

OVERALL

The development of the SW calculator was done in cooperation with many forum members on the Dutch forum some of them had SW machines.

We do not pretend that the System can offer exactly the same results as the RDC or other machines. But the difference between the machines and the Calculator were acceptable.

The intention was to make it easier for players an stringers to measure the SW (to compare racquets) and to know how much weight must be added to obtain a certain higher SW, without having to buy $2000 machines.
Compared to the swing test of the USRSA the test is easier to do and faster so it is easier to test a number of racquets.

Because the USRSA test is a real swing test the results can be more accurate.

Our experience with the different machines was that these also show quite a big difference in test results. Calibrating such a system is of major importance!

 

[Irvin]

I would like to know how RDC calculates swing weight.

@tregix’s explanation was good but in hopes of keeping it simple try this.

one thing I might mention is in the video he is explaining the perion for a mass hanging on a string. In machine like the RDC the mass isn’t handing on a spring it has to moved to a horizontal alignment. Therefore the mass can’t change the period, but the in inertia will. The deflection won’t change with a change in inertia but but the period will.

in a vertical system we already know the formula is

T = 2Pi * sqrt(Isupport / mgLcom) where mgLcom is the force applied

in a horizontal system the formula is very similar

T = 2Pi * sqrt(Isupport / k) where k is the force applied.

in the video above substitute inertia for mass. I believe he mentioned that briefly at one point in video. (4:35 in video)

 

[Irvin]

The intention (of Stringway swingweight calculator) is:
- To calculate the SW of a racquet without extra weight.
- To calculate how much weight must be added to raise the SW to a certain value.

Can you give us 1 example where the calculator works? Compute the SW of any racket you want and add 10 g to increase SW by 6 points.

 

[fritzhimself]

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

 

[Irvin]

Benefits and drawbacks of using a vertical or horizontal SW machine.

...................but now become very mean..........!

If he is going to persist in pushing his calculator I would just like to see 1 example of it working. I don't think that is asking too much. @fritzhimself aren‘t you on the Dutch forum? What is their consensus of this calculator?