Tachometer accuracy

[3l33ter]

Today I was curious about my tach so I decided to take a measurement and check it against a calculation. I turned on my GPS and I got the tach needle to point exactly at 2500rpm, and my GPS read 58mph. (My speedometer doesn't work.)

I calculated the tire radius of my 205/70/14 tires
205mm * 0.70 * 1in/25.4mm + 14in/2 = 12.65" ... round it down to 12.5" to account for about 1% squish (arbitrary)
4th gear, so 1:1 (correct?)
I have physically seen the 3.69 stamp on my differential

rpm = (1 rot / 2pi rad) * 3.69 * (58mph * 63360in/mi * 1hr/60min) / (12.5")

I get 2877rpm. So is my tach off by almost 400rpm? Or perhaps by a %? I just wanted to check in with the experts here and see if w116 tachometers are known to be inaccurate or if there is a problem with my gauge. Or some other part.

Or my math. 

[rumb]

you lost me at "I calculated"   

does any of this data help?
https://tiresize.com/tiresizes/205-70R14.htm

[raueda1]

Can't comment on tach accuracy on these cars.  Your math looks reasonable to me, though I didn't rework it all to be sure.  But I really think that's a kind of Rube Goldberg way to come at it.  I say this especially in light of the fact that I just ordered a old tach/dwell meter off ebay for about $15 incl shipping.  I'm using it for ignition work.  For these older cars it's a worthwhile investment IMO and they don't seem to make them anymore.

[3l33ter]

That's a handy link there, I'll bookmark that one, thanks!

raueda1, good idea, thanks!

[s class]

I think your assumption of 1% 'squish' is probably way short of what it actually is. 

[3l33ter]

If I make the squish 0%, the rpm calculates out to 2845 while my gauge reads 2500.

If I make the squish anything higher, the rpm goes higher (and further from the gauge reading). Realistically I think the squish is somewhere between 1-5% based on some reading around on the web.

[ptashek]

The most accurate approach would be hooking up an oscilloscope, or a simple digital counter to the TD pin on the ignition module. This is where the RPM signal for the tachometer comes from.

The signal is a square(ish) wave.
On the V8, at idle it should be around 47Hz, and about 390Hz at M117 redline of 5800rpm.

[3l33ter]

Cool, I didn't know where the signal came from so I'll see if I can borrow an oscilloscope.

For now, I downloaded a strobe light app, and I was going to put a white paint mark on my crank and try to match the strobe frequency to the engine speed, then compare it to the tach. I need a helper so hopefully I can con someone into helping this weekend