ABEX Azimuth Tape Specifications

This is just an academic exercise to pursue, let's see where it takes me ....

 

 

Reference tapes like ABEX quote azimuth errors of angular measure in degrees, minutes, and seconds, ie typically: 0º ±2' 0", 0º ±4' 0" etc.

 

Question: How will this translate into any L/R channel phase delay on the oscilloscope? What can I expect to see? 

I am going develop an expression where φ is a function of the quoted azimuth error. Remember, φ is the phase delay we see on the oscilloscope.

From earlier articles, the electrical (and physical tape) L/R channel delay D appears to be fixed, and is given by ...

Also, let's inspect this simplified cassette tape diagram below - one half only shown. The electrical/physical delay D in this context is relatively easy to compute since a right angled triangle has been formed.

 

From our knowledge of trigonometry we can see that the azimuth angle (anti-clockwise) from the 90 degree vertical is....

 

Where BC = cassette tape's centre-to-centre track distance, which is very approximately 0.9mm (ie, 9x10E-4 metres, SI units) Substituting D into the inverse tangent formula gives ...

 

The angle ACB is the quoted azimuth error/difference, but I want to find φ, a predicted oscilloscope phase shift trace. Rearranging the trig expression gives ...

At a typical 10,000Hz azimuth test frequency (f=10,000Hz), the ABEX quoted azimuth errors of their reference tapes were of the order ~ 0º ±2' 0", 0º ±4' 0". In decimal form this is 0.0333333°, and 0.0666666° respectively. (Note: I'm not using radian angular measure)

So then, the expected ABEX tape L/R channel phase error at 10,000Hz on the oscilloscope should be in the region of ... ±40º, and ±80º. Or in more practical terms approximately ±45º, and ±90º.

As ABEX and others cannot guarantee perhaps finer tolerances, I suppose the only way to get a near precise estimation of true azimuth would be to purchase a sizeable sample (say 6 or more?) of identical tapes, then devise a method that aims to achieve a median valuation from the set of acquired tapes?

(Articles are subject to the correction of mistakes, and amendments etc.)