Vehicle physics question regarding speed & tire size

[vjborelli]

So I'm trying to learn some physics, calculus, and fluid dynamics on my own through research material.

I understand that the max speed and acceleration rate of a vehicle can be modified by changing the radius of the tire/wheel. I know that older cars that used a vehicle speed sensor on the transmission would read incorrect vehicle speed if you change to larger or smaller tires.

Now I'm curious.... If the 2003+ B6 uses the ABS wheel speed signal to display current speed on the cluster, would it be accurately accounting for wheel size difference and display the correct speed, or would it still fall short of accounting for the correct dynamic wheel radius.

Here is a small chart I made using a few samples of logged data of my B6 on 205/65R15 tires. The unloaded tire radius @ 35psi is 1.0622 feet. The loaded tire radius in the chart is listed as "Eff. R", but I don't know if that is a wrong number based on the car coming with the 17" with a different dynamic tire radius. Dynamic tire radius is the effective tire radius under load from the weight, and also expansion from high rotation speed.

Velocity Formula:
V = ( π * R * ( RPM / ( G¹ * G² ) ) / 30 * ( 1/5280 feet per mile ) * ( 3600/1 seconds per hour )

Radius Formula:
R = ( V * 30 / ( 1/5280 ) / ( RPM / ( G¹ * G² ) ) / 3600 / π

Where:
R = Dynamic tire radius in feet
V = Velocity in miles per hour
G¹ = Transmission gear ratio for 3rd gear ( 1.429 )
G² = Final drive ratio ( 3.889 )



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[a4darkness]

In for maths. Nice topic OP.

[Charles.waite]

Not even going to broach the math here (I suck at it, ask tchuck) but I do know that when I was running 225/45R18 tires on my b6 the speedo read higher than my actual speed (as compared to the readout on a roadside speed warning sign I pass on my way to work every day. The difference was roughly 10%. With my more proper sized 235/40R18 tires the speedo now reads a bit more accurately, but still a few % off from actual speed (again, according to the roadside speedo sign). Now I can presume my car is accurately calibrated, but my gut tells me that the roadside speedo machine is properly calibrated given its sole purpose is read the speed of oncoming traffic. That and I think German automakers are notoriously optimistic when it comes to reporting speed in the cluster gauge.

[a4darkness]

Yeah where's Timothy Platinum.

[vjborelli]

Not even going to broach the math here (I suck at it, ask tchuck) but I do know that when I was running 225/45R18 tires on my b6 the speedo read higher than my actual speed (as compared to the readout on a roadside speed warning sign I pass on my way to work every day. The difference was roughly 10%. With my more proper sized 235/40R18 tires the speedo now reads a bit more accurately, but still a few % off from actual speed (again, according to the roadside speedo sign). Now I can presume my car is accurately calibrated, but my gut tells me that the roadside speedo machine is properly calibrated given its sole purpose is read the speed of oncoming traffic. That and I think German automakers are notoriously optimistic when it comes to reporting speed in the cluster gauge.

So the 2002 B6 uses a transmission speed sensor for vehicle speed. In the 2003+ B6, they eliminated the transmission speed sensor an opted to get vehicle speed from the ABS module using the wheel speed sensor.

Not sure which year you have, but that could be why. I'm trying to figure out if the ABS wheel speed system accounts for variable tire sizes, or if it is just as flawed as using the transmission speed sensor.

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[Rogue A4]

So the 2002 B6 uses a transmission speed sensor for vehicle speed. In the 2003+ B6, they eliminated the transmission speed sensor an opted to get vehicle speed from the ABS module using the wheel speed sensor.

Not sure which year you have, but that could be why. I'm trying to figure out if the ABS wheel speed system accounts for variable tire sizes, or if it is just as flawed as using the transmission speed sensor.

Sent from my Nexus 6

Don't think that the ABS system accounts for variable tire sizes but based on the S4 tuning Wiki it can be changed.

Wheel speed sensor

If you have different wheel rolling diameters from stock, and you want to log the correct speed:
AIMVM (0x12A56) - Number of speed pulses per m for signal normalization v

[vjborelli]

Don't think that the ABS system accounts for variable tire sizes but based on the S4 tuning Wiki it can be changed.

Wheel speed sensor

If you have different wheel rolling diameters from stock, and you want to log the correct speed:
AIMVM (0x12A56) - Number of speed pulses per m for signal normalization v

The S4 wiki is using information from the B5 S4, which also uses a transmission speed sensor if I'm not mistaken.

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[Skyler@Achtuning]

That and I think German automakers are notoriously optimistic when it comes to reporting speed in the cluster gauge.

IIRC German automakers are heavily penalized if the cars are found to be going faster than indicated, as such the speedos all read faster than actual.

http://www.unece.org/fileadmin/DAM/t...gs/r039r1e.pdf

5.3. The speed indicated shall not be less than the true speed of the vehicle. At the test
speeds specified in paragraph 5.2.5. above, there shall be the following relationship
between the speed displayed (V1 ) and the true speed (V2).
0 ≤ (V1 - V2) ≤ 0.1 V2 + 4 km/h

[Skyler@Achtuning]

I'm trying to figure out if the ABS wheel speed system accounts for variable tire sizes, or if it is just as flawed as using the transmission speed sensor.

I think it's just limited to essentially counting rotations, the car does not know if you are rocking 13" gold daytons or 33" mudders.

[Spike00513]

That and I think German automakers are notoriously optimistic when it comes to reporting speed in the cluster gauge.

This is why land speed records in cars are measured according to accurate GPS's, and not speedometers. Mine reads about 3mph faster than the car is actually going, on the highway.

[Charles.waite]

So the 2002 B6 uses a transmission speed sensor for vehicle speed. In the 2003+ B6, they eliminated the transmission speed sensor an opted to get vehicle speed from the ABS module using the wheel speed sensor.

Not sure which year you have, but that could be why. I'm trying to figure out if the ABS wheel speed system accounts for variable tire sizes, or if it is just as flawed as using the transmission speed sensor.

Sent from my Nexus 6

It would still be flawed. There is no way for the abs sensor to know what the rolling radius of the wheels is unless you program it.

[vjborelli]

This is why land speed records in cars are measured according to accurate GPS's, and not speedometers. Mine reads about 3mph faster than the car is actually going, on the highway.

The main reason I'm doing this is because if you can correctly calculate the dynamic tire radius based on vehicle speed, you would only need to know a very close approximation of actual vehicle weight to calculate torque at the wheels.

Mean Acceleration formula:
A = ( V² - V¹ ) / ( T² - T¹ )
A = Acceleration in feet per second squared
V¹ = Starting velocity in feet per second
V² = Ending velocity in feet per second
T¹ = Starting time relative to V¹
T² = Starting time relative to V²

Capable Acceleration formula:
A = ( T * (G¹ * G²) ) / ( m * R )

Wheel Torque from Acceleration formula:
T = ( A * ( m * R ) / ( G¹ * G² )

Where:
T = Wheel torque in lb-ft
A = Acceleration in feet per second squared
m = Total vehicle mass in slugs ( gravitational weight )
R = Tire radius in feet

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[Charles.waite]

I know the waste transfer center near my house has a car scale that is accurate down to the nearest 10-20lbs. That makes it relatively easy to know weight aside from variations in fuel level

[vjborelli]

It would still be flawed. There is no way for the abs sensor to know what the rolling radius of the wheels is unless you program it.

But it counts revolutions of the wheel based on a hall sensor, right? Wouldn't the axle rotation speed be relative to the dynamic tire radius?

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[vjborelli]

I know the waste transfer center near my house has a car scale that is accurate down to the nearest 10-20lbs. That makes it relatively easy to know weight aside from variations in fuel level

Gasoline weighs 6.02lbs per gallon.

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[vjborelli]

Oh, and I'm not sure if my equations accurately accounts for moment of intertia... Or if that torque value would have to be added to this one in order to see the full torque the wheels are putting to the ground.

Edit: Actually I'm almost certain this formula isn't accounting for wheel torque required to overcome drag force, mass moment of inertia, and climbing resistance.
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[vjborelli]

I think it's just limited to essentially counting rotations, the car does not know if you are rocking 13" gold daytons or 33" mudders.

Looking at the spreadsheet I made, the formula is calculating the difference in tire radius/circumference at different rpm/speed. I'm going to guess that this variance in radius is from the car shifting weight to the rear end under heavy acceleration?

Yeah, it does count just the rotations... But 1 rotation of the wheel hub still wouldn't complete without 1 rotation of the overall circumference, right?

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[Elliott]

You'll need to redifferentiate the angular momentum of the convergent peripheral arcs while at the same time quintizing the cosecants strict parabolic nature. Pretty straight forward really.

[vjborelli]

I may have come to an answer on my own.

Does anyone know how many splines the ABS trigger wheel has? Or what the distance impulse value is for the OEM 17" Sport wheels, and/or the Stock 16" wheel package?

the instrument cluster is coded for a specific distance per impulse, right? So if I can change that value (i think someone mentioned something like this above), then I should be able to change the unloaded tire radius the car is trying to calculate for?

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[Spike00513]

Are you trying to figure out how to correct the speedo reading to actual?

[vjborelli]

Are you trying to figure out how to correct the speedo reading to actual?

Initially, yes. Then use the correct speed values to get correct acceleration values, and in turn... Get a close approximation of wheel acceleration torque. I believe I would still need to calculate the torque mass moment of inertia, and add that to the acceleration torque to have a close idea of what actual wheel torque is.

Then it would be down to calculating the force requirements of: drag resistance, climbing resistance, friction resistance.... And it should give me a close approximation of actual engine brake torque.

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[vjborelli]

Here is a spreadsheet of the different tire sizes available as OEM options... except for the 2nd S4 AVUS listed, those are the all season tires currently on my actual set for B6 S4 wheels.

So if I can get the correct distance impulse settings for each OEM tire option, it should put me 1 step closer to calculating the wheel acceleration torque.



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[B-Time]

235/40-18 is a stock B7 and B6 size. When I jumped to 245/40-18, my speedo became accurate.

Not sure if this answers the question, as there was too much to read.

[vjborelli]

235/40-18 is a stock B7 and B6 size. When I jumped to 245/40-18, my speedo became accurate.

Not sure if this answers the question, as there was too much to read.

Yeah, I noticed that my GPS was reading the same as my speedometer when I had my 245/40R18 tires on. I wonder why that is... But yes, 235/40R18 is the OEM tire size for B6/B7 18" AVUS wheels.

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[B-Time]

Yeah, I noticed that my GPS was reading the same as my speedometer when I had my 245/40R18 tires on. I wonder why that is... But yes, 235/40R18 is the OEM tire size for B6/B7 18" AVUS wheels.

Sent from my Nexus 6

I believe it is some german mandate that speedo needs to read faster by 3 or 4 mph. Could be totally wrong. My B5 was the same way.

[vjborelli]

I believe it is some german mandate that speedo needs to read faster by 3 or 4 mph. Could be totally wrong. My B5 was the same way.

Interesting.... I wonder if they did that to bring down statistical data for their vehicles in speeding violations.

So that would mean that the Distance Impulse is set to a smaller radius/circumference from what the actual wheel is.

That would also mean the gas mileage and overall vehicle travel distance would be off a decent amount. That would explain quite a bit of everyone having different mpg values.

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[B-Time]

This may also be of interest to you.

http://www.caranddriver.com/features...d-tires-tested

[vjborelli]

I wonder if anyone has a close estimate of the weight of all the rotating parts (e.g. Flywheel, clutch, drive shaft, CV shafts, etc...)I would like to see if what the numbers look like when you take the torque from angular acceleration of all the rotating parts, and add that to the linear acceleration of the vehicle.

I'm also curious if anyone has the correct radius/diameter/circumference of the crankshaft trigger wheel. I counted 57 windows at 5mm each, 59 frame triggers at 3mm each, and a reference window at 19mm. This puts me at 483mm circumference, 153.74368mm radius. My issue is that I was using a Walgreen's ruler, so the measurements aren't exactly the most reliable.

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[ADCS]

Without being privy to the design drawings you will never be able to calculate an accurate inertia.

You used a Walgreen's ruler to measure parts but give a result with 5 decimal places? You will only be as accurate as your inputs.

Why don't you just download the android app Torque and call it a day.

[forevraudi]

Interesting topic but ADCS is right. Fundamental rule of hard science is that your accuracy (or decimal places) should at most match the accuracy of your measuring device. For example, if I use a mitutoya caliper accurate to within .0001" at work, I still could not report measurements/calculations to an accuracy of 5 decimal places. If you really want to understand what is going on, you are just introducing rounding error, which in turn makes your results questionable. Scientific method bro!

[vjborelli]

Without being privy to the design drawings you will never be able to calculate an accurate inertia.

You used a Walgreen's ruler to measure parts but give a result with 5 decimal places? You will only be as accurate as your inputs.

Why don't you just download the android app Torque and call it a day.

The 5 decimal place radius value was obtained by using an estimated circumference:
Radius = Circumference / π

The circumference was obtained by using a small Walgreen's ruler to measure the trigger windows and frames. 57 windows @ 5mm each, 59 frames @ 3mm each, 1 reference window @ 19mm ( reference window is actually 3 normal 5mm windows and 2 frames, except the frames are machined out to create 1 large window.

I put ink on the outside of the wheel and ran a piece of paper over.


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[ADCS]

First that is a projected area so you can't measure it like that.

Second, if you measure something with a tolerance +/- a few mm there is no point in retaining all those decimal places in your answer. It is not giving you a more accurate result. Garbage in garbage out.