ShadowsPapa

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Okay, so as promissed.

https://www.boeing.com/assets/pdf/commercial/airports/faqs/calctirecontactarea.pdf
Boeing Document #C1-APC-96-a072

Calculating Tire Contact Area
The tire contact area for any aircraft tire is calculated by dividing the single wheel load
by the tire inflation pressure. If the load is expressed in pounds, and the tire pressure in
pounds per square inch, then the area is in inches squared. The same thing works with
kilograms and kg/cm2 - the result will then be in square centimeters.
The shape of the footprint area is usually understood to be a 1.6 ellipse (as referenced
in the US Corps of Engineer's S-77-1 Report), wherein the major axis is 1.6 times the
minor axis. The calculation to solve for the minor axis is .894 times the square root of
the contact area. Note that the major axis runs parallel to the normal direction of motion
of the aircraft, and the minor axis is perpendicular to the major axis.

Example: 777-300 Main Gear Tire Contact Area
For this case, use the maximum taxi weight of 662,000 lbs configuration of the
777-300 as shown in Figure 7.2 “Landing Gear Footprint - 777-200/300” and
Figure 7.3 “Maximum Pavement Loads - 777-200/300.” Figure 7.2 provides the
main gear tire pressure of 215 PSI. Figure 7.3 shows the V(mg) per strut /
maximum load at the static aft center of gravity for this airplane configuration of
313,900 pounds. Given that the 777-300 has six wheels per main gear as shown
in Figure 7.2, to calculate the contact area first determine the load per tire
(313,900 / 6 = 52,317) then to calculate the contact area, divide the load per tire
by the PSI (52,317 / 215 = 243.3 in2 contact area).
The footprint area is a 1.6 ellipse determined as follows:
Minor axis is .894 x square root of the contact area (0.894 x sq root of 243.3 =
13.94 inches minor axis)
Major axis is 1.6 x minor axis (1.6 x 13.94 = 22.30 inches major axis)

So lets say we have Gladiator loaded to 6250lb at 30psi, 15psi & 8psi

6250lb / 4 tires = 1562.5lb per tire (yes I know, this is discounting weight distribution, go corner weight your own rig and do you own math)
1562.5lb / 30psi = 52.08333"^2 contact area
1562.5lb / 15psi = 104.1666"^2 contact area
1562.5lb / 7psi = 195.3125"^2 contact area

minor axis = .894 x sqrt (contact area)
@30psi = 6.451889052
@15psi = 9.124346372
@8psi = 12.49402982

major axis = 1.6 x minor axis
@30psi = 10.32302248
@15psi = 14.5989542
@8psi = 19.99044772

So...
30psi = 10.32 X 6.45
15psi = 14.60 x 9.12
8psi = 20.00 x 12.50

That's a pretty dramatic increase in contact area that oddly enough has nothing to do with the actual size of the tire. Tire size and subsequent load rating should then be the determining factor for how long and how well any given tire performs in this situation. To take a look at it in very basic terms Load = Patch and Patch should be physically limited by tire carcass dimensions; you should not have contact patch wider than the physical tread width. Which is a long way of saying contact patch determines tire size and not the other way around.

Or even another way, load dictates how much air pressure you can tolerate via tire deformation; the larger the patch gets, the less sidewall you have supporting the load AND the more work an incorrect part of the tire is doing.
Good grief - I keep saying that you can weigh your vehicle by using the foot print or contact area and psi for each tire. You just did it in reverse - weight and psi gives contact area. Pressure on an area gives the force -
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MrJeep

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Awesome analysis.
Two comments from a mech E who also worked in aerospace for a while.
Aircraft tires are way different from off-road tires in what they are designed for.
Sand is way different than tarmac. In fact, there are as many different kinds of sand as the "Eskimos have words for snow."
The sand wraps around the tires as much as the tires wrap around the sand and then there is the factor of how deep you have buried yourself.

All you sand lovers should DEFINITELY check out Matt's off road recovery on YouTube and see how even different weather can change how the sand reacts to tires. Most fascinatingly Matt has found that tires about 60% worn down are WAY better than when they are new.
 

aceisback

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Well I didn’t get any answers to my questions in post 9 so I’m just left with now being curious as to how many words Eskimos have for snow???
 

ShadowsPapa

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Well I didn’t get any answers to my questions in post 9 so I’m just left with now being curious as to how many words Eskimos have for snow???
50
But the Scotts have over 400 - but then it's not really the same comparison.
 

ACAD_Cowboy

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Well I didn’t get any answers to my questions in post 9 so I’m just left with now being curious as to how many words Eskimos have for snow???
To be honest they have a word for snow and then a huge collection of adjectives to describe the snow. It's somewhat like german with compound nouns.

Good grief - I keep saying that you can weigh your vehicle by using the foot print or contact area and psi for each tire. You just did it in reverse - weight and psi gives contact area. Pressure on an area gives the force -
It's the data point I have, the reason for finding it in the first place was a roiling discussion about wider tires == greater contact area and then that discussion came out. We were using it in the aired up direction but the concept applies either way and in either direction.

Awesome analysis.
Two comments from a mech E who also worked in aerospace for a while.
Aircraft tires are way different from off-road tires in what they are designed for.
Sand is way different than tarmac. In fact, there are as many different kinds of sand as the "Eskimos have words for snow."
The sand wraps around the tires as much as the tires wrap around the sand and then there is the factor of how deep you have buried yourself.

All you sand lovers should DEFINITELY check out Matt's off road recovery on YouTube and see how even different weather can change how the sand reacts to tires. Most fascinatingly Matt has found that tires about 60% worn down are WAY better than when they are new.
Hence why it is presented "for informational purposes only". Aircraft tires are slick balloon carcass tires that are designed to "pillow out" under load in ways that would frighten us on the road. Concrete and asphalt airport "roadways" are built very differently from some beach sand. This Boeing discussion doesn't in any way attempt to cover the complex 3d shape of a jeep tire tread in calculation of ground contact area and ground pressure, you are very correct that the sand will dish to accommodate the dish of the bagged out tire. On my typical beach the moist beach sand especially in the morning when it is cool and dense is much better for travel than the fishermans road in late day, the burma road as it is officially called by the county is somewhere between sugar sand and flour sand from all the traffic and in late day is dry and hot and flows fast. You will get stuck quick if you aren't prepared.

Matt's videos are great for demonstrating many flavors of inland sand. And yes a very worn tire that would be horrible in snow or rain will scoot right along on sand. I've seen pictures from friend's trips down in the Altar in Mexico and one year they went from XM47's to some borrowed "sand" tires, they are basically smooth and grooved like grader front tires and while amazing, they kept blowing beads because they weren't heavy enough to need enough air to hold the bead if you follow. But Matt's videos always remind me that these people drive among us; pulled a kid off the beach a few weeks back, he "never airs down because this nissan will go anywhere". Where he went that day was right to the frame in a bowl of super fine crystal sand after they blew a few hundred tons up on the beach after a storm. Guess you should have aired it down buddy.
 

Higher_Ground

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Engineers unite!

I wonder where the 1.6 major/minor axis ratio comes from - the ratio of the tire width to diameter? Or is from the rotation speed of the wheel? I figure they arrived at that value empirically but would like to know their guesses as to why.

I was curious what size tires airplanes even use. A 35x12.5 tire has a ratio roughly 1:2.8 width vs. diameter. From what I could google a 747 uses a H49x19 tires, roughly 49" tall and 19" wide for a ratio of 1:2.6.

If you had a ball sitting on the ground it's footprint would be a circle. Once it starts moving... consult a mechanical engineer!
 

ACAD_Cowboy

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Yes boeing was a little scant on supporting data. And yes we could do our own math to divine the nature of the elipse based on tire carcass geometry and see how consistant the math is.

I mostly use the calculations to demonstrate the principle, in the field I just air down until the main tread body is "flat" and the mud grousers are just making contact. For sand that is somewhere between 8 to 12psi. For dirt/mud it tends to be a little more like 12-14psi.

As for the real real reason behind the boeing math, I suspect it is useful for construction of the improved surfaces, psi of concrete mix, surface roughness etc and far less about the planes than we think, no one is asking about the best AT tires for their 707.
 

MrJeep

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Well I didn’t get any answers to my questions in post 9 so I’m just left with now being curious as to how many words Eskimos have for snow???
Well since you asked, Marine:
" Central Siberian Yupik has 40 such terms, while the Inuit dialect spoken in Canada’s Nunavik region has at least 53, including “matsaaruti,” for wet snow that can be used to ice a sleigh’s runners, and “pukak,” for the crystalline powder snow that looks like salt. "
From:
https://www.washingtonpost.com/nati...e3f4e0-59a0-11e2-beee-6e38f5215402_story.html

Same is true for mud, really, the one place I off road the most the mud can go from tacky to super slick with slight moisture level changes.

As for your dunes questions, find a local Jeep group, there HAS to be one around 29 Palms.

HTH - former Navy Squid
 
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jeepstertim

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UPDATE

12 psi this weekend (and turning the TC fully off) what a difference, soooo much more comfortable and flew up, along and down everything with ease. A complete blast and the JTR is now a hoot in the sand.
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ACAD_Cowboy

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Great report on performance and beautiful pictures
 
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