I agree with Cees.... the 1.6 factor is (was) not coincidental with the ratio of km/mile (1.609).
It's really a simple problem to deduce.... the pick-up gear is taken off somewhere after the tranny... whether before or after the rear-end is immaterial..... 4000k engine rpm at 1:1 (4th gear) is about 72-74 mph... so engine and drive-line revolves ~54 - 55 revolves times per mph in 4th. That's also 54 - 55 revs per minute per 1.609 kilometers per hour... or about 34 revs/min. per km per hr.
The pick-up has a gear on the cable's end... so the cable rotates at a fixed rate function of the engine's speed (in a given gear... using 4th since it's 1:1 to drive shaft). But that fixed rate function depends on the gear on the cable's pick-up end.
How many teeth on the gear on the cable's pick-up end? That depends on what speedo cable PN was purchased at the dealer.
Assume for a moment that the PN was purchased for a car with a km/hr speedometer unit. It has n teeth on the pickup gear. The cable therefore rotates x times for every revolution of the drive shaft.
Now assume the cable PN purchased was for a car with a mph speedometer unit in the car. It has m teeth on the pick-up gear. The cable therefore rotates y times for every revolution of the drive shaft.
In fact, number of teeth on the pickup gear on the cable for the mph speedo would have to have rotate 1.609 times more per revolution of the drive shaft than the pick-up gear on the km per hr speedo unit.
Assume further that the speedometer's mechanism for rotating the needle is of the centrifugal type.... the faster the mechanism spins the further the needle rotates.
The spinning mechanism is tied to the cable's rotation... and assumedly there's a set of gears within the speedometer unit between the cable's entrance and the spinning mechanism that drives the centrifugal pointer to rotate.
Now, if the speedo unit isn't changed when the PN for the cable is changed, the speedo unit will either spin at a rate 1.609 times what the gearing in the speedo unit is designed to spin the mechanism that drives the centrifugal pointer... so the pointer will be driven to a location on the speedo dial (degrees rotation) that is always 1.609 times further along the speedo dial, OR, it will spin at a rate of 1/1.609 = 0.622 times what the gearing unit in the speedo was designed for... i.e. read 62% of the actual speed.
r.bartl's story was to convert a mph unit to a kilometer per hr unit.... so the original cable's pick-up was designed with m teeth on the pick-up end of the cable.... and the gearing in the speedo unit was designed to spin the centrifugal spinner at the rate required for the m teeth mph PN cable unit.
I don't know whether the cable PN's are unique to a mph cable or a km per hr cable unit, but if r.bartl purchased a km per hr cable unit (with x teeth) at the pick-up end to replace the one with m teeth (mph cable unit), then the speedo (without changing anything from the mph speedometer unit) would spin at a rate 0.622x that for which the gears that drive the centrifugal spinner was designed... and the pointer would point to a speed that was 62% of the actual speed.... i.e. not rotate as far along the dial as it should have.
To correct this at the speedometer, the gears inside the speedometer needed to be replaced by ones that spun the centrifugal mechanism 1.609 times faster.... bringing the pointer back to the correct degrees of rotation to indicate the correct speed in mph on the mph dial on the speedometer.
But, r.bartl's statement was that the speedo (on return from PA the 1st time) read 1.6 x the actual speed. This means that the centrifugal device was spinning 1.6x faster than it should have been spinning. This in turn means that the gears inside the instrument had been changed to increase the speed of the centrigal unit by 1.602 times it's required speed. This in turn means that what PA actually did the first time the unit was returned was to modify the gear set inside to reflect a km to mph conversion... rather than the other way around. This stands to reason since I'd guess that 90% of PA's speedo business in conversions is from km to mph... not the other way around. Some tech simply read the order that said "speedometer conversion (mph to km) and didn't pay attention to the direction of the change requested). To correct this, either the pick-up end gears on the cable needed to be changed to one with 1.609 times as many teeth as was on the cable he was using (making the cable spin slower), OR the gears inside the speedometer unit that drove the centrifugal spinner needed to be changed to reduce the centrifugal mechanism's speed of rotation by 0.622 times... i.e. make the centrifugal spinner spin at a rate that was 62% of the rate it was spinning when he got the speedo back from PA the 1st time.
In any event, unless PA told r.bartl to provide the speedo cable along with the instrument to make the conversion from mph to km per hr on the speedo, or to tell them the number of teeth on the end of the cable pick-up end (or some other tell-tale for determining the cables rate of rotation for each revolution of the drive shaft (and or drive shaft + rear end), the entire conversion resides within the speedometer instrument's gears between the entrance of the cable and the centrifugal spinner.
There are probably small differences in the location of the km speed units on the dial compared to the respective corresponding mph units on the dial... the differences being due to using round figure ratio's for the gear drive mechanism's... like 1.6 instead of 1.609 or 0.6 instead of 0.622.
There is probably a small adjustment mechanism for the centrifugal spinner for fine tuning... but something on the order of +/- 5%... not +/- 60%!
Believe me... this isn't rocket science... it's simple ratio's of spin rates which rely on the number of teeth of one gear with to another.... and a simple centrigal spinner or other some-such analogue rotating device that rotates a fixed number of degrees of rotation per unit of input to it.... it could be a simple magnetic solenoid meter for example... the spin rate of the spinner driving the solenoid a given distance determined by the gears between the cable's input to the instrument.... but that actual analogue drive unit is probably independant of what's on the dial or whether everything is based on a km or mph unit.... or what rear-end is in which car.
Point being that PA goofed and used the wrong gear set (used a gear set that was normally used to change a km/hr unit speedo to an mph unit speedo) in their original conversion on the speedo instrument. And from r.bartl's brief statements (indicated speed 1.6x actual speed, and reading km/hr on the dial), the only thing PA did right the 1st time is change the dial from an mph dial to a km/hr dial.
So it's no wonder that PA didn't divulge their mistake.... who'ed want to admit to mis-reading the work-order.... or picking up the wrong gear set from the bin (absent mindedly using the normal gear set bin they're used to using). If r.bartl lived in the US he could file for redress in small claims court.... and win!!!! without the defendand (PA) even trying to offer a defense....since they already know they have none.
In fact, if I were r.bartl, I'd write a very nice letter (honestly... a nice letter... gentleman to gentleman) to the president of PA, explaining the amount of time having to be used to re-remove, re-reinstall the speedometer unit, the inconvenience experienced and the local MB Dealer's unit rate of remove & replace speedo unit, requesting compensation for PA's error. The only thing that's a little sketchy to me and which needs to be determined in fact, is what the end gears at the pick-up end of the speedo cable's are for a mph unit automobile and a Euro automobile, since if these are different, then part of the problem r.bartl experienced may have been due to the difference in the gear's at the pick-up end not being supplied at the time the conversion was originally requested. Other than that little detail, it's clearly a doo-doo head dufus mistake at PA's end of the business... and they'll know this as well as I do... so a gentleman will compensate you for their error.
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