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Now you are back to generalizing and resorting to the argumentum ad ignorantiam tactic. "Lack of proof is not proof."
speaking of lack of proof. you have yet to show me any calculations or show me any video or in fact, ANY proof whatsoever that I'm wrong. yet I have shown video, had others state the same thing, and even had others show me the calculations. if anyone here is guilty of lack of proof, it's you.
Go look at a dyno chart and tell me if you notice a difference in the area under the curve between 6000-6500 RPMS and 8500-9000 RPMS. Maybe that would help you see what issues may arise when you have to shift sooner.
actually, on the ap1, the torque curve remains fairly flat from 6000rpm to just about redline. your statement has very little relevance considering you are trying to take a snapshot of a single moment, vs looking at the entire picture. do the math if it makes you feel better. or just wait for crazyphud's graph plots and then you can try to pick at that all you want.
[QUOTE]
I am saying you are looking for facts that support your foregone conclusion.
Originally Posted by Wisconsin S2k,Aug 23 2005, 11:10 PM
so in other words, the real equation you need to be using here is F = ma
Thanks, I had forgotten that one. No wait, I hadn't.
F does not just come from nowhere. Nor does it come from the gears. It comes from the engine.
In a car with an infinitly continuous gear ratio, it is fairly trivial to calculate that there is a peak force that can be delivered to the car at any given moment, based on the max engine power and the speed of the car.
But we have a car with six fixed gears. So instead of the engine staying at a constant ideal speed as the car accelerates, the engine and the gearing go off from the peak. The reason we shift is to keep approximating that perfect infinitely continuous gear ratio.
The 4.57 diff gear is going to make those six speeds closer together. That should mean that you can keep the engine marginally closer to its perfect gear ratio, at the cost of shifting more and losing the top end to rev limitation. (If you shift well and quickly....)
But you aren't going to gain much. The whole system is still limited to only what the engine can put out.
The tradeoff here is that if you don't need the top end (or, for that matter, the bottom end), you can sacrifice it even further and close up the gear ratios even more. Lets say you know you will never get above 120. You might size the final drive so that you rev out at 130 (some safety margin, for tailwinds and the like). That gives you closer gearing, so that you can stay closer to your ideal gear.
On the other hand, if the car may get up to 150 (again, lets leave a margin for downhill or a tailwind and say 160ish), you would be screwed. Instead you would have to drop the final drive down a bit, accepting that the gearing will less perfectly approximate the ideal smooth peak power gear ratio.
If you know you only need first gear to get out of the pits and you will never be below 50 mph on the track, you can do what many race cars do and have a pretty substantial jump between first and second. That will allow you to reclose the gear ratios and still keep the top end speed limit.
Basically, you can tweak things a bit. You can get closer to the ideal limits of the engine by giving up some flexibility somewhere. But you can't mystically create power in the gears. They will make a small difference -- one that is important if two otherwise similar cars are running against each other, but one that is tiny compared to the difference between a car like an S2K and a car like a Viper.
All this talk about how much "performance" changing the gear ratio adds is fine IN CONTEXT. If you don't need the last bit of top end, and if you realize that the differences are going to be very small compared to something like adding F/I or pulling 300 pounds out of the car, then fine. Make your educated choice.
But "gears" are not some sort of magic speed wand, and way too many denizens of S2000 talk don't understand that.
way to dodge the subject. i have proof. what do you have? arguments and no proof.
That's why you need to look at the HP, which is also effected by engine speed.
sorry, horsepower is not used to determine acceleration. so in this case, it's irrelevant.
Ah, but you claimed it was a fact not a theory before the graphs have been provided...
before the graphs have been provided to YOU. the graphs were already made a long time ago, before i even got the gears.
That it takes time to learn how to do integrals and what they represent. And learning what they are, and how to do them, goes hand in hand.
right. which is something i know. however, since others are notably better at it than me, as well as have spreadsheets and things like that which help them do it in a timely fashion, i asked for their help. don't assume that I dont know how to do it myself.
Let's take as an illustration two AP1 S2000s. Let's also take two drivers who can shift so perfectly that it takes no time to shift from one gear to the next. The engines themselves produce the same torque @ any given rpm at the crank. Let's also say you're going from a straight line from 0 - 150.
Let's now create an imaginary transmission for the first S2000 with an axle ratio of 1.15. This means it relies on a single gear to go from 0 - 150 (I know this is not practical but bear with me). The gear takes up all of the usable RPMs on the engine all the way to 9000 RPM. We are in the range of 6000 - 9000 RPM (approx VTEC) from 100 MPH - 150 MPH. Not that great.
Now we have another imaginary transmission with an axle ratio of 4.50. It uses up all six gears. It's not too hard to see that because we're using the extra gears, we can stay in our usable powerband (6000 - 9000 RPM) for most of the 0-150 run (starting from 25 MPH).
The very best situation, theoretically, is if we had an infinitely high axle ratio, and an infinite number of gears, aka a continuously variable transmission. That way we can stay at the max torque RPM for almost the entire run.
I hope this shows that having a higher axle ratio is good because we can stay in our powerband for longer.
The second thing we need to know, aside from the fact that high axle ratio -> more gears -> more time in powerband, is whether or not accellerating in a single gear is faster with a higher axle ratio. A range of MPH common to both 4.10 and 4.57 is 43 - 58 in second gear. The accelleration you will see at this range is dependent on the torque driven to the wheels. Given the fact that the wheels are the same, the difference between the two cars is 9.72 stock, and 10.84 with the 4.57 gears. In the stock car, this range is between 5800 RPM and 8000 RPM. In the 4.57 car, the range is between 6400 RPM and 8900 RPM. It's safe to say that the total torque produced by the motor is going to be greater in the 4.57 car. This is multiplied by the higher gearing in the 4.57 car, giving you even greater accelleration. (Torque at the gears @ 7500 RPM is 153 * 1.16 * 4.10 * 2.045 = 1488 lb-ft in the stock car, and 153 * 1.16 * 4.57 * 2.045 = 1658 lb-ft in the 4.57 car.)
You could do the same thing yourself for any range of speeds, 0-60, 0-100, and you'll find that the 4.57 car will be faster, not only because it'll be using more of the high RPM range, but because the torque multiplication will be higher.
About the question of why not use 6.00 gears? Given perfect shifting, 6.00 gears will yield even higher torque multiplication and more use of the high RPM powerband. This will make for an even faster car. Of course, it's completely impractical, as the top speed is 113, but if you never go that high, and don't care about highway mileage, go for it.
Prior to doing this for myself, I had no idea why gears would make a difference, if any. Now I'm confident that getting a higher axle ratio makes a big difference. The math used was rudimentary, but I found it wasn't necessary to plot a big ol' graph to illustrate the point.
Originally Posted by mikegarrison,Aug 24 2005, 01:08 AM
Thanks, I had forgotten that one. No wait, I hadn't.
F does not just come from nowhere. Nor does it come from the gears. It comes from the engine.
There's nothing I can even say to this other than the fact that you're wrong. When you determine the FORCE that moves the car forward (the rotating force provided by the wheels, causing a linear force or forward motion) you use the gearing as part of the equation. So, increase the gearing (the final drive in this case) and you increase the acceleration, since mass remains constant.
you can then take this and plot it out for the entire rpm range using the torque curve provided.
then plot the shift points.
now you can plot the entire mph range all the way to the top of 6th gear. do this, and the area under the curve on this graph, will be greater under the 4.57 car than the stock 4.10 car.
as for how "big or small" you consider this difference to be is all in your own perception.
to me, 6 car lengths at 100mph is a significant difference.
The second thing we need to know, aside from the fact that high axle ratio -> more gears -> more time in powerband, is whether or not accellerating in a single gear is faster with a higher axle ratio. A range of MPH common to both 4.10 and 4.57 is 43 - 58 in second gear. The accelleration you will see at this range is dependent on the torque driven to the wheels. Given the fact that the wheels are the same, the difference between the two cars is 9.72 stock, and 10.84 with the 4.57 gears. In the stock car, this range is between 5800 RPM and 8000 RPM. In the 4.57 car, the range is between 6400 RPM and 8900 RPM. It's safe to say that the total torque produced by the motor is going to be greater in the 4.57 car. This is multiplied by the higher gearing in the 4.57 car, giving you even greater accelleration.
That overstates the advantage, because some of the time the car with stock gears will be in a lower gear. The car with the 4.57 will never be in a lower gear. In all cases, when the car with the 4.10 is in a lower gear, it actually has the torque advantage.
So you have to subtract the time when the 4:10 has the torque advantage from the time when the 4.57 has the torque advantage. When you do that, the differences close up quite a bit, and you get only a small change.
ok so I as asked to make another one of these graphs showing effective torque as a function of MPH. THe results are interesting and not quite as dramatic as I expected.
that said if you compare the two curves you will see that the 4.57 geared car has a greater torque advantage on average than the MY00-03 without gears(ignoring about 150 which is drag limited anyway)
08-23-2005, 10:43 PM
