optimal acceleration trough gears...academical question:

[beepbeep]

OK, i'm in a dispute with few car-guys over certaing things concerning choice of optimal revs to shift at.

Air drag is not in in the equation.

I believe that you need to shift in that way so that sum of areas under torque-curve under accelleration in every gears is as high as possible...

Other guy believes that you should shift so sum of areas under power-curves should be as high as possible.

I'm basing my statemet on the fact that acceleration in a gear is strongest troughout rev-range where torque is highest for the engine. (and thus torque at wheels is highest), and we want max sum of sustained accellerations trough every gear to achieve .

Be aware...this is inflamatory topic that easily degrades into flame-war...so argument with caution.

Thanx!

[930fan]

The way I understand it, a car with 200bhp and 175tq and an identical car with 200bhp and 140tq will accelerate and max out at the same speed provided that they are both optimally geared to their power curves.

Power is a measurement of rate of work done therefore you would want to keep the engine in the area where it gets the most work done so you should shift according to the power curve. I usually shift when I feel the power tailing off in a car. With a standard 930, that would be around 6000rpm.

I also find that the 4sp 930 is better for 0-1km races than a five speed. One less gearchange saves you 0.5-0.8 seconds plus the longer ratios keep the engine under load better so it produces boost better.

[beepbeep]

OK.

Of course, one should shift directly after power-curve begins to tail off.

But this question is not tied to any specific car but a quest for general formula for calculating shift-points for best acceleration trough gears...

[autobonrun]

I was thinking the same thing. If you look at the torque curves, you should be shifting where the curve drops off, somewhere between 4800 and 5500 rpm. However, I regularly accelerate up to red line before shifting during quick sprints. Also you see questions about rev limits. Under this scenario, one should never even reach red line through the first four gears and only in 5th (on the track of course).

[beepbeep]

Let me put few things straight before we dive deep down inte the subject:

Lets assume there is no aerodynamic drag and that shifting takes zero time.

How should i calculate my shift points to achieve best accelleration?

My idea is to arrange shift-points so "swept" area under torque-curves is as high as possible. That's beacuse we want integral of wheeltorque vs. time to be as high as possible and that integral is directly proportional to engine-torque integral i mentioned earlier.

Ideas?

[NYSCAR]

Well i think in theory, if your shift times take 0 seconds, you would have infinite gears that keep your rpm to an infinitely small sweep over your torque peak In reality we all know that shifting (especially with our older trannys) takes a *significant* amount of time. The idea is to get maximum acceleration, maximum torque. Ideally if shifts weren't an issue, we would hold revs at peak torque - but they are. So we try to gear the car so that the rpm range (assuming we're talking about winding the thing out) you're using is in the fattest part of the torque curve. That's why small displacement high output engines usually need close ratio trannys with a steep 1st gear, because typical 'beefy part' of the torque curves for these engines are high up and narrow (thus we need gears close together to sweep a narrower part of the rev range). 1st gear is to get you up there, and the close gearing keeps you up there. 930's can get away with a big wide 4 speed because they have very meaty torque curves (once the turbo spools). So I guess sweeping an rpm range during acceleration is a 'compromise' (unless you have a perfectly flat torque curve) because we can't shift infinitely fast. You want the highest average torque swept over an rpm range, without narrowing the swept range too much so you have to shift so often you hurt your acceleration times. Hope that all makes sense

Brad

[dickster]

i'm no expert but is max power (hp) the point??

gearing to stay around the power band = fastest acceleration??

five close gears will be quicker than 4 wide gears, thats how i understand it

example: london bus, it has shedloads of torque yes?? gear it to stay in that peak torque area, it going to win any 1/4 miles is it??

i'm still trying to get my head around the whole torque/hp issue

a bike has loads of hp but not much torque - it doesn't need alot of torque because its relatively lightweight??

[RarlyL8]

Torque and horsepower curves are only part of the equasion.

Vehicle weight, gearing, and type of tranny are equally important.
I used to do a lot of dragracing (the legal kind). You shift with two things in mind:
- peak horspower RPM and
- RPM drop after the shift
Ideally the shift should be made just beyond peak HP is achieved, and the RPM drop should put you right in the meat of the torque curve.

[Leland Pate]

I have no idea of what you guys are talking about.

[dickster]

RarlyL8 - thats how i understood it - so how does torque fit in??

Leland Pate - LOL - i'm just blagging

[rob911]

Theoretically I don't know my ar** from a hole in the ground.

Still here goes.

Maybe it is optimal to shift at peak torque, however the next gear ratio might drop the engine revs too low down the torque curve. This will cause the car to "bog". especially in a 4 speed AND a turbo.
So shift at approx max power and the next ratio should be right in the meat of the torque curve.

the weekly UK magazine Autocar publishes graphs with their "feature reports". These show the torque and power curve, with the gear ratios overlaid. For the gear ratio portion the x-axis is speed and the y-axis is RPM (I think). This looks like a series of overlapping triangles.

This should allow you to calculte the RPM of your NEXT gear, which might help to decide optimum shift point.

I just rev the nuts off it once it is warm Love the sound/feel/speed/sound etc. I believe it helps stretch the conrods or something (that's my excuse to the wife)

It also sounds great with the top down, ripping through 4000rpm (did I mention that already?)

[jluetjen]

I'm not going to delve into HP/Torque because I think that we just beat that to death a week or so ago on a different thread. Conceptually in performance driving, you want to shift in such a way that you are always accelerating the car as fast as possible.

As a rule of thumb, that usually means you should shift a little bit after the engine puts out it maximum HP (generally fairly close to the red line) into a gear that is at or above the engines maximum torque. So the engine always stays above the maximum torque point and below the red-line. If you want to be more precise and scientific, here are a couple of alternative methods. Both of these require that you know the detailed numbers behind your engine's HP numbers, usually from a Dyno sheet or if you are clever; intermediate times on a 1/4 mile. I'll assume that you know your torque and HP at specific increments for your motor. You also need to know your rear axle ratio as well as the different gear ratio choices that you have available.

1) A General Method (Not specific to a certain track).
A) Select a rear axle ratio based on your desired top speed and your available options. It seems that the most common ratio for 911's is 7:31.
B) At 500 or 250 RPM increments calculate the rear wheel torque in each gear across the rev range. You do this by multiplying the engine torque for a specific engine speed by the gear ratio and then by the rear axle ratio.
C) You will want to shift up when the rear wheel torque from the next gear is equal to or greater then the rear wheel torque in the current gear, or you reach the engine's red line.

2) A slightly more specific method is generally used when racing. The same calculations are often used, but a gear chart will do. On the chart, draw a line at the maximum torque point, this is the lowest that you will want to rev the motor. Draw a line at your desired red line. Pick a rear axle ratio and a top gear ratio by the expected top speed for a given track. You want to just be just reaching the red line when you are at terminal velocity on the longest straight. Select your 2nd gear so that you are just above peak torque at the slowest point of the slowest corner. 1st gear is usually only used for exiting the pits or for standing starts. Select the intermediate gears so that they are relatively evenly spaced, you are not shifting in the middle of any of the corners on the track nor are you dropping the engine out of the desired rev. range. Once you have done this, you generally have a fairly close set of ratios with a gear for every corner.

[island911]

"I'm not going to delve into HP/Torque because I think that we just beat that to death a week or so ago on a different thread. " by jluetjen

That *is* exactly where the misunderstanding starts. So I'll just add that bit to jluetjen's excellent post.

torque is static, Power is dynamic. That is, Power speaks to just how quickly the torque is applied. You may have more torque in the mid range, but it can't be applied as quickly as in the higher revs.

Sorry, I think the "Other guy" hit the nail on the head by saying; that you should shift so sum of areas under power-curves should be as high as possible.

[Early_S_Man]

John is very close to being right, but you need a VERY ACCURATE torque curve for the engine in question, and it should be in 50 rpm or 100 rpm steps! You also need a speed vs rpm chart for the transaxle and tire size on the car you are speaking of!

There is a 'calculation' involved ... and it is probably best done in a spreadsheet which has the gearing, tire, and torque curve data. What is calculated ... is 'thrust' available at the driving wheel. It is calculated by multiplying the torque available at a specific rpm level by the radius of the driving tire in feet ... and if you do an XY plot for all of the gears, look at the available thrust at the next rpm step, and if the thrust available in the next higher gear is higher than the thrust avalable in the current gear, then that is the correct shift point.

The selection of the shift point rpm is simply made graphically by comparing the thrust available that is declining in the lower gear, and comparing it to the rising thrust available in the next higher gear. The shape of the thrust curves follows the shape of the engine torque curve!

[930fan]

5sp are better than 4sp in 99% of situations because it gives you more options when entering and exiting corners so that the engine can be kept "on boil" i.e in the meaty part of it's torque curve. They also give you a much wider spread of ratios so that you can have acceleration and top speed. However, in a straight out drag race to say 160 mph, a 4sp will be quicker than a five because of that one less gearchange esp in a 930 since the engine always takes a moment to recover boost between shifts.

As for when to shift in a car, the ideal and most accelerative way is to keep the revs between peak torque and peak power. So I guess your friend is right.

[Clark Griswald]

Originally posted by beepbeep

Other guy believes that you should shift so sum of areas under power-curves should be as high as possible.

Your friend is correct, max out area under the power curve.

Originally posted by beepbeep

I'm basing my statemet on the fact that acceleration in a gear is strongest troughout rev-range where torque is highest for the engine. (and thus torque at wheels is highest), and we want max sum of sustained accellerations trough every gear to achieve .

You are forgeting that the transmission is a torque multiplier. Max torque at the engine is not the same as max torque at the wheels. This is the key to your answer.

A numeric example might help.

Imagine a hypothetical engine with a flat 100 ft/lbs torque from 3000 rpm to 6000 rpm. The trans has two gears. 1st gear is 2:1, 2nd gear is 1:1.

The car can be driven wot at 3000 rpm in 2nd gear and will be applying 100 ft/lbs of torque to the rear axle (neglecting drivetrain losses). The same car can be driven wot at 6000 rpm in 1st gear at the same mph and will be applying 200 ft/lbs of torque to the rear axle.

In both cases torque at the crank is the same. But torque at the drive axle doubles at 6000 rpm when the proper gear is selected to stay in the POWERBAND (not the torque band).

hp = torque X rpm / 5252

So in this example the engine is producing twice the HP at 6000 rpm as it is a 3000 rpm, applying twice the torque to the drive axle due to torque multiplication, and accelerating the car twice as hard.

This is why HP is the correct indicator.

[87 slant nose]

i,M NOT BYE ANY MEANS AN EXPERT BUT IF YOU HAVE A DYNO
NUMBERS FROM YOUR ENGINE I WAS ALWAYS TAUGHT TO SHIFT
AT PEAK HP RPM AND IF YOUR CAR WAS GEARED RIGHT THE NEXT GEAR WOULD BE RIGHT AT YOUR TORQUE PEAK FOR MAXIMUM
ACCELARATION. JMHO!
KEITH

[orbmedia]

This is definately an engineer's discussion.

You want to maximize the torque to the rear wheels, and this is acheived by sweeping out the best area under the power curve.

The key is the units:

HP has units of Force * velocity

The area under the Power curve has units of HP*time (X times Y axis)

OR Force*distance, or torque.

Maximizing the area under the power curve gives you the best torque.

[NYSCAR]

example: london bus, it has shedloads of torque yes?? gear it to stay in that peak torque area, it going to win any 1/4 miles is it??

well it might, depending on what you're racing against (i.e. an improperly geared london bus).

Brad

[beepbeep]

OK, i lived in impression that wheel-torque from a engine that has perfectly flat torque is also constant...albeit engine is disipating more power at higher revs, but *torque* at wheels from a perfect 100Nm engine geared trough 1:2 tranny will be constant 200Nm troughout rev-range....and car would accellerate at constant rate.

Accelleration in *any* gear will be best when reving trough range where engine-torque is reaching it's peak...that's why i believe(d?) that max accelleration trough gears would be sustained when sweeping trough highest sum of areas outlined by torque-curve ... in real world with real-world transmissions this would mean that you *would* actually shift somewhere around power-peek...and i'm *not* disputing about that...it's a fact that you should shift just after power-curve starts to fall...

It's just a purely academic question of calculating optimal shift-points that puzzles me.


I would do it this way: (being a Newton-rapson numeric guy)

I would enter exact torque-curve into my computer, wheel-radius and car mass.

Then i would simulate flat-out runs with perfect shifts starting at 4000 rpm and moving upwards in 100 rpm- increments.

Having all factors (and we can discard shift-times as they will not alter accelleration-times in non-linear fashion) i could calculate accelleration times for each shift-point and plot it into a graph.

On the end , we would get a parabolical-curve with peak at optimal revs.

Then (to make things more complicated), we could add a concept of aerodynamic drag which grows with quadrat of speed...

This would probably move shift-points upwards at higher speed...


Am i completly off the track here??