Gramophone styli and groove geometries

The cutting tool on the disc lathe yields a v-shaped groove which is 56μm or 2.2 thousandths of an inch (0.0022") at the top and with the groove walls at right-angles to one another. Consecutive spirals of the groove are separated by an area known as land. The land dimension for 200 grooves per inch (g.p.i.) translates to a groove separation of 125μm (0.005"). The maximum grooves per inch rarely exceeds this figure.

The groove is drawn to scale in the illustrations below. (Note that the illustrations are tilted over by 45° to make the geometry easier to understand.)

The depth of the groove is nominally 28μm (0.0011"). The bottom of the groove is not, in fact, a sharp corner but has a radius of 6μm or 0.25 thou' (0.00025").

A original, standard microgroove diamond stylus of conical (spherical) form has a radius of 25μm (0.001"). The groove width at the point of engagement with the stylus (half-way up the wall of the groove) is 36μm (0.0014") as illustrated at (a).

Arrival of stereo

The groove of a mono record possesses modulation which is entirely lateral (side to side). When a 0.001" stylus rides in such a groove, it rides at the same height at all times; comfortably half-way down the groove.

Stereo gramophone records are different from their mono forebears in that the groove is modulated vertically as well. The RIAA standards for the dimensions of gramophone records defines the depth of this modulation in terms of the minimum allowable-width at the top-edge of the groove. This specified to be 25μm (0.001") as this dimension is illustrated by the red line at (b).

As the illustration at (b) clearly shows, a stylus with a radius of 25μm (0.001") runs a very good chance of disengaging when the groove is that shallow. For that reason, monophonic styli are not recommended for stereo records. Stereo styli adopt a radius of 18μm (0.0007") so as to stand a better chance of staying in a vertically modulated groove as illustrated at (c). But this does, of course, mean that a stereo stylus is rides "lower" in the groove than the mono stylus as illustrated below. (The coloured arrows indicate the point of contact in each case.)

It's worth remembering that the bottom radius of the groove on monophonic microgroove records was not specified, which is why the converse is also true: that a stereo stylus is often unsuitable for listening to mono records.


Tracing

The first sounding turn of the groove of a 12" LP record has a radius of 146mm, and the last a 56mm diameter. The length of the first turn is thus 2 x π x 0.146m = 0.917 metres. And the last, 0.352 metres.

Given that a record turns at 33⅓ RPM, which equates to 1.8 turns per second, the velocity of the stylus within the groove is 0.509m/s (20 inches per second) on the outermost turn and 0.196m/s (8 inches per second) on the innermost. A 10kHz sinewave inscribed in the groove wall has thus a wavelength of (0. 509/10000) = 51μm on the outermost turn of the groove, and a wavelength on the innermost turn of 20μm.

Once again, these dimensions of the basic stylus within a groove are illustrated to scale in in the figures below. It's easy to see how a stylus of standard dimensions may negotiate 10kHz on an outer groove (d), but not on an inner groove (e).


One apparently obvious solution to this is to reduce the radius of the stylus. But, as illustrated at (e), a stylus with a dimension much smaller than about 25μm will ride too low and may even "bottom" in the groove where dust and dirt collect and generate unneccesary noise on playback.

Elliptical styli

The commercial solution to this need to trace high frequency details without bottoming the stylus in the groove came with the elliptical stylus which was invented by Grado in 1964 (although Edison invented a very similar idea in the button stylus forty years earlier). The elliptical stylus is illustrated below which is from Grado's patent.

The elliptical stylus has a major radius (R) of 18μm (0.0007") such that the stylus rides at the correct height in the groove, but has a minor axis (r - usually of about 10μm or less) which improves tracing. The combined dual-radius stylus being referred to, for example, as R/r = 18μm/10μm.

Line-contact styli

More exotic styli are formed by making further cuts to the diamond stylus so that the defining radius is even smaller than with a conventional elliptical stylus. The first of these styli was invented in 1973 to reproduce the high-frequency carrier signal for the extra two channels in CD-4 quadraphonic records and is known as a Shibata type after its inventor. It is illustrated below.

The minor axis of this type of stylus is about 6μm (0.0002"). The Shibata type has been greatly copied, re-invented and developed over the intervening years and is known by a range of different names: Hyper Eliptical; Line Contact; and so on.

Ten years after Shibata, Van den Hull in Holland invented a derivative in which both the front and the rear face of the diamond are cut so that the profile has an even sharper edge. This technique too has been widely copied and is now referred to by a number of names including Micro-line or Micro-ridge. These styli have minor axes of 4μm or less, the smallest being around 2.5μm (0.0001"). This is a very fine edge indeed and a considerable engineering achievement, for this dimension is only about 5 times the wavelength of light.

In addition to the smaller minor radius, the Shibata stylus and its derivatives have sides which are less rounded than a conventional elliptical. In fact, the major radii of these types of stylus are often actually described as >>25μm (0.001") which sounds counter-intuitive. How does a stylus with a major specified radius of >25μm stay in a conventional groove? The explanation lies in that the centre of the two major radii are not coincident as the diagram below illustrates. (Here, both major radii are 75μm or 0.003".)

This is how line-contact styli are referred to as having an apparently impossible radius-ratio of , for example, R/r = 75μm/2.5μm (0.003"/0.0001").

This greater major-radius helps the stylus makes contact with the groove wall over a greater area. The conventional spherical (conical) type theoretically only touches the groove at two points. The difference is well illustrated in the image below. The conical stylus is on the left and the Shibata on the right.

The increased footprint of the Shibata type stylus has a number of benefits. Because the stylus mass acts over a larger area, wear to the record is reduced and, more importantly, the stylus rides on parts of the groove wall where previous spherical styli have not worn away or damaged the information. Thus, even a damaged record, may become playable again with a hyper-elliptical stylus type. Lastly, because the high-frequency resonance of any cartridge is formed by the effective mass of the stylus tip bouncing on the compliance of the plastic record material, a larger footprint makes for a stiffer spring and a higher resonance frequency. These benefits have ensured that the Shibata stylus and its derivatives have gone on to remain the profile adopted in the highest quality cartridges despite the failure of LP-based quadraphonic sound.

Line-contact styli do however have the characteristic that the intersection of the two major radii is close to the bottom of the groove: both the diagram and photograph above illustrate this clearly. Sometimes these styli are truncated to reduce this dimension but these styli types are generally unforgiving of dirty records!

Tiny dimensions: huge forces

If we imagine a sinewave modulated track we can say that the dispacement of the stulus x(t) may be represented by,

x(t) = a . sin (ωt) ............ [eq.1]

where a is a is the amplitude scaling. Now, the voltage generated from a magnetic cartridge E(t) is proportional to the velocity of the modulating signal, or

E(t) = k. v(t) = k . dx(t)/dt ........... [eq.2]

The letter k being a constant which defines the sensitivity of the cartridge. If we let x(t) be the modulation as defined above, we can calculate the velocity (by differentiating), which is,

v(t) = (ω) . a . cos (ωt) ............ [eq.3]

which reveals that the output from a magnetic cartridge rises with (ω) or frequency.

The acceleration of the stylus is given by differentiating this last expression again, thus,

a(t) = -(ω)2 . a . sin (ωt) ............. [eq.4]

The maximum permisable modulation of a record groove utilises all the land between the grooves and thereby has the dimension of about 76μm peak to peak (or 38μm peak). Let's imagine a sinewave modulated groove at 400Hz and substitute these figures in equation [3] and [4].

The peak velocity is a relatively unsurprising 0.1m/s. But the peak acceleration has an (ω)2 term and is,

a(t) = -(6238)2 . 38μm . 1

= 240m/s/s, which is about 24 times the acceleration due to gravity. A surprising figure! And at higher frequencies, the accelerations involved become quite amazing.

Similarly surprising, although the tracking force of a modern cartridge is only perhaps a couple of grams, because the area of contact with the record is so small (about 10μm x 10μm on each side of the groove) the pressure at the contact point rises to,

0.001 / 1 x 10-10 = 10 x 106 kg/m2 (The 1 gram weight is half the total which is shared on the two sides of the groove.)

= 1 tonne per square centimeter. A pressure which causes sufficient friction due to heating that the plastic of the groove wall melts for an instant as the stylus passes over it.

Nude shank

Normally the diamond of the stylus is bonded to a metal shank and this is glued to the end of the cantilever which is flattened at one end to accept the adhesive and stylus assembly. In top-of-the-range cartridges the diamond stylus may be bonded directly to the cantilever without the intervening metal shank. This type of stylus is referred to as a nude-shank type and is generally considered better because the reduction in the mass of the stylus assembly ensures better tracking.

However, there is a proviso. Because the metal shank is not present, the cantilever rides very close to the disc surface and this makes nude-shank styli sensitive to clogging with dust and lint. One tiny thread of lint trapped around the tip can gather small particles and lint like a broom and in a very short time a ball of lint and dust surrounds the tip between the record and the cantilever and this lifts the stylus upward and away from the groove walls.

Nude-shank styli demand that the user keeps her records scrupulously clean.

Styli for "78" records

All the above concerns 33⅓ LP records (and 45's mutatis mutandis). For information on groove sizes and styli for 78 records go to the Help-page about "78s".


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