Minimum pressure
Posted: Fri Nov 22, 2013 8:32 pm
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.
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.
To avoid more cluttering of your deep snow tire article, I'll do it here instead.
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.