The tires on my '93 are worn out and I was thinking about getting Yokohama ES100s. I have the seven spoke OEM alloy rims. ES100s don't come in 195/55-14, so I was considering 195/60-14s instead of the stock
185/60-14s. The advantages are 0.6 inch wider tread and 2% lower revs at interstate highway speed; the disadvantages are slightly greater unsprung weight, 2% less acceleration, and maybe they wouldn't fit the wheels as well as 185s. What is your advice?
Alas I'm not sure. I've been thinking about this for a while trying to figure out where I got this sure intuition that a lower gear ratio (fewer revs per mile) gives you a proportionately lower rate of acceleration. I haven't ever done the math. Maybe it's what you might call "muscular intuition" based on riding ten-speed bikes, where the only way to pick up speed uphill at all is to shift to a higher gear ratio (more foot pedal revs per mile).
Well you're a physics guy, isn't that right, acceleration is linear with rear-axle torque divided by the radius of the tire? (Shows how long it's been since I did any physics, that I'm so uncertain I have to ask.) So with a lower rev per mile ratio wouldn't you accelerate more slowly, though to a higher top speed?
I'm not so sure that's correct. In fact, the force applied by the road to the axle through a smaller tire produces less of a lever arm, so the force required to overcome this (and therefore propel the car forward) decreases.
True. But average rear axle torque might be higher with the bigger tire.
The key to understand acceleration is not torque, but power. If the gears are extremely closely spaced, and correctly used, the smaller and bigger tires have exactly the same acceleration. Both cars will be operating only at the rpm of maximum hp, and in fact differences in gear selection will exactly compensate for the difference in "wheel gearing".
If the gear box is not continuously variable, it depends on which tire has the most advantageous average gearing at a given final speed.
At equivalent points in the acceleration process, the bigger tire has the engine going slower. That is bad in the first part of the power curve, where power goes up with rpm, but good at the end. This is especially so when the smaller tire needs to shift to the next gear.
In still other words, a smaller tire in second does obviously not have an gearing advantage over a slightly bigger tire in first. And even in the same gear, the slightly smaller tire does not have an advantage past the power peak, since the lower engine torque more than voids the gearing advantage.
Wrong. Axle torque does change with tire size unless *engine speed* is held constant. However, at fixed engine speed, the car with bigger tires would be going faster. Comparing torque is now unfair, because at higher car speed, more power is needed to get the same torque.
Note that above, I compare them at the same *car* speed, which makes all the difference.
Power characteristics of human muscle and engines differ, I believe. I seem to remember that muscle primarily are concerned with the force, not power, they provide.
I forgot the top speed issue in my other post. If your Miata runs out of puff *before* the power peak, and you want more top speed, you want to go to slightly *smaller* tires. This makes the engine run faster at that same speed, hence produce more power. Which means you now have some power to spare to go even faster.
After the power peak, you want slightly bigger tires. Don't really know which one is the case for the Miata. Also, gearing has changed with the generations, so what applies for one year may not for the other.
You are correct. Basically, a smaller wheel is (in this regard) the same as using a higher final drive ratio. At a given wheel speed, you will have slightly higher rpm, thus more power. That is, until: (a) you have passed the peak power pt (but in the Miata, you're pretty much at redline already) (b) you have to upshift because you've redlined. Now the larger wheel would have the advantage since it stays in the lower gear, is now at higher revs, makes more wheel torque, road force, and (synonymously, to avoid hp v torque debates) more power.
I think generally you come out ahead in accel with the smaller wheel (or higher FD), but not by as much as some might first think. And yes, you may lose out in top speed. But that's sort of for magazine racing.
That is what I already said in my post that you cut, yes.
Ah yes, I forgot about the possibility of getting stuck at the gap between the gears. You are right about a somewhat bigger wheel then being an advantage. Though the real answer, if you really want that sort of speeding tickets, would be to go to a smaller wheel, (or rather, final gearing change equivalent to a smaller wheel,) so that the top speed would now occur at the power peak of the highest gear. This will both give you the maximum top speed available, as well as space the gears more closely, which tends to be an advantage.
But while I have always maintained that hp and torque are
*mathematically* synonymous, it is somewhat awkward to describe a *power peak*, which plays a crucial role in all of this, in terms of torque, not? "Top speed will increase for a slightly smaller wheel if you are before the point where the torque curve *tangentially* meets, rather than crosses, the hyperbola y = C/rpm for some positive real number C."
Debates or not, hp is essential to understand, (rather than just mathematically derive, which can always be done), issues like this.
It is certainly plausible that the slightly smaller wheel will have some advantage at most final speeds. And certainly before the power peak in first, the smaller wheel will have a clear advantage. The bigger wheel can only get it back beyond the power peak and mostly after the upshift to two for the smaller wheel. But this was not the claim made.
I stand corrected :-) His last bit about "to a higher top speed" is incorrect. Is that what you referred to? The rest is, to the best of my knowledge, correct.
I didn't cut it to imply you were wrong. Just to save space. Hope this wasn't misconstrued.
Yep, set gearing/wheel size/whatever such that peak power occurs just at Vmax. But Vmax will be a fcn of temperature, altitude, grade, headwind, top up/down, sample variation, etc. So in theory doable, but in reality not.
And make for some painful freeway cruising (higher rpm).
I agree. A 2% change in wheel size (or in FD ratio) will not result in 2% faster accel across the board (ie, to every speed). It'll be less improvement than that. But it can be shown that it'll lead to faster accel, excepting when the 0-x is such that the x requires the additional upshift. Right?
Um, no. "Acceleration is linear with rear-axle torque divided by the radius of the tire" does not imply "with a lower rev per mile ratio wouldn't you accelerate more slowly", and in particular the
2% slower acceleration that is being defended.
Well, you say that the claim that I argue against is correct, implying that I must be wrong, cut out my reply, and then give an (equivalent) answer yourself. Just making sure the record is straight. :)
Well, you could average to ensure that most of the time you are using most of the power at top speed. But I would guess Mazda would think that top speed is of little concern to most of their customers, who live with speed limits, or do not have the miles of clear road to actually achieve it. Most posts that I seem to see here are "I wish they could cut down on those highway rpm", not "Why the heck did they gear it so that I have power left at top speed?" (Never seen one like the latter, actually, after all these years of reading this group.)
Personally, I can't say I worry much about engine rpm. Using 4 or 5 on the highway is pretty much the same to me.
What I really hate is the deafening noise from trucks passing by on the Interstates. Enough to take my arm off the door and close the window.
Miatas should not be on Interstates.
I would agree. In particular, I would think you would do better
0-60 if you would not have to shift to 3th just before getting there. Unfortunately, simple theory does not say; you would need to put a power or torque curve in a program and compute. Common sense however says that the gearing differences will mostly average out, (unless you stop at the power peak in first,) and there will be little difference, just as you said earlier.
Hmmm. We agree on the first part, accel=torque/radius/mass, right?
On the second part: At fixed engine rpm and torque, same gear ratio, with 2% smaller radius, you have 2% more force at road, thus 2% greater accel, right? So, lower mile per rev = greater accel (inverse of what he said, which also holds), right? Basically, it accelerates faster since it is making the same power, but at lower speed! (accel=power/velocity/mass)
This is, again, all provided that we are within the rev range (ie, haven't had to upshift the smaller tired car yet). It won't hold for the entire 0-xx since then you have to add the interval where the larger wheeled car is in the better gear. Plus potential added shifts.
Are we disagreeing?
Okay, just trying to make it straighter :-)
Yep, I would never speed! Seriously, that's why I said it was "magazine racing". Top speed to me is essentially irrelevant. Well, above say 150 :-)
I'm one of them. To me, if a car has 6 gears, then why not make the last very long-legged. No Miata (or S2000 for that matter) will see 6th gear in a race. So why keep it close-ratio'd? I guess in part to keep some modicum of accel in gear in highway conditions. Me, I'll downshift. Or if I want to have that feeling of accel on tap, I'll leave it in 5th. It's a matter of taste, but I think the 6th gear choices on the Miata and S2000 are poor. IMHO, 6-speeds are more about marketting than anything else.
I have occasionally grabbed for 7th.
I've been finding detours a lot more often than pre-Miata, but still on a 200+ mi drive to visit family, I'll spend roughly half on the interstate. And I admit to raising the window. At least the top is still down!
Definitely. Loses a few 10ths. But that's all magazine racing too. Alas, it is what we tend to focus on.
My thinking is that it benefits 1st gear, loses a bit on the shift, then is mostly a wash. If you took an idealized flat torque curve, and ignored shift time, I'm pretty sure you could come up with an easy analytical solution that, I think, would show an asymptoting decreasing 0-xx time with FD ratio. But it would be pretty flat at higher FD's. But yeah, you have to figure in real curves, shift times, drivetrain traction...
But in general, do not drag racers generally increase the FD for better times? Up to a limit, obviously.
I can nitpick. :) Before the torque peak in first, the loss in acceleration will actually be a bit more than 2%, because the smaller tires have the engine spinning quicker. And you did not include the (small) part in first beyond the power peak as being one won by the larger tires. All these will be small effects for a Miata, obviously.
Hum. When I was even younger, cars with far less than 100 hp did not run such rpm at a lot higher highway speeds. I am guessing the problem is that it would destroy the sports car image to have a "cruising gear".
Well, with more closely spaced gears, you can squeeze just a little bit more average power out of an engine with a peaky power curve. I guess that might be particularly true for the S2000, though I have not seen a power curve for that car.
I admit I have grabbed for sixth on my 5 speed.
It might be a little bit messier. Taking asymptotes, your top speed would contract to zero, for example, or you would need to add more and more imaginary gears.
Actually, startup might be the real difficulty. What do you assume? That the slipping clutch is producing a given torque? That the wheels provide maximum trust?
Don't know. Drag racing is a funny area of technology. I am still trying to figure out how they can get far more traction than the textbooks say rubber tires can produce. I have been told they burn the rubber in the asphalt on the trial.
On Fri, 25 Jul 2003 00:21:15 GMT, snipped-for-privacy@zmiata.net (Leon van Dommelen) wrote in news: snipped-for-privacy@4ax.com:
Eau Rouge at Spa produces 4g according to the BAR circuit guide. F1 does not produce the highest cornering forces. Some of the non-open-wheel formulas will be higher.
Of course those forces are the result of downforce at high speed.
I think Leon's example was for grip off the line, no downforce. Eau Rouge could be upside down and the F1 cars would still stick to the track at speed.
Exactly. I was talking about tire performance. Maybe a drag racer can pick up some aerodynamic down force near the end of the run, but it can hardly be three times its weight, let alone what is needed to compensate for lack of traction at the start of the run.
Like I said, it can obviously be done, it is just not obviously to me exactly how.
I dunno, Leon. Last time I paid any attention to drag racing--a couple or three decades ago--only elapsed time and trap speed were measured. Actually, the only thing that mattered was crossing the finish line before your opponent. Each run is a separate race unto itself, and while times may be interesting, they don't determine who gets the big trophy at the end of the day: it goes to the winner of the last elimination match. You see, the clock starts when you cross the start line...but if you react slowly, your opponent will leave first, and you could lose the race despite a lower elapsed time and higher terminal speed.
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