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Dunlop Swingweight Machine Linearity Testing

Recently, I had the opportunity to test a Dunlop swingweight machine, so I measured the set of reference rods from the Briffidi SW1 Linearity Testing. I had previously seen data from an old Babolat RDC (Spurr) that showed significant non-linearity across the measurement range, but I expected the modern Dunlop machine to be better. The following data is from just one machine, and I hesitated to share it, but if I were any other tennis nerd without a competing product, I would have shared it without even thinking.

I verified that the Dunlop machine was calibrated and level. As describe in the SW1 testing, the reference rods were calculated from mass and length measurements. I measured the swingweight of each reference rod, in both orientations, on the Dunlop machine. The results are summarized in Table 1, and the deviation is plotted in Figure 1.

Calculated
(kg·cm²)
Mean Measured
(kg·cm²)
Deviation
(kg·cm²)
0.00 (empty)27.027.00
25.2146.020.79
50.0766.015.93
100.23108.07.77
149.89149.00.89
202.74198.5-4.24
250.37244.0-6.37
303.71299.0-4.71
355.61356.51.89
400.75397.0-3.75
Table 1 – Measurements of Reference Rods with Dunlop Machine
Figure 1 – Plot of Measured Swingweight Deviation by Reference Rod

Except for the outlier at ~400 kg·cm², there is a clear pattern to the deviation results. I don’t know enough about how the machine works to explain that outlier. The Dunlop calibration rod is marked 200±1 kg·cm², but there is significant deviation even there. It measured 204 kg·cm² on an SW1. There is both a shift due to the out-of-spec. calibration rod and significant non-linearity across the measurement range.

My goal is not to disparage the Dunlop machine, but I don’t mind pointing out that a big brand name or price tag doesn’t ensure greater accuracy. Even with the considerable inaccuracy, the Dunlop is still a useful tool. It looks and feels like a device you’d see in a professional setting, and the racket cradle is quite nice. Most importantly, it provided repeatable measurements, and that’s enough to match rackets. However, even at equal cost, I’d pick the SW1, as the accurate measurements (along with my spreadsheet) usually allow me to hit my target specs on the first try.

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Effect of Leveling on Briffidi SW1 Measurements

I previously completed some linearity testing as described in Briffidi SW1 Linearity Testing, and I recently repeated the testing with the SW1 intentionally not level.

First, I leveled the device and then raised the rear foot by two turns (1 mm). I took measurements at ten points, as described in the prior post, except I reduced the number of measurements from five to two in each configuration, as five seemed like overkill. Then, I returned the rear foot to level and raised the left-side foot by two turns (1 mm), and repeated the testing.

The plots below show the results of the prior, level testing and the two non-level configurations. For each, I calculated the calibration values in two ways. For Figure 1, similar to the standard calibration procedure, I used the measurements nearest to 150 and 300 kg·cm². For Figure 2, I used the measurements at zero (empty) and nearest to 150 kg·cm².

Figure 1 – Swingweight Deviations with 150 and 300 kg·cm² Calibration

With the standard calibration, using the measurements nearest to 150 and 300 kg·cm², the deviation is fairly small in the range of normal tennis rackets, regardless of leveling. With the rear raised, the effect of gravity is seen at higher swingweights. Gravity adds to the spring force and reduces the period of oscillation. With the left side raised, there is an effect at low swingweights that I don’t fully understand.

Figure 2 – Swingweight Deviations with 0 and 150 kg·cm² Calibration

With the 0 and 150 kg·cm² calibration, the non-linearity of the measurements is a bit more apparent. Raising the rear actually seemed to offset some of the non-linearity present when level. Raising the left side seemed to add to it.

My take-away is that for measuring typical tennis rackets, calibration does a good job of compensating for leveling error. If you’re going to calibrate after, it’s not necessary to spend much time leveling. If your surface is fairly level, it’s probably fine to just leave the leveling feet all-the-way in. Leveling would still be important if you wanted to move the SW1 and not re-calibrate, perhaps if you were taking the device somewhere without the calibration rod. If the device is level when calibrated and level after being moved, the measurements should be good.

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Briffidi SW1 Android App Open Beta

1-NOV-2022 UPDATE: The Android app is out of beta. I have published updated Getting Started videos, and I’ve not received any reports of incompatibility (except virtual gyroscope sensors).

I’m pleased to announce that the Briffidi SW1 Android app is available in open beta. You can join the beta and then download the app from the Google Play Store.

Device Requirements

  • Android 8.1 (Oreo) or later
  • NFC capability
  • a physical (not virtual) gyroscope sensor (see Gyroscope Sensors)
  • a shape/size that fits securely in the cradle of the SW1 (see Physical Size/Shape)

Differences from the iOS App

  • To add your SW1 to the app, just scan the NFC tag under the Briffidi decal. There’s no need to navigate to the device page in settings and tap an “Add Device” button.
  • To delete a measurement or measurement group, long-press it and confirm instead of swiping it to the left.
  • The main button on the Measure tab displays “Place in Cradle” and is disabled until after the phone is in the mounted position.

Tested Phones

  • Google Pixel (original): Working
  • Google Pixel XL (original): Working
  • Google Pixel 6a: Working
  • Google Pixel 6 Pro: Working
  • Huawei Mate 20 Pro: Working
  • Samsung Galaxy Note 20: Working
  • Samsung Galaxy S20 FE: Working
  • Samsung Galaxy S21 Ultra: Working
  • Xiaomi Mi 10 Pro 5G: Working
  • Xiaomi Redmi Note 9: Not Working (virtual gyroscope)

If you try another phone, please leave a comment below or send a note to support@briffidi.com to tell me how it works. I’ll update this list as I hear from people.

NFC Scanning

The NFC reader in an iPhone is located at the top of the phone, so it’s easy to scan the NFC tag on the SW1. Many Android phones have the NFC reader located further down. You may need to lift the SW1 to gain sufficient access to the NFC tag. Because of this, I suggest scanning the tag before leveling the SW1.

Some Android phones have NFC scanning disabled by default. If you have trouble scanning, make sure that NFC is enabled.

It’s not necessary to scan the NFC tag except during initial setup. If it is easy to scan with your phone, you can scan it to open the app (and select the scanned device if you use more than one SW1)

Gyroscope Sensors

Some lower-end Android phones provide gyroscope capabilities via a virtual gyroscope. One tester who tried using the app on a device with a virtual gyroscope reported poor results.

There are apps, such as Gyroscope Test, that will provide details about the gyroscope sensor in your phone. If it reports the gyroscope as “virtual_gyro” or something similar, the app probably won’t work.

I also show a way to test the gyroscope using the app in the video at the top of the page.

Physical Size/Shape

Android phones come in many shapes and sizes. The SW1 was originally designed for the iPhone, which has typical size and shape. The phone-holding features of the SW1 cradle are able to accommodate most but not all phones. The phone must be secure in the cradle for accurate measurements.

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Racket Twistweight from Spinweight and Swingweight

A commenter recently asked on the Effect of Orientation post whether twistweight is really equal to the difference between spinweight and swingweight. It’s a common approximation based on the perpendicular axis theorem. That theorem is valid for planar (two-dimensional) objects. A tennis racket is nearly planar, but as mass deviates from that plane, twistweight will increase slightly.

To quantify the error, I looked back at the CAD model I had created for the Effect of Orientation post.

Here are the moment of inertia properties from CAD:

  • Swingweight: 306.82 kg·cm²
  • Spinweight: 320.01 kg·cm²
  • Twistweight: 13.58 kg·cm²

The difference between spinweight and swingweight is 320.01 – 306.82 = 13.19 kg·cm². The twistweight is 13.58 kg·cm², so there is an error of -0.39 kg·cm² or -2.9%. As expected, the actual twistweight is higher than approximated. This error will vary based on the accuracy of my CAD model and the geometry of the racket, but it should be somewhat close to that value.

I have a prototype device to measure twistweight more directly, as I’ve found a practical issue with determining it from spinweight and swingweight. That issue is a crooked butt cap. When I measure the swingweight of a racket and then flip it 180° and re-measure it, the measured value is often different by tenths of a kg·cm². That’s a small difference in terms of swingweight, but it’s large relative to twistweight determination.

I also have been 3D printing pallets with integrated caps. As seen in the photo, the pallet is two pieces, so the face of the butt end should be nearly perfectly square in the wider direction (affecting swingweight) and perhaps not quite square in the shorter direction (affecting spinweight) if the two halves aren’t perfectly aligned. The door is slightly recessed, so it won’t interfere with measurements.

I measured the racket in the photo using both methods on my SW1. In the first (bottom) measurement group, I measured the swingweight of the racket twice in one orientation and twice at 180°. In the second group, I measured spinweight in the same way. As expected, there was a bit of deviation in the spinweight measurement, likely due to misalignment of the pallet halves. The difference of 13.70 kg·cm² is circled in red. Then, I measured my twistweight device empty and finally with the racket. The more directly measured twistweight of 13.88 kg·cm² is circled in green.

In this sample measurement, there was less difference between the two methods than there was in CAD. I haven’t explored why. There is error in all the measurements, and I haven’t used the prototype twistweight device enough to fully understand its capabilities.

So, back to the original question: is twistweight really the difference between spinweight and swingweight? Not exactly, but it’s a pretty good approximation. Practically, as long as the butt cap of the racquet is square, it’s useful, especially when the goal is to match the twistweight of similar rackets.

Thanks for the question, Ryan.

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Effect of Orientation Error on Racket Swingweight Measurement

A customer with an SW1 recently asked if it matters whether the racket is oriented with the head perfectly vertical, for swingweight, or perfectly horizontal, for spinweight measurements. I suspected that the result wouldn’t be very sensitive, but I wanted to quantify it.

I modeled a racket in CAD and adjusted the material densities to get a string bed of 17 grams and overall mass properties close to a typical tennis racket:

  • Mass: 333.5 grams
  • Balance: 33.2 cm
  • Swingweight: 306.8 kg·cm²
  • Twistweight: 13.6 kg·cm²

Then, I twisted it in 1° increments and output the moment of inertia about the swingweight axis:

Twist (°)Swingweight (kg·cm²)Difference (kg·cm²)
306.82
306.82+0.00
306.83+0.01
306.85+0.03
306.88+0.06
306.92+0.10
306.96+0.14
307.01+0.19
307.07+0.25
307.14+0.32
10°307.21+0.39

From the data, it seems unnecessary to be extremely accurate with racket orientation for typical swingweight measurements. At 5° of twist, which is easy to see, the swingweight result is only off 0.1 kg·cm². However, if measuring swingweight and spinweight to determine twistweight from the difference, orientation accuracy is more important. An error of 0.1 kg·cm² is more significant relative to the magnitude of twistweight.

These results should be valid for any swingweight measurement method.

If you have any questions about the SW1 or racquet measurement, leave a comment below.