KirklandM5

Ok, with all this talk about gearing and drag racing...It's now time to turn our attention to OPTIMAL SHIFT POINTS!

The idea here is to "maximize area" under the hp curve...(an integral for calculus types!)

Ideally, this means hp before and after the shift is EQUAL!

This is not always practical because:

the spacing between gears may be too large AND the rev limiter does not allow the engine to reach the optimal shift point!

Based on our earlier discussion we realized that maximizing acceleration meant MAXIMIZING HORSEPOWER sent to the wheels...

So what this mean? Let's look at the horsepower chart again....(540i non Vanos and M5)



HP peaks at 6600 rpm for the M5 and is basically flat until the rev limiter kicks in at 7000 rpm.

Ideally, if we had custom super close ratio gearing we would shift at 7000 rpm and the rpm in the next gear would be 6600 rpm.

This way we would maximize the available horsepower.

I've done a spreadsheet on the M5s speed vs. rpm for each gear...

From what I can tell...the optimal shift points for each gear is 7000 rpm for stock s/w.

With Dinan S/w letting it out to 7300 rpm is a good idea except for the 5-6 shift.

Since, the motor cuts out at the rev limiter you really don't want to hit it because you interrupt the power...

Let's test this out...

Consider the 1-2 shift. 1st gear is a low 4.23 gear and 2nd is 2.53.

If we shift at 7000 rpm = 40 mph, the new rpm after the shift is 4200 rpm.

This means hp at the wheels goes from about 330hp to 255hp before and after the shift, respectively!

Since hp drop before and after shift is so big it means that the gear spacing is too wide to be optimal OR the rev limiter kicks in too early!

Let's consider "short shifting" ie. shifting early. Now let's shift at 5000 rpm. HP at 5000 rpm is 300 at the wheels = 29mph. After the shift we'd be at 3000rpm or only 170 hp at the wheels.

By short shifting...We never use all the horsepower available in 1st gear AND HP after we shift is also lower!

In a HONDA S-2000 with a 8900 rpm redline and peak hp at 8200 rpm...Short shifting at 5000 rpm results in a 0-60 time of 11 seconds up from about 5.5 doing it right!

Let's look at Ben Treynor's dyno chart with Dinan s/w at: http://www.treynor.com/M5_Mods.htm

Looks like Ben's Car makes about 325hp AT 7300 rpm.

If we shift at 7300 rpm from 1-2 we're at 42mph and 325hp.

After the shift we're doing 42mph at 4200 rpm or about 265 hp.


Note that this is slightly better than shifting at 7000rpm!

Below: I detail optimal shift points for 7000 rpm cutoff and 7300 rpm cutoff.

Assumptions: Gears 1-6: 4.23, 2.53, 1.67, 1.23, 1.00, 0.83, 3.15 Rear End.

1-2 Shift
7000 rpm Shift Point (40mph) HP Before: 330
HP After 255 at 4200 rpm.

7300 rpm shift point (42mph) HP Before: 325
HP After: 265 at 4400 rpm.

7300 rpm shift pt is better as we pick up 10 hp after the shift!

2-3 Shift
7000 rpm Shift Point (67mph) HP Before: 330
HP After: 275 at 4600 rpm.

7300 rpm shift point (70 mph) HP Before: 325
HP After: 290 at 4800 rpm.

3-4 shift:
7000 rpm: 101 mph, HP Before 330, HP After 305 at 5100 rpm.

7300 rpm: 106 mph, hp before 325, HP after 315 at 5400 rpm.

NOTE: How the hp drop after shifting is narrowing AS Gear SPACING GETS CLOSER!!

4-5 Shift:
7000 rpm: 137 mph, hp before 330hp, HP After:
317 hp at 5700 rpm.

7300 rpm: 143 mph, hp before 325, HP after: 320 hp at 5900 rpm.

5-6 shift: (I assume engine has hp to achieve these speeds, Big IF!)

7000 rpm: 169mph, hp before 330 hp, HP After: 328 at 5800 rpm.

7300 rpm: 176mph, hp before 325hp, HP after 330 at 6050 rpm.

For the 5-6 shift 7300 is NOT more optimal because hp is greater after shift than before.

The 5-6 gear spread is the narrowest in the gear set...And basically would allow us to keep the engine in the flattest portion of the hp curve!!! Too bad wee need to be going SUPER GONZO SPEEDS to test this!!!

JL

greg

Kirkland - I'm confused. Wouldn't best accel be to maximize the area under the torque curve? To quote from http://www.vettenet.org/torquehp.html,

In his article he goes on to explain why HP is important, but I THINK (if I am interpreting it right) he would claim shift points should be chosen to deliver the most torque.

Can you clarify?

AndyMenard

All,

I would agree with Greg on this. I always shift my car to optimize torque delivery, hence I very seldom make it to redline in my BEAST; except for an occasional slip in first gear that is...

I have always been a believer that if you go past the point where the torque curve starts to fall off, you've gone too far?.. Just my personal preference however...



------------------
Andy

2000 Imola M5 / Black Nappa - Titanium Trim

KirklandM5

Ok guys...Let's go for drag race...I'll shift at 7000 rpm...you can shift at the torque peak at 3700rpm.

We just did a big thread on how hp to the wheels is what we're looking for...so shift accordingly!

Greg: If you read the article you refer to...it compares the 245hp L98 Vette vs the 300hp LT1 Vette...Both have similar PEAK torque, but the LT1 maintains the torque to a higher RPM level...IT MAKES MORE POWER because of this...

In Essesnce you are following the torque curve, but the engine is also making more power too!

KirklandM5

Not sure if you read my entire post...it was SUPER LONG...He're a quick excerpt examining the 1-2 shift:

Consider the 1-2 shift. 1st gear is a low 4.23 gear and 2nd is 2.53.

If we shift at 7000 rpm = 40 mph, the new rpm after the shift is 4200 rpm.

This means hp at the wheels goes from about 330hp to 255hp before and after the shift, respectively!

Since hp drop before and after shift is so big it means that the gear spacing is too wide to be optimal OR the rev limiter kicks in too early!

Let's consider "short shifting" ie. shifting early. Now let's shift at 5000 rpm. HP at 5000 rpm is 300 at the wheels = 29mph. After the shift we'd be at 3000rpm or only 170 hp at the wheels.

By short shifting...We never use all the horsepower available in 1st gear AND HP after we shift is also lower!

MarcK

I agree with Greg and the excerpt of the article he has posted. In ANY GIVE GEAR, the acceleration follows the torque curve, and not he HP curve. However, I think that Andy's conclusion that "going past the point where the torque curve starts to fall off is going too far" is not correct. The reason is that you don't care about the torque on the crank. What you want to optimize is the torque on the wheels, i.e. you have to take gearing into consideration. The optimal shift point is where the torque on the wheels before and after the shift is equal.

I realize that this conflicts with Kirkland's statement about the HP before and after the shift being equal. So I made the same calculations that Kirkland has made, but with torque instead of hp. It turns out that the conclusions regarding the optimal shift points are virtually identical with either theory:

The numbers are based on the dyno sheet of my own car, which is virtually identical to the one Kirkland has posted (337.1 vs 335.1 hp, 324.6 vs. 323.1 torque). My torque numbers are "normalized" to 1st. gear, ignoring the 3.15 rear end factor, since it is the same for all gears.

1-2 Shift:
7000 rpm: torque from 245@7000 to 192@4200
7300 rpm: torque from 230@7300 to 192@4400

7300 is best shift point.

2-3 Shift:
7000 rpm: torque from 147@7000 to 126@4600
7300 rpm: torque from 138@7300 to 124@4800

7300 is best shift point

3-4 Shift:
7000 rpm: torque from 97@7000 to 90@5200
7300 rpm: torque from 91@7300 to 89@5400

7300 is still the best shift point, but it is getting close

4-5 Shift:
7000 rpm: torque from 71@7000 to 70@5700
7300 rpm: torque from 67@7300 to 69@5900

Here we gain rear wheel torque when shifting at 7300, so we have shifted too late. The best shift point is around 7100. Here the hp and torque approach give a different result, since according to Kirklands numbers 7300 is optimal.

5-6 Shift:
7000 rpm: torque from 58@7000 to 57@5800
7300 rpm: torque from 54@7300 to 55@5900

As for the 4-5 shift, the best shift point is below 7300, around 7100 or 7200. Here the result is the same as with Kirklands numbers.

Make your own decision, whether hp or wheel torque should be optimized. Either way, the optimal shift points are at redline for all gears with 7000 rpm limit. With a higher rev limit of 7300, you still get best acceleration with shifts at redline up to 4th. gear.

Marc

KirklandM5

Mark K: Nice work..., since HP is a function of torque...I'm NOT surprised that our results are similar.

HP (at wheels) = torque (at wheels)x rpm (at wheels)...

Now gears do multiply torque, BUT they also divide rpm by the same amount!!

So-ex frictional losses, hp is the same!! (I've thought about this for awhile!)

So here's the full formula:

Torque at Wheels = (Torque at Crank)x (Trans Gear Ratio) x (rear end Ratio) - (Frictional Losses of DriveTrain)

HP at Wheels=(Torque at Wheels)* (engine rpm)/(trans gear ratio*rear end ratio)

Now if we wanted to maximize area under the torque curve, we would shift at 5000 rpm, and keep the motor in the FLAT portion of the torque curve...See the Chart.

We know that this is not optimal.

MarcK

Kirklan, I'm not surprised either, given the relationship between HP and torque. What I am wondering though, is whether the results are just similar, or whether the results will always be identical, since we just calculate the same thing in a different way.

It all comes back to the torque curve at high rpms. Depending on how steeply the torque curve falls off, the HP will keep going up, stay about the same (as in the M5 engine) or drop. So if you take a variety of different engines with different torque curves, would you get the same optimal shift points if you make the calculation based on HP or wheel torque? Or can you find a (real or constructed) torque curve, where the results are significantly different, in which case there would indeed be a difference between optimizing HP and optimizing rear wheel torque?

tonyo

You almost have it right. You want to shift your car to optimize torque delivery (at the wheels!).

At 7000 rpm in second gear, you still have more torque to the wheels than you do at 4600 rpm after the shift, despite the engine having more torque at 4600 rpm. This is too bad, since we fall out of our power band, but it only gets worse if you shift earlier.

It's always the same. Figuring with HP instead of torque simply includes the already integrated speeds. If you want to work with the two components of HP, torque and speed, you need to remember to use both of them all the time. Whenever you do use both, you have the same thing.

For example, when we shift from 7000 to 4600 rpm, from either the horsepower or the torque frame of reference, the same "reality" is still in effect. This means that torque at the wheels (you must including gearing while in the torque frame of reference) times the speed of the wheels equals the power at the wheels. If you use HP figures, the gearing, other than contributing to choosing the spot on the power curve, simply cancels itself out.

MarcK

Tonyo,

You state that choosing shift points based on torque at the wheels and based on HP is the same. There is one point that confuses me, and keeps me from agreeing. Perhaps you can clear this up.

If I move back from looking at shifting points to just looking at the acceleration within one gear, let's say 1st gear. At 6600 rpm (HP max), I have 337HP at the wheels, and about 260 torque at the crank. At 3800 rpm (torque max), I only have about 240HP, but 324 torque. Comparing torque at the crank is the same as comparing torque at the wheels in this case, since we are in the same gear. So where does the car pull stronger in first gear, at 6600 or 3800? Whatever the answer is, doesn't this mean that either HP or torque at the wheel determines the acceleration? And if so, then doesn't this mean that shift points should be chosen based on either HP or torque, and the fact that both methods give similar results for the M5 just means that the torque curve of the M5 engine (and perhaps most or even all real world engines) are so that the results will be similar?

Where am I going wrong?