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

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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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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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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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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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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Nice thing about

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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. ullinghair:

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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).

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. ullinghair:

I will be doing a real world measurement test as soon as I am on vacation (in a few days).

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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.grimjeeperand 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 aboutgrimjeeperis 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

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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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