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Discussion Starter #1
The circumference of the tire does not change (mounted on rim and under vehicle weight vs mounted on rim but not on vehicle) therefore the revolutions per mile also does not change.
This being the case why do I read over and over again I should base my new gear ratio on the height (diameter) of the tire under the weight of the vehicle?
 

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I don't believe your premise is correct. The tire is rotating on a diameter that is defined by the tire with the weight of the vehicle on it. Therefore the actual circumference is smaller than what you measure. The distance from the middle of the hub to the ground is what you would use to represent the circumference that defines the revolutions per mile. Rather than using the diameter when calculating the correction factor for my speedometer I used the number of revolutions in a set distance. say 100 feet. I figured that was more accurate than eyeballing a tape measure to the center of my hub.
 

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Discussion Starter #3
I don't believe your premise is correct. The tire is rotating on a diameter that is defined by the tire with the weight of the vehicle on it. Therefore the actual circumference is smaller than what you measure. The distance from the middle of the hub to the ground is what you would use to represent the circumference that defines the revolutions per mile. Rather than using the diameter when calculating the correction factor for my speedometer I used the number of revolutions in a set distance. say 100 feet. I figured that was more accurate than eyeballing a tape measure to the center of my hub.
Circumference (distance around the tire) will not change, except for expansion slightly as the tire spins - centripetal force... I think it's called.
"Distance around" might get oblong instead of perfectly round but is still the same distance.
 

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Think about a caterpillar tread as the logical extreme of your argument. the portion of the tire flat to the surface doesn't contribute to the calculation
 

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Think about it. The tire is flat on the bottom. And it stays that diameter as the tire rotates. You are rotating around a smaller circumference than the unloaded tire measures in at. The tire is bulging out on the sides to make the volume the same, but the effective diameter is smaller and the effective circumference is also smaller.
 

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Instead of using diameter use the radius from the center of the axle to the ground x2 = effective diameter.
 

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Instead of using diameter use the radius from the center of the axle to the ground x2 = effective diameter.
That would be the best way, IMHO

The circumference does change, ever so slightly, as does the radius/diameter, when the vehicle is putting its weight on the tire. How much depends on tire pressure. What matters is where the rubber meets the road, ha ha. But seriously, that is the effective tire radius and it is what will drive your final drive ratio. BTW, I use radius because the distance from center of hub to the ground does not equal the distance from the center of the hub to any other point around the perimeter of the tire.
 

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Circumference is defined as follows from Wikipedia

The circumference of a circle relates to one of the most important mathematical constants in all of mathematics. This constant, pi, is represented by the Greek letter π. The numerical value of π is 3.14159 26535 89793 ... (see OEIS A000796). Pi is defined as the ratio of a circle's circumference C to its diameter

C=pi x diameter = pi x (2 x radius)

The circumference is going to change between unloaded and loaded due to the change in the radius due to the compression of the tire as it is loaded.


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Should be easy to see which is correct. Mark the tire where it contacts the ground and then roll the Jeep until that mark again is at the point where it contacts the ground and measure the distance. A couple of revolutions might make it easier to measure. Without having done this, I'm leaning towards the circumference like the OP.
 

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This is an interesting question! The OP is correct that there is a fixed "length" of tread on the tire and every revolution of the axle you should move forward that length. Hmmmm. Gonna have to think about this.
 

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This is an interesting question! The OP is correct that there is a fixed "length" of tread on the tire and every revolution of the axle you should move forward that length. Hmmmm. Gonna have to think about this.

Yes the OP is correct that there is a "fixed length" of tread, BUT the rolling circumference WILL change due to as how the OP put it "the diameter of the tire off the vehicle and the diameter of the tire under load on the vehicle". These measurements will be different due to the compression of the sidewalk under vehicle load which will then change the diameter of the tire. As I listed above the formula for finding the circumference of a circle is

C= pi x d = pi x (2 x radius)

There is no changing this as pi is a constant.

Example...... a 40" diameter tire will be used to keep the math simple. Off vehicle unloaded the radius is 20". Your radius from the axle center to the outside of the tire is 20".

C = 3.14 x (2 x 20) = 125.6" circumference.

Now mounted on the vehicle under load the sidewall is now compressed 1". Your radius from the axle center to the road is now 19".

C = 3.14 x (2 x 19) = 119.32"


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the above is correct.
I'm sure if someone wants to get really involved, they can create the formula that relates % of circumference in contact with the ground under deformity of the loaded tire (contact patch) backwards through the revolutions of the circumference to show the loss in "roll out"... but in the end the simple method of radius from center of hub to ground is the measuring stick.
So, a portion of the circle, "chord" has been flattened, making a larger contact patch, so while the circumference length has not changed, the radius has (because it is no longer a circle) and since the tire rotates about the center of the hub (center of the circle as it relates to the ground), radius still rules the day, just, more of the deformed circumference is now flat on the ground.
Since the distance we travel is the measured along the ground, as result of hub rotations, it is the radius between the ground and the center of hub that is again the measuring stick.
 

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so... take one of those triangle shaped "tracks" that folks use for snow...

Stretch that track out into a circle, lots of length (circumference).
In it's current shape it has a tonne of contact patch, but, the center of the drive hub to the ground is still going to determine how far it goes per revolution of the hub, and revolutions of the hub are what is driving your odometer, and speedometer. (sure the sensor may be mounted to the trans output shaft or some other rotating part, but in the end it's math is based on wheel revolutions, and tire "diameter", or as we have illustrated, radius of hub center to ground).
 

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Discussion Starter #14
Ok, with all that's been said assumed true... are the gearing charts compiled using real world diameter or advertised diameter?
 

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I do not know the answer to that, but if you use sites like grimjeeper and input the true numbers you will get true data, vs some random chart made by someone who is basing recommendations of personal opinion/requirements.
Nice thing about grimjeeper is you can input factory numbers in one column to get factory rpm/mph, then in the column next to it play with variables and compare what happens to rpm/mph and decide for youself based on your needs/requirements/tolerance.
 

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OK, I thought I knew the answer, but talking about it changed my mind. Take that same 40" tire

C = 3.14 x (2 x 20) = 125.6" circumference.

Now deflate it until it is 2" tall and flattened out. The radius is 1", but the circumference didn't change to 6.28". It is still 125.6" circumference, so it travels 125.6" per revolution. The distance traveled doesn't change depending on the air pressure. :pullinghair:
 

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Discussion Starter #17
OK, I thought I knew the answer, but talking about it changed my mind. Take that same 40" tire

C = 3.14 x (2 x 20) = 125.6" circumference.

Now deflate it until it is 2" tall and flattened out. The radius is 1", but the circumference didn't change to 6.28". It is still 125.6" circumference, so it travels 125.6" per revolution. The distance traveled doesn't change depending on the air pressure. :pullinghair:
Your argument is also where I'm coming from. But I think you need to look at it from side wall bulge too. Not that I fully believe the arguments made above regarding circumference changing to a noticeable amount, I do agree that diameter (measured perpendicular to the ground) will change due to the sidewall bulging under pressure/ weight of the Jeep. The sidewall can only bulge so much though since it is mounted to a rim (regardless of the material composition limiting the bulge).
I will be doing a real world measurement test as soon as I am on vacation (in a few days). :)
 

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Discussion Starter #18
I do not know the answer to that, but if you use sites like grimjeeper and input the true numbers you will get true data, vs some random chart made by someone who is basing recommendations of personal opinion/requirements.
Nice thing about grimjeeper is you can input factory numbers in one column to get factory rpm/mph, then in the column next to it play with variables and compare what happens to rpm/mph and decide for youself based on your needs/requirements/tolerance.
Thanks for the link... can you tell me what auto trans and transfer case the JKU (2015) has? I don't know gear ratios to enter so I need model #'s I guess.
Thanks
 

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I just want to throw my 2 cents in here to maybe help you guys make heads or tails of this.

I see a bunch of comments talking about the circumference changing when the height of the tire changes and talking about the circumference of a track rather than a round tire.

Unless you're talking about a circle, you are NOT talking about a circular circumference and the formulas do not apply. If the tire has a 20" radius unloaded and that radius goes down to 19" when it's aired down, then it is no longer a circle and you can't use the same formula.

The OP is right in that the distance around the tire tread remains the same. Bulging at the sides doesn't lengthen or shorten it (unless it's particularly stretchy... which I don't think is a tangible factor here).

One revolution of the wheel should move the jeep the same distance forward regardless of the tire pressure so long as the tire isn't slipping.

Comparing it to any track system isn't valid since in a track, the wheel is moving around within the track. With a tire, unless the bead slips, this isn't the case.
 

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If you need evidence, you can look at what your tire size in the Jeep's computer is programmed for. The stock tire being 32" when inflated to max PSI an unloaded is programmed as 30.75", which is it's loaded and normal PSI diameter. A lot of people make this mistake when they put larger tires on their Jeep, buy a FlashCal to reprogram the tire size, and set for 33" or 35" rather than an actual measured diameter. Typically the loaded diameter is an inch to an inch and a half less than the specified diameter.
 
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