Verifying BTU Spacing for 50.8mm Ball Compatibility

[robbiemu]

Hi,
I have a question about ball compatibility. I can source a very high-quality 50.8mm diameter ball that I'd prefer to use if possible, but I need to verify it will fit properly. The device listing mentions it works with 52mm and 55mm balls. I wanted to understand the geometry to see if 50.8mm would also work.
I attempted to measure the BTU spacing in the STEP file using FreeCAD (though I'm not experienced with CAD tools). When I measured the distance between what appear to be the centers of the three BTU contact holes, I get 44.31mm.
Using this measurement, I calculated the geometry:

For three BTUs in an equilateral triangle with 44.31mm sides, the support radius is $44.31\div3 = 25.58mm$
This means the minimum ball diameter that can rest on all three BTUs is approximately 51.2mm ($2 * 25.58mm$) -- which is shockingly close to the circumference of the smaller ball that is offered so I probably am doing something wrong. A 50.8mm ball has a radius of 25.4mm, which is smaller than the 25.58mm support radius, it cannot physically contact all three BTUs simultaneously.

Could you confirm:

• Is 44.31mm the correct center-to-center spacing between the BTU contact points? If not, what is the actual BTU spacing?
• Based on the actual geometry, would a 50.8mm ball be compatible, or is the valid range strictly 52-55mm?

I suspect I may be measuring the wrong dimension in the STEP file, which is why I'm reaching out to verify.

[efogdev]

Hi! It's actually not just about the size. These sensors are particularly picky to color. However, the smaller the ball, the more optimal the distance to the lenses becomes. I've tried 50.8 mm from Adesso T50 — works perfectly, and also I have some 49.6 mm balls which work either, but I'd guess it's borderline acceptable. Btw, not sure where you've seen info on 52-55 mm, I'm specifying 50-55 mm everywhere. I even sell 50 mm POM and PC balls.

P.S. Distance between the sensors is not equal. The triangle is isosceles not equilateral.

[robbiemu]

The smaller ball is listed as 52mm in the shop. That is where my confusion came from.

Im surprised about the color concerns. Can you describe that a bit more?

I can get either a fine grade zirconia or Si3N4 -- so white or black. Both are "mirror" polished, so the friction would be very, very low. I was going to get Si3N4 for the lower weight ( still twice the density of resin ). The idea is something that is relatively heavy, but not fatiguing, and super low friction.

Ive seen a similarly "bearing grade" zirconia control ball working with the ploopy adept sensor.

I understand you were thinking about upgraded sensors later as well, so this comes into consideration too.

[robbiemu]

I think I got a satisfying answer about the reflectivity needed with such materials, thanks to models like chatGPT (et al). I think it is not so much about the color as the reflectivity, although a mirror finish on a dark material is marginally worse than on a light material. Adjusting the roughness increases diffuse reflection at the cost of higher friction (the low friction is the reason you might want to go with an exotic material in the first place):

Si₃N₄ bearing balls — how surface roughness and material optics affect PMW3610 laser tracking

The PMW3610 uses a near-infrared VCSEL whose light falls mainly in the 830–865 nm band. To track motion, the sensor relies on diffuse speckle contrast. It cannot track a clean mirror reflection; it needs the surface roughness to scatter light back into the aperture.

A standard rough-surface model gives the specular fraction:

$$ R_{\text{specular}} \approx e^{-(4\pi Ra/\lambda)^2}. $$

If we require a usable signal floor (sufficient diffuse photons returning to the sensor), the physics dictate a critical roughness threshold relative to the wavelength:

$$ Ra_{\min} \approx 0.057\lambda. $$

Using the actual PMW3610 band (830–865 nm) produces:

Raₘᵢₙ ≈ 47–49 nm ≈ 0.05 μm

Below this, the surface is “optically smooth” at NIR wavelengths.

Material optical behavior (The "Dark Mirror" Factor)

Silicon nitride and zirconia behave differently in the infrared, which dictates their safety margins:

• Si₃N₄ (Dark Mirror Risk):
  Bearing-grade Si₃N₄ is dark gray or black. It has low natural reflectivity (~11%) in the IR spectrum.
  Because the material itself returns so little light, you cannot afford to lose signal to specular reflection. You need higher roughness to force a larger percentage of that meager light back to the sensor.
• ZrO₂ (Higher Albedo):
  Zirconia is typically opaque white or ivory. It has a higher refractive index and optical albedo.
  Even if the surface is smoother, the material reflects more total light, giving the sensor a stronger baseline signal to work with.

This difference explains why zirconia allows for slightly less roughness—it has a "brightness" buffer that Si₃N₄ lacks.

---

What this means for your Si₃N₄ ball (Ra = 25 nm)

Your Si₃N₄ ball at Ra = 25 nm (0.025 μm) presents a critical failure mode.

1. The Geometry: At 25 nm, the surface is effectively a mirror to the 850 nm laser.
2. The Material: Because Si₃N₄ is dark, the light that enters the ball is lost, and the light that hits the surface bounces away specularly.

Result:
Signal Starvation.
The sensor will likely see a total signal return of <1.5%, which is well below the reliable tracking floor. The sensor will interpret this as "Lift-Off" or simply fail to register motion.

A comfortable “safe” tracking range for Si₃N₄ is:

Ra ≈ 80–150 nm
Smooth to the touch, but optically rough enough to ensure the signal rises above the noise floor.

---

TL;DR — Zirconia comparison

• Si₃N₄: Low Reflectivity + Smooth Surface = Invisible to Sensor.
• ZrO₂: Higher Reflectivity = More forgiving.

ZrO₂ minimum Ra: ~40–45 nm
Practical reliable range: ~60–120 nm

This is why zirconia is the safer choice if you are forced to use a smoother, high-precision bearing grade.

Despite appearing black, ceramic Si₃N₄ can still work fine with an optical mouse sensor as long as:

• Surface roughness is in the 50–200 nm Ra range → gives enough speckle contrast.
• Reflectivity ~5–15% at 830–860 nm → still usable for VCSEL sensors.
• No translucent diffusion (balls are opaque, which is ideal).

--

I have a custom spreadsheet for overall "ball feel" that I spent a couple of days building. It models how different materials will behave at different size, sphericity and roughness, and I used the above formula to adjust the minimum roughness for materials. (So for example, using the above we need at least 55nm - a bit above mirror grade, for Si3N4.) You may not find this useful in the slightest, it reflects my biases for agility, inertia, and fatigue, but anyway:

	34	38	40	44	50	55
Overall	Polished Steel	Polished Steel	Zirconia	Zirconia	Si3N4	Glass (Soda Lime)
Second	Brass	Zirconia	Polished Steel	Alumina	SiC	Si3N4
Agility	Tungsten Carbide	Polished Steel	Zirconia	Zirconia	Si3N4	Si3N4
Inertia	Teflon	Teflon	Teflon	UHMWPE	UHMWPE	UHMWPE

Here is the table adjusted for RSI/sensitive users (much more weight dependent):

	34	38	40	44	50	55
Overall	Alumina	Si3N4	Glass (Soda Lima)	"pool ball" Resin ($1.8 g/cm^3$)	Resin	UHMWPE
Second	Si3N4	SiC	Si3N4	POM	Nylon	Nylon
Agility	Alumina	Si3N4	Si3N4	Glass (Soda Lima)	Resin	Nylon
Inertia	Si3N4	Teflon	"pool ball" Resin ($1.8 g/cm^3$)	POM	UHMWPE	UHMWPE

I also calculated the same for the Ploopy adept's optical PMW3360, and the table really doesnt change even though the optical sensor is more forgiving.

[efogdev]

FYI the sensors I'm making an upgrade for are PAW3805EK-CJV1 and PAW3395DM

[robbiemu]

Ok cool! So the first is for people who want to track on glass (and still dont demand a gaming sensor), and the second is maybe MY NEXT SENSOR.

The material issues I was talking about won't change much.. the first sensor is even more dependent on surface features, the second is more like the one I know from Ploopy.