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.
Arm side: The effective length and offset angle are little variable when mounting cartridge on the slot holes of shell.
Cartridge side: IEC 98 (1987) recommended the distance from the centre of mounting holes of cartridge to stylus tip should be 9.5mm +/-1mm at recommended tracking force.
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  (Arm distance:237mm) 251 14 20 as per leaflet 63/109
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  Alternative alignment (underhang) 215 -19.6? 0 93.86?
A-1 original setting (overhang 0 as ancient arms) 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 & WE-4700(2019)
English manual for WE-407/23 uploaded at Vinyl Engine indicated  Effective Length 221, which is mistranslation of Arm Distance. Similar case as Sound.
WE-407/TM is unknown in Japan though its design L236mm/offset angle 24 degrees/overhang 15 mm is strange. 24 degrees might be bending angle of pipe (not offset angle).  I would not meddle in this kind of MESS anymore.

SAEC's tradition: they don't care much about alignment while their mechanical precision work is superb.
The front end of shell to arm pivot is indicated as 233mm.
Then the stylus point should be located just under the front-end of shell.

Rather peculiar arrangement or instruction.
12 18.8
(18 as per  manual)
(no null point if L233 Overhang 12 and offset 18 degrees)
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 with slide base & ST-14S(standard) without slide base (same geometry as Guya STO-140). Distance 237 was wrongly quoted as effective length. Similar misleading description is repeated in Japan due to language and preference (bad practice) of indicating mounting distance for exchanging arms. For example: Catalogs from 1980s quoted 227mm for Stax short arms and 300mm for Stax long arms. Maker should clarify the meaning of numbers. Often makers skimp on making explanatory manual.  251 (237 should be distance). When effective lateral length is 237mm, then error angle +1.5 degree/-1 degree as mentioned in leaflet cannot be obtained. 14 20 63/109
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)
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 angle 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.

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.

Importance of Linear Offset length rather than offset angle in arm alignment design. Effective length x SIN(offset angle)=Linear offset length. Offset angle is ASIN(Linear offset length/Effective length). (Total of null points if any)/2 equals Linear offset length. Often users discuss offset angle without questioning why some alignment tools can be applied on many different arms with certain linear offset length.  Arms with same linear offset length have potential for same alignment irrespective of arm length  - this is the basis of each alignment tool for two null points. Of course linear offset length can be different as per arm alignment design.

Null points b, c = Linear offset length +/- alpha.  Proper alignment is obtained by adjustment of alpha: see Alignment Gauges.

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 AT-1120 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 various alignment tools.

BTW:Most of straight arms including SME/Denon DP-7F etc are not straight actually because stylus-arm pivot-countershaft line is not exactly straight. When seeing from stylus point to arm pivot, the countershaft is biased a bit in order to counterbalance laterally the rear part of cartridge whose centre of gravity is set aside to centre line of straight arm. Thus such straight looking arms might be called just slim type of S-shaped arms. Do you like slim one (so-called straight pipe) or fatty one (S-shaped pipe)? AT-1100 sold in Japan around 1979 had interchangeable pipe system: Integral spare pipe ASP-1(straight pipe with fixed shell), Universal spare pipe ASP-11(detachable shell and S-shaped pipe as usual Japanese users prefer) and sub-counter-weight W-3 for using ASP-11. Meanwhile AT-1120 cannot change its straight arm pipe. Both AT-1100 & AT-1120 do not have lateral balance weight, whereas their stylus-arm pivot-countershaft line is exactly straight!

In 1989 Mr. Ho in Taiwan proposed "perfect dynamic balanced arm" and lateral balancing device for shell+cartridge by GB 2229848 (possible improvement for AT-1100/1120).

Though above design looks better and simple for lateral balancing, but its head weight is increased. So I admit that slim type of S-shaped arms is preferable as practical compromise.

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). Example of overhang gauges distributed together with cartridges: One from Denon (stylus location adjusted to the recommended distance from shell neck: usually around 50mm), another from Audio-Technica (measuring overhang directly from spindle). By these devices "Nominal effective length together with overhang" is attained 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 the end of my recspecs 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.

ASPECTS ON ARM DESIGNS: There are more or less important factors than simple tracking angle error. Tracking angle error of swing arm has been discussed for long time (Wilson/Loefgren/Bauer/Baerwald and others) and its calculation to reduce "expected" tracking angle error is almost established.  THEIR DOCUMENTS LOOK GREAT! Hence there are so many followers or "playing groups" for every alignments. On the other hand "how far tracking angle error distortion is audible or not" was not discussed clearly so far.  Mr. Richard Tollerton aka AXON published at AES convention 127 (Oct. 2009): "Digital Simulation of Phonograph Tracking Distortion". I believe his conclusion is "it is not audible in usual music" and his method has been supported by some audio engineers (Axon made test CDR and nobody can discern between original sources and their distorted editions to certain value). Interestingly in case of pure single tone and its distortion, the audible threshold became lower than music consisting of various tones and fluctuating amplitude.  In my humble opinion: alignment calculations are related to something scientific, but difference of alignment effect is not confirmed scientifically. I think every tweak is concerned with taste and not science. One holds what one has.
By the way recently in Japan some "Pure Straight Arms" [PSA] without any offset angle and with underhang (minus value overhang) alignment appeared. In SP era PSA was rather common. Early case of this modern revival in Japan is YAMAHA YSA-2 (limited production in 1985 as option against YSA-1 since arm distance is same 248mm). The comparison of measured distortions between these arms was indicated by Yamaha. In my understanding this is measured by tracing 45 degree sweep L channel (located at outmost) of test record so that these 2nd harmonic distortions are combination of lateral/vertical tracking distortions and vertical tracing distortion - tricky a bit in rushing for their conclusion that lateral tracking error is of no importance. The points of view of PSA supporters: 1) Tracking angle error is not so important. Usually error null point for PSA is designed at the centre of music band i.e., around radius 8cm from the centre spindle. 2) Conventional overhang-and-offset alignment in swing arm has fatal demerit because stylus cantilever is always swayed according to the fluctuating frictional forces - the fixed offset angle as designed tends to be reduced under actual operation by the frictional forces (so to say stretch the end of bow without string).  3) There is such gimmick as inside force canceller or anti-skating bias prepared for swing arm. Its design target is based on the certain fixed coefficient of force divided from frictional force between stylus and record groove. But the frictional forces are changing rather radically and never constant. 4) In case of PSA, the stylus cantilever angle is not affected laterally by the above force (tension) and the cantilever direction remains at the centre of cartridge since stylus point, cantilever pivot and arm pivot are arranged in a straight line as seen from above. 5) The absolute value of side forces inside and outside at PSA is smaller (roughly half) than that (only inside force) of offset arms when arms with same effective length are compared. I will not support any "playing group". We need various points of view. Please note that there are various designs at the corner of the world though one would like to think one is always at the centre of world or playing group!


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

Effective Length L from arm pivot to stylus tip 
Arm Distance from arm pivot to spindle centre
Overhang O extension (Overhang) of arm/stylus point over spindle
Groove Radius groove radius from record (spindle) centre to stylus tracing point
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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