Guys, I have seen and now understand the relationship between torque and HP, and it would seem that in a straightline, two cars with the same HP level and nearly same weight should accelerate the same....so why does the 911 turbo (420 lb ft @2700) floor the modena every time? It irkes me, I just dunno why...anyone know why? and does this mean that realistically turbo's work "better"? i hope not, cuz i love the ferrari sound, and the fact that they rev forever, but if a turbocharger just makes a better car That F40 was pretty nasty...

thats because it has so much more torque. I think it has something like 415 ft-lbs, and it makes it all down low where the 360 only has like 275, which it makes high up in the rev range. The turbo also has awd, so it can put all its torque down to the ground when it leaves the line.

NSXprime.com How Japan may get instant torque on tap from the next NSX. (this car IS the extra wide torque curve, not like the typical high revving strung out engine, or the low revving but narrow peak torque with say a v-8) The more I think about it, the more a hybrid powerplant makes sense. With a whole flew of high perf cars and supercars out there now, it will be nearly impossible to make the NSX a standout with just good performance alone. The first NSX was something very special for its time. It was a high performance exotic that had the reliability of Honda. It also showcased Honda's new technologies including independent 4 channel ABS, VTEC, traction control, etc. If the NSX were to be released now with a sequential tranny, 400hp, great handling, and good looks - would it really be very special? Now with a hybrid powerplant, Honda is able to do things the competition is not able to do: 1. With instant torque on tap, you no longer need to rely on VTEC. You can now build the car with only high RPM HP in mind. This makes it easier to get more HP per liter out of the car. I would think that 120 - 130 hp per liter would not be too difficult to attain since they already get 120 hp per liter with the S2000. 2. So take a 3.5 liter engine making say, 455HP (130HP per liter) then throw in 50HP - 100HP from an electric motor and now you have over 500HP. Plus, you get a lot of low end power from the electric motor AND all wheel drive - both of which will dramatically help exit speed. 3. Now, with the electric motor, the NSX is able to now also to give you better mileage. So you get this high HP car that will get you say, 30+ miles per gallon. Just speculation of course. I personally wouldn't mind having a hybrid car. I'm sure Honda wouldn't create a hybrid sports car that runs out of juice at track events. -J quote: -------------------------------------------------------------------------------- Originally posted by apapada actually, on cars WITH COMPARABLE WEIGHT, a hybrd powertrain would allow to shave some serious seconds from your laptime as it would seriously flatten out that power curve, creating an artificial extra-wide powerband (what the current NSX lacks big time, IMHO). As you already know, torque is what is really pushing the cars forward out of corners, and electric motors have plenty of it at low RPMs! -------------------------------------------------------------------------------- I realize you are new to the track with the NSX, but the idea behind the wonderful motor in this car IS the extra wide torque curve, not like the typical high revving strung out engine, or the low revving but narrow peak torque with say a v-8. Due to the extremely flat torque curve, you can still salvage a missed downshift or just not down shift at all if you would just upshift within a couple of seconds after the turn. Would I like more torque? Yes. Would I give up a flat curve to have a higher number? No. Do I want regenerative battery power to an IMA motor? Give me a paddle shift 7 speed transmission and 2700 pounds, and I will take on anyone on any track that has straights of less than 1 mile in length, and probably win. (As did the LMP675 at Sears this year) __________________ http://www.nsxprime.com/forums/showthread.php?s=&threadid=25106&perpage=50&pagenumber=3

I think that would be an awesome feature for Ferrari to use. High output motor with an electric motor, awd, and sequential transmissions. 5.0L V12 with over 600bhp along with an 150bhp electric unit. hehe Ferrari needs a car like the Audi LeMans and new NSX put together. Reliable, better fuel economy than 10mpg, and high tech speed. It could be the new mid engined V12 below the rare supercar and above the V8 and GT models. A new TR.

Posted on Friday, July 25, 2003 - 2:10 pm: -------------------------------------------------------------------------------- I wish I could take credit for the following, it is very well written and concise. Excellent examples. I have tried to contact the author, he has not returned my inquiries yet. I personally have not written any of the following text, though I agree will the entire contents. Best regards, Rob Schermerhorn _______________________________________________________ Torque and Horsepower - A Primer From Bruce Augenstein, rba@augenstein.ultranet.com [Before I let Bruce explains the stuff, here's a quick summary. Remember that the magic number 5252 works only with torque in ft-lbs units. Torque in other units such as Newton Meters or kg-m require a different number. - Maximum acceleration at any speed occurs at the HP peak. - Maximum acceleration in any gear occurs at the torque peak - HP = torque * RPM / 5252 - torque = HP * 5252 / RPM - torque = HP at 5252 RPM HP is not measured directly, it is simply calculated from torque. However the HP to torque formula is useful to figure out how much torque the engine is making at peak HP. I wish when the car magazines do a road test they would include the torque and HP graph, gear ratios vs speed, 0 to top speed table in every 10 miles with G (acceleration) values... etc. - Frank] There's been a certain amount of discussion, in this and other files, about the concepts of horsepower and torque, how they relate to each other, and how they apply in terms of automobile performance. I have observed that, although nearly everyone participating has a passion for automobiles, there is a huge variance in knowledge. It's clear that a bunch of folks have strong opinions (about this topic, and other things), but that has generally led to more heat than light, if you get my drift . I've posted a subset of this note in another string, but felt it deserved to be dealt with as a separate topic. This is meant to be a primer on the subject, which may lead to serious discussion that fleshes out this and other sub-topics that will inevitably need to be addressed. [Bruce hit it dead on. Anyone who's read UseNet for a period of time knows how much crap is on it. There are many knowledgeable folks posting quality discussions (in all newsgroups) but they are easily overshadowed by stupid posts. - Frank] OK. Here's the deal, in moderately plain English. [size=+1]Force, Work and Time [/size] If you have a one-pound weight bolted to the floor, and try to lift it with one pound of force (or 10, or 50 pounds), you will have applied force and exerted energy, but no work will have been done. If you unbolt the weight, and apply a force sufficient to lift the weight one foot, then one foot pound of work will have been done. If that event takes a minute to accomplish, then you will be doing work at the rate of one foot pound per minute. If it takes one second to accomplish the task, then work will be done at the rate of 60 foot pounds per minute, and so on. In order to apply these measurements to automobiles and their performance (whether you're speaking of torque, horsepower, newton meters, watts, or any other terms), you need to address the three variables of force, work and time. Awhile back, a gentleman by the name of Watt (the same gent who did all that neat stuff with steam engines) made some observations, and concluded that the average horse of the time could lift a 550 pound weight one foot in one second, thereby performing work at the rate of 550 foot pounds per second, or 33,000 foot pounds per minute, for an eight hour shift, more or less. He then published those observations, and stated that 33,000 foot pounds per minute of work was equivalent to the power of one horse, or, one horsepower. Everybody else said OK. For purposes of this discussion, we need to measure units of force from rotating objects such as crankshafts, so we'll use terms which define a *twisting* force, such as foot-pounds of torque. A foot-pound of torque is the twisting force necessary to support a one-pound weight on a weightless horizontal bar, one foot from the fulcrum. Now, it's important to understand that nobody on the planet ever actually measures horsepower from a running engine. What we actually measure (on a dynamometer) is torque, expressed in foot-pounds (in the U.S.), and then we *calculate* actual horsepower by converting the twisting force of torque into the work units of horsepower. Visualize that one pound weight we mentioned, one foot from the fulcrum on its weightless bar. If we rotate that weight for one full revolution against a one pound resistance, we have moved it a total of 6.2832 feet (Pi * a two foot circle), and, incidentally, we have done 6.2832 foot-pounds of work. OK. Remember Watt? He said that 33,000 foot-pounds of work per minute was equivalent to one horsepower. If we divide the 6.2832 foot pounds of work we've done per revolution of that weight into 33,000 foot pounds, we come up with the fact that one foot pound of torque at 5252 rpm is equal to 33,000 foot pounds per minute of work, and is the equivalent of one horsepower. If we only move that weight at the rate of 2626 rpm, it's the equivalent of 1/2 horsepower (16,500 foot pounds per minute), and so on. Therefore, the following formula applies for calculating horsepower from a torque measurement: Horsepower = (Torque * RPM)/(5252) This is not a debatable item. It's the way it's done. Period. [size=+1]The Case For Torque [/size] Now, what does all this mean in car land? First of all, from a driver's perspective, torque, to use the vernacular, RULES . Any given car, in any given gear, will accelerate at a rate that *exactly* matches its torque curve (allowing for increased air and rolling resistance as speeds climb). Another way of saying this is that a car will accelerate hardest at its torque peak in any given gear, and will not accelerate as hard below that peak, or above it. Torque is the only thing that a driver feels, and horsepower is just sort of an esoteric measurement in that context. 300 foot pounds of torque will accelerate you just as hard at 2000 rpm as it would if you were making that torque at 4000 rpm in the same gear, yet, per the formula, the horsepower would be *double* at 4000 rpm. Therefore, horsepower isn't particularly meaningful from a driver's perspective, and the two numbers only get friendly at 5252 rpm, where horsepower and torque always come out the same. In contrast to a torque curve (and the matching pushback into your seat), horsepower rises rapidly with rpm, especially when torque values are also climbing. Horsepower will continue to climb, however, until well past the torque peak, and will continue to rise as engine speed climbs, until the torque curve really begins to plummet, faster than engine rpm is rising. However, as I said, horsepower has nothing to do with what a driver *feels*. You don't believe all this? Fine. Take your non-turbo car (turbo lag muddles the results) to its torque peak in first gear, and punch it. Notice the belt in the back? Now take it to the power peak, and punch it. Notice that the belt in the back is a bit weaker? Fine. Can we go on, now? [size=+1]The Case For Horsepower [/size] OK. If torque is so all-fired important, why do we care about horsepower? Because (to quote a friend), "It is better to make torque at high rpm than at low rpm, because you can take advantage of *gearing*. For an extreme example of this, I'll leave car land for a moment, and describe a waterwheel I got to watch awhile ago. This was a pretty massive wheel (built a couple of hundred years ago), rotating lazily on a shaft which was connected to the works inside a flourmill. Working some things out from what the people in the mill said, I was able to determine that the wheel typically generated about 2600(!) foot pounds of torque. I had clocked its speed, and determined that it was rotating at about 12 rpm. If we hooked that wheel to, say, the drive wheels of a car, that car would go from zero to twelve rpm in a flash, and the waterwheel would hardly notice . On the other hand, twelve rpm of the drive wheels is around one mph for the average car, and, in order to go faster, we'd need to gear it up. To get to 60 mph would require gearing the wheel up enough so that it would be effectively making a little over 43 foot pounds of torque at the output, which is not only a relatively small amount, it's less than what the average car would need in order to actually get to 60. Applying the conversion formula gives us the facts on this. Twelve times twenty six hundred, over five thousand two hundred fifty two gives us: 6 HP. Oops. Now we see the rest of the story. While it's clearly true that the water wheel can exert a *bunch* of force, its *power* (ability to do work over time) is severely limited. [size=+1]At The Dragstrip [/size] OK. Back to carland, and some examples of how horsepower makes a major difference in how fast a car can accelerate, in spite of what torque on your backside tells you . A very good example would be to compare the current LT1 Corvette with the last of the L98 Vettes, built in 1991. Figures as follows: Engine Peak HP @ RPM Peak Torque @ RPM ------ ------------- ----------------- L98 250 @ 4000 340 @ 3200 LT1 300 @ 5000 340 @ 3600 (Numbers for 94 Integra LS/RS and GS-R) Engine Peak HP @ RPM Peak Torque @ RPM ------ ------------- ----------------- B18B 142 @ 6300 127 @ 5200 B18C 170 @ 7600 128 @ 6200 If you overlap the torque curve for B18B and B18C, you'll see that B18C's maximum torque (127 vs. 128 ft-lbs) is about the same as B18B, except B18C's torque curve just keeps on climbing, thus the much higher HP. B18B and B18C are quite similar, but not identical. Mostly notably the B18B has slightly longer stroke, which gives it the displacement of 1835 cc vs. B18C's 1797 cc. The stroke explains why the B18B has better low end, and it is also a factor why it revs slower and has lower redline than B18C. [Monitor YAHP for an article that will talk about the basic relationship between bore and stroke. - Frank] The cars are geared identically, and car weights are within a few pounds, so it's a good comparison. First, each car will push you back in the seat (the fun factor) with the same authority - at least at or near peak torque in each gear. One will tend to *feel* about as fast as the other to the driver, but the LT1 will actually be significantly faster than the L98, even though it won't pull any harder. If we mess about with the formula, we can begin to discover exactly *why* the LT1 is faster. Here's another slice at that formula: Torque =(Horsepower * 5252)/(RPM) If we plug some numbers in, we can see that the L98 is making 328 foot pounds of torque at its power peak (250 hp @ 4000), and we can infer that it cannot be making any more than 263 pound feet of torque at 5000 rpm, or it would be making more than 250 hp at that engine speed, and would be so rated. In actuality, the L98 is probably making no more than around 210 pound feet or so at 5000 rpm, and anybody who owns one would shift it at around 46-4700 rpm, because more torque is available at the drive wheels in the next gear at that point. On the other hand, the LT1 is fairly happy making 315 pound feet at 5000 rpm, and is happy right up to its mid 5s redline. So, in a drag race, the cars would launch more or less together. The L98 might have a slight advantage due to its peak torque occurring a little earlier in the rev range, but that is debatable, since the LT1 has a wider, flatter curve (again pretty much by definition, looking at the figures). From somewhere in the mid range and up, however, the LT1 would begin to pull away. Where the L98 has to shift to second (and throw away torque multiplication for speed), the LT1 still has around another 1000 rpm to go in first, and thus begins to widen its lead, more and more as the speeds climb. As long as the revs are high, the LT1, by definition, has an advantage. Another example would be the LT1 against the ZR-1. Same deal, only in reverse. The ZR-1 actually pulls a little harder than the LT1, although its torque advantage is softened somewhat by its extra weight. The real advantage, however, is that the ZR-1 has another 1500 rpm in hand at the point where the LT1 has to shift. There are numerous examples of this phenomenon. The Integra GS-R, for instance, is faster than the garden variety Integra, not because it pulls particularly harder (it doesn't), but because it pulls *longer*. It doesn't feel particularly faster, but it is. A final example of this requires your imagination. Figure that we can tweak an LT1 engine so that it still makes peak torque of 340 foot pounds at 3600 rpm, but, instead of the curve dropping off to 315 pound feet at 5000, we extend the torque curve so much that it doesn't fall off to 315 pound feet until 15000 rpm. OK, so we'd need to have virtually all the moving parts made out of unobtanium , and some sort of turbocharging on demand that would make enough high-rpm boost to keep the curve from falling, but hey, bear with me. If you raced a stock LT1 with this car, they would launch together, but, somewhere around the 60 foot point, the stocker would begin to fade, and would have to grab second gear shortly thereafter. Not long after that, you'd see in your mirror that the stocker has grabbed third, and not too long after that, it would get fourth, but you'd wouldn't be able to see that due to the distance between you as you crossed the line, *still in first gear*, and pulling like crazy. I've got a computer simulation that models an LT1 Vette in a quarter mile pass, and it predicts a 13.38 second ET, at 104.5 mph. That's pretty close (actually a tiny bit conservative) to what a stock LT1 can do at 100% air density at a high traction drag strip, being power shifted. However, our modified car, while belting the driver in the back no harder than the stocker (at peak torque) does an 11.96, at 135.1 mph, all in first gear, of course. It doesn't pull any harder, but it sure as hell pulls longer . It's also making *900* hp, at 15,000 rpm. Of course, folks who are knowledgeable about drag racing are now openly snickering, because they've read the preceding paragraph, and it occurs to them that any self respecting car that can get to 135 mph in a quarter mile will just naturally be doing this in less than ten seconds. Of course that's true, but I remind these same folks that any self-respecting engine that propels a Vette into the nines is also making a whole bunch more than 340 foot pounds of torque. That does bring up another point, though. Essentially, a more "real" Corvette running 135 mph in a quarter mile (maybe a mega big block) might be making 700-800 foot pounds of torque, and thus it would pull a whole bunch harder than my paper tiger would. It would need slicks and other modifications in order to turn that torque into forward motion, but it would also get from here to way over there a bunch quicker. On the other hand, as long as we're making quarter mile passes with fantasy engines, if we put a 10.35:1 final-drive gear (3.45 is stock) in our fantasy LT1, with slicks and other chassis mods, we'd be in the nines just as easily as the big block would, and thus save face . The mechanical advantage of such a nonsensical rear gear would allow our combination to pull just as hard as the big block, plus we'd get to do all that gear banging and such that real racers do, and finish in fourth gear, as God intends. The only modification to the preceding paragraph would be the polar moments of inertia (flywheel effect) argument brought about by such a stiff rear gear, and that argument is outside of the scope of this already massive document. Another time, maybe, if you can stand it . [size=+1]At The Bonneville Salt Flats [/size] Looking at top speed, horsepower wins again, in the sense that making more torque at high rpm means you can use a stiffer gear for any given car speed, and thus have more effective torque *at the drive wheels*. Finally, operating at the power peak means you are doing the absolute best you can at any given car speed, measuring torque at the drive wheels. I know I said that acceleration follows the torque curve in any given gear, but if you factor in gearing vs. car speed, the power peak is *it*. An example, yet again, of the LT1 Vette will illustrate this. If you take it up to its torque peak (3600 rpm) in a gear, it will generate some level of torque (340 foot pounds times whatever overall gearing) at the drive wheels, which is the best it will do in that gear (meaning, that's where it is pulling hardest in that gear). However, if you re-gear the car so it is operating at the power peak (5000 rpm) *at the same car speed*, it will deliver more torque to the drive wheels, because you'll need to gear it up by nearly 39% (5000/3600), while engine torque has only dropped by a little over 7% (315/340). You'll net a 29% gain in drive wheel torque at the power peak vs the torque peak, at a given car speed. Any other rpm (other than the power peak) at a given car speed will net you a lower torque value at the drive wheels. This would be true of any car on the planet, so, theoretical "best" top speed will always occur when a given vehicle is operating at its power peak. [size=+1]"Modernizing" The 18th Century [/size] OK. For the final-final point (Really. I Promise.), what if we ditched that water wheel, and bolted an LT1 in its place? Now, no LT1 is going to be making over 2600 foot pounds of torque (except possibly for a single, glorious instant, running on nitromethane), but, assuming we needed 12 rpm for an input to the mill, we could run the LT1 at 5000 rpm (where it's making 315 foot pounds of torque), and gear it down to a 12 rpm output. Result? We'd have over *131,000* foot pounds of torque to play with. We could probably twist the whole flour mill around the input shaft, if we needed to . The Only Thing You Really Need to Know Repeat after me. "It is better to make torque at high rpm than at low rpm, because you can take advantage of *gearing*." Thanks for your time. Bruce

Torque smque. Just keep the foot to the floor until the little guy stops going faster. Me, my top speed is faster than any German car. I-15 makes beliefers of the German cars. Bonzi. Smile

Essentially, its just the average area under the power curve that matters most. Thus, given identical gearing/weight/etc, the car with the better 'average' hp will accelerate faster. So, with 2 cars having identical hp peak figures but different tq values, their peak acceleration rates will be the same but one will have a higher average acceleration value. Thus, it'll generate a greater velocity. Similarly, one would expect a car that makes a constant 500 hp from 5k-7k rpm redline to be faster than an identical car that makes 300 hp at 5k rpm that rises to 500 hp at 7k rpm redline.

Dead on? Hardly. Torque Rules? This is a ridiculous statement. A mantra repeated ad nauseaum by the great unwashed masses. Give me a 24" breaker-bar with a 17mm deep socket on the lug bolt of my wife's Mini Cooper. Since I weigh 200 lbs, just by standing at the end of the bar I am generating 400 lbs/ft of torque AT THE WHEELS! As Homer Simpson would say "WOO HOO!". The problem is the Mini is just sitting there not moving, because the parking brake is on. Torque rules indeed. Esoteric? There is nothing the slightest bit esoteric about horsepower measurement. And if Bruce were sitting in my wife's Mini as I stood on the breaker bar I bet he would really "feel" that 400 lbs/ft of torque. Tell that to John Force as he pilots his 6,000 hp Funny Car down the 1/4 mile, Bruce. And on and on and on........

So if a 420 or whatever generates near 500 ponies, then it should be as fast as the Turbos and ford GT yes? sounds good, and with 7 gears too...and that 4.44 rear end...give me 25 lbs of torque! doesnt matter! bc first gear will get us to about 200!

Torque and gearing, teak. All you've demonstrated is that you cannot overcome friction forces with 400 ft-lb. Do you drive the car with the parking brake on? Of course not. Part of the confusion is the concept of torque has not been promoted by marketing departments like horsepower has been. The general public, without the physics and engineering background, doesn't understand horsepower is a function of torque and rpm. A broad, flat torque curve is what sells a commuter car to the general public. Best regards, Rob Schermerhorn

Well stated! This is correct. Power rules, not torque. The area under the power curve is the critical factor in determining the potential acceleration rate. Take two cars each developing a peak 400 hp. One develops peak torque of 150 lbs/ft, the other 300 lbs/ft. There best 1/4 mile times are IDENTICAL. HP RULES Take two cars each developing a peak 300 lbs/ft of torque. One develops a peak 150hp, the other 300 hp. The best 1/4 mile times are WAY DIFFERENT. The 300 hp car is WAY quicker. How come this is true? BECAUSE HP RULES. The torque gods have brainwashed almost everyone! (Except tiggs)

That's because torque in and of itself is meaningless when determining work done (i.e. acceration rates). Rob, I guarantee you if I apply 400 HP to your car with the parking brake on you'll notice something going on!

No, I sold it to Rob for $20,000!! He couldn't believe I had an object that weighed only 2 pounds that he could use on his Ferrari to develop an additional 400 Lbs/ft of torque!

Yes, you're right. Torque is work (time independent), HP is power (work over time, or dW/dt). HP is time dependent, torque is not. HP is a function of torque and time (rpm). Yes, in a low gear, not in overdrive. It's gearing dependent. 1 hp = 550 ft-lb/s We're on the same page, though I think you may be confused over the differences between work and power. No biggie. 400 units of a force quantity is not directly comparable to 400 units of a power quantity. One must utilize common unit conversion. Otherwise it's apples and oranges. We need both HP and torque, and as my post summed up, torque at high rpm makes us all happy, gives us big HP numbers. We want to make a lot of torque, as quickly as possible, this results in big HP. Rob

Torque is NOT WORK. This is very basic. It is simply a force. I fully understand the difference between work and power. Power along with time, is simply a component of the amount of work being done. Applying 400 hp to a car in ANY gear will do the same amount of work per unit time. It doesn't matter what gear you are in. Applying 400 hp to an overdrive gear at a standstill will probably result in a lot of the work being done to the drivetrain (i.e. smoking it). Torque, along with rpm, is simply a component of hp, nothing more. By the way, I appreciate your non-confrontational and polite responses. A rarity in today's world! Respectfully, Scott

Integrate the torque vs RPM curve to fine total accelerative potential. It's really quite simple Best! Ben.

Silly,and meaningless, statement QUOTE=ENZOFORZA] HP= how quickly the "work" can be done[/QUOTE] [/QUOTE] Correct, but no quotation marks needed around the word "work"

the reason tubo cars make higher HP+Tq is that forced induction will increase the volumetric efficiency of the motor to over 100%. Any NA motor can only hope to achieve 100% volumetric efficiency (none can due to frictional losses etc.). The turbo "cheats" the laws of physics by increasing the volume of the cylinders, not by actually increasing the size of each cylinder, but by compressing more air/fuel mix into each. This will make a 3.5L engine that NA might produce 380 HP NA to a car that can produce 760 HP under boost levels of 2 bar (2X atmospheric pressure) or about 28PSI and "increases" the displacement of the motor to 7.0L (2x the Volume of a 3.5L motor) this of cours is a much simplified equation. This theoretical 3.5L motor would most likely produce more like 650HP. Variables like increasing intake temps (increased temps = lower oxygene+ lower Power #'s), detonation, and a laundy list of other crap that can drop power. Sorry for any misspelled words. Im a better engineer than an English teacher I guess

[/QUOTE] Correct, but no quotation marks needed around the word "work"[/QUOTE] whats silly and meaningless, its correct

Correct, but no quotation marks needed around the word "work"[/QUOTE] whats silly and meaningless, its correct[/QUOTE] Teak360 I just got this from Websters. 2. <machinery> A unit of power, used in stating the power required to drive machinery, and in estimating the capabilities of animals or steam engines and other prime movers for doing work. It is the power required for the performance of work at the rate of 33,000 English units of work per minute; hence, it is the power that must be exerted in lifting 33,000 pounds at the rate of one foot per minute, or 550 pounds at the rate of one foot per second, or 55 pounds at the rate of ten feet per second, etc. Perhaps you could email them and tell them how stupid and meaningless they are.