Someone better than me, please check my math.

[thesameguy]

This is a stupid thread, but I know one (or all) of you guys is better at math than I am:

Vehicle Speed Sensor = 9832 pulses per kilometer
9832 pulses per kilometer = 15860 pulses per mile

At 60mph, one mile per minute, I should see 15860 pulses per minute or 264 pulses per second. The VSS pulses four times per rotation, so that means 66 VSS rotations per second.

A 195/60-15 tire has a 24.21" height and a 76.0194" circumference. At 60mph, that tire is at 833.47rpm (63360" per mile/76.0194" tire circ.), or 13.9 tire rotations per second.

Tire speed is mechanically connected to ring gear speed. The ring gear drives the VSS.

If:

o The tire is at 13.9 rotations per second,
o The VSS is reporting 264 pulses per second

66 (whatever the symbol for gear reduction is :lol:) 13.9 * 4

= 4.75:1

Seem legit?

[LHutton]

I think so, but I wouldn't bet your life on my opinion right now.

[CudaMan]

Not understanding exactly what you're dealing with as far as this project goes... how easy is it to change values for this thing? Mechanical or software? You could always do the trial/error method using a GPS speed tracker app on the road to get your speedometer right. Right?

[Crazed_Insanity]

Yeah, not sure what you're getting with this...

Also, VSS does 9832 pulses per kilometer so what happens if you're stationary? That means no more pulses?

The pulses must just be pulsing at how ever many times per second or something, right? Not really based on distance traveled?

[Yw-slayer]

Are the pulses only emitted a bit at a time? ;)

[thesameguy]

Not understanding exactly what you're dealing with as far as this project goes... how easy is it to change values for this thing? Mechanical or software? You could always do the trial/error method using a GPS speed tracker app on the road to get your speedometer right. Right?

I can't change values, unfortunately. And I really want to be sure I understand the In and the Out before tackling this to avoid unnecessary cost and possible severe damage to the pieces involved. :) I really want a bench test, so that's what I'm trying to design.



Also, VSS does 9832 pulses per kilometer so what happens if you're stationary? That means no more pulses?

Correct, no pulses. The pulses are a measuring tape, not a timer. That is a hard thing to wrap your brain around, but that's how it works. :)



Are the pulses only emitted a bit at a time? ;)

Obviously. That's how you maximize the VALUE.

...

But, nevermind the pulses and what I'm doing - is my math solid?

Part A:

A. A thing that measures distances in New Units (NU) thinks 9832NU is equal to 1km
B. That thing would thus think there are 15858NU in a mile (9832/.62)
C. Traveling at 60mph, that thing would count 15858NU every minute
D. It would count 264 New Units per second (15858 / 60)

Part 2:

1. A round thing with a 24.21" diameter has a 76.0194" circumference
2. A round thing with a 76.0194" circumference is at 833.47rpm at 60mph (63360" per mile/76.0194" circumference)
3. That round thing is at 13.9 rotations per second (63360" per mile/76.0194" circumference)

We'll get back to the last part if all this is correct. :D

[Rare White Ape]

I think your numbers check out (I started with a very rough calc to convert kilometers to miles (miltiply by 1.6) so it won't be 100% accurate beyond two decimal places) but my back-of-the-computerised-envelope mashings got the same result as you.

All you want to find is the correct gear ratio to drive your speedo, yes/no?

[LHutton]

I get 15823 pulse per mile based on 9832 per km, but that still comes out at 264 per second to the nearest pulse.

[thesameguy]

I think your numbers check out (I started with a very rough calc to convert kilometers to miles (miltiply by 1.6) so it won't be 100% accurate beyond two decimal places) but my back-of-the-computerised-envelope mashings got the same result as you.

All you want to find is the correct gear ratio to drive your speedo, yes/no?

Basically, yes. I need to discover that gear ratio so I can simulate driving the sensor.

Ring gear rpm = tire rpm (they're attached by the axle!) and the ring gear drives the speedo gear. I need a way to equate road speed to speedo gear rpm, so the way to do that is discover the ring gear:speedo gear ratio.

So Part III is:

Given that:

o The tire (and ring gear ) is at 13.9 rotations per second at 60mph and
o The VSS is reporting 264 pulses per second at 60mph and
o The VSS reports four pulses per rotation, so
o The VSS at 264 pulses per second is 66 rotations per second

So:

66/13.9 = 4.75:1

[SportWagon]

I get 15823 pulse per mile based on 9832 per km, but that still comes out at 264 per second to the nearest pulse.
I get those results, too.

awk 'BEGIN{p=(5280 * 12 * 2.54) / 100000 * 9832; printf("%9.2f\n%9.2f\n", p, p/60) ;}'
15823.07
263.72

But
awk 'BEGIN{printf("%9.2f\n", 15860.0 / 60.0) ;}'
264.33

It's almost like they got the 15860 by multiplying back on the 264. Although 264 * 60 is only 15840.

So is it your math that needs checking, or the problem presenters?



A 195/60-15 tire has a 24.21" height and a 76.0194" circumference. At 60mph, that tire is at 833.47rpm (63360" per mile/76.0194" tire circ.), or 13.9 tire rotations per second.

I get 76.0580 tire circumference with pi 3.14159265 but if you were given both the numbers I would guess the circumference could be accurately measured (though,depending how the measurement was done, perhaps not really taking into account speed distortion or slippage) and diameter would be almost irrelevant.
The difference in diameter between 76.0580 and 76.0194 is almost signicant.
76.0194 gives only 24.198, IICC. So that's a whole 1/100 inch. (Hmm. I erroneously thought 1/10 for a while; 1/100 is pretty small).



B. That thing would thus think there are 15858NU in a mile (9832/.62)


.62 is a very rough calculation for the number of miles in a kilometer.

awk 'BEGIN{p=100000 / (5280 * 12 * 2.54); printf("%9.6f\n", p) ;}'
0.621371


And if I divide any of the close approximations of 264 by 66 I get about 4.75. (though as low as 4.7432 for 263.72)

But I'm having a difficult time convincing myself of the significance of that number.

[thesameguy]

But I'm having a difficult time convincing myself of the significance of that number.

HA! Me too! There is certainly a 1-2% margin of error, and legally maybe as much as 5%.

The only number *for sure* is actually 2458 pulses per kilometer, which is what the fuel injection system is designed around. I don't know why that number, maybe something to do with computer things like clock timing or something. I really have no idea. This is legacy from the '80s, who knows why anything was done. But, 2458 pulses per kilometer in a DC square wave is what's expected.

There is a sensor in the transmission that generates a signal, the VSS. I assume the sensor is a two coil magneto that by design makes four pulses per rotation. Being a magneto, its output is AC sine. According to the factory manual, the output from the sensor is "four times the rate of the fuel injection input." There is no more detail - because who would ever reverse engineer this? :lol: I am reading this to say "The VSS rotates 2458 times per kilometer and pulses four times per rotation, or 9832 pulses per kilometer.

I know the rpm vs. road speed of the ring gear because it's mechanically linked to the tires. The tires are 195/60-15, which have a nominal height (aka diameter) of 24.21" - obviously there is variation by specific tire so more room for error there. I know the tire has to rotate X times to go a mile, so I know the ring gear does too.

I know the rpm of the VSS because I know what it's expected output is.

Comparing the two gives me the ratio - 66 VSS rotations per second divided by 13.9 tire rotations per second = 4.75:1 gear ratio.

The missing piece is the actual speedometer. You'll recall the VSS outputs AC sine, but the fuel injection requires DC square. The factory speedometer does that conversion. I am replacing the factory speedometer, so I need a thing that does the conversion - and I have that thing.

The point: I am trying to design a bench test - I want to spin the VSS at a given speed and verify its signal is what I expect for the speed. Then, I want to hook up the new converter thing and watch it's output, to verify the VSS at a given speed goes through the new converter and comes out a "matching" square wave output. I want to do this before I plug the converter thing into my car and wreak havoc on the fuel injection. Admittedly it *may* be moot, I have read the fuel injection only cares about three things: 0, >0, or approaching 0 and the details aren't important. That makes sense to me - it probably just wants to know what to do with idle control - but I don't know that, and don't want to take a risk.

Hence, all the math.

Sadly, my initial test came out poorly.

A 700rpm indicated drill speed would equate to a 10.2 mph road speed - 700rpm VSS speed / 4.75 gear reduction = 147.37 tire rpm * 76.0194" tire circumference = 11202.86" inches per minute / 63360" per mile = .17 miles per minute * 60 = 10.2mph

At 10.2mph, I should be seeing approximately 15860 VSS pulses every ~5.88 minutes, or 44-45 pulses every second. But the multimeter showed 189.4Hz.

Something is wrong and I can't figure it out - either my math or the multimeter (or, maybe I don't understand my multimeter!) The thing that gives me the most pause is that given the VSS is four pulses per rotation, at 700rpm I should see 700 rpm * 4 pulses per rotation / 60 seconds per minute = 46.67 pulses per second - about 46Hz, bloody close to my calculation above!

189.4Hz at the VSS should equate to 2841 pulses per minute at the fuel injection - 189.4 * 60 seconds per minutes / 4 VSS pulses per rotation = 2841
2841 pulses per minute * 60 minutes = 170460 pulses per hour / 3965 pulses per miles = 43mph!

I just don't know where I'm going wrong and I'm not good enough at math nor is there sufficient documentation on the electronics to help me figure it out.

[Godson]

Why would the revs per mile have anything to do with the fuel delivery?

[thesameguy]

Absolute road speed *probably* doesn't matter, but referenced against load road speed can be valuable. The problem is I have no way of knowing what the margin of error on the signal is, how far off it can be before it's completely discarded or trips a code. A few (hundred) pulses per mile obviously wouldn't matter in any way, but a double or half rate pulse would as likely as not be a real problem. I really don't have much choice other than get it right.

[thesameguy]

I can't leave well enough alone, so I kept kicking...

Through disassembly I found the actual speedometer drive ratio is 1.23:1.

2485 square pulses per kilometer = approx 3965 square pulses per mile expected at the computer

VSS is 4x the square pulse rate, or approx. 15860 sine pulses per mile

Indicated drill speed was 700rpm, divided by the 1.23:1 ratio of the speed drive, means approximately 569rpm at the wheel.

A 195/60-15 tire is approximately 76.0194" around. 569rpm * 76.0194" tire circumference is 43263" per minute, or approximately .68 miles per minute

.68 miles per minute * 15860 sine pulses at one mile per minute is approximately 10829 sine pulses per minute

10829 sine pulses per minute divided by 60 seconds per minute = 180 sine pulses per second.

I measured 189.4Hz. 189.4Hz is SO CLOSE to the expected 180Hz I think it's fair to say it's close enough. That's 4% error, well within speedometer inaccuracy and possibly explained by a different tire size (195/60-15 c900 vs. 195/65-15 or 205/55-16 9000) or possibly explained by a slight error in the speedo drive ratio (900 vs. 9000), a sampling error/inaccuracy on the multimeter, or a misreporting on the drill tach. *Plenty* of room for a 10Hz error.

I am pretty satisfied this is an accurate test with good math.