FormulaIntegra

You're the resident aero guru, and I figured this might be an interesting topic for everyone, warranting a post rather than a pm.

I've been thinking about final drive ratios for my 1995 ITA EX Coupe (D16Z6). Stock is 4.25; at Auto Club Speedway (the fastest track I've run on), I top out around 120-125mph or so on the front straight before scrubbing off some speed going around the oval. I've looked at the the online gear ratio calculator (http://www.fatboyraceworks.com/gears/) and switching to a 4.9 final drive still keeps me within that 125mph top speed range, albeit in 5th gear instead of 4th.

I know that changing final drive ratio will let me accelerate more quickly via a higher rate of torque multiplication, but those gear ratio calculators don't take aerodynamic drag into consideration, and I just finished re-reading a Honda tuning book including some articles written by a certain E. John Thawley III for a prominent sport compact car magazine back in the day talking about a top speed project in an EG civic that they decided could only happen in 4th gear, as 5th dropped them out of the power band, and further acceleration would not happen due to the inability to overcome aerodynamic drag at that point.

Therein lies my question. I'm afraid of running out of gears on the super fast tracks, and although the calculator says I won't considering the current top speed I'm reaching, will the fact that I'm accelerating at a higher rate reasonably mean I will be at a higher top speed by the time I reach the end of the straightaway? And secondly, how much of an aerodynamic impact will there be on potentially attaining said higher speeds.

My thought is that any car moving through air, with a fixed amount of power (gear ratios won't affect horsepower, but will affect torque), has an ultimate top speed aerodynamically, and changing the rate of acceleration at which one attains said top speed will not affect the fact the the car simply can't go any faster than it's aerodynamics will allow. Will my car simply not go over 125mph in current engine tuning trim, no matter what gearing I have, or do I need to worry about redlining in 5th gear 3/4's of the way up the straight, and furthermore, the Hondata is currently tuned conservatively for endurance racing, and I know I can extract more ponies out of it with a more aggressive tuning, meaning potentially more power to overcome said aerodynamic drag, and therefore higher straightline speeds......

I don't want to spend (alot) of money on several final drives to find out which one is still tall enough for Auto Club Speedway, yet still gives me the acceleration boost I crave for tighter tracks like Buttonwillow. Is there a empirical way to figure out how high is too high a ratio, or should I not take any chances and start with a 4.5 or 4.7 and go from there?

Any of this make sense? Johnny Mac, Help????

RR98ITR

You are overestimating the benefits of gear ratio changes, and possibly overlooking negatives that might arise from changes. Look at how your current ratios match up to the key corners at the tracks you run at. Are you in the powerband as you start adding throttle? Do you run out of gear before you get to any braking zones? Etc. If you're stuck with your stack, and all you can change is the final, and your 5th isn't That tall, then you're talking about very little gain total - maybe a tenth or two. I have painful personal experience with this. I paid good money for a close 4th and 5th from Houseman (my 3rd was perfect where it was). That 5th put me at 8500 indicated at the end of my longest straight. Incidentally the gears broke and alot of money got flushed down the toilet. It was after all that that I modeled my home track using Mitchells software and determined that at most those gears were worth 1-2 tenths.

Think about it - you're not changing your speed leaving corners, your motor has the same torque and power curves, in 5th the aero drag is so exponential that a typical gearing change is going to give a mynoot effect, and beyond that you're really just moving your shifting points around.

Scott, who hates wasting money to not actually go any faster...sometimes you don't know how relatively well off you are already...we always assume there's a solution for the problem we imagine we have...

descartesfool

I did a bunch of modeling using Lapsim on gear ratios and differentials, and came to the same conclusion as Scott. Spending money on gears is a waste of good money that could be spent on engine upgrades, as they will buy you seconds while gear changes will buy you tenths, and will be only better on some tracks and worse at others. Only if you cannot modify anything that makes more power might you want to spend money on gears, and then again, suspension mods would be better. As for aero mods, without real data from a logger, you can increase drag so much with little other benefit, that I would be very hesitant to make too many changes there.

beanbag

I won't speak to the aero aspect, but I'll point out one fundamental misconception you have - that somehow a shorter (or higher number, whatever) final drive somehow gives you more torque and thus you can accelerate faster. Your ability to accelerate is limited by horsepower, not torque, and don't gimme that torque is related to acceleration crap. IF you change the final drive, what happens is that for a given engine rpm, you have more wheel torque BUT you also happen to be moving at a slower speed than before, so it doesn't mean anything.

Put another way, lets assume currently 1st gear tops out at 40 and 2nd at 60. If you get a new final drive that is 20% shorter, you can accelerate 20% faster, but only until you hit 32 mph. Now you are suddenly screwed because you have to upshift into 2nd, while previously you kept pulling in 1st. Now you're accelerating 33% SLOWER than before. From 40-48, you are ahead again, but now you have to shift into 3rd, while previously you kept pulling in 2nd. etc etc. IOW, it really takes horsepower to make acceleration, and you can't get it for free by changing the final drive.

The better way to look at it is to get your engine dyno and plot out the horsepower curves as a function of wheel speed. So basically what you will have is an overlapping series of 5 sawtooth-shaped curves, with each sawtooth stretched out horizontally. Where they overlap is the shift points. If you get a shorter final drive, the entire graph compresses horizontally, but the average horsepower doesn't change much.

What you want to do is look at the speed ranges you are interested in, and see if the shorter final drive will put more horsepower into that range. As for the top speed case, look at the plot at 120 mph and note the horsepower (in 4th gear, I assume?). Now compress everything over horizontally by that 20%, and see if you have more or less power at 120 mph. If more, you can go faster, if less, you will end up going slower.

The only way to get more average horsepower via gearing is to get a close ratio gearbox. This decreases the dips in the horsepower between shift points coz it keeps you in the powerband better.

Edit: I guess a CVT gearbox would also work.

A Blue Lude

This is what I get when I compare a 4.266 (stock US H22) vs 4.71 FD on an old version of my car, which illustrates some of what beanbag is talking about. It's a bit rounded off since it is only based on 500rpm increments, but you get the idea.

http://img203.imageshack.us/img203/9707/finals2.gif

HP against Speed is also a good chart to look at.



edit: 50rpm increments make it a lot prettier to look at, here's a similar comparison (the engine is being short-shifted very hard)
http://img408.imageshack.us/img408/483/finals3.gif

descartesfool

You can calculate acceleration from horsepower? Say I am going 10 mph, and car weighs 2500 lbs, and I have 100 hp. How fast can I accelerate?

beanbag

100HP =75kW
Power = force * velocity
force = 75kw / 4.5 m/s = 16.7 kN
acceleration = force / mass = 16.7 kN / 1100 kg = 15 m/s^2

IF you had a RWD dragster with a CVT transmission, you could accelerate at 1.5g.

If you had a wimpy civic econobox with overly tall 1st gear, obviously less.

This calculation makes more sense if you ask me what's the best possible acceleration you could possibly hope to get (by playing with the gearing) coming out of turn 3 at 60 mph.

Aquafina

iTrader: (3)

The FD doesn't add torque or power, the engine still makes the same and puts down the same numbers (within a couple percent). It won't change your speed at a given point either (assuming corner exit, entry, etc speeds are the same as they were prior to the FD change). What it will do, is allow you to accelerate faster.

FormulaIntegra

It seems I have been outright schooled in my train of thought. It appears that I forgot the cardinal rule of torque vs. speed. Leverage, i.e. shorter gear ratios, increases torque, but at the cost of speed for any given moment of power.

So, shorter gearing means you accelerate more quickly through the gearing, but increases the number of shifts you need to do to get to a given speed, per se, and time is obviously lost during the actual shifting, which potentially negates acceleration gains. I may get to 30mph faster with a shorter gear ratio, but I'm still only going 30mph at that shift point rather than being able to continue to accelerate to 40 before shifting.

I need relook at gearing as a means to keep the ENGINE within in it's POWER BAND, rather than a means to get to a particular speed FASTER. And I need to maximize the engine's power before worrying about anything downstream of that.

On that note, I would have to say, yes, I've found some instances on particular tracks that I feel like I'm in between gears on certain corners. I also know, however, that I'm still behind the curve enough that there's more speed in the car on it's own, and I need to work on my driving skills, and maximizing the car's setup (like Claude said, money spent on suspension upgrades far outweighs money spent on gearing changes) before worrying about changing my final drive ratio.

The simple fact is, there is more horsepower to be gained in my engine, and I need to work on that before deciding if my gear ratios are at their optimum. I guess that answers my original question (funny enough, without Johnny Mac ever piping in), that horsepower will determine my top speed at the end of the straight, not torque or gear ratios, and yes, aerodynamic drag will increase with higher speeds (exponentially, as Scott so rightly pointed out), but more horsepower offsets some of that. Therein lies the compromise.

I was just looking for an edge at the the tracks I'm deficient at. My car outhandles the Miatas and RX-7's (and the odd Protege) at tight, twisty tracks like Buttonwillow, but I was hoping for something that gave me a better shot at the horsepower tracks like Willow, and the main straight at ACS. I guess I need to head to the dyno shop more than anything (and seat time, it's always about seat time, isn't it? lol)

Thanks, guys, for enlightening me. Sometimes it's a matter of perspective, and sometimes it's a matter of experience, and usually, it's a pretty healthy amount of both.

FormulaIntegra

And Blue Lude, those charts are interesting. With the shorter final drive, torque is obviously higher at the initial gear engagement, but falls off more quickly than the taller gearing. Very good food for thought.

It makes me think that my taller stock gearing is more of an advantage at the longer straights, higher horsepower tracks, and that shorter gearing would be more beneficial at the tracks I already seem to have the edge at: the tighter, twistier ones.

beanbag

If I were u, I would do the overlay of the 5 horsepower curves, and see what you can do to minimize the dips in terms of engine mods. Next, you can play around with the gearing in Excel. Probably it would help to decrease the spacing between 3,4,and 5. This is NOT similar to getting a different final drive, because that won't affect the spacing between any of the gears, and won't help the problem of feeling "in between" gears.

With all that being said, it might still be helpful (and easier) to just get the final drive, since it does let you use the close spacing between 4th and 5th. U have to do the analysis to see.

PS: I'm not a big fan of "improving as a driver" crap. That takes time, effort and skill. Too much trouble. Why not sit around and think, and then throw money at the problem?

descartesfool

But therein lies the difference between torque and horsepower at the wheels for the acceleration calculation, and why I put in the velocity in my example. If you use torque, you do not need the initial velocity. You can simply calculate the acceleration at any speed with a=F/m, since you are not stuck with getting F from P=FV. Without the velocity, you could not have found the answer, but with torque you could, at any velocity. You do of course need the wheel radius to convert torque at the axle to force at the pavement.

beanbag

In this context, it is about optimizing gearing to achieve maximal acceleration, and maximal acceleration occurs near the HP peak, not the torque peak. (I know this sounds weird but it's true. Also, I don't want to get into a HP vs torque debate) My original statement was that HP LIMITS acceleration, so all you need to know from your car is a single number (HP) and then you will realize that you can't use gearing to cheat your way out of more acceleration.

In any case, if you wanted, say, maximal acceleration in the range of 50-60 mph, you would do the analysis with HP curve, not torque curves.

RR98ITR

Hold on now FormulaIntegra...you still haven't heard from Johnny Mac...your schooling is not yet complete and your enlightenment not full...

Scott, who needs to seek some additional enlightenment from the guru that inhabits the land of cows and silos...

Johnny Mac

Sorry, but I've been busy working on a car that must make it to round one of World Challenge and I haven't even been able to sign on here until now. I will take a look at the question in depth and give a different perspective to gearing and aero as they pertain to horsepower or torque. By the way, torque drives cars and horsepower wins arguments. Its the torque that arives at the axle that spins the wheel and then the longitudinal force that drives the wheel can be easily computed (F= Torque(axle)/(distance from contact patch to axle centerline)). Horsepower numbers can be used to find torque and vice versa, but really your car's acceleration is directly related to your instantaneous wheel torque, aero and rolling drag, inertia and rotational inertia. Your transmission gearing and wheel diameter will just determine at what car speed will you have a given amount of torque.

beanbag

Since JMac is Busy Doing Better Things, I'll take a crack at the aero part, although you'll have to settle for something I Just Made Up Right Now. Namely that to a first approx, aero drag force is proportional to v^2. However, power loss due to aero drag is then proportional to v^3. So lets assume that right now your car maxes out at 125 mph, and at that point, the engine is making 100 HP. It is the balance point, where the engine HP is totally cancelled out by drag. If you do the engine mods or change the gearing around and get 10 more HP out, then you can now get up to 129 mph, coz (129/125)^3=1.1. IOW, chasing top speed give you pretty small gains.

IMHO, the top priority is to fill in the dips in horsepower, which contribute to your feeling of being "in between gears". If I were in your situation, I would make an excel spreadsheet that has your engine dyno data, and then plots out the 5 HP curves for you, letting you play around with the gearing. You can also very easily add in the aero drag and from that, you can calculate top speed, acceleration time from one speed to another (e.g. 60-90 times), subtract out the shift times, etc etc.

I did find this spreadsheet here
http://www.offroadvw.net/exceldyno/index.htm

which sort of has some of these features, but again, it only shows the 5 torque curves, not the 5 HP curves, so you have no idea how to lay out the gear spacing.

A Blue Lude

Shifting where there is more wheel torque in the next gear or shifting where there is more flywheel horsepower in the next gear gives you the same result either way....you just need more information to work out the former.

descartesfool

Drag racing simulations are good for, well, drag racing.

For road racing, since for any gear setup you come off different corners at different tracks at different parts of you torque curve, you need a lap time simulator. You can play with straight line simulators all you want, but they aren't going to tell you much about your lap time. Try doing it in Bosch LapSim. It's free. It will be much more useful. And by the way, it also does straight line simulations, if you care about those, and you can store engine curves and gearboxes so you can play with it as much as you like. Then come back and let's see how many seconds you can gain on a given engine and track by changing gear ratios.

You can also evaluate different types of engine torque curves, say with all the same area under the power or torque curve, or same average or peak power. That will tell you a little about the effects of aero and how it relates to horsepower and torque in terms of lap times. You can also simulate the effects of aero drag and downforce on the laptime.

So unless you have access to a wind tunnel, spend your money on the engine.

A Blue Lude

Are there any freebie Honda models floating around for that program? It's already got Mosport by default (there's half the battle), but it takes a whole lot of details for the car...which I guess isn't a bad thing.