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Re: A4 & '80's Coupe rpm-mph values (LONG!)
Hey gang. As I have mentioned before, my Dad is really bugged by the
high rpms that his A4 1.8tq 5-speed turns at 80mph on the highway. He was
able to get the spec sheets containing the gear ratios for the '97 1.8tq,
'97 2.8 v6 12v, and '98 2.8 v6 30v. I used those values to calculate the
theoretical rpms turned by the engine at 80mph, but I do not know if I
have done the calculation correctly or if the values are accurate. Based
on the four or five data points I have from listers and my father about
rpms at 80mph in 5th, I see conflicting results (three seem close, the
other two are way off).
The first issue that concerns me is the fudge-factor I used to reduce the
radius of the wheel when loaded. Is 1/2" too much? Not enough"
The second item involves the gearing itself. Is there a 1:1 correlation
between final drive rotations and wheel rotations? I assumed so in my
calculations.
So, if some of you guys could review this (sorry for the length) and
give me some feel for whether the values are correct or where I made a
mistake, I would appreciate it.
BTW, this is all done with a non-proportional font. Sorry for all those
who use proportional fonts, as it will not align correctly.
Thanks,
Eric
'85 Coupe GT, turns 3500rpms @ 80mph, not 3600-3700! :(
---
Eric J. Fluhr Email: ejfluhr@austin.ibm.com
630FP Logic/Circuit Design Phone: (512) 838-7589
IBM Microelectronics Div. Austin, TX
> Dad,
>
> Here are the values I used to calculate rpms vs. mph. I used a fudge-factor
> of 1/2" for the change in rolling radius due to the compression of the
> tire when loaded.
>
> Rolling radii: 205/55-16 tires
>
> 16" 205mm 1"
> --- + x ------ x 0.55 = 12.4" full radius
> 2 25.4mm
>
> 12.4" full radius - 0.5" = 11.9" rolling radius
>
>
> Rolling circumference (distance): PI = 3.1415926
>
> 2 x PI x 12.4" x 1ft
> --- = 6.51ft per tire rotation
> 12"
>
> 2 x PI x 11.9" x (1ft/12") = 6.25ft per tire rotation
>
>
> Now, in the following calculations, I will use these definitions:
>
> Erot = 1 Engine rotation, i.e. as in engine RPM
>
> Trot = 1 Transmission rotation, rotation of the transmission shaft
> after passing through a gear, but before entering into the
> final drive unit (i.e. rotations of input shaft to final drive)
>
> Drot = 1 Driveline rotation, rotation of the output shaft of the
> final drive unit, assumed equal to one rotation of the wheels
>
>
> MPH vs. RPM calculations:
>
> I use the following formula to calculate the values:
>
> 80mph 1hr 5280ft 1 Drot ??? Trot ??? Erot Erot
> x ----- x ------ x ------ x -------- x -------- = ------ = RPM
> 60min 1 mile 6.51ft 1 Drot 1 Trot min
>
>
> Note the following:
>
> (??? Trot / 1 Drot) is the final drive ratio.
> (??? Erot / 1 Trot) is the fifth gear ratio.
>
>
> '97 A4 1.8t quattro 5speed:
>
> 80mph 1hr 5280ft 1 Drot 3.889 Trot 0.838 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3524 RPM
> 60min 1 mile 6.51ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 3.889 Trot 0.838 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3671 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
>
>
> '97 A4 1.8t FWD 5speed:
>
> 80mph 1hr 5280ft 1 Drot 3.700 Trot 0.838 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3353 RPM
> 60min 1 mile 6.51ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 3.700 Trot 0.838 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3493 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
>
>
> '98 A4 30v V6 quattro 5speed:
>
> 80mph 1hr 5280ft 1 Drot 3.889 Trot 0.789 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3318 RPM
> 60min 1 mile 6.51ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 3.889 Trot 0.789 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3456 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
>
>
> '98 A4 30v V6 FWD 5speed:
>
> 80mph 1hr 5280ft 1 Drot 3.700 Trot 0.789 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3157 RPM
> 60min 1 mile 6.51ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 3.700 Trot 0.789 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3288 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
>
>
>
> Rolling radii: 195/60-14 tires
>
> 14" 195mm 1"
> --- + x ------ x 0.60 = 11.61" full radius
> 2 25.4mm
>
> 11.61" full radius - 0.5" = 11.11" rolling radius
>
>
> Rolling circumference (distance): PI = 3.1415926
>
> 2 x PI x 11.61" x 1ft
> --- = 6.08ft per tire rotation
> 12"
>
> 2 x PI x 11.11" x (1ft/12") = 5.81ft per tire rotation
>
>
> '82 Coupe:
>
> 80mph 1hr 5280ft 1 Drot 4.11 Trot 0.60 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 2855 RPM
> 60min 1 mile 6.08ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 4.11 Trot 0.60 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 2983 RPM
> 60min 1 mile 5.82ft 1 Drot 1 Trot
>
>
>
> '85 Coupe GT w/ ABV 093 5speed:
>
> 80mph 1hr 5280ft 1 Drot 4.90 Trot 0.64 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3631 RPM
> 60min 1 mile 6.08ft 1 Drot 1 Trot
>
>
> 80mph 1hr 5280ft 1 Drot 4.90 Trot 0.64 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3793 RPM
> 60min 1 mile 5.82ft 1 Drot 1 Trot
>
>
> So, things don't look good. Going to the 5th gear from the V6 engine
> and using 225/65-16 tires will get you down close to 3200 rpm @ 80mph,
> but that is a couple thousand dollars worth of changes. You would
> probably be better off selling me the A4 :) and buying another car
> that turns < 3000rpm at highway speeds. Interestingly, the '98 A4 30v V6
> with Tiptronic AUTOMATIC transmission looks to turn around 2750rpm at
> 80mph:
>
> 80mph 1hr 5280ft 1 Drot 3.292 Trot 0.742 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 2751 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
> Similarly, the '97 A4 1.8t FWD or quattro with AUTOMATIC 5speed (not
> the Tiptronic) yields the following result:
>
> 80mph 1hr 5280ft 1 Drot 3.730 Trot 0.742 Erot
> x ----- x ------ x ------ x ---------- x ---------- = 3117 RPM
> 60min 1 mile 6.25ft 1 Drot 1 Trot
>
> Note that both of the above calculations were done with the fudged
> rolling radius. I still don't yet know how accurate the values are.
> Perhaps you can drive the automatic A4 and find out.
>
> I don't know why most auto trannies now-a-days turn much lower RPMs than
> their manual counterparts, but that seems to be a common occurrence. I
> assume it has something to do with top speed.
>
> I hope all this was relatively clear. Let me know if you need any
> explanations. Like I said, I would be more than happy to buy your A4
> from you for what you paid for it. If you still like the A4, perhaps
> you should look into an automatic transmission version, whether 1.8t
> or 30v V6 (which should be quieter, regardless of the rpms), since both
> of them appear to turn significantly fewer rpms at speed.
>