TS-Aligner Accuracy
TS-Aligner is designed to be the premiere precision alignment tool specifically designed for industrial use on woodworking machines. Other devices make claims about being accurate, TS-Aligner really delivers. When I say it's accurate, I'm not kidding!
The vertical motion of the dial indicator on TS-Aligner is precisely calibrated to be accurate to less than +/-0.001" from perfect squareness. That means that no point along the travel will be more than 0.001" away from perfect squareness. Calibration is verified using a Laboratory Grade AA granite square on a Laboratory Grade AA surface plate - both with NIST traceable certification. A 0.0001"/div dial indicator is substituted for the standard 0.001"/div indicator. No unit is shipped unless it passes this strict qualification.
In order to make angle measurements to within 1/60 degree (the same as saying +/-1/60 degree) using a device accurate to 0.001", you must be able to measure over a distance of at least 3.4377" (ATAN(0.001)*60). The vertical travel on the TS-Aligner is slightly more than 3.875" and the short side of all our angle blocks is at least 4". So, even with the +/- spec of 0.001", TS-Aligner can resolve angles to better than 1/60 degree. But, proper analysis doesn't stop here.
In order to detect a change of 1/60 degree using a 4" machinists angle block, you need to be able to discern a measurement difference of 0.0011" (4*SIN(1/60)). This is just within the published specification of TS-Aligner and very easily accomplished. Some alignment tool manufacturers might not bother to do this much analysis on their products. Others might just stop here. But, this still isn't a proper error analysis - read on!
It takes combinations of two angle blocks and the MTB to cover the entire range from 0 degrees (square) to 45 degrees in one minute increments. Stacking errors come into play when more than one angle block is used so a proper analysis of TS-Aligner's capabilities must take this into account. Each angle block contributes 0.0001" error. This assumes that a micrometer is used to set the MTB (since the Tangent function isn't linear, use of the thumbwheel results in 0.0004" error at it's maximum 5 degree setting). For TS-Aligner, I use 0.0003" for the standard deviation and +/-0.0005" for the worst case tolerance (0.001" TIR). These two figures are based on actual results from measuring calibrated units.
Worst case analysis of the tolerances reveals 0.0008" maximum error (0.0003" for three angle blocks and 0.0005" for the TS-Aligner itself). This is a possible outcome but an extremely unlikely situation. It would require all of the items to exhibit their maximum error simultaneously and it doesn't take into account any uncertainty in the measurement abilities of TS-Aligner. This uncertainty must be considered in order to obtain a real world estimation of accuracy so a proper analysis is still not complete.
Finally, a statistical analysis of the tolerances is necessary. This takes into account the worst case tolerances of all the components and includes the minute random variations associated with the measurement capabilities of TS-Aligner. As stated earlier, these random variations exhibit a standard deviation of 0.0003". Such an analysis of the tolerances and instrument uncertainty reveals a 2.3% chance that the measurement accuracy will fall outside the +/-1/60 degree specification. In other words, 97.7% of all angle measurements made by all units will be accurate to within 1/60 degree. Further analysis suggests a three sigma tolerance of +/-0.0012" for TS-Aligner.
What does it all mean? When you use TS-Aligner in conjunction with angle blocks to setup your machine, you are using the finest products available to achieve the finest possible results. You can be absolutely sure that your measurements will be accurate. You won't need to waste any time or materials on test cuts.
Last revised: January 21, 2006.
