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Discussion Starter · #1 ·
Optimal shift point analysis is just what it sounds like: identifying the shift points to achieve maximum speed. The premise is to keep torque to the ground at its maximum possible value at all times, because this maximizes the tractive force and the acceleration. I didn't invent this, someone else did - if you disagree with the premise, take it up with them, not me. The analysis factors in the engine torque curve, the gear ratios and final drive ratio, and tire size.

With a E153 transmission the gear ratios are:
75616


Ignore 6th gear. There is no sixth gear in a e153.

Typical characteristics for a race tire - this is a Hoosier A6.
75617


Typical 2GR torque curve (from Alex W. dyno chart)

75618


Let's go ahead and digitize this, but with a twist, of extrapolating tq and HP past the 7200 rev limit, with declining torque and hp - in a minute, you'll see why I did this.

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And these are the data points
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It's elementary to produce a chart showing how fast the engine needs to rev for a given speed in a given gear.
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:Ignore 6th gear. There is no sixth gear.

It's also elementary to produce charts of how much torque the engine puts to the ground in every gear - this accounts for the wheel size and for every overall gear ratio including final drive.

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Again, ignore 6th gear. I keep repeating this because I know that someone is going to get hung up on 6th gear. Ha ha.

Next the columns for speed and torque can be matched to produce charts of torque versus speed in any gear .

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Now the idea is in order to maintain maximum acceleration, you have to maintain the maximum torque at any speed. So you hop-scotch from one gear to the next - in other words, shift - where the torque produced in a given gear becomes less than the torque produced in the next gear. This gives the shift points - with a little bit of programming magic

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And with a little bit more magic the shift points can be overlaid on the speed vs rpm chart.
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Do you see what I see? 7200 rev limit is definitely an improvement over the factory 6400, but 8000 would be even better, even on stock engine, no camshafts.The 2GR wants to be shifted well over 7000 for maximum acceleration.

I wrote this spreadsheet to help my dyno tuning clients develop their race strategies. Shift points change drastically with different torque profiles and boost profiles. The spreadsheet is completely automated and spits out the shift points given the data for gear ratios, tire size, and torque profile. If there is interest, I can make this available on google sheets.
 

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Nice. I did a similar analysis on my car a few years ago to select gear ratios. I've attached the excel files to find ideal shift points below:


Now if only you had the luxury of getting a custom gearset made...

edit: the KAAZ gearset looks like a great match for a 7500RPM redline. And if you need higher speeds, maybe swap in the 3.93 R&P from the Camry. Not cheap. But perhaps more reliable for endurance racing.
 

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Very nice. I would be interested in playing with it a little if you end up sharing it.
 

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Cool stuff.

I'll add that being able to rev an engine out farther typically needs stiffer valve springs to control valve motion, which does tend to affect power everywhere. Additionally, at some point you'll just lose control of the valve. The valve float makes the power really take a nose dive down. That's assuming the bottom end holds up. Friction also tends to build on a 2nd order relationship to RPM, so falling VE + rapidly rising friction makes power tend to fall off much faster than you might guess at lower RPM.

Just putting it out there that sometimes it's difficult to even keep a linear relationship to the power curve up high for anybody thinking of going north of 8k RPM.
 

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Discussion Starter · #6 ·
I am going to test launch this link here. I have tried to protect all but the input cells of the worksheet so it cannot be mangled by users. Maybe you could give me feedback on what access you have, usability, et cetera.

 

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I am going to test launch this link here. I have tried to protect all but the input cells of the worksheet so it cannot be mangled by users. Maybe you could give me feedback on what access you have, usability, et cetera.
Works great for me!

One hint - highlight the gear ratios, rear tire size, and engine dyno cells with a brighter color like this:


Or you could optionally have a macro run at page load to step the user through updating those values.
 

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I found a couple of errors.

The tire diameter calculations references a fixed value for sidewall height, rather than the sidewall height cell just above it. So the speeds don't change with tire changes. Not a huge problem as tire diameter and final drive effect all gears, and so they don't effect shift points vs RPM, just the road speed at which the shift occurs.

Also, where did those E153 gear ratios come from? 1st and 5th match the numbers I have always seen in the past, but 2nd-3rd-4th are all all shorter than what's listed in the BGB.


Your RatiosBGB Ratios
1st3.233.23
2nd2.1421.913
3rd1.5181.258
4th1.258.918
5th.731.731
FD44.285

This is why there is such a large drop from 4th to 5th in your charts. Is that maybe an alternate close ratio set for the e153?

The result is that the new optimal shift points are:

Old Optimal ShiftNew Optimal Shift
1-279758293
2-377238004
3-472437622
4-583597312

Which only further underscores your point that the 2GR needs to be revved higher!

One note, if you don't want to see 6th gear on the charts, just put in 0 for the 6th gear ratio. It throws divide by zero errors in some of the cells, but everything seems to work, and it simply removes the 6th gear traces from the charts.
 

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Typical 2GR torque curve (from Alex W. dyno chart)

View attachment 75618
Worth noting also that this isn't exactly a "typical" 2GR torque curve, as that is from my X-pipe exhaust systems. And while the bulk of the gains from the X-pipe are in the mid range (which don't effect our shift point calculations), the X-pipe also showed gains in the top end starting at about 6500 RPM, and increasing from there. So that throws the extrapolation off as RPM increases. The difference is about 5 ft-lb at 7000 RPM. When I reduce the torque values up there to match what you would expect with a more typical y-pipe exhaust, all of the shift points drop by a couple hundred RPM. They are all still well above the typical 7200 RPM redline, but not by quite as much.

X-pipe vs Y-Pipe:
 

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Discussion Starter · #10 ·
Thanks for checking this out, hope you can get some use out of it.

The tire diameter calculations references a fixed value for sidewall height,
I don't know how this feature got into the worksheet, or how it got out - it's not in my original worksheet, and it is gone now. I've tried locking the working cells of the worksheet so users can change the input values but nothing else.

Also, where did those E153 gear ratios come from? 1st and 5th match the numbers I have always seen in the past, but 2nd-3rd-4th are all all shorter than what's listed in the BGB.
I may have read them off the wrong line in wikipedia or read them wrong entirely or if they are on the google drive worksheet they may have been values someone else using the worksheet put in for a different transmission.

One note, if you don't want to see 6th gear on the charts, just put in 0 for the 6th gear ratio.
I saw that someone did that. Ha ha.
 

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Thanks for checking this out, hope you can get some use out of it.

I don't know how this feature got into the worksheet, or how it got out - it's not in my original worksheet, and it is gone now. I've tried locking the working cells of the worksheet so users can change the input values but nothing else.

I may have read them off the wrong line in wikipedia or read them wrong entirely or if they are on the google drive worksheet they may have been values someone else using the worksheet put in for a different transmission.

I saw that someone did that. Ha ha.
The tire sidewall thing, who knows. It's fixed now because I fixed it. Same goes for the 0 for the 6th gear ratio, I did that. I didn't realize it was letting me save those changes to your worksheet, but I guess that makes sense for shared worksheet.
 

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Discussion Starter · #15 · (Edited)
I did a thing - I made a time slip calculator based on this shift point calculator.

How it works: uses a finite difference calculation to estimate speed, acceleration, and distance traveled stepping in small time increments. This is based on the vehicle characteristics of torque vs rpm curve, gear ratios, tire size, vehicle weight.

It's in beta so it does not have any provision for reaction time, tire slip on launch, or shift delay - but these could be easily added. Also no aerodynamic drag and no rolling resistance - both could be easily added.

I have never seen a calculation of this kind done by anybody anywhere so I believe it is an original concept.

I'd be interested in feedback and comments and how it jives with people's racing experience.

By the way I have no idea whose dyno chart and gear ratios those are.


Colorfulness Rectangle Product Slope Font
 

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Discussion Starter · #16 · (Edited)
I've added the aerodynamic drag force. You can make changes to your vehicle's drag coefficient and cross sectional area and see how it affects the trap speed and ET.

Rectangle Font Slope Line Parallel



PS. I was not specifically looking to do this but this calculation worksheet should be able to estimate the vehicle's top speed where aerodynamic forces (and frictional forces when added later) will be equal and opposit of the tractive foce of the engine.
 

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Discussion Starter · #17 ·
And... i've added a shift delay, meaning, while shifting gears, the car travels at constant speed, no acceleration. Strictly speaking, it should be slowing down because of drag, but this makes the calculation too complex, and does not really add much accuracy. You can vary the shift delay and see the effect on trap speed and et.
 
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