Differential calc

[XfireZ51]

My math teacher sister in law says engineers can't solve anything correctly unless the formula is already set up for them.
We are splitting hairs and at the end of the day the 4.10 is likely the most practical solution. I'm just going to continue the disagreement because it's fun.

Proportionality is the most accurate method of solving this:

Effective gear:Actual Gear::Effective gear:Actual Gear

Paul,

You can't accuse me of the Bugger Factor because I was not "looking" for a particular answer. In fact, I had originally thought of 3.90 gears.
The .156 is the error of the indicated speed not the actual. That's why your proof does not work.

WVZR-1,
The error is 15.6% whether you arrive at it by (74/64)-1 or (74-64)/64. The divisor is the indicated speed because that's what I'm trying to solve for.
I use proportionality because I want to maintain the same relationship (since I'm keeping the wheels and speedo gear) I currently have between the 3.45 gear and what it acts like (2.91) when I swap gears.

ZeeAreOne,

That was my suspicion also. Car had 4.10s and at some point 3.45s were installed but the speedo gear never swapped. Of course that under reports the mileage. HMMMMM! No matter.

[Jagdpanzer]

I found this tool handy when I switch over to 19" wheels and larger diameter tires on the rear:
http://www.rimsntires.com/specs.jsp

Prior I was running stock 17" wheels and tires, 4.10 rear gears and 13/43 speedo correction gears. With this combo the speedometer and GPS more or less matched. However, after changing to 19" wheels and larger diameter 345/30ZR19 tires the speedometer showed 4 mph slower with 60 mph indicated on the GPS. Changing to 13/41 speedo gears narrowed the difference to around 1 mph which I find acceptable.

[RHanselman]

You guys are killing me sitting in your loungers at 1 G...

Us old Fighter Pilots just try to use the KISS principle...

Keep the 3:45's, put the stock wheels back on and then put the stock trans spedo gear back in. Problem solved...

But its kind of fun to see you guys go out to 10 digits and then cut it with an axe!

(4:10's are more fun...)

[XfireZ51]

Dyno,

Thanks for all the higher math. . This was going to be my next step.
But let me clarify again the objective. I don't really care about the speedo accuracy. What got me started on this is the realization that I have gone through my upgrades and I am killing performance by having the equivalent of a
2.90 some odd rear gear. So the real purpose of this exercise is to at come up w gearing that approximates the performance of the stock setup. If the speedo is off, I honestly couldn't care.

The other objective of the thread is to give Ron fun.

[XfireZ51]

This also points to why my trap speeds dropped originally when I installed the 19's.

[RICKYRJ1]

I have WAZOO installed 3.73's. I run both 18" and 19" rears depending on what look I prefer at the time. Where does that put me? We installed the correction gear at the time of install. I have only driven her with the 19's on since the install, car feels good.

[XfireZ51]

Originally Posted by RICKYRJ1

I have WAZOO installed 3.73's. I run both 18" and 19" rears depending on what look I prefer at the time. Where does that put me? We installed the correction gear at the time of install. I have only driven her with the 19's on since the install, car feels good.

Just using Dynos calc, I'd estimate u have an effective 3.22 gear.

[WVZR-1]

Originally Posted by RICKYRJ1

I have WAZOO installed 3.73's. I run both 18" and 19" rears depending on what look I prefer at the time. Where does that put me? We installed the correction gear at the time of install. I have only driven her with the 19's on since the install, car feels good.

Where does that put you? Your 3.73 is "still" a 3.73 gear

These are 1:1 4th gear calculations:

Using Phil's 345/30/19 (27.1) and your 3.73 gear 65 MPH: 3006 RPM, 100 MPH: 4625 RPM

Using a 315/35/17 and your 3.73 gear 65 MPH: 3170 RPM, 100 MPH: 4877 RPM

Your speedometer error actual/displayed: 60/56.8 - 100/94.6 - 140/132.4 These are calculated using advertised diameters not "rolling radius" but it's very close to what Phil mentions using the GPS.

To regain the RPM if you're "performance minded" I'd think it would require a 3.92 gear 65 MPH: 3159 RPM, 100 MPH: 4860 RPM

If you wanted to relate what the 345's did to your present 3.73 I'd guess you'd do the 3.73/3.92 = .9515 X 3.73 = 3.55

Seems logical to me but then again..........

[ZRapid-1]

Originally Posted by XfireZ51

Dyno,

Thanks for all the higher math. . This was going to be my next step.
But let me clarify again the objective. I don't really care about the speedo accuracy. What got me started on this is the realization that I have gone through my upgrades and I am killing performance by having the equivalent of a
2.90 some odd rear gear. So the real purpose of this exercise is to at come up w gearing that approximates the performance of the stock setup. If the speedo is off, I honestly couldn't care.

The other objective of the thread is to give Ron fun.

Changing from the stock ZR-1 tire diameter to one that is an inch larger doesn't have a huge effect.

25.7 x 3.45 = 26.7 x (Effective Dif Ratio)

Effective Dif Ratio = 3.31

Another way of stating it is that a 26.7 inch tire diameter (Z06) with a rear dif ratio of 3.45 is the equivalent of a 25.7 inch tire diameter (stock ZR-1) with a rear dif ratio of 3.31.

Not sure of the weight difference between rims/tires you are using, but acceleration could suffer. With the larger diameter tire, most of the weight is at the tread and thus further away from the axle centerline. A larger rim diameter also puts more metal at a larger radius from the axle centerline. The added rotational inertia will slow the tire's rate of acceleration.

[Paul Workman]

Oh, hell...Going all the way around the barn here; rpm, inches per second...

Cutting to the chase:

Let the (effective reference) radius from the center of the wheel (A) to the contact patch = 1
Let the (effective) radius from the center of then new wheel (B) to the contact patch = 1.2
Let the current differential drive shaft to axel ratio (C) =1:1
Let "X" = the new differential ratio.

X = Bx2xPi/Ax2xPi x C
simplifying...
X = B/A(reference) x C
substituting values...
X = 1.2/1 x 1 = 1.2

Checking:

The reference case: The (effective) circumferance of (A) = DxPi, or radius x 2 x Pi = 1 x 2 x 3.14 = 6.28
The (effective) circumferance of (B) = 1.2(radius) x 2 x 3.14 = 7.536

The new driveshaft axel ratio: X = B/A x C = 7.536/6.28 x 1:1
The new ratio = 1.2:1 (check)

B (7.536) / 1.2:1 = 6.28 = A...Check!!

Proof #2:

Using a proportional computation: A is to B as 3.45 is to X expressed as-

1:1.2 :: 3.45:X

solving the proportion-

X = 1.2x3.45/1 = 4.14 (in this hypothetical case)

4.14/1.2 = 3.45 Check (again)

Cliff (Dynomite) is right, far as using the speedo reading and GPS doesn't address the gear ratio directly, leaving a lot to chance, unless you assume 100% accuracy of the speedo and GPS values. Direct measuring is always less likely to introduce hidden factors.

Dom, you measure the effective radius of your wheel (center to patch), and I'll measure mine (currently a F1 GS D3 315x35x17) and then we'll have a pretty good basis for predicting final ratio to equate to the 3.45:1 on stock wheels. K?

My radius = 12.25"

X = (your radius)/12.25 x 3.45 = your new ratio to exactly equate to the 3.45

I'm outta here. Oh, wait!...I'm outta here except to trade friendly jousts with your sister: Being a math teacher in public school is no glowing recommendation . I've had to teach logarithms to high school grads that couldn't balance their checkbook. I made a good living for several years teaching math to HS grads that didn't have a grasp of the 4 basic principles of arithmetic. (Did your sister teach you math too??)

P.