Pinz math

[pinzinator]

I bought an automotive mathematics book, and started doing some calculations. Tire diameter in inches can be calculated by multiplying the width X height and dividing by 2540, then multiplying by 2, then adding 16, which is the wheel size. In a formula- (285 X 75/2540) X 2 + 16. I came up with 32.8”, and I’m sure a ruler would have told me the same. If I multiply the diameter X pi (3.14), the circumference of the tire measures 8.58’. Dividing 5280’ (one mile) by 8.58’, I calculated that the tires on the Pinzgauer make 615.4 revolutions every mile. According to the Pinzgauer owner’s manual on page 208, the final gear ratio in top gear is 5.678-1, which means the crankshaft turns 5.678 times for every rotation of the axle. This takes into consideration the transmission ratio, auxiliary gearbox, differential, and wheel drive. Since the tires rotate 615.4 times per mile, and the crankshaft rotates 5.678 times per tire revolution, the crankshaft rotates 3494 times per mile. At 60 MPH (about 97 KPH), the tach should read 3494 in my Pinzgauer, yours may vary due to tire size. Too bad my tach doesn’t work right, as this would be a good way to verify its accuracy. That’s assuming my math is correct.

Using another formula in the book, I calculated the Pinzgauer piston speed to be 24.46 MPH at 60 MPH. This translates into the pistons travelling at 41% of the vehicle speed. This speed occurs only momentarily when the piston is halfway between TDC and BDC, because the piston has to slow down and stop twice with each crankshaft revolution. Something to think about the next time you are out in the Pinzgauer!

[waterdog]

O......K.......

[Tibbermore]

Detailed analysis of the data seems to suggest that there is not a lot of entertainment in Indio during October!!

[undysworld]

Equally intriguing, in a rather inverse manner, is the fact that each of those four pistons actually comes to a complete STOP, twice every rotation of the crank. For those of you still counting, that's a FULL 100% SLOWER (as calculated in AU's) than your Pinzgauer is traveling, EVEN IF YOU ARE IN NEUTRAL!!

EVEN IF YOU HAVE THE BRAKES APPLIED!!!

It's a wonder we aren't all killed.

Now this is something else to consider while you're toodling around town feeling smug.



Pinz,
Not pickin' on ya. Just having a grin.
I'm not sure why you did those calcs either, nor how it would be applied. But my hat's off to you for going through the work, even if only as mental exercise.
With a 712, I'm pretty sure I'm not speeding, but if I actually cared much about the accuracy of my speed, I'd just turn on my cheap GPS. As far as a tach goes, I'd just verify it against a decent shop tach and call it good.
Paul

[pinzinator]

Here's the book, it's quite interesting! Amazon probably has it.

[Jimm391730]

the fact that each of those four pistons actually comes to a complete STOP, twice every rotation of the crank.

Wow, now I know what they mean by "Stop and Go" driving!

[Stekay]

This speed occurs only momentarily when the piston is halfway between TDC and BDC

Not exactly... It happens when the crank throw and rod are at 90 degrees to each other, so slightly after halfway heading towards TDC and slightly before halfway when headed for BDC.