Effect of unequal tyre pressures on Detroit Locker 1

[JimAttrill]

From the Owner's Manual, page 3:
"Anything that improperly causes a difference in individual wheel speeds, such as mismatched tire diameters due to differences in tire wear or tire pressure ... can cause the NoSpin differential to deliver power to only one side of the vehicle ... "

This comes with a picture to show how you should measure the diameter of each wheel and adjust tyre pressures to get these equal. However, I think that this reasoning is suspect. What is important regarding wheel speed is not the diameter of the wheel/tyre but the circumference. Tyres of different sizes or wear will alter the circumference whereas unequal loading or pressures will not. If one thinks of a tracked vehicle as an extreme example, the distance from the ground to the centre of the driving wheel will vary, but the length of the track cannot, just as the 'length' of a tyre cannot, especially with the modern steel-belted radials. So a wheel with a deflated tyre will go round at the same speed as a wheel with a tyre at the correct pressure.

I am not saying that driving with under-inflated tyres or unequal loading will not affect the steering, but that the effect will not be caused by differential wheel rpm as the wheels will go round at the same speed.

I e-mailed Tractech pointing out this error in their manual but never received a reply.

 

[evelrod]

All I can say, after using Detroit Lockers in my race cars since 1967, is that I have, generally, had few problems...in fact, I am still using the first one purchased in 67! I also still have all the original paperwork and it has nothing relating to this matter. Pre PC paperwork?

In the race car it is quite common to have different tire diameters (stagger) for different track conditions as well as varrying tire pressures (by a pound or two--- I have had a flat rear on occasion).

I will point out that if used on the street, they do make a bit of noise when you turn a tight corner at slow speed, at least in my experience.

Rod

 

[JimAttrill]

Hi evelrod, you and I have used the Detroits for different purposes - mine is in a Land Rover 110" Defender and yours are in race cars. Mine is fitted to a Salisbury axle, which I believe is a sort-of Dana made in England. (Also fitted to Aston Martins etc).

This 'stagger' you refer to - is that helpful in the oval race tracks that you have there? In other words, if you went around the track in the opposite direction you would swop the wheels left to right?

I use my Land Rover on the street most of the time. I avoid turning into parking places with the clutch 'in' as I get lots of clonking from the back axle which tends to frighten passengers. On the other hand, the Land Rover emits so much noise anyway that most passengers don't notice it

One thing that attracted me to the use of a Detroit is that they seem to work for ever with no problems. The
ARB lockers from Australia require air pumps, others require vacuum pumps etc.

It doesn't work well with a short wheelbase vehicle, which they define as < 120". It is ok with my 110", but the other 93" version is not good. The Range Rover and Discovery (both 100") are a bit borderline.

If you send me a pic of your car I will send one of mine

jimattrill@xsinet.co.za

 

[ivymike]

So a wheel with a deflated tyre will go round at the same speed as a wheel with a tyre at the correct pressure.

you think so, eh? Why not halfway deflate one tire, put a chalk mark on a couple, roll forward ten feet, and check? $5 says you're wrong.

 

[ivymike]

(without a locked diff, of course)

 

[JimAttrill]

Ok. What I should do is mark tyres with a chalk mark then push my 2-ton truck up and down my driveway to see what happens.

As its bloody hot here in Johannesburg I don't reckon this is a good idea, though I might lose some weight

 

[ivymike]

I'm sure there's a hill around there somewhere...

Regardless, if you want to calculate the rotational velocity of a tire at a given vehicle speed (assuming insignificant slippage), you take the tangential velocity at the point of contact, and divide by the radius to rotational center.

The fact that a particular patch of rubber may travel a certain distance every revolution has no bearing on the relationship of rotational speed to vehicle velocity. Any particular piece of tread may have significantly varying tangential velocity as it goes around the rotational axis (since radius can vary), what makes the car go is the velocity each patch has when it is in contact with the ground.

To go back to your tracked vehicle example, does the vehicle move forward by the length of the track for every revolution of a drive cog? No. If there is no slippage, it moves forward with the tangential velocity of the portion of the track that's on the ground. Whether the track itself is very long or very short makes no difference.

 

[JimAttrill]

Thanks Ivymike. Now what I want to know is whether you are agreeing or disagreeing with the Locker manual: ie. does altering tyre pressure alter the rotational speed of the wheel?

 

[ivymike]

I thought I was being clear enough.

In short, I disagree with both you AND the manual:
* manual says the diameter of the wheel is what matters, and I disagree. It's the radius from the rotational center to the ground that matters (the tire won't be round).
* The manual says that the difference in rotational speeds can cause the diff to deliver power to only one side of the vehicle. That can happen, but I think the wording is misleading - in the case where wheel slippage is a concern (why you got a locking diff in the first place), the power delivered to each wheel (excluding the little stuff) will depend on its rotational speed, the radius from the rotational center to the ground, and the friction force generated at the contact region. If the diff is locked, the rotational speeds will be equal. If the radii are different (due to pressure, wear, or whatever) and the friction at each wheel is different (due to mud or whatever), then the fraction of power to wheel 1 will be r1f1/(p_total) and wheel 2 will get r2f2/p_total.
* you say that the circumference of the wheel is what matters, and I disagree. It's the radius from the rotational center to the ground that matters. The circumference will depend on the shape of the tire away from the contact area, which (as your tank tread example demonstrates) has nothing to do with distance of vehicle travel vs number of wheel rotations. Put another way: if you have a pair of tires on an axle, and the differential is not locked (allowing different rotational speeds), and you're moving in a straight line, and one of the tires has lower pressure than the other (assuming they would be the same size if equally pressurized), then the low-pressure tire will complete more revolutions for a given distance of vehicle travel.

 

[ivymike]

even shorter answer: yes, pressure affects rotational speed.

 

[Rob45]

There's a very simple explanation here:
Changing the tire pressure changes the rolling radius, i.e., the distance from the road to the center of the hub.

The circumference relates to the rolling radius as one might expect... C= 2*pi*r

Less air = less circumference.
-----------------
That note that a Detroit Locker requires a wheelbase > 120" is a new one on me: the first Locker I ever used was in a bugeye Sprite, which had a wheelbase not much more than a foot and half, as I recall. LOL!
I'll bet the wheelbase guideline, if any, should relate to the ratio of wheelbase to track width.

 

[ivymike]

The circumference relates to the rolling radius as one might expect... C= 2*pi*r

flat tires are round?!?

 

[NormPeterson]

Effective rolling radius is neither the loaded radius nor the free (unloaded) radius but somewhere in between. Obviously (and assuming zero slippage), the entire circumference of the tread surface must contact the road surface during each revolution, but due to compliances the tread compresses slightly in the contact patch zone, and somewhere within that region the tangential tread velocity equals road speed.

To put some rather rough numbers on this, the effective rolling radius of a steel belted radial tire is in the neighborhood of 98% of the free radius, while the loaded radius is more like 92% of the free radius. My reference for the above values is nearly 35 years old, so the current numbers might vary a bit from those, but I'd certainly expect the general relation to remain.

FWIW, the same ancient reference gives the effective radius for bias-ply tires at 96% of free radius and the loaded radius at 94%. Those are relatively close dimensions and tend to support the use of loaded radius for simplified calculations for such tires. Kind of a moot point these days, though . . .

Norm