Table of Arm Data

Linear Trackers & Arms equipped on system players are omitted from list.

Data about Effective Length & Overhang are taken from Stereo Guide (SS) and Maker's catalogues and Internet pages.
There are many discrepancies among them-see also detailed NOTES(1-6).
Offset angle and Null Points are only calculation so that the actual performance of arms may differ from these results.
MAKER MODEL NAME Effective LENGTH OVERHANG OFFSET(degree) Null Points
Audio Craft AC-30/300/3000/3300 237 15 21.5 (22) 61/113 (57/120)
Audio Craft AC-400/4000/4400 283 13 18.5 (17.5) 60/119 (78/92)
Japanese manuals  indicated Offset 17.5degrees for AC-4000/4400 and 22 degrees for AC-3000/3300.
Audio-Technica AT-1501II 282 12 18 56/118
Audio-Technica AT-1501III, IV 285 12 18 56/121
Audio-Technica AT-1503II 254 15 21 61/121
Audio-Technica AT-1503III, IV, IIIa   257 15 21 61/124
Audio-Technica AT-1100/1010/1120 240 15 21.5 60/116
Audio-Technica AT-1001/1005II/1007/1009 240 15 21.5 60/116
Azden PU-402 (SYNTEC S-220) 220 15 22 62/103
Azden PU-547 & PU-550 237 15 21.5 61/113
Azden PU-549 244 15 21 64/111
Denon DA-303/305/307/309/401  244 14 20.5 (21) 60/111 (56/119)
Denon DA-302/304/308/1000 282 12.5 18 61/114
Dynavector DV-501/505/507 241 15 21.5 60/117
Excel ES-801 237 15 22 57/120
Excel ES-1000 & Pro S1TA 240 17.25 22.9 66/121
Fidelity Research FR-12 230 14.5 21.4 60/108
Fidelity Research FR-34 237 15 21.5 61/113
Fidelity Research FR-14/FR-24/FR-54/FR-64 245 15 21.5 59/120
Fidelity Research FR-66S 307 12 16.66 65/111
Fidelity Research FR-66fx 307 12 16.82 63/115
Grace G-540F/640P/704/707/714/727/945 237 15 21 67/103
Grace G-565F/660P/860F/860FB/960 285 15 20 63/132
Guya STO-140 251 14 20.75 56/122
Ikeda IT-407 307 12 16.66 65/111
Ikeda IT-345 & IT-245 245 15 21.5 59/120
Jelco SA-250 & SA-750D (S-shape wand) 229 15 22 59/113
Jelco SA-250st (Straight wand) 228 18 23.75 68/115
Jelco SA-750LB (S-shape wand) 305 15 19 69/130
Lustre GST-1  237 15 21.6? (21) 60/114 (67/103)
Lustre GST-801 240 15 21.6? (21?) 60/117 (65/107)
Micro MA-202 237 15 21.833 (21) 58/118 (67/103)
Micro MA-303 222 15 22.5 (23) 57/113 (54/120)
Micro MA-701, CF-2 (static) 237 15 21.833(2150') 58/118
Micro MA-505, MA-707, MAX-237, CF-1(dynamic) 237 15 21.833(2150') 58/118
Micro MAX-282 & MA-505L 282 12 17.5 61/109
Pioneer PA-100 237 14.5 21.5? 57/117
Pioneer PA-1000 237 15 21.683 (2141') 60/116
RS-Lab   re 215 -19.6? 0 93.86?
A-1 original setting 215 0 0 rotary shell
Saec WE-308N & WE-308SX 240 5 12 39/61
Saec WE-308L 270 5 11.2 44/61
Saec WE-407/23 & WE-317S 233 12 18.8 61/89
Saec WE-317 248 13 19.3 61/103
Saec WE-506/30 295 9 14.4 61/86
Saec WE-8000/ST 306 13 18 60.6/128.5
Satin AR-1/1M/1S 250.5 15.5 21.5 62/122
Sony PUA-237 & PUA-1500S 237 15 22.22 56/124
Sony PUA-286 & PUA-1500L 286 13 18.65 58/125
Sony PUA-1600S 237 15 21.5 61/113
Sony PUA-1600L 286 14? 18degrees? then no null point. 
Offset 19degrees for overhang 14mm might be far better to have null points 64/122mm. Or overhang 13mm for 18degrees might be correct to have null points 65/112mm. see note 3)
Sony PUA-7 235 14 21 58/111
Sony PUA-9 264 14 20 59/121
Sound ST-14 237 14 21 57/113
Supex 6140 245 15 21.5 59/120
Stax UA-7/7N/7cfN/9N 240 13 20 56/108
Stax UA-70/70N/90N 312 12 17 60/122
Technics EPA-100/250/500 250 15 21 62/117
Technics EPA-101S & EPA-121S 220 14 22 54/111
Technics EPA-101L/101T/102L/102T/121L/121T 242 15 21.5 60/118
Technics EPA-99 & EPA-110 235 14 21 58/111
Victor (JVC) UA-7045 245 15 21.667 (2140') 58/123
Victor (JVC) UA-7082 282 12 17.5 61/109
Yamaha YSA-1 262 14 20 60/119
Yamaha YSA-2 pure straight arm 228 -20 0 97.6
ADC LMF-1 & LMF-2 237 15 21.6 60/114
ADC ALT-1 237 19 24.6 69/129
Alphason Opal/Delta/Xenon/HR100S 229 18 24 66/121
AudioQuest PT-6/7/8/9 229 18 24 66/121
Belcanto Unipivot 10" 243 16 21.75 66/114
Belcanto Unipivot 12" 307 14 18.35 66/127
Breuer Type 5A 228 20 25.5 68/128
Breuer Type 6A 262 17.2 22 68/128
Breuer Type 7 & 8 249.44? 18? 23.1? 68/128
Brinkmann 10.5 266.7 15.4 20.5 66/121
Clearaudio Unify 9"  239.3 17.3 23 66/121
Decca International & Professional for transcription 12-16inches and SP record as well? 228.6 (9inch) 15.875 (0.625inch) 26 45/155
Empire 980 & 990 228.6 (9inch) 17.5? (manual indicates  5/8inch=15.875mm) 23.8 64/121? (53/131 and error+/-0.65degree?)
EMT 929 (it is questionable that RF229/RMA229 made by Ortofon for EMT 930 turntable had exactly same geometry as EMT 929) 244 14 20.833 57/117
Graham Model 1.5t (US Patent 4686664: "for purposes of explanation only, one arm has the following dimensions: effective length 235 mm, offset angle of 23.5 degree and overhang of 17.638 mm." )   Baerwald "1" or Loefgren "2" overhang can be selectable. 235=Baerwald 17.6 (17.638) 23.4 (23.5) 66/121 (65/122)
235.5=Loefgren 18.1 (18.138) 23.38 (23.45) 70/117 (70/118)
Gray  108 Viscous Damped (Uni-Pivotted) Transcription  Arm in MONOPHONIC AGE Effective length 11inches [279.4mm] is unchanged while arm distance & overhang should be adjusted per playing record sizes as per instructions 9.525mm for 12" records [IMO: applicable also to 16" records] Geometrically fixed around 15 or 16 degrees. But to obtain null point with overhang more than 11mm, the cartridges should be mounted askew. 51/103 if offset is 16 degrees
12.7mm for less than 16" records, though unreasonable NIL
25.4mm exclusive for 16" records, though unreasonable NIL
Hadcock GH228  228.6 15.75 23 57/121
Hadcock GH242 Special Edition 243.8 17.8 23 69/122
Helius Orion 252? 16? 21.5? 65/119?
Helius Aureus & Scorpio 228.6 18 24 66/120?
Immedia RPM-2 254 16 21.5 65/121
Infinity Black Widow 237 15* 21* 67/103*
JML Co. TA-3A 229 18.156 24.102 66/121
Keith Monks M9BA Laboratory Arm MKIII 228.6 12.7* 19.7* 60/94*
Kuzma Stogi 230 18 24 65/122
Linn Akito/Basik/Ittok/Ekos 229 18 24 66/121
Logic datum S 228 17.3 23.5 65/117
Magnepan Unitrac-1 241.3 17.145 22.8 66/121
Manticore Musician/Magician 227.48 16.78 23.6 60/122
Manticore Magician 12inch 304.8 20 21.967 79/149
Mayware Formula 4 Model PL S4/D 224 15 22.023 60/108
Mayware Formula 4 MK III/IV/V 229+/-3 around 17 around 23.5 around 63.5
Mission 774 Original 229 13.6 20.5? 60/100?
Moerch DP-6 & UP-4 230 18 24 65/122
Naim Aro 230.5(230) 18 24 65/122
Odyssey RP1-XG & RP1 Gold 230 17.2 23.5 63.5/120
Ortofon RMG-212 & RS-212 228 16 22.7 61/114
Ortofon RMG-309 320 11 15.9 60/115
Ortofon SMG-212/SKG-212/AS-212 228 16 22.7 61/114
Rega RB250 & RB300 237 15 21.63 60/115
Roksan Artemiz/Tabriz 240 17.5 22.9 68/118
Schroder Model 2 and Model DPS 239.3 17.3 23 66/121
SME 3009 Series II improved with non-detachable shell and imp/S2 with detachable shell: (early=Serial Number less than 439606). Don't mix up previous Series II with imp/S2. See pdf arranged by SME for the identification of specific models IMO: S2 was named after the lightweight shell type S-2. 231.2 15.86 22.6 60/117
SME 3009 II imp & imp/S2: (later=S/N 439606 or above) 231.2 17.95 23.84 66/121
SME 3009III &3009IIIS (original/smaller shell) 229 16 22.8 60/117
SME 3009III &3009IIIS with modified wand (larger shell) 233.2 17.8 23.62 66/121
SME 3009R 233.2 17.8 23.62 66/121
SME 3010R 239.3 17.3 22.985 66/121
SME 3012R 308.8 13.2 17.615 66/121
SME V/IV 233.15 17.8 23.635 66/121
SME 309 232.32 16.97 23.204 64/119
SME 310 238.5 16.5 22.569 64/119
SME 312 308.19 12.59 17.278 64/119
SME M2-9 233.2 17.8 23.62 66/121
SME M2-10 239.3 17.3 22.985 66/121
SME M2-12 308.8 13.2 17.615 66/121
SUMIKO  MMT/FT-3/FT-4 239 17.3 23 66/121
Syrinx PU-2 with minimum shell sliding on wand/PU-3 with fixed shell 228 16.6 23.4(23)? 60/121(64/114)?
Thorens BTD-12S 207.5 17.5 25.25 59/118
Thorens TP16II with TP-62 230 14.4 22 54/118
Thorens TP16III with TP-63 232 16.4 23 61/120
Wheaton/Tri-Planar Tri-Planar MKIV Ultimate 250 16.5 22 65/122
Wilson Benesch ACT2& ACT 0.5 237 17.5 23.22 66/121
Zeta Zeta 228.6 18 23.75 68/116

NOTES: there are many discrepancies in the descriptions/performance of arms due to the following reasons.
1) Manual and model do not always coincide (manual is not enough if there are too many modification:
history of models may be required). Some dimensions (esp. effective length) of same model may differ between early manual and later manual even though the product itself remains unchanged. And vice versa: same model may change dimensions without referring to them. Often we find irregular conversion from inch to mm in the manuals for UK/US products.
2) Incorrect worked angle: the processed tube will tend to change the angle after a while
(someone said that Mr Breuer was watching his arms for more than 3 months).
What is the worked allowance for the offset angle of bent arm?
3) Misprint or dubious description in original documents or repetition from secondary sources. Moreover many documents show unreliable descriptions on error angles irrelevant to the geometry of arm. There is no standard style of description/definition about error angles. Some adopted average error angle divided by groove radius (for example: 0.1degree/cm). Other adopted maximum error angle at optional radius of groove or size of record. Usually maximum error range +/-degrees are mentioned without specifying the range of groove radii. Who knows: the designer is nonchalant about geometry or the manual is wrong from typo or the manufactured arm is not made in accordance with drawing/manual etc?
4) Strained to some fixed ideas such as Baerwald/Loefgren designs. For the honour of them, please note that so-called Stevenson/Baerwald/Loefgren designs are not directly related with them who gave mathematical solution, method and thought on lateral tracking error.
Some fixed ideas of designs will lead us to overlook the actual product as it is produced.
In case of my KMAL M9BA MK3 Serial No. 75187(fixed shell with 2 thread holes for inch screws),
the linear offset measured is 77mm(19.7degree)
- far from 89mm(23degree) as proposed by Audio Magazine 1980 which stated O16.2 A23 NP60/118.
*Keith Monks M9BA MKIII L228.6 O12.7 A19.7 NP60/94 when linear offset is 77mm.
I suppose that the actual geometry of my arm is similar to the above simulation.
Arm Distance (Spindle Centre to Base Centre) Mounting template indicates 8.5inch
Arm Effective Length (from arm pivot to stylus): nominal 9inch
Overhang: 0.5inch as a result and also matching to my arm. There were various headshells so that the offset angles might be differing among these shells (perforated one/black thin plate shell of mine/big and robust one as seen in the picture gallery of The Vinyl Engine). Anyway incredible offset angle 23degrees and overhang 12.7mm were described in documents for early M9BA with robust shell (M9BA MK I) originally produced by Audio & Design around 1967. But alignment under such geometry shall indicate funny null points such as 41/137mm - it might be intended for transcription disks: effective 9inch arm for 12inch records, 12inch arm for 16inch records? See also null points on Decca International/Professional.
In case of my Infinity Black Widow with silicon oil bath and SME type bedplate 60.5x41mm.
Audio Magazine 1980 stated L237 Distance222.641 O14.359 A21.017 NP60/110.
*But original setting template indicated distance 222mm and I think that L237/Offset 21degrees/Overhang 15mm/Distance 222mm shall be more realistic design figures. Then Null points 67/103mm though I could not confirm these figures since I have not original alignment template. Anyway the linear offset length is approx. 85mm as I measure.
5) In case of Thorens, there is much confusion due to the different exchangeable head tube (Endrohr) types such as TP62 & TP63. Actual offset, Overhang & Effective length shall be determined with the combination of head tube/shell and arm tube.
6) Some old & longer arms are designed for transcription or sound track record (16inches). I think there was standard broadcasting equipment recommended by NAB in USA or BTS in Japan though I could not find any specific document but  suggestion in old catalogues. It is interesting to note that the distance (from arm pivot to turntable spindle) of such arms (Audio-Technica AT-1501II, Denon DA-302, Grace G565 & Gray 108 etc) is mostly around 270mm. Decca International/Professional arm has strange geometry in order to play back SP, EP and LP as well. This is the meaning of "Professional" or "Broadcasting" use.

General Dimensions of Disks SP 30cm EP 17.5cm MP 25cm LP 30cm(12inch) Transcription 16inch Disks as specified in IEC98-1958
Innermost radius (mm) of music groove 47.6 RIAA(1963) 53 JIS(1973) 57.6 JIS(1973) 57.5 DIN(1981)/57.6 JIS(1973)/60.325 RIAA(1963)  60 for fine groove 33.3rpm*see remark, 47.5 for coarse groove 78rpm, 95 for coarse groove 33.3rpm
Outermost radius (mm) of beginning or music groove  146.3 IEC(1964)/RIAA(1963) 84 JIS(1973) 121 JIS(1973) 146.3 IEC(1964)/146.5 JIS(1973)  196.85
Remark*:  In the first edition of IEC98 (Section F5 Page 21) the "minimum diameter of recorded surface"  120mm (4 3/4inches) is quoted for transcription recordings  (for broadcasting use) only. There is no corresponding description about minimum diameter for commercial disk records (Section E).  However RIAA indicated 4 3/4inches for LP. Sometimes in actual records we find irregular disks which are not complying with any standard.

I believe the users know the worked products better than designers or manufacturers. Hence please email to me if you find reliable data confirmed/measured by yourself (hearsay evidence is unwelcome - I've had quite enough of such kind).

Above and following calculations are based on my EXCEL sheets about Overhang adjustment on shell & comparison of arm designs which can be used at your end after saving it if you like.

Please note that "geometrical offset angle" is not same as headshell offset. Headshell offset or German wording for offset "Kroephung"( "bending the pipe") is leading us often to misunderstand the geometrical meaning of "offset angle". See above drawing. HO=Headshell offset angle to the straight pipe measured at the neck of shell or at the centre of slots for mounting cartridge. A=true offset angle is measured at stylus point against the imaginary straight line from stylus tip to arm pivot. Hence it is not easy to measure the offset angle from appearance. Linear offset can be measured with a carpenter's square. The overhang adjustment on shell is not changing linear offset length as far as the cartridge is mounted square within shell (see above right drawing) - that is changing the effective length and the distance between two null points-  see the details on another sheet: Alignment.xls    IMO: The discernible limit on our adjustment of cartridge azimuth on shell is: 0.5mm in length and/or 1 degree only so that I cannot believe too much in any method of alignment. The thickness of grids on protractor must be made very thin and we must discern the difference of 0.1mm order for obtaining exact angle alignment as seen in the following table. Man confident of having such good sight ability might be happy enough. Now I have poor sight. [15inch monitor screen (4:3=12x9inch) having 1024x768pixcels : one pixel size is about 0.3mm - Can you find any dead pixel/dot on your screen?] It resembles "the problem of mice who bell the cat" in Aesop's Fables. There is much difference between armchair theory or calculation and actual practice. According to another chart indicated in my recspecs page, the adjusting method of anti-skating bias by seeing the deflection of cantilever is also not valid. But in real world, self-assurance or conceit prevails among some audiophiles who would say "we did it perfectly", but nobody can testify their performance.

angle deviation (degree) deviation in mm  
When the side of cartridge body having straight 20mm outline is aligned to grid lines on any given protractor: deviation in mm (front and rear ends of cartridge) 0.5 0.17
1 0.35
1.5 0.52
2 0.70
When the direction of cantilever  having whole length 8mm is aligned to grid lines: deviation in mm (front and rear ends of cantilever) 0.5 0.07
1 0.14
1.5 0.21
2 0.28
In either case, there arises parallax or deviation due to one's observing point because "the whole cantilever" cannot be seen from just above or under.

SME drawings for series V/IV (& 300) are also misleading or confused by indicating: 

  1. headshell offset D instead of true offset angle (=D minus included angle between grey line and wand centre line) 

  2. pivot to tip distance (A) projected laterally to horizontal line instead of straight effective line from pivot to tip

If stylus tip is located at the centre of C, then effective length indicated by SME is incorrect.
If we take the given dimensions as design drawing and not for the template for alignment, 
then what should be calculated dimensions based on drawing?
True effective length straight from pivot to tip 233.181 mm
True offset angle when headshell offset angle D to wand is 23.635degrees 22.699 degrees
Linear offset length 89.983 mm
With given overhang F=17.8mm.   Null points: 79.381mm &  100.584 mm
Hence if SME is truly intending Baerwald type alignments (Linear offset around 93.5mm),  then we should amend the data on drawing as follows (or amend the drawing itself - it might be better for user since overhang definition F is not correct) When stylus tip has 9.5mm distance from the centre of mounting holes.
Headshell offset angle D to make true offset angle 23.635 as a result 24.6 degrees
Lateral projected length A to make true effective length 233.15 233.116 mm

The above confusion seems to be arising from shell design. The following drawing of AT1120 for example shows various cartridges with 103mm distance from the centre of mounting holes to tip can be used/aligned on this shell. This allowance 103mm (no mention of tracking force) should comply with JIS standard(1979) about pick-ups. IEC(1987) recommended cartridge mounting holes centre to tip:  9.5mm +/-1mm at the tracking force recommended by the manufacturer though the latter recommendation is not adopted by many cartridge makers except Audio Technica/Shure etc.

Here headshell offset angle equals actual offset angle because of the following reasons:

1) centre headshell line is parallel to the headshell offset line to wand in drawing 
2) stylus tip is located at the extension of wand centre line

Thus there is no fixed alignment in design, make and performance (so that I believe alignment with protractor is effective as compromising method). Please also look into my another page about various alignment gauges in the past.

Alignment Table & Designs of Arms

I calculated offset angle and suitable overhang based on conventional/expedient linear offsets each specified for Stevenson and Baerwald types (these linear offsets were based on disputable/dubious recorded groove radii: inner groove radius 60.325 and outer radius 146.05mm). I assume that Stevenson in type 1B tried to compromise with smallest music radii of record formats: 7inch records for 45rpm & 33 1/3rpm (RIAA 2 1/8inch=53.975mm) and 12 inch LP records (DIN 57.5mm). His method is not differing from Baerwald essentially. It is a matter how to set inmost groove and outmost groove of actual records to be played on. Most Japanese arms seem to be designed similar to Stevenson type for EP/LP and have often constant overhang 15mm for arm length ranging from 230 to 260mm.  See also my reading of Stevenson paper.

Effective Length of Arm: L Linear Offset 88.873mm Linear Offset around 93.5mm
Stevenson Overhang Baerwald Overhang
mm degrees mm degrees mm
200 26.4 18.6 27.9 21.1
205 25.7 18.1 27.1 20.5
210 25.0 17.6 26.4 19.9
215 24.4 17.2 25.8 19.4
220 23.8 16.7 25.1 19.0
225 23.3 16.3 24.5 18.5
230 22.7 16.0 24.0 18.1
235 22.2 15.6 23.4 17.6
240 21.7 15.2 22.9 17.2
245 21.3 14.9 22.4 16.9
250 20.8 14.6 22.0 16.5
255 20.4 14.3 21.5 16.2
260 20.0 14.0 21.1 15.8
265 19.6 13.7 20.6 15.5
270 19.2 13.5 20.2 15.2
275 18.9 13.2 19.9 14.9
280 18.5 12.9 19.5 14.6
285 18.2 12.7 19.1 14.4
290 17.8 12.5 18.8 14.1
295 17.5 12.3 18.5 13.8
300 17.2 12.0 18.1 13.6
305 16.9 11.8 17.8 13.4
310 16.7 11.6 17.5 13.1
315 16.4 11.5 17.3 12.9
320 16.1 11.3 17.0 12.7

Generally for the Japanese arms, the overhang is instructed while the place of Null points is often neglected. "Japanese record-philes" have usually several cartridges ready to use equipped on head shells (there was an accessory named "cartridge keeper or headshell stand") and are exchanging the cartridges along with head shells so frequently to enjoy the respective reproducing sound. Hence simple adjustment method (lengthwise adjustment on shell) is enough for them. Overhang is not measured directly in many cases and usually overhang adjustment is done indirectly by measuring the stylus point on shell lengthwise from the neck of exchangeable headshell when arm is pre-mounted on record player (i.e. arm distance from arm pivot to turntable spindle is already fixed so that proper overhang is obtained by adjusting effective length of arm as designed). On the other hand the method for adjusting null points and offset angle is very clumsy thing: I doubt that  users can adjust their specific arms perfectly in accordance with alignment tools as designed. Moreover the distortion due to lateral tracking angle error is not so great as compared with other distortions (i.e. tracing distortions).  We can calculate an expected distortion due to lateral tracking angle error, but there is no actual measuring data of this distortion respectively because this rather small distortion (less than 2%) is usually masked by other much bigger distortions (often exceeding 10%) in playing a record actually. As far as I know, any authentic measuring method of this distortion due to lateral tracking angle error is not yet established. Also read my recspcs about the comparison of various distortions. Very often we discuss an expected distortion due to lateral tracking angle error while we neglect an expected distortion due to vertical tracking angle error. Maybe it is again not so big problem when we hear monaural recordings (lateral recordings) only. Also read my VTA page.

GEOMETRY OF ARM: LATERAL TRACKING ANGLES

Explanations of drawing: the arc of radius L is tracking with pivoted arm while the arc of radius r is groove . 

Definition:
Effective Length L from arm pivot to stylus tip 
Arm Distance from arm pivot to spindle centre
Overhang O extension (Overhang) of arm over spindle
Groove Radius groove radius from record (spindle) centre to stylus tracing point
Equations:
No.1 L=D+O
No.2 Tracking angle An=90-c a=ACOS ((D^2+L^2-r^2)/(2*L*D))
No.3 COS c=(L^2+r^2-D^2)/(2*L*r) b=ACOS ((D^2+r^2-L^2)/(2*D*r))
c=ACOS ((L^2+r^2-D^2)/(2*L*r))
No.4 Tracking Angle An=90-ACOS ((L^2+r^2-D^2)/(2*L*r))
Note on Equation No.3 (cosine theorem): C^2=A^2 +B^2 - 2*A*B *cos c

VARIOUS EQUATIONS of tracking angle (An) at specific groove radius.
(based on D) =Equation No.4 90-DEGREES(ACOS((L^2+r^2-D^2)/(2*L*r)))
(based on O) 90-DEGREES(ACOS((2LO+r^2-O^2)/(2*L*r)))
(based on D) DEGREES(ASIN((L^2+r^2-D^2)/(2*L*r)))
(based on O) DEGREES(ASIN((2LO+r^2-O^2)/(2*L*r)))
(based on O) DEGREES(ASIN(0.5r/L+(L/r)*(O/L-0.5*(O/L)^2)))
(based on O) DEGREES(ASIN(0.5r/L+(2LO-O^2)/(2*L*r)))
These six equations are essentially identical.

Tracking angle at specific groove radius - Fixed offset angle = Error angle at specific groove radius. 

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