Tires-Why Are Rolling Circumference And Loaded Radius Not The Same?

[npalen]

In other words, why isn't dividing rolling circumference by 6.28 (two times pi) equal to loaded radius? I guess what I'm asking is the exact definition of loaded radius and rolling circumference.

Edit: An example http://www.titanstore.com/info/412373

Rolling circumference shows 118" so dividing that by 6.28 equals 18.8 but the specs show 17.7 for the rolling radius.

Edit: Should read "loaded radius" previous sentence.

 

[dickfoster]

In other words, why isn't dividing rolling circumference by 6.28 (two times pi) equal to loaded radius? I guess what I'm asking is the exact definition of loaded radius and rolling circumference.

Edit: An example http://www.titanstore.com/info/412373

Rolling circumference shows 118" so dividing that by 6.28 equals 18.8 but the specs show 17.7 for the rolling radius.

The tire is flat on the bottom when loaded, thus the loaded rolling radius while the circumference is just the circumference of the tire unloaded.

 

[bcp]

I've read that the RC measurement method is different for ag tires than for highway tires. Maybe it allows for tire lug penetration into the ground when working.

Bruce

 

[dickfoster]

Loaded radius depends on variables like load and tire pressure, Just go measure it. Use a tape measure, yard stick or even a string with knots in it to measure from the ground to the center of hub.

 

[npalen]

I always assumed that the loaded radius is the distance from the center of the wheel/tire to a hard surface when maximum rated weight is applied at the recommended tire PSI. I'm guessing that most would agree with that.
So why wouldn't rolling circumference be calculated using that same loaded radius?

Here's some info that would lead me to believe that the rolling circumference SHOULD be determined by the loaded radius x 2 x pi. So why is that not the case in the Titan spec in post #1?

 

[zzvyb6]

Tires 'slip' when they roll. Slip is affected by pressure, load, camber and steer angle. Sometimes its excessive and will show up on a concrete surface as rubber tread marks.

All tires slp, thats how they react to a round tire running on a flat road. Even steel train wheels have this characteristic. Not much, but that's also one reason why they can't stop quickly (besides the coefficient of friction for steel on steel). And your pi is not accurate enough for the rocket scientists.

 

[npalen]

That's interesting! I ran across the info below on tirerack.com which seems to coincide with your comments: It sounds like "rolling circumference" would factor into tire diameter matchup for FWD tractors.

Pi - Wikipedia (To satisfy the rocket scientists:laughing



Revolutions Per Mile
Revolutions per mile indicates the number of times a tire revolves while it covers the distance of one mile. Depending on the tire manufacturer, revolutions per mile may be either measured in a laboratory or derived from calculations based on their previous test experience.

Tire revolutions per mile cannot be calculated by simple math because the tire tread and sidewall bend and stretch (deflect) when the load of the vehicle presses the tire against the road.

Since the resulting loaded or rolling radius is less than half the tire's published overall diameter (which would only reflect the tire's unloaded radius), calculating the tire's absolute rolling circumference isn't possible.

Additionally, a tire transitions from an unloaded to loaded state as it rolls, continuously flattening where the tread footprint comes into contact with the road. These continuous transitions result in some tread slippage, again increasing the tire revolutions per mile beyond what simple math would indicate.

 

[Texasmark]

Tires 'slip' when they roll. Slip is affected by pressure, load, camber and steer angle. Sometimes its excessive and will show up on a concrete surface as rubber tread marks.

All tires slp, thats how they react to a round tire running on a flat road. Even steel train wheels have this characteristic. Not much, but that's also one reason why they can't stop quickly (besides the coefficient of friction for steel on steel). And your pi is not accurate enough for the rocket scientists.

That's the first explanation I have read that makes sense on using something other than the actual circumference of the tire when considering things like matching front to rear tires on 4wd machines. Will give the AG tire sinking factor the #2 spot......course both depend upon soil/contact conditions so there is some tolerancing in the numbers.

Worst case I saw was a coworker with a long bed Ford P/U years ago. Put hot dog tires on his hunting truck and in 4wd on concrete/asphalt, the front end would actually hop in a hard turn......bad mismatch.

 

[zzvyb6]

Most of the slip (in going forward) occurs at the trailing edge of the contact patch surface. That's where the highest tread heat develops, rolling resistance is highest, and belt fatigue appears. Keeping pressures up helps eliminate problems with fuel economy, tread separation and tire longevity, but reduces stopping ability (smaller patch area) and hurts ride (because the spring rate increases).

I live with the ride penalty but like the better wear and fuel economy of higher pressures in all my vehicles because most of my driving is on highways (expressways). I usually run then 5 psi over door placard. Don't worry, grampa, tires can take a LOT higher pressure than that. Well above the sidewall rating. In fact, its the wheel and suspension parts that are most likely to fail if you ran above 60 psi in some vehicle's tires. That excludes PU trucks (usually 3/4 or 1 ton trucks on singles instead of duals). They have to run 90 psi or so because of their load rating.

And remember folks, the bottom of the tire doesn't hold the wheel up, it hangs from the top part of the tire. Take an old bicycle wheel and cut the spokes starting at the bottom. It's OK (when stationary) until you start removing the uppermost spokes. Air pressure keeps the suspending tire ring structure intact. When it collapses (buckles), you are gonna get hurt.

 

[bcp]

Probably also makes a difference if it is a powered or an unpowered tire, especially for ag tires.

Bruce

 

[bcp]

I've read that the RC measurement method is different for ag tires than for highway tires. Maybe it allows for tire lug penetration into the ground when working.

Bruce

Found it. Maybe someone can track down the document.



Bruce

 

[LD1]

And remember folks, the bottom of the tire doesn't hold the wheel up, it hangs from the top part of the tire. Take an old bicycle wheel and cut the spokes starting at the bottom. It's OK (when stationary) until you start removing the uppermost spokes. Air pressure keeps the suspending tire ring structure intact. When it collapses (buckles), you are gonna get hurt.

I like that one :thumbsup:

 

[MHarryE]

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The effective rolling radius

The effective rolling radius is not the same as the*loaded tyre radius*Rl, with the latter being defined as the vertical distance between the wheel centre and the horizontal surface. A free rolling tyre rotates around a point near the contact patch. For a rigid wheel on a flat horizontal surface, this point coincides with the single contact point between tyre and road, and the forward speed Vx*equals angular speed time (loaded = unloaded) radius.

For a pneumatic tyre, the distance between points at the circumference of the tyre and the wheel centre varies from a value close to the unloaded radius just before entering the contact area to the same value as the loaded radius just at the projection point of the wheel centre on the contact area. At that point, the peripheral velocity of the tread (relative to the wheel centre) coincides with the horizontal velocity V of the wheel centre.

Moving out of the contact area, the tread regains its original length and the peripheral velocity returns to Ω.R with R the unloaded radius. As a consequence, the spin speed of the wheel with a pneumatic tyre under conditions of free rolling is less than that of a rigid wheel and:



It means that the centre of rotation of the wheel usually lies somewhere below the surface. The effective rolling tyre under free rolling also behaves different with varying tyre load compared to the loaded tyre radius. A loaded radius behaves almost linear in the tyre load Fz, i.e. the tyre behaves as a linear spring in vertical direction. The effective rolling radius varies significantly with tyre load. This can be described based on empirical fit as follows [1]:



with tyre deflection ρ, tyre deflection ρ0*for*nominal tyre load*Fz0, and fitparameters B, D, E which may vary according to:

3 < B < 12 :*********** B stretches the effective tyre characteristic curve along the Fz*-axis (ordinate). B large means a large slope at Fz= 0.
0.2 < D < 0.4 :******* shift from asymptote at high wheel loads
0.03 < E < 0.25 : ****with low values of E for stiff tyres



Effective and loaded tyre radius under conditions of free rolling

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An example of the variation of Rl*and Re*is shown in figure above for B = 10, D = 0.25 and E = 0.05. The tyre stiffness is taken as 2·105*N/m. The unloaded radius R is taken as 0.32 m and we choose Fz0*= 4000 N. We have also varied the parameters to illustrate the range of possible effective rolling radius characteristics.

The effective rolling radius turns out to increase with increasing speed and increasing inflation pressure. The variation with speed is strongly dependent on the tyre carcass structure.

A*radial-ply*tyre rolling radius appears to be almost constant for varying speed in contrast with the diagonal-ply (bias-ply) tyre. This phenomenon has to do with the radial response of the tyre to higher circumferential speeds.

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