BFG Mud Terrain actual sizing?

srimes said:
View attachment 349856

No issues with your math. Kinda gotta take issue with the claim that "rolling radius isn't really related to the rolling circumference." Seems like by definition they're related by šŸ„§ šŸ„§ (2 pies).

And I wasn't claiming that rolling circumference is 2pi(hub height). Pointing out that is itsn't is a very interesting observation and I had to chew on that for a while. I got to thinking about the tire tread like a tank track. But the distance/rev does change, just not as dramatically hub height. And this implies some amount of slippage or compression/expansion at the tread blocks.

re: rolling circumference vs speed and pressure, see below. But they're talking about car tyres so maybe it doesn't apply to tires?

[URL]https://www.researchgate.net/p...ement_of_dynamic_radii_for_passenger_car_tyre[/URL]
View attachment 349852
Click to expand...

Good find on the data, I think 1% difference between 20-38psi being far less than the diameter lost as the tire wears through it's lifetime, and probably on par with the most precise measurements any of us use to measure speed; I think it's close enough to be negligible for the purposes of gearing calculations on grimm Jeeper.

But because I like math, I'm gonna propose this for the group to chew on. Maybe the difference you inferred in tread block compression/distortion is accounted for in compressing the arc length of the contact patch into the associated chord?

1660137806209.png
 
Mr. Bills said:
Yes, I will, if you provide the data as I did.

First do my experiment.

Then do yours using the "rolling circumference" method.

Compare Grimm Jeeper calculator results.

If there are differences, it will be your turn to explain why.
Click to expand...

Okay, I did my testing today, as promised. First, some vehicle data:

05 LJ Rubicon
Stock NSG370 6 speed
Stock NP241OR Transfer Case
Stock 4.11 Rubicon Gears
285/75R16 Tires (Load Range E) with about 7,500 miles on them
Speedometer Calibrated via SpeedoHealer v4

Next, a description of the test procedure. I used a Bluetooth ODB2 scanner (ODBLink MX+) with my iPhone (sorry, Zorba!) so that I could include GPS speed in the dataset. The PCM's vehicle speed and engine speed data streams, in addition to the iPhone's GPS speed, were logged during the tests. I performed the test twice. Once with 51 psi in the tires and again with 12 psi in the tires (both measured with hot tires). For the test, I drove the country road near my house with the cruise control set at approximately 40 MPH in 4th gear and recorded data. Each time, after completion of the data logging, I returned home and put my LJ in the shop on a level surface to measure the following:

Tire pressure (psi)
Hub height (inches) - measured with a tape measure
Rolling circumference (inches) - measured by putting a paint dot on the tire and driving forward to get two dots to measure between with tape measure

Here's the data collected from the first test:

Tire pressure = 51 psi
Hub height = 16.1 inches
Rolling circumference = 100.38"
Vehicle speed = 42.7 MPH (from GPS speed)
Engine speed = 2,314 RPM

Data (data point circled in blue):
Tire Diameter Test 1.jpg


Here's the data collected from the second test:

Tire pressure = 12 psi
Hub height = 15.6 inches
Rolling circumference = 99.25"
Vehicle speed = 41.9 MPH (from GPS speed)
Engine speed = 2,280 RPM

Data (data point circled in blue):
Tire Diameter Test 2.jpg


So, with data in hand, I went to GrimmJeeper's Gear Ratio Calculator to calculate the tire diameter from the vehicle and engine speed data (Mr. Bills' Test). Here's what I got from there for the two tests:

Test 1 - In fourth gear, to get 43 MPH at 2,314 RPM, the tire diameter has to be from 31.8" to 32.4"
Test 2 - In fourth gear, to get 42 MPH at 2,280 RPM, the tire diameter has to be from 31.5" to 32.1"

As shown, getting a tire diameter with this method is tricky due to the speed being calculated to the nearest whole MPH. For instance, with the first test, if the first number you try is 31.8", and you stop there, you'll conclude that it's 31.8", but if you start at the other end and stop there, you'll conclude that it's 32.4". That's over a half inch of difference. I decided to do the math myself to get the tire diameter to the nearest tenth of an inch, since it seems possible to measure a tire diameter to that level of accuracy. Am I splitting hairs? Absolutely. Is this necessary for gearing calculations? Probably not. However, remember the point of this exercise was to try to determine the best method for measuring tire diameter with regards to gearing. So, doing the math myself, I get the following results:

Test 1 - In fourth gear, to get 42.7 MPH at 2,314 RPM, the tire diameter has to be 31.9"
Test 2 - In fourth gear, to get 41.9 MPH at 2,280 RPM, the tire diameter has to be 31.7"

Now, the other two methods I employed in this testing to measure tire diameter were the hub height (or rolling radius) and the rolling circumference. Multiplying the hub height by two gives a diameter, and dividing the rolling circumference by pi gives a diameter. Doing those calculations gives the following summary of test results:

For Test 1:
Tire Diameter from Hand Gearing Calculations = 31.9"
Tire Diameter from GrimmJeeper (worst case) = 32.4"
Tire Diameter from Hub Height = 32.2" (16.1" x 2)
Tire Diameter from Rolling Circumference = 32.0" (100.38" / pi)

For Test 2:
Tire Diameter from Hand Gearing Calculations = 31.7"
Tire Diameter from GrimmJeeper (worst case) = 32.1"
Tire Diameter from Hub Height = 31.2" (15.6" x 2)
Tire Diameter from Rolling Circumference = 31.6" (99.25" / pi)

Conclusions
  1. If we use the diameter from the hand gearing calculations as the most correct one (since it's accurate to a tenth MPH), the worst-case errors from using the GrimmJeeper calculator to estimate tire diameter are 0.5" (Test 1) and 0.4" (Test 2), or less than 2%.
  2. The error from using the hub height to estimate tire diameter are 0.3" (Test 1) and 0.5" (Test 2), or less than 2%.
  3. The errors using the rolling circumference to estimate diameter are 0.1" for both tests, or about 0.3%.
  4. As I mentioned in an earlier post, the rolling circumference method is the most accurate, and the reason for this is that when you measure that, you're measuring the actual distance the vehicle rolls with one revolution of the tire.
  5. The manufacturer lists the diameter of my tires as 33.07" (but they also have 7,500 miles on them). The error from using that number is only about 4% compared to the two diameters arrived at by hand calculations in the two tests I did, and that's probably accurate enough for gearing changes, too.
  6. All of these methods are likely accurate enough for gearing calculations, depending on how accurate you want to be. For instance, the range of engine speed in 6th gear at 70 MPH from the GrimmJeeper site for the range of tire diameters from the four methods (31.2" to 33.07") is 2,455 to 2,603 RPM - just 148 RPM, which is not likely to be a problem if you're off by that much. Tire size is just not that critical.
So, I guess Mr. Bills and I were both correct. Using hub height times two for gearing calculations will be accurate enough, but using the rolling circumference is the most accurate of the four methods (GrimmJeeper, hub height, rolling circumference, and manufacturer's diameter).

Further Thoughts
Even though it was just about 1%, the change in rolling circumference surprised me some, so I checked hub height and rolling circumference for two other pressures (5 psi and 26 psi), but I didn't drive the LJ with those pressures. Here's a summary of those numbers:

1660433005735.png


These data show that the hub height change with tire pressure is very non-linear, especially when pressures get into the single digits. The fact that rolling circumference for 26 psi is less than that for 12 psi is probably due to measurement inaccuracies (the paint dots are faint and slightly different shapes so it's difficult to be perfect).

However, while the hub height grows about 16% (2.2"/13.9") from 5 psi to 51 psi, the rolling circumference only grows about 3% (2.76"/97.62") for the same pressures. As I said earlier, the 3% change in rolling circumference due to tire pressure is insignificant, but the 16% change in hub height is not insignificant. Then again, how many times do we do gearing calculations for tires at 5 psi, right?

I suspect that rim width has a lot to do with the rolling circumference and the resulting tire diameter calculated from it, and since the manufacturer's don't give rim width information with their diameter data, those numbers seem to be the most inaccurate.
 
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sab said:
Okay, I did my testing today, as promised. First, some vehicle data:

05 LJ Rubicon
Stock NSG370 6 speed
Stock NP241OR Transfer Case
Stock 4.11 Rubicon Gears
285/75R16 Tires (Load Range E) with about 7,500 miles on them
Speedometer Calibrated via SpeedoHealer v4

Next, a description of the test procedure. I used a Bluetooth ODB2 scanner (ODBLink MX+) with my iPhone (sorry, Zorba!) so that I could include GPS speed in the dataset. The PCM's vehicle speed and engine speed data streams, in addition to the iPhone's GPS speed, were logged during the tests. I performed the test twice. Once with 51 psi in the tires and again with 12 psi in the tires (both measured with hot tires). For the test, I drove the country road near my house with the cruise control set at approximately 40 MPH in 4th gear and recorded data. Each time, after completion of the data logging, I returned home and put my LJ in the shop on a level surface to measure the following:

Tire pressure (psi)
Hub height (inches) - measured with a tape measure
Rolling circumference (inches) - measured by putting a paint dot on the tire and driving forward to get two dots to measure between with tape measure

Here's the data collected from the first test:

Tire pressure = 51 psi
Hub height = 16.1 inches
Rolling circumference = 100.38"
Vehicle speed = 42.7 MPH (from GPS speed)
Engine speed = 2,314 RPM

Data (data point circled in blue):
View attachment 350721

Here's the data collected from the second test:

Tire pressure = 12 psi
Hub height = 15.6 inches
Rolling circumference = 99.25"
Vehicle speed = 41.9 MPH (from GPS speed)
Engine speed = 2,280 RPM

Data (data point circled in blue):
View attachment 350722

So, with data in hand, I went to GrimmJeeper's Gear Ratio Calculator to calculate the tire diameter from the vehicle and engine speed data (Mr. Bills' Test). Here's what I got from there for the two tests:

Test 1 - In fourth gear, to get 43 MPH at 2,314 RPM, the tire diameter has to be from 31.8" to 32.4"
Test 2 - In fourth gear, to get 42 MPH at 2,280 RPM, the tire diameter has to be from 31.5" to 32.1"

As shown, getting a tire diameter with this method is tricky due to the speed being calculated to the nearest whole MPH. For instance, with the first test, if the first number you try is 31.8", and you stop there, you'll conclude that it's 31.8", but if you start at the other end and stop there, you'll conclude that it's 32.4". That's over a half inch of difference. I decided to do the math myself to get the tire diameter to the nearest tenth of an inch, since it seems possible to measure a tire diameter to that level of accuracy. Am I splitting hairs? Absolutely. Is this necessary for gearing calculations? Probably not. However, remember the point of this exercise was to try to determine the best method for measuring tire diameter with regards to gearing. So, doing the math myself, I get the following results:

Test 1 - In fourth gear, to get 42.7 MPH at 2,314 RPM, the tire diameter has to be 31.9"
Test 2 - In fourth gear, to get 41.9 MPH at 2,280 RPM, the tire diameter has to be 31.7"

Now, the other two methods I employed in this testing to measure tire diameter were the hub height (or rolling radius) and the rolling circumference. Multiplying the hub height by two gives a diameter, and dividing the rolling circumference by pi gives a diameter. Doing those calculations gives the following summary of test results:

For Test 1:
Tire Diameter from Hand Gearing Calculations = 31.9"
Tire Diameter from GrimmJeeper (worst case) = 32.4"
Tire Diameter from Hub Height = 32.2" (16.1" x 2)
Tire Diameter from Rolling Circumference = 32.0" (100.38" / pi)

For Test 2:
Tire Diameter from Hand Gearing Calculations = 31.7"
Tire Diameter from GrimmJeeper (worst case) = 32.1"
Tire Diameter from Hub Height = 31.2" (15.6" x 2)
Tire Diameter from Rolling Circumference = 31.6" (99.25" / pi)

Conclusions
  1. If we use the diameter from the hand gearing calculations as the most correct one (since it's accurate to a tenth MPH), the worst-case errors from using the GrimmJeeper calculator to estimate tire diameter are 0.5" (Test 1) and 0.4" (Test 2), or less than 2%.
  2. The error from using the hub height to estimate tire diameter are 0.3" (Test 1) and 0.5" (Test 2), or less than 2%.
  3. The errors using the rolling circumference to estimate diameter are 0.1" for both tests, or about 0.3%.
  4. As I mentioned in an earlier post, the rolling circumference method is the most accurate, and the reason for this is that when you measure that, you're measuring the actual distance the vehicle rolls with one revolution of the tire.
  5. The manufacturer lists the diameter of my tires as 33.07" (but they also have 7,500 miles on them). The error from using that number is only about 4% compared to the two diameters arrived at by hand calculations in the two tests I did, and that's probably accurate enough for gearing changes, too.
  6. All of these methods are likely accurate enough for gearing calculations, depending on how accurate you want to be. For instance, the range of engine speed in 6th gear at 70 MPH from the GrimmJeeper site for the range of tire diameters from the four methods (31.2" to 33.07") is 2,455 to 2,603 RPM - just 148 RPM, which is not likely to be a problem if you're off by that much. Tire size is just not that critical.
So, I guess Mr. Bills and I were both correct. Using hub height times two for gearing calculations will be accurate enough, but using the rolling circumference is the most accurate of the four methods (GrimmJeeper, hub height, rolling circumference, and manufacturer's diameter).

Further Thoughts
Even though it was just about 1%, the change in rolling circumference surprised me some, so I checked hub height and rolling circumference for two other pressures (5 psi and 26 psi), but I didn't drive the LJ with those pressures. Here's a summary of those numbers:

View attachment 350740

These data show that the hub height change with tire pressure is very non-linear, especially when pressures get into the single digits. The fact that rolling circumference for 26 psi is less than that for 12 psi is probably due to measurement inaccuracies (the paint dots are faint and slightly different shapes so it's difficult to be perfect).

However, while the hub height grows about 16% (2.2"/13.9") from 5 psi to 51 psi, the rolling circumference only grows about 3% (2.76"/97.62") for the same pressures. As I said earlier, the 3% change in rolling circumference due to tire pressure is insignificant, but the 16% change in hub height is not insignificant. Then again, how many times do we do gearing calculations for tires at 5 psi, right?

I suspect that rim width has a lot to do with the rolling circumference and the resulting tire diameter calculated from it, and since the manufacturer's don't give rim width information with their diameter data, those numbers seem to be the most inaccurate.
Click to expand...

Ya'll work way too hard at this. I drive the rig, get numbers from the speedo and tach in a known gear. I take those in the house, log into the calculator, punch in the tire diameter until they match what I see on the dash. Done with an exact tire size to use for when I want to know what gears I want.
 
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mrblaine said:
Ya'll work way too hard at this. I drive the rig, get numbers from the speedo and tach in a known gear. I take those in the house, log into the calculator, punch in the tire diameter until they match what I see on the dash. Done with an exact tire size to use for when I want to know what gears I want.
Click to expand...
Mr. Blaine - I know you work very hard to understand things, too. Your work shows that.
 
sab said:
Mr. Blaine - I know you work very hard to understand things, too. Your work shows that.
Click to expand...

Ya'll are doing the equivalent of measuring the flame front temperature when the spark plug fires to extrapolate what the engine running temperature is.

All we need to know is what tire size will give us reasonably accurate results when used with a basic calculator to see where we'd like our engine RPM to be at a given speed and use that to pick a gear ratio that works for what we do.

That tire size is easily determined via a short test drive, noting the speed and RPM and then changing the tire size in the calculator until we get a match.
 
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mrblaine said:
Ya'll are doing the equivalent of measuring the flame front temperature when the spark plug fires to extrapolate what the engine running temperature is.
Click to expand...

How so? Yes, I spent a few hours analyzing different ways of measuring tire diameter for use in gearing calculations, but that analysis shows that measuring tire diameter isnā€™t complicated or difficult and can be done successfully several ways.

mrblaine said:
All we need to know is what tire size will give us reasonably accurate results when used with a basic calculator to see where we'd like our engine RPM to be at a given speed and use that to pick a gear ratio that works for what we do.

That tire size is easily determined via a short test drive, noting the speed and RPM and then changing the tire size in the calculator until we get a match.
Click to expand...

And it can also be determined in other ways that may even be easier, depending on the situation. Personally, Iā€™d rather paint a dot on the tire, roll the vehicle forward for one revolution and measure dot to dot. However, doing it your way works just as well, so if that works for you, thatā€™s great, too. Does there only have to be one way to do it?
 
mrblaine said:
Ya'll work way too hard at this. I drive the rig, get numbers from the speedo and tach in a known gear. I take those in the house, log into the calculator, punch in the tire diameter until they match what I see on the dash. Done with an exact tire size to use for when I want to know what gears I want.
Click to expand...

Funny, that sounds exactly like my experiment.

Wait, I designed that experiment specifically to test your method. The results proved your method effective with more meaningful results than using published tire diameters.

But you already knew that. ;)



I'm still going to read and digest @sab 's post. I owe it to him and I'm always willing to learn something new.
 
Last edited:
sab said:
And it can also be determined in other ways that may even be easier, depending on the situation. Personally, Iā€™d rather paint a dot on the tire, roll the vehicle forward for one revolution and measure dot to dot. However, doing it your way works just as well, so if that works for you, thatā€™s great, too. Does there only have to be one way to do it?
Click to expand...
Only an engineer would ever say that taking a short drive, noting a few dash readings and then plugging those into a calculator is harder than anything else.
 
mrblaine said:
Only an engineer would ever say that taking a short drive, noting a few dash readings and then plugging those into a calculator is harder than anything else.
Click to expand...

Some of us are doing this to select a gear ratio before we have the tires in our possession. What his experiment had demonstrated is that you can use the stated revs per mile and get way better than close enough without having to worry about your specific load and inflation pressure or any of the other variables people worry too much about.
 
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freedom_in_4low said:
Some of us are doing this to select a gear ratio before we have the tires in our possession.
Click to expand...
Great, another fucking engineer. You really are NOT going to find enough of a discrepancy between the commonly available tires in a given size like 31, 33's, 35's or 37's to miss a gear step. That and at the end of the day, the most you are going to be off is 5% unless you're just being silly.
freedom_in_4low said:
What his experiment had demonstrated is that you can use the stated revs per mile and get way better than close enough without having to worry about your specific load and inflation pressure or any of the other variables people worry too much about.
Click to expand...
We have to go back to why all of this stuff started. It started with folks plugging the sidewall stated 35" into the calculator believing erroneously that they would get accurate info. I've had many conversations with folks who said the calculator was crap because it didn't match what they see on the dash. I'd explain over and over that the mechanical math is a known quantity and the only variable that skews their readings is tire size. Stop using the size on the sidewall and it all gets better.

Iffen ya'll wanna play fuck fuck games with dots and measuring shit, fine by me. Us technically challenged folk have a way to find the answer and so do all ya'll smart folk.
 
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mrblaine said:
Only an engineer who lives a mile down a rough gravel 15 MPH private road, but has a nice 40' concrete pad in his shop would ever say that taking a short drive, noting a few dash readings and then plugging those into a calculator is harder than anything else.
Click to expand...

Fixed it for you. ;)
 
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