Low Range Gearing Ratios

[wasarangie]

My cats breath smells like cat food

What's this thread about again?

[I should know as I'm the OP]

x2

The low range is not in the rock crawler region. But it does give a lower ratio.
You can buy a gears set to lower the ratio. They are around $1500 plus fitting. You would be looking at approx 40% lower low range. That is in the really useful area, but not a simple change.

To the others.

So you are saying that the wheel will travel exactly the same even with 40% less pressure?

I take the opposite opinion. If you take a passive TPMS (Tyre Pressure Monitoring System) in modern cars they monitor, via the ABS, the actual wheel speed. If the wheel speed is "seen" to show a difference between wheels an alarm is triggered. This system picks up a difference in tyre pressure of approx 25%

If the tyre travels the exact same distance then the systems do not work and manufacturers have been fitting these systems for no good reason.

Are you forgetting that the tyre will deform at different pressures and could allow the tread face to buckle in a wave pattern? This could be just one reason why running at low pressure builds heat in tyre.

[fuelconsumption]

It is time I stopped playing games and swapping hats, and write a posting that explains exactly what I believe is the 'correct answer', and why. Any satisfactory explanation must be able to account for every argument and observation that has been raised. In other words, it is not good enough for me to say that the 'constant tread length' argument is watertight and therefore correct, I must also be able to convincingly explain why the 'effective rolling radius' argument is not correct.

First some history. Many years ago when I was an ignorant young whipper-snapper (as opposed to an ignorant old fart) I believed in the 'effective rolling radius' theory. Sure, it is bleeding obvious that 'lever arm length' is less when the tyre is partially deflated, resulting in an increased driving force and a reduction in road speed.

Then an old mate of mine threw a spanner in the works, pointing out that the tread length (circumference) is fixed, and so logically the vehicle must always move the same distance (one circumference) for every revolution of the wheel, which is another way of saying that the road-speed-per-engine-RPM and effective gearing ratio is a constant, independent of inflation pressure and 'sag' in the tyre. I reluctantly had to agree that this appears to be an irrefutable argument, though my mate never did explain why the ‘effective rolling radius’ approach is wrong.

This led to a few sleepless nights way back then, after which I concluded the following.

The ‘effective-rolling-radius’ argument assumes the small part of the tread in contact with the road is ‘driven’ by the sidewall at that point, where the ‘effective radius’ is smaller. It is not. In fact the opposite is true, that part of tread in contact with the road actually ‘drives’ the sidewall, and very much against it’s will at that. WTF is FC talking about!

The key to understanding this explanation is to view the tread as a fixed-length ‘caterpillar track’. Because it is fixed length, the entire tread must move at a constant speed. If one part of the tread was moving at a different speed to the rest of the tread, the tyre would be very rapidly destroyed!

So far so good, but what speed does the tread move at? In the case of a bulldozer track, the effective drive ratio to the ground is set by the diameter of the sprocket driving the track. In the case of our tyre, the sidewall acts as that sprocket, ie, the sidewall drives the tread. Here is the crunch. Most of the sidewall is undeflected, so the effective ‘drive sprocket radius’ is given by the full-inflation, undeflected tyre radius. In other words, the speed and driving force applied to the tread is predominantly based on the undeflected tyre radius. This view of the world (well, of a tyre, anyway) takes some getting used to. The section of tread in contact with the road, is actually ‘driven’ by the section of sidewall above, sort-of analogous to the driving a caterpillar track, where the track is not actually driven at the point where it touches the ground.

This leads to the very curious situation where the section of tread contacting the ground will be travelling faster than the sidewall at that point 'wants' to travel at, because the rolling radius is smaller there. Yes indeed. That speed differential is taken up by the bulging, flexing, deflection and general localised torture of the sidewall at that point. That is why the sidewall heats up, and is also why the sidewall is always built to be thin and flexible, even in a heavy-duty tyre.

The ‘speedometer error’ test will show for certain whether this theory is correct, but I reckon it probably is, at least predominantly so, in which case the ‘reduced gearing ratio’ from an underinflated tyre is mostly a myth.

More precisely, I would expect that what actually happens is a combination of effects. At inflations down to say 60% of normal operating pressure, I would expect the ‘constant tread length’ prediction to predominate. That is, I would expect any reduction in effective ratio to be significantly less than predicted by the reduction in rolling radius. The speedo error test will show if this is true. At ridiculously low inflation pressures where the entire tyre and tread and all are distorted out of their tiny minds, with the tread waving and wagging and flopping then anything could happen, with the limiting case being zero inflation with the rim on the ground.

Wasarangie makes an excellent point re onboard tyre monitoring that detects a change in rotational speed of an underinflated tyre. Yes, as per the previous paragraph, I would expect a small change in rotational speed which could be detected by these systems, but the real question is whether the effect is small compared to what would be predicted from the reduced rolling radius.

Comments? Can anyone poke a hole in the above?

[fuelconsumption]

My cats breath smells like cat food

What's this thread about again?

[I should know as I'm the OP]

I apologize for hijacking your thread. The problem is that technical discussion is sort-of like relationships, it just happens without prior planning, and may fizzle out quickly or really catch fire and go on and on, and you never know in advance what turns and twists it might take.

My only defence is that I did contribute to the original thread, and others made excellent contributions such that the original topic has been fairly well covered.

In retrospect I probably should have started a new thread. Sorry about that.

[mrdenn1s]

All good

Discussion is just way over my head!

[fuelconsumption]

Gentlemen, I believe I now have this wrapped up with the addition of some experimental data confirming my prediction.

Firstly, a paper on the subject here: www-nrd.nhtsa.dot.gov/pdf/esv/esv19/05-0082-O.pdf

Observe Figure1, which is a plot of Rolling Radius as a function of Inflation Pressure. Note the linear increase in rolling radius as the pressure is increased, which is how the indirect tyre pressure monitoring systems work. Now look at the teenzy extent of the effect. To be precise, a change in inflation pressure from 7.5 PSI to 29 PSI causes the rolling radius to increase a negligible 1.75mm from 275mm up to 276.75mm. The change in axle height corresponding to a drop in pressure from 29 PSI down to 7.5 PSI would be comparatively huge, at least 30mm I would think. The conclusion is clear. Changing inflation pressure has a negligible effect on rolling radius.


OK, so maybe you are not so much into graphs and technical papers. Then try this U-tube video www.youtube.com/watch?v=_2l5bOhHNxU where the rolling circumference is measured directly by placing a mark on the tire and the floor, then rolling the vehicle for one or two revolutions, and marking the floor again where the mark on the tyre meets the floor. They did this for normal inflation, then let let the air out so the tyre looked vey saggy, and over two full revolutions were not able to measure any change in rolling circumference. They rightly concluded that rolling circumference is negligibly affected by inflation pressure.

And so another myth bites the dust.

Reducing tyre inflation will not significantly lower the effective gearing, will not make the vehicle slower for a given engine RPM, and will not increase the driving force.

Engineering and sound logic triumph again.

[RedSector]

Gentlemen, I believe I now have this wrapped up with the addition of some experimental data confirming my prediction.

... ...

Engineering and sound logic triumph again.

Wow nice work

[fuelconsumption]

Some more experimental data, this time from a member of another 4WD forum, where this topic raged for 6 pages, though the 'tread length' and 'rolling radius' camps never did figure out why their approaches gave different predictions. The conclusion from this data is the same. The actual change in rolling circumference was negligible compared to what it should have been based on the change in axle height, even though the pressure was dropped by an absurdly large factor of x3.8 - the rim must have been all but on the ground! I consider the topic done and dusted. FC


Measured Results

Tyre: Rear Bridgstone Dueler 694 - 31 x 10.5 x 15 - Unladen Vehicle
Start Pressure: 2.3
Measured Radius (from centre to bottom): 365mm
Measured Distance for one rotation (Circumference): 2350mm

Second Pressure: 0.6
Measured Radius (from centre to bottom): 340mm
Measured Distance for one rotation (Circumference): 2330mm

Measured Differences:
Radius: 25mm
Circumference: 20mm

Calculations: (C = r x 2 x 3.14)
Using the measured radius, the calculated circumferences are
1. 365 x 2 x 3.14 = 2292
2. 340 x 2 x 3.14 = 2135
That gives a calculated difference of 157mm (compared to the actual 20mm)

Using the measured circumference, the calculated radius are
1. 2350 / (2 x 3.14) = 374
2. 2330 / (2 x 3.14) = 371
That gives a calculated difference of 3mm (compared to the actual 25mm).

My conclusion....
Lowering the tyre pressure will not dramatically change the final gearing.

[fun510]

Excellent input from all.

Great to see a discussion with no friction - appart from that between the rubber and the road.

So......... What's next..... (In a new thread of course)

[fuelconsumption]

Here is some more information that some may find of interest. I have been reading the incredibly comprehensive text 'Mechanics of Pneumatic Tires', which confirms what has already been concluded. You can find the first chapter of this book here: http://media.wiley.com/product_data/...0471354619.pdf

For radial ply tyres, their experimental data shows a 2% change in rolling circumference for an 8% change in axle height, again confirming that rolling circumference (=effective gearing to road) changes very little with axle height.

We would expect this to be true for steel-belted radial tyres where the tread length cannot significantly change, but less true for the old-fashioned bias-ply tyres, and this is indeed the case. For bias ply tyres, they found a 4% change in rolling circumference for a 6% change in axle height.

If the tread really did change speed and dimension over the contact patch, we would expect this to be lossy and heat up and wear out the tyre, for this represents slippage, a wiping motion between the tread and road. This was another reason I had concluded that the tread behaves predominantly as a fixed-speed caterepillar track. Again, this prediction is borne out by reading the book, quote :-

For the radial-ply tire, flexing of the carcass involves very little relative movement of the cords forming the belt. In the absence of a wiping motion between the tire and the road, the power dissipation of the radial-ply tire could be as low as 60% of that of the bias-ply tire under similar conditions, and the life of the radial-ply tire could be as long as twice that of the equivalent bias-ply.

I love it when everything adds up and makes sense.

PS. Traditional bicycle and mororcycle tyres are not of the radial, steel-belted type, so for these we would expect a greater variation of rolling circumference with inflation pressure, as well as higher drag compared to a radial tyre of the same dimensions and pressure.