|
|
12-06-2007, 06:25 PM | #177 | |
Captain
13
Rep 689
Posts |
Quote:
If you know engine HP at any given time, you can calculate acceleration as long as you also have weight. If you know engine TQ, well, you cannot calculate jack without knowing a lot of additional information beyond weight. Or put another way, knowing just a cars power to weight is an execellent approximation of acceleration. TQ/weight won't tell you a thing unless you also start talking about gearing and RPM at which point you know HP and could have just used it to start. But by all means continue to worship at the alter of engine TQ. |
|
Appreciate
0
|
12-06-2007, 07:58 PM | #178 | |
Major General
382
Rep 8,033
Posts |
Quote:
Not sure where this coming from? My point is the Tq vs. Hp distinction is not particularly meaningful since they are directly coupled. On the other hand, max Tq vs. max Hp distinction is meaningful. Going back to Bruce's original statement: so how come the redline does not matter? |
|
Appreciate
0
|
12-06-2007, 08:11 PM | #179 | |
Captain
13
Rep 689
Posts |
Quote:
You need rear wheel TQ, not engine TQ which is the number people always talk about. RWTQ is engine TQ modified by gearing. So its useless to factor in engine TQ without knowing that other factor. Now HP already factors this in. Now stop and think for a second, which car is faster one with 100ft/lbs or torque and a 6000rpm redline or one with 200ft/lbs and a 3000rpm redline. Now lets the higher reving engine always makes the same hp at 2x the rpm of the other motor. So we have a high torque motor and a low torque motor. Which is faster? Now what if you just change the final drive by 2x on the higher RPM motor? I simply cannot believe how dense some people are on this subject. Its really sad. |
|
Appreciate
0
|
12-06-2007, 08:21 PM | #180 | |
Major General
382
Rep 8,033
Posts |
Quote:
READ post #175. I am talking about Tq at the wheel. Who said anything about Tq at the shaft? You still need to convert the hp number to tq so that you can calculate the force so that you can calculate the instantaneous acceleration. What part of that are you opposing? Read my previous about max tq vs. tq. You are using the terms loosely. What does it mean to have a 100ft/lbs or torque and a 6000rpm car? That means the car has 100ft/lbs MAX tq and a 6000 rpm redline. Yes, the MAX hp number will account for that, and therefore be a correlate for AVERAGE acceleration. Do you understand the difference between that and instantaneous acceleration? Did you even read my post? |
|
Appreciate
0
|
12-06-2007, 08:32 PM | #181 | |
Captain
13
Rep 689
Posts |
Quote:
|
|
Appreciate
0
|
12-06-2007, 08:34 PM | #182 |
Major General
382
Rep 8,033
Posts |
Then, don't respond to posts you haven't read. There is no point in getting upset at an imaginary post that you think is talking about shaft Tq, whereas the real post has clearly referenced Tq at the wheel.
|
Appreciate
0
|
12-06-2007, 11:33 PM | #183 | |
Colonel
99
Rep 2,000
Posts |
Quote:
As for gearing, perhaps the best way to illustrate my point is to visualize identical vehicles except for gearing. One is stock, and the other has been treated to a more aggressive final drive ratio. In a drag race, the geared car, given reasonable traction, will launch harder than the stock vehicle, and begin to pull away - and the reason for this is that it's making more power because it's operating higher in the rev range. Sure, you can do the mechanical advantage/torque at the drive wheels thing if you so desire, but you'll find that horsepower is a great shorthand in this environment. Enigma may be impolite, but he's exactly correct. OK, now the cars are well underway, and the geared car grabs second. At this point the stocker is still in first and higher in the rev range so it's now accelerating harder than the geared car - because now it's making more power at that point. Then the stocker has to shift, and the geared car is now higher in the rev range and making more power, so it will again be pulling harder at that point. Then the geared car shifts, and... You see the point. Once the cars are well underway, it becomes a seesaw battle. First one car is pulling harder, then the other. The geared car has the theoretical drag race advantage because it's got the early advantage, mostly off the line given copious traction, but also because it gets an early advantage in each gear, while the stocker's advantage points are delayed. This is mostly an ET thing, but terminal speeds are often mildly affected because the geared car may have an overall average power advantage during the course of the race. This is by no means a given however, and is dependent on the vagaries of shift points and where the finish line falls in the race. For a good, though incomplete, analysis of a gearing change on an E46 M3, just click on this. That note illustrates the see-saw battle quite well, I think. It does in fact ignore traction issues, however, and since the M3 in our garage always has trouble in first gear even with stock gearing, that may be an issue. Perhaps more important is the fact that it also ignores rotational inertia, and the additional rotational inertia penalty given as a freebie to the geared car will limit its advantage - primarily because its penalty is enacted early in each gear, while the stocker is penalized only after the geared car has shifted (each time). The geared car still wins, but by a reduced margin. I know that nobody talks about this (rotational inertia), but it's far from a tiny issue. As an example, if you have a car with a three to one first gear and a two to one second gear, you would naturally expect first gear to accelerate 50% harder in first gear than in second. Not so, however. The least loss I've encountered during instrumented testing on many cars over the years is about 12%. The most is near 20%. That particular record was achieved in a German car, and we well know that German cars use flywheels that may as well have been liberated from old Panzer tanks, or U-boats. OK, I'll shut up now. Too many points Bruce |
|
Appreciate
0
|
12-07-2007, 01:01 AM | #184 | |
Captain
13
Rep 689
Posts |
Quote:
I keep hoping that the move away from MT gearboxes will reduce their usage of heavy flywheels since drivability won't still be an issue. I have always been a fan of taller 1st and 2nd gears in high HP cars. It makes little sense to use a 1st gear that always traction lmited. 50mph 1st and 72mph 2nd would be about right in my mind. A while back I was instructing someone driving a superchared Atom. It turned out to be best to launch the car in 2nd and save the time of the shift and focus on the first zig in the course. If you are putting drag radials on the car, then a lot changes. For street or DOT-R tires a super short first gear isn't really usefull. |
|
Appreciate
0
|
12-07-2007, 02:56 AM | #185 | ||
Lieutenant General
634
Rep 10,407
Posts |
Quote:
By the way I’ll never let you forget that you are the one so foolish to claim here on this very form that you “contributed” to a similar simulation software tool capable of validation with actual tests to within HUNDREDTHS OF A SECOND. Let me quote you, just to remind, Quote:
This all comes right back to your infamous quote above. There is simply no way to make a simulation tool that matches a widely variable real world test “perfectly” (with my basic definition of perfect here being +/- 1/100th second – right from the horses mouth). Now drag racing IS significantly more consistent than magazine tests. This is their business – consistency. How does simulation account for this? You simply need more accurate physical tests to determine the best set of input parameters. As well you will likely need an improved simulation tool; specifically an improved friction/tire spinning/tire growth model than available in CarTest. However, the same basic numerical integration scheme based on torque and gears and drag will still work beautifully. Once these and oher SYSTEMATIC ERRORS are reduced guess what? One will be able to get a nice match between these very consistent tests and a simulation. As good as you might get it though your previous claim about 1/100th second is still a farse and a pipe dream. What else have I said about simulation? Simulation is almost always better at relative predictions compared to absolutes. For instance what change would I see if my M3 had 30 more hp or what is the difference between the M3 and RS4 in a given performance contest. The whole new car vs. old car thing is so simple I don’t even feel it warrants a reply but here you go. A broken in car will typically produce more power than a new car. If you can measure that effect on an accurate ENGINE dyno and put the results into the simulation guess what – you could predict these differences, again, “reasonably”. I also disagree with your closing PS. A high redline and gear ratios absolutely have a large impact on vehicle performance both directly and indirectly. Sure, as I have stated and agreed with many on the point, time and time again, the key figure for either track or strip performance is simply power to weight. But gearing and redline matter as well. Gears provide torque multiplication and they do so in all gears at all times. Larger ratios either gear or final = more torque multiplication = more acceleration, period (with the caveat that indeed the wheels are not spinning). Of course there is a limit to this, there is no such thing as a free lunch, you can’t simply raise and raise the gear ratio endlessly, traction is a limiting factor at lower speeds as well is keeping the engine in its best operating rpm band where is produces high torque lastly there is the limit of having such large ratios that it requires too much shifting. A high redline allows one to stay in a gear longer and maximize time spent accelerating instead of shifting (slowing down) and shifting to the next gear where acceleration will be markedly less. Would you disagree that raising the redline on a car, all other things equal (and assuming it still produces reasonable torque in the increased band) it will make the car accelerate better through the gears? The indirect benefits of a high redline and numerically larger gears is more evident on the track than the strip. Vehicles designed as such are typically low torque, high power, high redline, and light/low intertia drivetrain. All of these add up to a car that can not only accelerate but one that can handle. |
||
Appreciate
0
|
12-07-2007, 02:57 AM | #186 |
Captain
36
Rep 625
Posts |
One huge advantage of the DCT M3 will be that it has 7 gears, allowing shorter spacing between gears, quick and seamless shifts, and still a reasonable cruising gear. I agree 1st gear should be reasonably long in high HP cars, and I find BMW loves to use a short 1st gear for a snappy feel off the line followed by too big of gaps between 1st and 2nd and 2nd and 3rd. This could be solved by using a taller 1st gear, just slightly taller 2nd gear, and the same 3rd gear.
The DCT m3 could be 0.3 seconds faster than the 6-speed in the 1/4 mile with a 2-3 MPH higher trap speed, depending on just how fast it shifts and what gearing they choose.
__________________
Driving sideways: It's not faster, but damn it's more fun!
|
Appreciate
0
|
12-07-2007, 03:10 AM | #187 | |
Captain
13
Rep 689
Posts |
Quote:
Off the line the DCT may suffer depending on what form of LC we get. Good drivers can easily beat the SMGII off the line (us version). |
|
Appreciate
0
|
12-07-2007, 03:20 AM | #188 |
Captain
13
Rep 689
Posts |
Swamp,
I have also used car-test in the past. I found it to produce reasonable result IF you were able to feed it detailed enough info. The last time I used it was over 5 years ago so I cannot speak to the current version. |
Appreciate
0
|
12-07-2007, 11:07 AM | #189 | ||
Major General
382
Rep 8,033
Posts |
Quote:
1. How come redline does not matter? In the sense that it will allow you to apply Tq at even a greater rate and result in more power. You are saying the same thing above, and as far as I can see, contradicting what you said in your PS unless I am missing something here. 2. I looked at the M3 example with the different final drive ratios. Of course it will be a seesaw battle, and that the more aggressively geared car will win although that depends on when the race ends since it will take a hit on top speed, but for most practical purposes, that’s not an issue. What you are claiming is that the aggressively geared car is winning because it has some kind of an acceleration advantage early on ONLY, which forms the basis for the rest of the race. That part seems inaccurate to me. The aggressive gearing will give it an acceleration advantage throughout the race overall—ignoring the details around shit points—and not just at the start. That’s just physics. I don’t see how the aggressive final drive ratio all of a sudden will cease to be an advantage just because you are past a certain distance in the race since it is a static factor. Quote:
That said, Hp is indeed, as you put it, a shorthand. It is how the capability of the engine to do work per unit time is measured, which is a very useful number to have because it incorporates a “rate”, or a delta t, whereas a Tq number does not. Technically speaking, Hp does not cause acceleration. Cheers, |
||
Appreciate
0
|
12-07-2007, 01:09 PM | #190 | |
Lieutenant General
634
Rep 10,407
Posts |
Quote:
|
|
Appreciate
0
|
12-07-2007, 01:34 PM | #191 |
MacroRisk
111
Rep 2,523
Posts |
My take on the IS-F is you have to take Lexus (aka Toyota Posh) seriously. They may not be there today, but you know they - as the largest global manufacturer - will keep pouring $$ into that brand to take share away from arch-rivals MB/BMW.
And the quality control is amazing. Wish my 5ers were as consistent . Lexus' success in the U.S. is staggering (and shows that they know how to get to those who want total reliability / quality more than any other attribute). But I also agree that this brand lack passion / precision (funny, Clarkson says the same about German cars vs lambos, massas, alfas and ferraris) - I test drive my boss's demo gs 430 - ugh, give my old e39's any day ... my boss eventually went w/ e500 (better). So, hot Lexii are to be watched - and hey, more competition means all marques have to get better / more R&D - good for us, the drivers
__________________
Just thinking of something not so witty ///M3 E92 '09 Jerez Black | 6MT | Ext Fox Red | Tech | Prem | 19s |Heated Seats | iPod |Smartphone | Euro Deliv June 09 Sold: 540iT / 530i / 323i |
Appreciate
0
|
12-08-2007, 02:12 PM | #192 | ||||||
Colonel
99
Rep 2,000
Posts |
Quote:
Quote:
Not only was ShiftMaster capable of delivering results at that level of accuracy, it pretty much had to be that accurate. We bought a number of such packages available at the time (this was a number of years ago), and pretty much all of them could deliver results down to around that level. In other words, not only was it possible amongst a number of available packages, it was routine. I should qualify this a bit, I think, since the last time you and I had a dust up (about time to speed having essentially nothing to do with time to distance), it was due to a misunderstanding. What I'm talking about is taking actual drag strip results, documented along with weather conditions, starting line techniques, subjective traction levels and whether the car was able to hook or not off the line and during shifts, plus shift points and style, plus etc if I've forgotten something. I used to write notes on the back of the timeslips. (Anal? Who me? I was potty trained at gunpoint.) At the time, it was pretty straightforward to get extremely good accuracy with packages we bought before ShiftMaster came into being, and that package eventually got accuracy as close as anything else we tried. We also bought a ton of SAE papers on the subject, especially those we could find on rotational inertia and the vagaries of traction coefficients at various levels of slip. I should also mention that we only tested in depth on material we knew we could trust, which was essentially our timeslips with our intimate knowledge of what had gone on during those runs. Still, the result was a package that was competitive with others we had hands-on knowledge of at the time - and to repeat, they were all accurate to a level that you say is impossible. All of them. As a final sort of disclaimer, let me also say that I'm quite sure that we would've stumbled from time to time on a car that more or less refused to be accurately simulated, for whatever reasons. Hadn't happened up to the point I lost interest, however, and I'm also quite sure that that would be the exception rather than the rule. Quote:
Wow. Tell me I'm wrong. As an aside, my guess is that CarTest really *is* an accurate tool, but not in your hands just yet. Quote:
Quote:
Quote:
As we've said before, horsepower is the great simplifier in this context. You can certainly go through the torque-at-the-drive-wheels calculations, but when you do, you'll see that you didn't have to. Bruce Last edited by bruce.augenstein@comcast.; 12-08-2007 at 09:55 PM.. Reason: Change 295 foot pounds to 590 foot pounds |
||||||
Appreciate
0
|
12-08-2007, 02:44 PM | #193 | |
Captain
13
Rep 689
Posts |
Quote:
The other point you touch on is what i always refer to a a good powerband. You want to choose your shift points to maximize the area under the HP curve from the HP plot. In a car like the M3 where peak HP is so close to redline its easy, you just shift at redline. However, if you had the same engine but with a 10k redline you would want to shift higher, past the HP peak. In an ideal world you would shift very close to the point where the HP had dropped the same hp value the car is going to make in the next gear after your shift. With the current motor thats not possible. However, this is why some engines that produce less peak hp sometimes get better acceleration numbers. From the graph its likely the engine will spend most its time most its time between 6500 and 8400. In that range it will make between 360 and 420hp. You could integrate the area under the curve and get a good aproximation. Just eyeballing it we look like we will on average be using about 93% of the cars power. Sometimes 100% and sometimes 85% The Lexus has a flatter HP curve in its dyno. As a result its going to utlize a greater average % of its peak power. This gives is a slight edge that just comparing peak numbers would not make aparent. |
|
Appreciate
0
|
12-08-2007, 11:16 PM | #194 | ||
Colonel
99
Rep 2,000
Posts |
It's in the numbers
Quote:
Quote:
Now, let's flash forward to 182 mph, the last data point shown in that note. At 182 mph, the geared car has a .8489 car length advantage, call it about 13 feet. At 182 mph, that's about .05 seconds. You see the point, I think. In the first couple of seconds into the race, the geared car gets a four foot advantage at 36 mph, and then in the next 146 mph and what, maybe a minute? it gets another nine feet, and actually loses some time (from a .075 second advantage to a .05 second advantage) against the stocker. Yeah, once you get up into the power range, gearing kind of disappears in the noise. Edit: Furthermore, if you get into a race from a rolling start, either car may in fact be able to win, based on who got the early advantage. That early advantage will be determined by the starting speed, and whether the stocker can be in a lower gear at the onset. Bruce |
||
Appreciate
0
|
12-09-2007, 06:17 AM | #195 |
Major General
1208
Rep 8,034
Posts |
Bruce,
Myself not being a technical man are you saying that changing the gears makes really very little difference on the overall result. Like you said in the first few hundreds it's more noticeable but this advantage doesn't grow to anything like the advantage some here believe it can be. Take two cars for example the E63 and the M5, both have 7 gears and both roughly produce the same power but their really difference is in the amount of torque and at what revs. From what you are saying would I be right in thinking that the E63 should be able to pulls daylight between it and the M5 based on the fact it has more torque regardless of where it is produced. I have always had a problem understanding what some more technical guys here have said that it not the amount that is important but where it's produced. Surely that is determined by the gearbox and gearing as each car roughly makes the same speed in each gear or there abouts. Please can someone explain this in to layman terms for us thickies. |
Appreciate
0
|
12-09-2007, 09:27 PM | #196 | |
Lieutenant General
634
Rep 10,407
Posts |
Quote:
Bruce, ever heard of apples to apples? That is simply what this is about. What you (or your buddy as it sounds like) did and how you did it, although using basically the same method (physics/numerics) is very different that what I am doing and how I am doing it. Here is why: You are using a very controlled and small set of data points. You are controlling the set of cars, the driver, the tires, the technique, the track, as well as likely controlling more variables than that. Then, as I understand it, you tweak the simulation to match the measured results. You even admit some subjective factors such as quality of hook up and traction, etc. CarTest by the way offers no such qualitative inputs, all of them have a close or directly quanifiable meaning/interpretation and tests are then possible to determine these input parameters. How does that quality of hookup adjustment work exactly? Is it just a lookup table that adds or subtracts some number of tenths to the simulation based on asking the driver was it "excellent", "good", "fair" or "poor". Or maybe you have an "exotic" curve fit for corrections for these inputs that use langauge to translate to numbers. Bruce this is called HEURISTICS, not simulation. . Once you have enough repeatable runs this type of "tweaking" of a simulation (be it with quantitative or qualitative factors) is what most in the business call at best simply curve fitting, or at worst cheating. How good would your infamous method work if all of a sudden you changed the trans, tires, driver, removed 300lb from the vehicle and hopped it up with 15% more power and a 1k rpm higher redline ON THE FIRST RUN? This is a KEY question as the the capability of the tool and of the operator of such a tool. So on top of how you did this, which I addressed above, there is also what you did. I still contend that it is not possible to match within hundredths of a second, time to distance nor time to speeds ALL the way along the strip. I think you are simply losing sight of reality and orders of magnitude. I'd be suprised if you got within tenths the entire way down, let alone TEN TIMES BETTER than that. Do you realize how much a simple factor like a transmission loss affects 1/4 mi times? A mere 1% error in this crucial input parameter (from either a bad estimate or test with not enough fidelity) results in about FIVE hundredths difference in the 1/4 mi time (in a MT car in something like the E92 M3). Perhaps you can explain how you obtained your transmission losses to less than a 0.2% . What about friction as a function of temperature, tire growth with rpm, or any of the dozen inputs I have shown that CarTest uses: YOU WOULD HAVE TO KNOW THESE FACTORS MORE PRECISELY THAN YOU CAN ACTUALLY MEASURE MOST OF THEM. Christ we did not even mention rounding. To be withing a hundredths (or was it only hundredths) you really have to be within five thousandths. Starting to see the point ... yet...? Doubtful, but many others here will. Now back again to what I am doing. Your serious misunderstaning of my last reply, which you dismiss as simply "defensive hyperbole", again shows just how ignorant and confused you are about this whole simulation thing. What I am doing is predicting tests that are known to vary widely from a variety of uncontrolled factors including, driver, tires, track, temperature, age of car, car to car variations, etc. I am using purely analytical techniques and some combination of tuning or better yet using an enveloping process to determine drive train loss parameters. What is the bloody spread of 0-60 times or 1/4 mi times reported by a group of magazines for a typical car? Multiple tenths of seconds is the answer. So what is THE real time? THERE IS NO REAL TIME nor "best" time or whatever you want to call it, all of the times are valid data points and predicting somewhere in the middle is again the hallmark of a REASONABLE and accurate simulation. Do you see yet why you are making an apples to oranges comparison? Why did I bring up old car vs. new car results? Because you brought it up first as evidence that my simulations were so incapable of accuracy. Again, measure the hp, input it to the sim, voila you can easily show the difference between the two cars. Better yet look at some dyno results for a similar car, new vs. well broken in and then you could probably establish a reasonable hp gain. With your harsh criticisms of my lack of ability, my hideous and systematically (do you even know what that means...) incorrect results, I think there is only one way to settle this. Dust of that old TRS-80, all of those valuable old time slips and track down your buddy (who probably did most of the work) and BRING THE EVIDENCE. It is so easy for you to sit in front of your computer now, reference the magic of the glory days and how terrible of a job someone else is doing. First you can prove your claim on the hundredths of a second issue. Then you can show me how you can better hit a constantly variable and moving target such as results from magazines. You can't really do it, almost by definition. I am definitely not one to say I am a leading expert on this topic, I also do not claim my results are perfect and I readily admit that a lot of the input parameters need to be known more accurately. But again given what we all have access to, these simulations are in my opinion, and in the opinion of quite a few folks here, reasonable and accurate. Really, Bruce, put up or shut up. Finally, I do think I know our differences about the importance of hp, tq, gearing and redline as well and how they relate to acceleration. Folks like lucid and myself take a sort of reductionist view of the systems of a vehicle where everything can change independently. You look at vehicles as they actually exist where they are mostly already optimized in that the transmission, redline and torque curve all are chosed to maximize acceleration. If you took a vehicle so optimized and drastically altered its gearing or redline of course it's performance would change in a correspondingly predictable way. So your POV is when a vehicle is totally optimized for its engine, redline and gearing do not predict how fast that car is in the 1/4 (right?). My POV is that power to weight is indeed the critical factor but that all systems must be matched carefully to an engines characterisitics. Then of course to the extent that you can adjust and engines tq/hp/redline independently, if you made such changes the gearing would then be critical to get right. Sound about right? |
|
Appreciate
0
|
12-09-2007, 11:13 PM | #197 |
Captain
13
Rep 689
Posts |
Not sure where this thread is going but I am not dusting off the TRS-80 or the Apple IIc.
I have been on both sides of this. The problem with pure simulations is you always end up estimating the effects of components that you don't have sufficient information on to make an accurate model. Good examples are drive train loss, tire grip at launch, shift times, effect of flywheel mass on shifts (next gear lurch), energy wasted as stored rotational energy in the drivetrain (you bleed much of it during shifts), and atmospheric effects. Unless you have an accurate model for those you are just guessing. The guess are educated based on previous real world result being fed back into the simulation. However as a predictor they are still guesses. |
Appreciate
0
|
12-09-2007, 11:46 PM | #198 | |
Lieutenant General
634
Rep 10,407
Posts |
Quote:
These indeed are some of the differences between an OK simulation and a great simulation as well as the difference between using a fairly advanced engineering type tool vs. an out of the box, use it as is type of tool. All of the above variables are able to be taken in to account in CarTest, with either a simple or sometimes a complex model. One should not look at all of the unknowns and conclude that simulation is simply intractable. As much are cars are vastly different; they are in many wasy very common/similar. Much of the value of a good software tool is the appropriateness of its default parameters. This is true with ANY simulation software. I have found that for CarTest, these are pretty darn good, right out of the box. CarTest is noticeably weaker with regards to turbo charged engines and modern low loss/high performance automatic transmissions as well as for any transmission that shifts very quickly (although I learned the hard way how to deal with that one and deal with it with great accuracy). Much of this observed difficulty is likely to NOT be related to the sufficiency of the softwares model and method but related to poor/unknown inputs. Lastly, population of the various parameters is absolutely not always a trial and error or a feedback type of approach, many parameters are without doubt such as tire size and air temperature. Other such as transmission losses can be obtained (although not perfectly) from dyno tests, rolling resistance can be obtained from coast down speed vs. time (subtracting any relevant aerodynamic effects), lastly shift times are now these days often cited direct by manufacturers for automatics and DSG type boxes. If we remember that the the critical inputs to such a software tool are the power or torque curve, redline, weight, gearing (including tire size) and transmission losses we can do some pretty good absolute simulation and even better RELATIVE simulation without a tremendous effort and without tremendous uncertainly. PS: The TRS-80 comment was not directed at you in any way! Last edited by swamp2; 12-10-2007 at 02:57 AM.. |
|
Appreciate
0
|
Post Reply |
Bookmarks |
|
|