44 replies to this topic

[genespleen]

Folks,

I have trouble understanding the rationale for the continued use of grooved dry-weather tyres in F1. I realize that they were introduced as a hack-measure to slow down cornering speeds, lengthen brake zones, perhaps induce passing.

They caused a stir when introduced; are we now just used to them? I still find them visually just awful.

What keeps them in the regulations?

[Melbourne Park]

Originally posted by genespleen
Folks,

I have trouble understanding the rationale for the continued use of grooved dry-weather tyres in F1. I realize that they were introduced as a hack-measure to slow down cornering speeds, lengthen brake zones, perhaps induce passing.

They caused a stir when introduced; are we now just used to them? I still find them visually just awful.

What keeps them in the regulations?

Without grooves, the tyres would be narrower, hence much better aero, and the cars would be a lot faster, so they have to change the whole formula.

IMO the grooves are good - in fact if I was the FIA, I would just make the tyres wider to slow the cars down - make the tyres wider, and at the same time increase the width of the grooves, but all the same keeping the contact patch the same.

[J2NH]

Width of the grooved tires helps to keep straight line speeds down. Can't imagine how fast these cars would be with a narrower slick but it would be significant. I would imagine that is why they have kept the grooved dry tire.

With one manufacturer I would think that you could make a very hard wide slick with no grooves and keep the cornering speeds down.

[Choda-Boy]

Why would the slicks have to be narrower? It would be enough for the FIA to specify the minimum tyre width. Now, with only one tyre company, going back to slicks shouldn't increase speeds at all.

[Oho]

Originally posted by Melbourne Park

Without grooves, the tyres would be narrower, hence much better aero, and the cars would be a lot faster, so they have to change the whole formula.

I don't buy this. Not with rear tyre grip being the limiting factor on acceleration to pretty high speeds.

[Clatter]

Originally posted by J2NH
Width of the grooved tires helps to keep straight line speeds down. Can't imagine how fast these cars would be with a narrower slick but it would be significant. I would imagine that is why they have kept the grooved dry tire.

With one manufacturer I would think that you could make a very hard wide slick with no grooves and keep the cornering speeds down.

Grooved tires keep the cornering speed down, not the straight line speed.

[Mauseri]

Grooved tyre has more connection to civil tyres. And Bridgestone is a civil tyre manufacturer. They don't sell that many slicks.

[rhm]

Originally posted by micra_k10
Grooved tyre has more connection to civil tyres. And Bridgestone is a civil tyre manufacturer. They don't sell that many slicks.

That's not it is it? They only started making groved tyres for F1 when the FIA introduced a rule to say they had to. They happily supply slicks to champcar.

The reason was to reduce cornering speeds without having to either change the sizes of the tyres, or impose other parameters such as compound or construction.

Now there is only one supplier, the FIA can just say "don't make them any faster than they were in X year", so they don't really need the grooves. I have heard driver reports that indicate the grooves make the tyres slip more progressively than slicks do, but that was champcar drivers comparing the two. In any case I'd say the real reason is that they didn't want to spend the money to develop a completely new tyre and so they've brought the tyres from a few years back.

[Melbourne Park]

Originally posted by Choda-Boy
Why would the slicks have to be narrower? It would be enough for the FIA to specify the minimum tyre width. Now, with only one tyre company, going back to slicks shouldn't increase speeds at all.

If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

[Clatter]

Originally posted by rhm


That's not it is it? They only started making groved tyres for F1 when the FIA introduced a rule to say they had to. They happily supply slicks to champcar.

The reason was to reduce cornering speeds without having to either change the sizes of the tyres, or impose other parameters such as compound or construction.

Now there is only one supplier, the FIA can just say "don't make them any faster than they were in X year", so they don't really need the grooves. I have heard driver reports that indicate the grooves make the tyres slip more progressively than slicks do, but that was champcar drivers comparing the two. In any case I'd say the real reason is that they didn't want to spend the money to develop a completely new tyre and so they've brought the tyres from a few years back.

I agree with the cost factor. I suspect that BS could well put pressure on the FIA to maintain the status quo, rather than have to develop a slick for F1 use.

[angst]

Originally posted by Melbourne Park


If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

Agree with everything here.

[Clatter]

Originally posted by Melbourne Park


If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

Blood doesnt flow away from the brain due to side loads. Anyway the corners in F1 are not long enough to cause a blackout, you require a sustained G-force for this to occur.

[Mauseri]

Originally posted by Melbourne Park
If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

Agreed.

The tricky handling might have had more to do at that time with unoptimised narrow cars than grooved tyres.

[Risil]

In the hope that they may be vaguely relevent/interesting (to anyone with a subscription, that is):

An article from early 1999 detailing why slick tyres must be returned to as quickly as possible

And another from the same issue, which argues the opposite

I think that it must be said that the quality of racing didn't appreciably drop between 1996-2000, despite this new change coming in the middle of that period. Other factors may have been at work...

[Calorus]

Originally posted by micra_k10
Grooved tyre has more connection to civil tyres. And Bridgestone is a civil tyre manufacturer. They don't sell that many slicks.

That's just daft. If that were the case, we'd still have one set per race, and all weather tyres.

[Calorus]

Originally posted by Melbourne Park


If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

But if the tyres were slicks they could go back to 1997 spec tyres instead of 2004 ones, meaning that the grip would fall to even more manageable levels. The single supplier literally allows the FIA to pick an ability and specify it.

[Oho]

Originally posted by Melbourne Park


If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased.

The increased size of the contact patch probably is not the key factor in performance differential between grooved and slick tyre, well thats my guess. The real advantage would be in increased lateral stability of the thread and consequently reduced thread hysteresis especially under lateral loads. I would assume the performance differential would not be so marked in longitudinal direction but what do I know.

[Calorus]

Originally posted by Oho


The increased size of the contact patch probably is not the key factor in performance differential between grooved and slick tyre, well thats my guess. The real advantage would be in increased lateral stability of the thread and consequently reduced thread hysteresis especially under lateral loads. I would assume the performance differential would not be so marked in longitudinal direction but what do I know.

Arguably not, since towards a tyre's End of Life, the variance of X-sec decreases almost to nothing.

[Oho]

Originally posted by Calorus


Arguably not, since towards a tyre's End of Life, the variance of X-sec decreases almost to nothing.

Well the grooves pretty much penetrate through the thread, and for what its worth, my understanding is that the grooved thread forces different tyre construction and harder compounds. In particular because of the reduced lateral grip the tyre must have stiffer lateral profile, wild guess.

[angst]

I believe that you are on the right ttrack, Oho (for what it's worth). It's not just about contact patch.

Why is everybody so hung up about whether tyres have grooves? I'm far more concerned with the ridiculaous aero sensitivity of the cars.

[Choda-Boy]

Originally posted by Melbourne Park


If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

The braking would be much later too which doesn't assist passing.

They'd then have to further change the wings, which as the FIA has shown, is never quite what they'd expect, the teams do seem to recover downforce despite putting wings up higher and generally trying to limit their effect.


And high front wings are most effected by aero disturbance from the car in front: hence it becomes impossable to overtake, because your car slows down as you get near the cars wind wake in front of you.

F1 cars IMO should have the front wings on the ground, so that front downforce is not sensitive to the car in front. And in order to slow the cars down, just make the tyres much wider, which would increase drag. And keep the contact patch the same, by increase the width of the grooves, or maybe adding another groove or two.

Who cares about having a slick" The driver's in F1 don't, the handling on the grooved tyres was tricky a few years ago, but now they work just fine.

And also, the groove is where BS is going to put the tyre compound colour!

You are tight, of course, physics would work that way. But I wanted to say that in the era of a single tyre supplier, the FIA could ask for hard enough compounds to actually reduce speeds on slicks.

OTOH, I'm not against grooved tyres at all. I don't think slicks are something that should be a given for a F1 car. Why should they be? In fact, I consider the grooved tyres a compliment for F1 cars: they are so powerful, so capable, so mighty, that using slick tyres would simply make them too dangerous for mere humans driving them!

About the aerodynamics...we remember the ground-effect cars of 1982 and how they were banned after being deemed too dangerous and going beyond drivers' physical capabilities. However, today's cars generate even more downforce with no underbody profiles.

Wouldn't it be a good idea to return to the use of dimensionally-limited (or specified) underbody venturis? I'm not an aerodynamicist but I presume that the air flowing within an enveloped channel, defined in all sides (the underbody venturi), would be much less prone to spoiling than the air flowing over wings and bodywork. Therefore, the ground-effect cars would be much less aerodynamically sensitive when following another car, provided their wings are limited enough in width, chord and number of elements.

[Melbourne Park]

Originally posted by Choda-Boy
Wouldn't it be a good idea to return to the use of dimensionally-limited (or specified) underbody venturis? I'm not an aerodynamicist but I presume that the air flowing within an enveloped channel, defined in all sides (the underbody venturi), would be much less prone to spoiling than the air flowing over wings and bodywork. Therefore, the ground-effect cars would be much less aerodynamically
sensitive when following another car, provided their wings are limited enough in width, chord and number of elements.

I think the negative issue with that is if the connection with the road is disturbed, the sudden loss of downforce makes the car almost take off. But I too like the concept.

I recall Juan Pablo Montoya, who was keen on overtaking, saying that if all the downforce was generated in between the front and rear tyre, to the side of the car, then drafting on the straights and the bends would work, because the aero wake would not effect the area where the downforce was being generated.

[Melbourne Park]

Originally posted by Oho


The increased size of the contact patch probably is not the key factor in performance differential between grooved and slick tyre, well thats my guess. The real advantage would be in increased lateral stability of the thread and consequently reduced thread hysteresis especially under lateral loads. I would assume the performance differential would not be so marked in longitudinal direction but what do I know.

But you are not including the significant extra frontal area of the wider tyre which a grooved tyre has. And I recall how sensative F1 cars are to a small amount of extra contact patch, such as was demonstrated in 2003 with the claimed use of the edge of the tyres which increased the contact patch and increased grip. Ferrari then brought out a squarer front tyre which increased the contact patch and Ferrari then was faster than the Williams. So contact patch is relevent. And IMO the frontal area of the tyres is a major aero issue.

[Choda-Boy]

Originally posted by Melbourne Park


I think the negative issue with that is if the connection with the road is disturbed, the sudden loss of downforce makes the car almost take off. But I too like the concept.

I recall Juan Pablo Montoya, who was keen on overtaking, saying that if all the downforce was generated in between the front and rear tyre, to the side of the car, then drafting on the straights and the bends would work, because the aero wake would not effect the area where the downforce was being generated.

No, it would not take off ;) But what it would do in that case is run (very) wide in a corner, if a sudden seal-with-the-ground breakage occurs and the outside air is allowed to enter the low pressure area.

However, those problems were solved already back in 1980 with suspended skirts (that were banned for 1981 by an idiotic FISA's move) so I don't think it would be a problem to make a reliable system today.

JPM's words do make a lot of sense, at least as far as I'm able to understand aerodynamic phenomena. Turbulent air is "disciplined" when forced to enter sealed underbody tunnels.

[Choda-Boy]

Originally posted by Melbourne Park


But you are not including the significant extra frontal area of the wider tyre which a grooved tyre has. And I recall how sensative F1 cars are to a small amount of extra contact patch, such as was demonstrated in 2003 with the claimed use of the edge of the tyres which increased the contact patch and increased grip. Ferrari then brought out a squarer front tyre which increased the contact patch and Ferrari then was faster than the Williams. So contact patch is relevent. And IMO the frontal area of the tyres is a major aero issue.

I think it's a trade-off that could be resolved the best way only by experimenting. Contact patch is certainly of importance as it influences the lateral force that could be transmitted (or at least I think so ). On the other hand, wider tyre would induce more aerodynamic lift (directed upwards) and that way artificially lighten the axle load, thereby decreasing the transmittable force. So the point is to find the optimal combination of parameters. That Ferrari first went down the wrong path is only a testimony that it's not easy to determine what's the best thing to do.

[Hacklerf]

is there anything you can put on tyres to give them super grip? like say they painted the tyres with some thing that gets worn off over a certain amount of laps? its off topic, but just curious.

[Calorus]

Originally posted by Hacklerf
is there anything you can put on tyres to give them super grip? like say they painted the tyres with some thing that gets worn off over a certain amount of laps? its off topic, but just curious.

Yes, lots of things, but they're all illegal in F1.

[Hacklerf]

Originally posted by Calorus


Yes, lots of things, but they're all illegal in F1.

i know its illegal,

but what kinds of things could you put on them to make them super sticky ?

[Nathan]

If you went back to a slick and made them harder, how would that effect pit stops?

[tifosi]

Originally posted by Calorus

That's just daft. If that were the case, we'd still have one set per race, and all weather tyres.

I say pump fuel and tyres anyone can get at Sears

[Calorus]

Originally posted by Hacklerf


i know its illegal,

but what kinds of things could you put on them to make them super sticky ?

I use this. http://www.griptyres...ner.com/faq.asp

[metz]

Originally posted by Hacklerf


i know its illegal,

but what kinds of things could you put on them to make them super sticky ?

I can't immagine anything more sticky than a set of current super softs.
You do realize that when they are at operating temperature one can dent them with a finger.
Or pinch them and rip off a chunk. It's where the marbles come from.
Seems to me that more stick would start to affect roll resistance, what some have called the "flypaper" factor.
Spraying on anything would only be good for a lap max.

[Calorus]

Originally posted by metz

I can't immagine anything more sticky than a set of current super softs.
You do realize that when they are at operating temperature one can dent them with a finger.
Or pinch them and rip off a chunk. It's where the marbles come from.
Seems to me that more stick would start to affect roll resistance, what some have called the "flypaper" factor.
Spraying on anything would only be good for a lap max.

The current tyres could be far softer as it stands, but it would last very long.

[metz]

Well, they make 4 different compounds.
We'll see the supersofts at Monaco.

[Calorus]

Originally posted by metz
Well, they make 4 different compounds.
We'll see the supersofts at Monaco.

No, we'll see some more "fairly softs". A "Supersoft" would be equivalent to a 1990 Qualifier: good for about 10 miles.

[metz]

I thought they call them Hard, Medium, Soft and Supersoft and at Monaco BS will only bring the last two... :
You can call them what you like.

[Calorus]

Originally posted by metz
I thought they call them Hard, Medium, Soft and Supersoft and at Monaco BS will only bring the last two... :
You can call them what you like.

I don't think they're formally named, just coded.

[Dudley]

Originally posted by micra_k10
Grooved tyre has more connection to civil tyres. And Bridgestone is a civil tyre manufacturer. They don't sell that many slicks.

That doesn't tie, they supply GP2 and had no problem with that series swapping grooves for slicks in 06.

If the tyes were slicks, and they were the same width, then the contact patch would be greatly increased. Running on the same compound, with more contact patch, this would mean more grip, and then the cars would likely exceed safe side G levels, and the driver's brains would be under too much pressure, the blood would flow too much away from the brain too, they'd pass out.

We're a long, LONG way from 8g cornering. And even that is surivable.

Plus we have spec tyres now. They can just make the tyres a different compound.

Plus slicks have a much better slick angle. You can slide without spinning, watch GP2.

In short, go away and do minimum research, you're just plain wrong in virtually the entire post.

If your post was accurate CART, GP2 and Nascar would be very dangerous places.

[Hacklerf]

Originally posted by Calorus


I use this. http://www.griptyres...ner.com/faq.asp

nice one mate, going to try that on my old karting tyres

[Melbourne Park]

Originally posted by Dudley


That doesn't tie, they supply GP2 and had no problem with that series swapping grooves for slicks in 06.



We're a long, LONG way from 8g cornering. And even that is surivable.

Plus we have spec tyres now. They can just make the tyres a different compound.

Plus slicks have a much better slick angle. You can slide without spinning, watch GP2.

In short, go away and do minimum research, you're just plain wrong in virtually the entire post.

If your post was accurate CART, GP2 and Nascar would be very dangerous places.

Maybe you need to re read the post. What I was saying was that if slicks came in, the cars would require a major re-design. Why do it, when its working now? Its not as if its expensive technology either. But if you want to re-design, then why not concentrate on changes that will improve overtaking, I listed some factors, such as having a front wing that's always efficient.

Unfortunately I won't be able to debate this though as I am away for a few weeks.

Cheers

[Locai]

I remember reading before something along the lines of this:

When there's 2 or more tire manufacturers involved, they don't want to change because they each think that the other will get an advantage.

When there's only 1 tire manufacturer involved, the 1 doesn't want to change because it will make it easier for another manufacturer to jump in (since they would both have "a clean slate").

So, basically, it's paranoia that will probably keep the grooves in F1.


One other thing I thought of this week: Why didn't the FIA think of painting all of the grooves back when they first got competing tire makers? It would have seemingly made the rule concerning "discernable grooves" much easier to police (no paint = no groove).

[HBoss]

You ask too much of them.

=)

[Dudley]

Originally posted by Locai
I remember reading before something along the lines of this:

When there's 2 or more tire manufacturers involved, they don't want to change because they each think that the other will get an advantage.

When there's only 1 tire manufacturer involved, the 1 doesn't want to change because it will make it easier for another manufacturer to jump in (since they would both have "a clean slate").

So, basically, it's paranoia that will probably keep the grooves in F1.

WEll that's not a factor since BS are guaranteed to be the only tyre in F1 for what? 5 years is it?

[roadie]

There is no reason not to go with full slicks with a harder compound. However, it's probably a case of the FIA having to suspend some ideas in order to force through others.

[OO7]

Regarding wider slicks, as well as having a larger contact patch I've heard they allow you to run a softer compound as they dissipate heat at a greater rate.

Regarding overtaking and aerodynamic degradation in-close:

I don't believe the level of downforce is the problem, I think it is the way the cars generate downforce. I would think peak low-pressure areas exist under the front wing, about the leading edge of the floor, at the throat of the diffuser and under the rear wing. It seems that basically downforce is created at the front and rear of the car with not much comparatively in the middle. The problem with this is that if you were to lose 30% of front downforce when following a car closely the car will become very unbalanced because the front wing contributes a great deal.
Many remember the Mercedes CLR flip over the brow at Le Mans back in 1999. Back then downforce was created in a similar fashion to F1 cars, at the back and front, so when the front lost downforce the car became unbalanced and seriously unstable.

Assuming ground effects is less susceptible to wake turbulence, particularly the closer to the ground you run it, flat bottoms (last used in early 1994) with tunnels about or slightly ahead of the cars c of g may alleviate much of the problem. Using such tunnels will mean less front wing is necessary (Compare the front wing of an F1 car and GP2 car from head-on in Monaco it is immediately apparent how much more frontal area lies in the F1 wing. More downforce generated by the F1 front wing means a greater percentage of downforce is lost in wake turbulence, plus greater imbalance due to the fact that it is solely front downforce being effected). The level of downforce created by the under body can perhaps be regulated with mandated holes near the leading edge of the tunnels that are connected to the top of the side pods? The tunnels diffuser section should be of a constant gradient, (and maybe height also should be limited to assist in controlling the underbody downforce levels) to limit up wash. The lower tier rear wing should be deleted or regulated in such a way as to devalue its effect on the tunnel and the up wash produced.

The front wing could be regulated using the method the ACO developed for the Le Man series in which the wing in profile view must fit within a theoretical box of a predetermined size. This could be used for the lower tier rear wing as well.

Raising the rear wing may help in raising the overall low pressure wake region.

Increasing the cars width to 2000mm or 2150mm may create better slipstreaming opportunities.

Obi