Minimum pressure

Discussion about deep snow wheeling, vehicle builds, trip reports, etc
Post Reply
Roger
Posts: 11
Joined: Fri Nov 22, 2013 7:34 pm
Location: Seattle

Minimum pressure

Post by Roger »

Matt - First, sorry about cluttering up the 101 class with more advanced techniques. ;)

To avoid more cluttering of your deep snow tire article, I'll do it here instead. :D

I ran some quick calculations based on some of the numbers (if I remember correctly) that you have given for your rig. Here are the numbers I am using: Tire size - 36X12.5X15, Weight 4200 lb with a front weight bias. So, I will use a weight of 1100 lb on a front tire. And, I will make a wild guess that the average with of the contact patch when the tire is aired way down is 14 inches.

Now, if the tire is at zero psi, the center of the tire/rim is going to be about 8.5 inches off the ground (15" rim is about 16" in overall diameter, plus 2 layers of tire sidewall for a total diameter of 17 inches). So how long is the contact patch when the tire is flat?

Well .... Draw a 17" circle in the center of a 36" circle, and then draw a horizontal line at the bottom of the 17" circle. Now, the length of the line between the two places where it crosses the 36" circle represents the maxim length of the contact patch that your tire can have. We can use the Pythagorean theorem to find this distance:

(36/2)^2 - (17/2)^2 = (contact length/2)^2

This gives a contact length of just under 32 inches. If we multiply this by the 14" with I guessed at, we get 445 square inches. Divide the weight on the tire by the area -- 1100/445 = 2.5 psi. So, I'm going to suggest that 2.5 psi is the minimum pressure that would be helpful given the size of your tires. Below that, the tire will be fully collapsed at the bottom and the rim will push through to the inside of the tread increasing the ground pressure in that area. This of course assumes flexible sidewalls.

This is where you can tell me my theoretical treatment of this subject is BS because you find pressures below 2.5 psi continue to improve performance in soft snow. :devil:
User avatar
Nobody
Site Admin
Posts: 1140
Joined: Fri Aug 07, 2009 6:58 pm
Location: Stanwood, Wa
Contact:

Re: Minimum pressure

Post by Nobody »

Welcome to the forum. Thanks for starting the discussion!

I love seeing the mathematics applied to the discussion. There are two big factors that really screw up your calculation. The first being the sidewall of the tire. The sidewall is passing 2-3+psi. Back when EBSTEVE was running SX's we used to pull the cores and run his tires at ZERO psi. Even that wasn't enough. Taking a wild guess, at zero psi, I'd say he was still at the equivalent of 5-6 PSI compared to a tire with a more flexible sidewall.

The second big factor is that the ground pressure is not distributed evenly over the area of the footprint. It actually varies widely based on many different factors. Including motion!

Here's an example footprint of what I believe is a Bias ply tire.
Image

What we need is TekScan. I actually reached out to them to see if I could get some generic footprint images, but they never followed up.
Image

WINTER IS HERE
Roger
Posts: 11
Joined: Fri Nov 22, 2013 7:34 pm
Location: Seattle

Re: Minimum pressure

Post by Roger »

Nice pressure plots. Do you have any more information about the conditions under which they were made? For example, road speed, tire size, weight on tire? With the 30+ inch contact length in the 6 psi condition, it must be a large tire. Also, the tire seems to be wider than the 20" shown in the plots. By doing a rough off-the-cuff integration, It appears there is over 2500 pound of load on the tire. I also assume that for these plots, the tire was on a hard surface. On a soft surface, I would expect things to be a bit different. But and you imagine trying to measure ground pressures dynamically in deep snow!

First, the 6 psi plot shows basically what I was trying to say in my original post. That is, as you get to very low air pressures, loading on the ground is concentrated to the area directly under the rim beads. Now, in the 18 psi plot there is high ground pressure near the center of the tread and it gets lower toward the edges. Conversely, at 6 psi the ground pressure is low in the center and high near the edges. It seems likely that at a pressure between 6 and 18 psi, say 10 psi, that he ground pressure would be more even across the width of the tire. It also seems reasonable that a more even ground pressure distribution would give better mobility than either of the cases shown.

Now, before you say the 10 psi is way too high (which I would agree with), lets consider that the tire shown seems to have a heavy load on it. What if the 18 psi plot is similar to what your tire looks like 5 psi, and the 6 psi case is more like your tire at 1.5 psi. Is it possible that some in between pressure, maybe 3 psi would give the best results for the weight on your tires?

Second, I agree with you completely that softer sidewalls are better. Stiff sidewalls just causes the ground pressure shift seen in the 6 psi plot to occur at a higher pressure. I suspect you would agree that tires that are stiff enough to run at zero psi are not ideal for deep snow.

Finally, regarding the ground pressure shifting forward of the axle center line. Do you have any more information on why this occurs? My first guess is that a lot of it is due to acceleration of the tread is it contacts and lifts from the road surface. That is, the tread is moving downward before it touches the pavement and reaches a zero vertical speed shortly after contact. This is an upward acceleration requiring an upward force on the block of tread. Since the air pressure in the tire is constant, this upward force must be due to higher ground pressures at the front of the tire. Assuming a smooth flat road, the total force on the ground must always be the same -- otherwise the vehicle would accelerate up or down. So some other part of the tire must have less ground pressure, for example the rear part of the contact patch.

If I'm correct about this (admittedly a big IF), then speed should have a large impact on the shift of the pressure distribution forward of the axle line. At low speeds, I would expect to see much less shift to the front of the axle.
User avatar
Nobody
Site Admin
Posts: 1140
Joined: Fri Aug 07, 2009 6:58 pm
Location: Stanwood, Wa
Contact:

Re: Minimum pressure

Post by Nobody »

I'm impressed. You're exactly right about that image being from a large tire. I got it from a publication on farming and soil compaction, but it didn't include any specifics about the conditions or tire specs.

While searching for one of the publications I remember reading. I came across this. Tons of great info... I haven't had a chance to digest it all yet. There is rarely a moment of silence in my house :tongue:
http://ethesis.helsinki.fi/julkaisut/ma ... endix5.pdf
WINTER IS HERE
Post Reply