Two more calculators went up this afternoon, which rounds out the tools section for now. One deals with arm height, the other with alignment geometry. Both live at boolaudio.com/tools alongside the resonance calculator, the loading calculator and the cartridge database.
Arm height in millimetres, rake angle in degrees
Raise or lower a tonearm pillar and the stylus tilts in the groove. Height and angle are the same adjustment described from opposite ends, and spec sheets swap between them freely, so the VTA calculator converts in both directions. Type a height change and read the angle, or type the angle you want and read the height.
The conversions run smaller than most people expect. One 0.5 mm graduation on the Clear Wave's VTA scale is an eighth of a degree at the stylus. Swap a thin pressing for a 180 g one and the playing surface rises about 0.6 mm, which moves the angle by more than a graduation before you've touched anything.
It deals in changes only. Finding your absolute stylus rake angle takes a microscope; finding what 2 mm at the pillar does to it takes nothing but the arm's effective length.
Null points and tracking error
A pivoted arm sweeps an arc, and an arc can only be tangent to the groove at two radii. The alignment calculator plots what happens everywhere else. Enter an arm's pivot-to-spindle distance, overhang and offset angle, and it draws the tracking error across the record, marks the null points, and works out what the three standard alignments would ask of the same arm at its mounting distance.
The Clear Wave makes a worked example. Its published geometry, 211 mm mounting distance, 18 mm overhang, 24 degrees of offset, puts the null points at 65.7 and 120.6 mm with a maximum tracking error of 1.93 degrees. The spec sheet quotes the textbook Baerwald pair, 66.0 and 120.9, and the half-millimetre gap between the two is the rounding inside an 18 mm, 24 degree spec. The calculator calls it what it is, effectively a Baerwald alignment.
There was one trap in the build. Löfgren B looks like a straightforward optimisation, so the natural way to code it is to let the maths choose both the overhang and the offset angle. Doing that gives null points about 0.3 mm away from the ones Löfgren actually published, because his method holds the offset at Baerwald's value and only re-optimises the overhang. Our solver reproduces the published figures for all three alignments to within 0.02 mm, and that check is why you can trust the table.
Why there is no printable protractor
The obvious companion would be a printable protractor, and we stopped short of it on purpose. Home printers don't hold scale reliably, and a grid that comes out 2 percent long mis-aligns every cartridge set to it. The calculator's numbers agree with any properly printed Baerwald protractor, and a good one costs less than a record.
Both calculators work without JavaScript, and every result keeps its own address. The full set is at boolaudio.com/tools.
If a result looks off to you, or there's a cartridge we should add to the database, leave a comment below or use the contact form. Every correction makes the tools better for the next person.