Wheel ground pressure vs wheel size

[Baluncore]

I refer you to; Mechanics of pneumatic tires. NBS monograph 122. 1971.
By Gehman, S. D.; Ludema, K. C.; Backer, Stanley; Takeyama, T.; Matsui, J.; Clark, Samuel K.; Gough, V. E.; Walter, Joseph D.; Schallamach, A.; van Eldik Thieme, H. C. A.; Pacejka, H. B.

58 Mbyte; https://ia800702.us.archive.org/15/items/DTIC_AD0621045/DTIC_AD0621045.pdf

I quote Page 472;
“
In this section attention is directed first to the normal pressure distribution components caused by contact of the tire with some other surface. As a basic primary concept, one might state that
p = po+ f (Tire structural characteristics, tire driving or braking torque, tire side forces, tire velocity, etc.) (5.9)
where p is the vertical pressure component at any point, po is the inflation pressure of the tire and f is some general functional relationship which insofar as is now known is extremely complicated, and can best be described in a qualitative sense.
In eq (5.9), we postulate that the net pressure distribution at any point depends primarily upon the inflation pressure, and there is considerable experimental evidence to indicate that this is indeed true.
“

 

[hutchphd]

I couldn't get past p164 on your link (?) so I recommend this one:

https://archive.org/details/mechanicsofpneum122gehm/page/472
Thanks, it is a very interesting reference (I think I have defined myself as a nerd by that comment).
Notice the immediately subsequent equation eq.5.10, which mirrors what I was trying to say in comment #25 above!

 

[Baluncore]

Notice the immediately subsequent equation eq.5.10, which mirrors what I was trying to say in comment #25 above!

Eq.5.10 is referring specifically to where a tyre is tested against a rotating cylindrical roller. I agree that any test against a convex surface will give higher roller pressure results, which is the point of eq.5.10. But a road or an agricultural field is flat, not tightly curved.

Getting back to the OP.

I need to drive a tractor across and area of soft ground without leaving deep tracks.

I am talking about agricultural tractor tyres for use on soft ground. Internal pressures between about 12 and 25 psi, with large flat contact patches that do not leave ruts. Tractor tyres have a very flexible sidewall.

1, in cases where the ground is soft and deformable.

Under that situation the soil flows below the traction tyre to balance the ground pressure against the contact patch. Examine the track left by an agricultural tractor and you will see an equally compacted soil, with depressions where the tread lugs displaced soil. Soil flow is encouraged by horizontal soil shear due to traction.

The sidewall of a tractor tyre is folded with a short radius of curvature at the sides of the contact patch, which clearly precludes surface tension as a dominant factor. The front and rear of the contact patch have a tyre to ground separation angle that indicates surface tension will taper ground pressure from inflation pressure to zero at the entry and exit only.

 

[hutchphd]

Eq.5.10 is referring specifically to where a tyre is tested against a rotating cylindrical roller. I agree that any test against a convex surface will give higher roller pressure results, which is the point of eq.5.10. But a road or an agricultural field is flat, not tightly curved.

Unless it is mud...or other very viscous fluid. The fact that the resulting track is flat does not necessarily indicate that the instantaneous contact patch is flat. Mostly I was responding to a categorical statement about pressure and the contact patch. I did give a similar caveat in #25...
Clearly the biggest deviation in the real world comes from the rigidity of a tire and that analysis is well beyond my pay grade.

 

[Baluncore]

Mostly I was responding to a categorical statement about pressure and the contact patch. I did give a similar caveat in #25...
Clearly the biggest deviation in the real world comes from the rigidity of a tire and that analysis is well beyond my pay grade.

I was mostly pointing out that the "its just the interior pressure" argument fails in even the simplest case.

I do not claim that it is only interior pressure. I stand by my earlier statement for tractor tyres.

The ground pressure of a tyre is simply the tyre pressure.

All the pneumatic tyre references I have seen, and all my experience with tractor tyres indicates that primarily, the ground pressure is the same as the internal pressure.

You can argue that it does not hold around the edges, or for special cases of curved ground, or free flowing mud, but in any rational analysis it must be the first principle of pneumatic tyres.

 

[hutchphd]

I do not claim that it is only interior pressure. I stand by my earlier statement for tractor tyres.All the pneumatic tyre references I have seen, and all my experience with tractor tyres indicates that primarily, the ground pressure is the same as the internal pressure.

You can argue that it does not hold around the edges, or for special cases of curved ground, or free flowing mud, but in any rational analysis it must be the first principle of pneumatic tyres.

Then we agree. It is something many folks miss I fear.
Also I bet you can show that (even considering "surface tension" and a curved interface) the net upward load has to be the interior pressure times the contact area projected onto the horizontal plane. But who really cares!