VPI tonearm geometry
An attempt to understand the geometry of VPI tonearms
The geometry used by VPI tonearms is presently undefined and this article will attempt to provide a better understanding of VPI’s tonearm geometry. I’m not the first to have questioned VPI’s tonearms. John Elison, for instance, contacted Harry Weisfeld several times over past years requesting VPI’s geometry parameters. Except for the numbers provided on VPI’s website, John never received an answer to his questions concerning the second null point or his request for more precise and exact data.
My point is not to criticize VPI because all vinyl fans know the high quality of VPI products. In fact, I am a very happy user of a VPI 16.5 RCM imported from the United States at a time when VPI didn’t have distributors in Europe. However, I would love to own a VPI turntable in the future. Therefore, my approach is one that any customer aware of tonearm geometry theory might have when looking at the rather unconventional data provided by VPI.
We will discover (if you can finish this long and boring paper) that, finally, the alignment proposed by VPI and by their jigs is really interesting.
Harry, why didn’t you tell us before!
Official data for VPI tonearms can be found here
|JMW 9||JMW 9 +||JMW 9 Sig||JMW 10||JMW 10.5||JMW 10.5i|
|Spindle to pivot||223mm||223mm||223mm||250mm||250mm||262mm|
What is the problem with this data?
The problem is that when you combine data to calculate the null points, you’re not obtaining the first null point at 66 mm.
With the JMW-9, JMW-9 PLUS and JMW-9 SIGNATURE, following the indicated mounting distance, angular offset and overhang, you’ll obtain null points at 49.16mm and 140.6mm.
With the JMW-10 and JMW10.5, the pair of null points you’ll obtain will be 53mm and 145.4mm. With the JMW10.5i, the null points will be at 52mm and 155.5mm (out of the LP).
Since the first null point is declared to be 66mm, the real data behind VPI tonearms are not the data provided by VPI.
In fact, this is not that important since VPI provides a jig to help users align their cartridge. This jig is rather unconventional since there is a unique null point but, when using the jig, you must point it to the pivot of the tonearm. Two jigs were evaluated in this report—a black one and a white one.
Let’s now understand certain issues regarding alignment.
We’re about to present some calculations. These calculations are not related to any assumptions made by Löfgren, Baerwald and others who provided various pairs of null points we’re usually using. This is just simple geometry.
Let’s begin with this first question: “What is a null point?”
At a null point, the projection of the cantilever onto the record’s surface is exactly perpendicular to a line passing through the platter’s spindle and the stylus. In other words, tracking error is zero at a null point and there can be a maximum of two null points for pivotal tonearms.
Let’s make a drawing to visualize the null points:
Null points are measured by their distance to the spindle centre i.e. AC (NP2) and CB (NP1). The angle formed by the line passing through the stylus and the pivot of the tonearm and the projection of the cantilever onto the record’s surface is named the offset angle (AOffset). Once set up, the offset angle is fixed.
The linear offset is given by OA* Sin (offset angle) = OB* Sin (offset angle) (since OA and OB are equal to the effective length).
This linear offset is equal to DB and AE. Therefore, it follows that:
Linear offset = NP1+DC
Linear offset = NP2-CE
Let’s now take a look at the triangles ODC and OEC with right angles at D and E. Those triangles share one common side, OC. and OD = OE = OA * Cos (offset angle) =OB * Cos (offset angle). It follows that DC=CE
And then the linear offset is (NP1+NP2) / 2
DC = CE = (NP2-NP1) / 2
Whatever the effective length, if you choose a pair a null points, the linear offset is simply a function of the pair of null points you choose.
I asked VPI jig users to measure the angle OCB on their jig. What is the theoretical value of this angle?
Let’s begin with the DCO angle – once we have this angle, OCB will be 180-DCO.
DCO is given by: ArcCos ((NP2-NP1) / (2OC))
And then, OCB is 180 - ArcCos ((NP2-NP1) / (2OC))
Remember that OC is the mounting distance and for a given pair of null points, the angle OCB is a function of the mounting distance.
Let’s call the angle measured by users, Alpha.
Our goal here is to obtain the value of the second null point (since it’s not provided by VPI). Let’s consider the mounting distance as known. We now need to resolve this equation:
Alpha = 180 – ArcCos ((NP2-NP1) / (2OC))
180 – Alpha = ArcCos ((NP2-NP1) / (2OC))
Cos (180 – Alpha) = ((NP2-NP1) / (2OC))
NP2 = 2OC * Cos (180 – Alpha) + NP1
Once we know the second null point, all other data relating to the geometry of the tonearm alignment can be calculated from the following equations:
Effective length = (OC² +NP1*NP2)0.5
Angular offset = ArcSin ((NP1+NP2) / (2*Effective length))
Overhang = Effective length – mounting distance
Measurements of the VPI jigs
I asked users of the VPI jigs on various vinyl forums (Vinyl Engine, Vinyl Asylum and the LS3-5a French forum to take their jigs and measure the inner null point as well as the angle of the grid to the stylus/pivot line. (And I would like to thank those users: John Elison (VA), Musikmike (VE & VA), Lanny (VE), Naturalman, bbill (;-)) (LS3-5a))
There is no real doubt about the position of the null point on the black VPI jig, which is 68.75mm. About the white one, I have only one measurement of 68.0 mm.
Now, the grid angle for the white jig has been measured at 96.2°. For the black jig, things are rather complicated. Most users measured that angle to be 96°. Now, John Elison indicated to me that the spindle hole is closer to the edge than the centre of V by about 2.2 mm. Because of this, John Elison measured his black jig’s grid angle to be 95.5°. I’ll provide numbers for those two values.
The black jig is supposed to work with JMW 9, 10 and 10.5 tonearms; the white jig is supposed to work with 10 and 10.5 series. We supposed in our previous calculations that the mounting distance is known. For the JMW 9, a mounting distance of 223 mm is given by VPI on their website. Now, on VPI turntable, this arm is mounted at 222mm (measured by users with a Feikaert jig). Since, our results depend on the mounting distance, this explains why, in the next tables, we’ll indicated the second null points and so on for various mounting distances.
In the center column of the table there are three columns of numbers. The first two columns represent the black jig while the last column (with an angle of 96.2°) represents the white jig. There are no values for the white jig with the JMW-9 because it was applicable only to the longer tonearms.
First result: there is no clear outer null point. This is a direct consequence of the construction of the jig.
Please understand that the data is determined by the VPI jig.
Let’s now compare the pairs of null points we obtained with more traditional approaches (Löfgren A (aka Baerwald) and Löfgren B).
For the 9” tonearm, I took the mean value of the outer null point (113,43) and a mounting distance of 223 mm.
In the two last lines of the table, I calculate the average %RMS distortion over the record length and over the last third of the LP. Our idea here is to have a single number represent the distortion caused by one or another pair of null points. I’m providing the %RMS for the last third of the LP side because, when searching on the Internet about VPI geometry, Bbill (LS3-5a forum) found this text:
Harry Weisfeld once said: "I use a Mitch Cotter system described by Peter Axcel in The Audio Critic. I find it to be the best sounding of the bunch. On the JMW-9 the jig we supply will give you lower distortion in the final third of the record. Just a point of view difference but they sound a bit different. Listen to both and you decide in your system with your cartridge which matches better. Both work, but they are different. We don't publish the specs because we want you to use our jig! No matter what anyone says cartridge alignment is a matter of taste."
I do agree with the later affirmation!
The overall measure of distortion is very good and comparable to that obtained with Löfgren B alignment (whose aim is to minimize overall distortion). Now, one can even considerer this alignment better than the Löfgren B since the distortion at the end of the LP (the weakness of Löfgren B null points) is lower with the VPI null points. On the other hand, one could also consider VPI’s alignment to be worse than Löfgren B since VPI simply traded lower inner groove distortion for higher outer groove distortion. The next drawing confirms this fact.
Here’s something interesting to consider:
All LPs have outer grooves that start at approximately the same place—somewhere between 144-mm and 146-mm. However, the position of the innermost groove seems to vary considerably among LPs—anywhere from 60-mm to 70-mm. Therefore, by shifting the alignment curve to favour inner grooves at the expense of outer grooves, you will always be listening to more distortion if you always begin playing the LP at its outermost groove. Just a thought!
The data used to build this drawing can be seen in the previous table.
The distortion curves pictured above are called weighted tracking error curves. They are weighted in order show the audible effect of tracking error distortion across the entire grooved area. For example, the blue Baerwald curve shows approximately 0.6% distortion at the innermost groove, in-between the null points, and at the outermost groove. The audible effect of this distortion will be the same regardless of groove position. The Löfgren and VPI alignments produce lower distortion in the middle of the LP at the expense of higher distortion at the inner and outer grooves. Some people prefer this type of alignment because even thought distortion is audibly higher at the beginning and end, it is lower for a longer period of time in the middle of the LP.
If you’re now using the jig with a 10” tonearm, things could be a little different.
Distortion for the last third of the LP is now lower with Löfgren B than with VPI’s alignment. Now, if the real angle is 95.5°, the distortion for the final third of the LP remains inferior to the distortion obtained with Löfgren B null points.
The next drawing shows the distortion curves.
Finally, for the longer 10.5, even if I’m using the value of the outer null point obtained by an angle of 95.5°, the lowest average %RMS distortion will always be given by a Löfgren B alignment. That is the definition of Löfgren B.
In this later case, the VPI alignment forced by the jig is similar to Löfgren A (Baerwald) alignment during the first 50% of the LP side. At the end, it is very similar to a Löfgren B alignment.
Well, you’ll certainly think that I’m crazy but I had a great time analyzing the geometry of VPI tonearms forced by the use of the VPI jig. The solution proposed for the 9” series tonearm is quite interesting due to its very low distortion in the middle of the LP. The outer null point moves out farther for the 10 and especially for the 10.5i.
Now, regarding the jig by itself, I think that VPI is providing a very good tool. We generally align our cartridge with some piece of paper and our eyes. Both those tools have their limitations and between the real null points and the null points presented by the paper protractor, there is always a gap.
You say you’re using a basic protractor (like the “stupid protractor” you can download here)? Well, are you sure that you’re able to see a 0.5° difference between your cartridge body and the lines printed on the piece of paper?
You say you’re using an arc protractor (like a WallyTractor, one of mine or one made by Stephlouv from the ls3-5a forum)? Are you sure that the mounting distance stated by the drawing is the one you actually have on your turntable? Are you able to accurately measure the mounting distance? Are you sure that you’re really following the arc?
You say you’re using something like a Geodisk for which you need to point toward the pivot of the tonearm. Are you sure that you’re pointing exactly that pivot?
So there will always be a gap between your null points and the ones indicated on your protractor. Most of the time, there won’t be any consequences because misalignment problems arise only in some extreme cases and you’re guessing that alignment is not that important as long as set-up is done properly and accurately.
Some people don’t like Löfgren alignment for instance. They’re hearing a tracking problem at the end of the LP side. To me, this is because Löfgren alignment is more “risky” than the more standard Löfgren A alignment, better known today as Baerwald’s alignment. The gap between your real null point and the Löfgren null points certainly explains that mistracking. If accurately set up, I’m not sure you could hear a real difference (but I don’t have golden ears).
Now, should we burn all our paper protractors? Certainly not! But if you choose to use this kind of protractor, please have in mind that, when it is said, for instance, the cartridge body must be parallel at the two grids, this means: the cartridge body MUST be parallel at the two grids, not “almost”.
And that VPI jig? By its construction, the effective length will be quite accurately set up. Now, regarding the offset angle, you’re still having one pair of eyes but the gap between the actual and the theoretical null point will be minimized by the fact that you’re controlling the effective length.
There is always a unique outer null point with the VPI jig based on its inner null point, mounting distance, and grid angle. I tried to show that average distortion is quite good and comparable to what the other popular alignments could theoretically provide (but things could be improved for the 10 and 10.5i tonearms). In my opinion, VPI’s alignments are comparable to other, more popular alignments, especially in the case of the JMW-9. Furthermore, the alignment method employed by VPI is certainly far superior to flimsy paper protractors, arc protractors and sight-line protractors. It is therefore clear to me why VPI customers are generally happy with their VPI tonearms.
A special note to Harry Weisfeld who may read this article
You have provided some very interesting answers to alignment issues by the construction of you alignment jig. Please understand that this paper is an attempt to understand what was on your mind. Your choice was to not communicate much about the specific data relating to your tonearms. In fact, you chose to actually publish proxies (some might say erroneous data) on your website. Well, this is your choice, but now, you know that some customers want to know more.
I know that this kind of analysis is not your cup of tea. Please understand that the tools I’m using are the ones used by people interested in understanding tonearm geometry and issues regarding cartridge alignment. Those tools are as old as geometry and trigonometry.
Löfgren’s paper (published in 1938) is the base of all subsequent papers published on the subject including Baerwald (1941), Bauer (1945), Seagrave (1956), Stevenson (1966) and Kessler & Pisha (1980). Interested reader will find an excellent paper by Graeme Dennes reviewing and analyzing those historical papers here
If I have presented any incorrect data in this paper, I take pride in knowing that I am in good company. However, if you would like to provide more accurate data that can be verified mathematically, I will be happy to improve my analysis to reflect the greater truth.
My deepest thanks to John Elison who checked my very bad English and to Graeme Dennes who accepted to read preliminary versions of this paper.
All errors in this paper remain mine.
Many thanks to sjg for the corrections