APR versus Stock Power Curves and Optimal Shift Points

[spindlewood]

While I sit on the fence about giving up my warranty at 25k, I wanted to understand how power delivery (torque at rpm) is related to gear ratios and how optimal shift points are calculated. I took the APR graphs for stock versus 91 tune and plotted their numbers for each gear. This is what I came up with:

at-the-crank-stock.jpg
at-the-crank-apr.jpg

When I compared my theoretical numbers against the one Draggy Youtube of a stock 2018 S5, I was surprised at how well my numbers fit the Draggy. When I added in 8% losses (drive train, weight, wind, road, etc), the mph calculations at the shift points were pretty spot on. I know losses vary by rpm and increase with speed, but still interesting how close the mph fit.

In the APR thread, I asked why at WOT you don't shift before red-line, since torque decreases after 5k and you'd fall back to a higher torque band at the next gear. The answer was "gear ratios" and, with the graph, you can see the ending point of each gear ideally just touches the next gear's curve because of this. Not shown on these graphs (wanted to keep it simple), is that if losses are higher at higher rpm (17% at 6500 versus 14% at 5000 according to the APR At the Wheel numbers), it looks like shifting earlier might actually be beneficial (e.g. 6k rpm from 3rd to 4th).

One thing (I think) I learned, is that the At the Wheel torque numbers that APR shares must be a number calculated without the gear ratio but showing losses. The torque I'm showing on the graph is theoretical "true" torque at the wheels due to including gear ratios.

Curious if this is interesting to anyone except me. I'd be happy to post graphs for At the Wheel instead of Crank or share the underlying data.

I know I need to a) get a life and b) just bite the bullet and send in the ECU, which I will soon (read, working on convincing my wife - and myself - this is essential right now).

[OverBoosted]

I'm trying to follow the charts but the torque seems literally off the charts, why is it in the thousands?

All about nerding out on data but did you calculate tire height in addition to the gear ratio when calculating these numbers? I don't believe the 6500 rpm shift point accurately displays the correct max speed (MPH) for the gearbox. (see below)

Numbers I used are:

Gear Ratio
1st 4.71
2nd 3.14
3rd 2.11
4th 1.67
5th 1.28
6th 1
7th 0.84
8th 0.67

R&P 2.85
Tire Height 25.75

[Kondax]

I'm trying to follow the charts but the torque seems literally off the charts, why is it in the thousands?

All about nerding out on data but did you calculate tire height in addition to the gear ratio when calculating these numbers? I don't believe the 6500 rpm shift point accurately displays the correct max speed (MPH) for the gearbox. (see below)

Numbers I used are:

Gear Ratio
1st 4.71
2nd 3.14
3rd 2.11
4th 1.67
5th 1.28
6th 1
7th 0.84
8th 0.67

R&P 2.85
Tire Height 25.75

The original calculations seem to be a bit more accurate. Couple of people have topped the car out low 190s at the end of 7th gear.

[spindlewood]

To derive the Torque formula, I used these two sources:
Optimal Shift Point
How do you calculate torque / power at the wheels? (4th & 6th post down)

Torque
Torque was calculated as follows:

Torque at Crank * Gear Ratio * Final Drive Ratio * Efficiency
For example (using the APR 91 tune at 6500 rpm in 1st gear):

torque = 348 @ 6500 rpm
1st gear ratio = 4.71
Final Drive Ratio = 3.2
Efficiency w/ 8% losses = .92

= 348 * 4.71 * 3.2 * .92 = 4825

Speed
The speed difference between yours and mine is due to my having adding losses at a flat 8% (yours has none).
APR shows 17/4% loss @ 6500 rpm (comparing crank and wheel torque). Using this didn't line up well with the Draggy in lower gears so I stuck to 8%, basically trying to reverse engineer losses based on Draggy observation. Air resistance and other factors at top speed require more sophisticated modeling and this data just isn't available.

To calculate speed, I used:

Tire Diameter = 29.06 inches (255-45/20 tires - I should have used 29.035, but it makes no significant difference in rounded mph)
Circumference = 91.295 inches
Miles per revolution = circumference in inches/ (5280*12)
= 91.295 / (5280*12)
= .00144

To calculate top speed in 8th
8th Gear Ratio = 0.67
Final Drive Ratio = 3.2
rpm = crank rpm /gear ratio
rpm = 6500 / 0.67

mph = (revolutions per hour / gear ratio) * (miles per revolution)
mph = (rpm *60 / final drive ratio) * (miles per revolution)
mph = ((6500/0.67) * 60 / 3.2) * .00144
mph = 262 (you show 261)

At 8% losses
final mph = mph * efficiency
final mph = 262 * .92 = 241

At 17.4% losses = 216
At 25% losses = 197

I appreciate you playing along and giving feedback. I just got the OK from my wife to send in the ECU. So, I can be done playing with numbers and get to the real fun.

[HurrayFive]

This is the most engineered answer to talk yourself into a tune I've ever seen, lol, I love it.

I've got a '19 SQ5, I ran the JB4 for about a year, on map 5 with an E30 blend it rips, 4.4 0-60, and a consistent 12.5 in the quarter. That's about the edge of its capabilities on the stock hardware.

I recently added the APR 91 octane tune (I've always been a flash guy, third APR tuned Audi, but the JB4 has been great on this platform)...you won't be disappointed. With only the 91 tune (granted I still had E30 in the tank), it feels about as quick as the JB4 on map 5 up top, but down low it feels much faster, and is way more responsive. Stacked with the JB4 on map 2 and an E30 blend the car ran 4.1 0-60 on my first try and (probably) a ~12.2 quarter, all stock hardware (except the intake), though that's definitely the limit of the factory intercooler, you heat soak after two runs with the factory intercooler at that power level and can see the car pulling timing in the logs from there on out.

I've done about ~20 total LC quarter mile runs, and the car is consistently 3-4 tenths quicker short shifting before redline. I get the best results letting the 1-2 shift happen on its own, and then shifting around 6250RPM in every gear after that, it's consistently repeatable. That may be different with a larger intercooler that doesn't start to heat soak towards the end of the run, but it's definitely been the case on the stock one. Enjoy the tune!

[spindlewood]

This is the most engineered answer to talk yourself into a tune I've ever seen, lol, I love it.

lol. You got that right. Never having done a true tune before with warranty on the line, it's like standing at the top of a cliff watching the water below, getting up the courage to jump. And I want to know that I will feel it and it's worth giving up the warranty. I had the JB4 for a few months when it first came out. Could only run on Map 2 with my 92 ethanol free. Gains weren't huge and I didn't know about heat soak back then. I got too many codes, some self induced plus it was a pain to remove every time I had to go to the dealer (far more often than I liked). I sold it when I found out a true tune was coming.

I've got a '19 SQ5, I ran the JB4 for about a year, on map 5 with an E30 blend it rips, 4.4 0-60, and a consistent 12.5 in the quarter. That's about the edge of its capabilities on the stock hardware.

I recently added the APR 91 octane tune (I've always been a flash guy, third APR tuned Audi, but the JB4 has been great on this platform)...you won't be disappointed. With only the 91 tune (granted I still had E30 in the tank), it feels about as quick as the JB4 on map 5 up top, but down low it feels much faster, and is way more responsive. Stacked with the JB4 on map 2 and an E30 blend the car ran 4.1 0-60 on my first try and (probably) a ~12.2 quarter, all stock hardware (except the intake), though that's definitely the limit of the factory intercooler, you heat soak after two runs with the factory intercooler at that power level and can see the car pulling timing in the logs from there on out.

I've done about ~20 total LC quarter mile runs, and the car is consistently 3-4 tenths quicker short shifting before redline. I get the best results letting the 1-2 shift happen on its own, and then shifting around 6250RPM in every gear after that, it's consistently repeatable. That may be different with a larger intercooler that doesn't start to heat soak towards the end of the run, but it's definitely been the case on the stock one. Enjoy the tune!

I've been following your posts a long time - especially because you've got the SQ5. Your comments on short shifting corroborate what my numbers predict with the APR tune. Because the losses increase as rpms go up, it becomes advantageous to shift earlier. Shifting from 2nd through 5th, the numbers say the ideal shift is between 6000 - 6200. Seems like you're in-tune with the car (forgive the pun). Awesome numbers. You're pushing the envelope with stacking the JB4 right out the gate. It'll be curious to see "no JB4" runs (and please, even with just straight up 91 gas runs) in comparison so you have a baseline and can see how much each component is adding.

[HurrayFive]

lol. You got that right. Never having done a true tune before with warranty on the line, it's like standing at the top of a cliff watching the water below, getting up the courage to jump. And I want to know that I will feel it and it's worth giving up the warranty. I had the JB4 for a few months when it first came out. Could only run on Map 2 with my 92 ethanol free. Gains weren't huge and I didn't know about heat soak back then. I got too many codes, some self induced plus it was a pain to remove every time I had to go to the dealer (far more often than I liked). I sold it when I found out a true tune was coming.



I've been following your posts a long time - especially because you've got the SQ5. Your comments on short shifting corroborate what my numbers predict with the APR tune. Because the losses increase as rpms go up, it becomes advantageous to shift earlier. Shifting from 2nd through 5th, the numbers say the ideal shift is between 6000 - 6200. Seems like you're in-tune with the car (forgive the pun). Awesome numbers. You're pushing the envelope with stacking the JB4 right out the gate. It'll be curious to see "no JB4" runs (and please, even with just straight up 91 gas runs) in comparison so you have a baseline and can see how much each component is adding.

Oh man, if all you've got is the same 92 that I've got when not blending E, the 91 tune by itself is going to be night and day. I could only run map 2 safely on 92 in the summer with the JB4, I had to add octane booster or blend E to run any of the higher maps. The 91 tune is waaayy stronger than that, you'll def enjoy it.

I've not had warranty issues so far, but I also haven't kept these cars long term (2-3 years avg). '13 A5, '15 S3, and now the SQ were all APR tuned. Flashed them back to stock before dealer visits or a trade in and it's always been fine, never TD1 flagged. Major warranty repairs needed and you're likely SOL, but so far I've not had any trouble. Statistically you're unlikely to encounter any major trouble, but it's always a possibility for sure. ...the tune is just so much fun though 😂

[HurrayFive]

https://youtu.be/NefdJdstVZk

Idea on power with the APR 91 tune + JB4 on map 2, E30 blend. I had my phone on a lanyard around my neck, sorry for the shitty shaky vid, hah.

[OverBoosted]

The original calculations seem to be a bit more accurate. Couple of people have topped the car out low 190s at the end of 7th gear.

You would have to take into account their wheel size and speedometer error to get the true number or have the speed verified by GPS. On paper given the transmission specs and wheel size these are the theoretical speeds it can hit in each gear.

[OverBoosted]

Torque
Torque was calculated as follows:

Torque at Crank * Gear Ratio * Final Drive Ratio * Efficiency
For example (using the APR 91 tune at 6500 rpm in 1st gear):

torque = 348 @ 6500 rpm
1st gear ratio = 4.71
Final Drive Ratio = 3.2
Efficiency w/ 8% losses = .92

= 348 * 4.71 * 3.2 * .92 = 4825

Thanks for sharing those articles. Where are you getting the final drive ratio of 3.2 for the B9 S4/S5? That seems closer to the reverse R&P ratio. The final drive should be 2.85.

https://www.caranddriver.com/audi/s4...4_audi-s4_2018
https://www.iseecars.com/car/2018-audi-s4-specs

Speed
The speed difference between yours and mine is due to my having adding losses at a flat 8% (yours has none).
APR shows 17/4% loss @ 6500 rpm (comparing crank and wheel torque). Using this didn't line up well with the Draggy in lower gears so I stuck to 8%, basically trying to reverse engineer losses based on Draggy observation. Air resistance and other factors at top speed require more sophisticated modeling and this data just isn't available.

To calculate speed, I used:

Tire Diameter = 29.06 inches (255-45/20 tires - I should have used 29.035, but it makes no significant difference in rounded mph)
Circumference = 91.295 inches
Miles per revolution = circumference in inches/ (5280*12)
= 91.295 / (5280*12)
= .00144

255/45/20 won't fit on our cars. The correct aspect ratio would for 20" wheels on our cars is 30, i.e 255/30/20 which would give you a tire height of 26.02"

I appreciate you playing along and giving feedback. I just got the OK from my wife to send in the ECU. So, I can be done playing with numbers and get to the real fun.

Congrats, enjoy the tune!

[Kondax]

You would have to take into account their wheel size and speedometer error to get the true number or have the speed verified by GPS. On paper given the transmission specs and wheel size these are the theoretical speeds it can hit in each gear.

This is on a dyno, but I do agree with you in any other case. I believe you might be correct in that the top end is higher though - I think the TCU is limiting it to an extent.

[spindlewood]

Congrats, enjoy the tune!

Thank you. ECU went in the mail today. Should have it back on Thursday if overnight is really overnight (UPS isn't making promises any more).

Thanks for sharing those articles. Where are you getting the final drive ratio of 3.2 for the B9 S4/S5? That seems closer to the reverse R&P ratio. The final drive should be 2.85.

https://www.caranddriver.com/audi/s4...4_audi-s4_2018
https://www.iseecars.com/car/2018-audi-s4-specs

255/45/20 won't fit on our cars. The correct aspect ratio would for 20" wheels on our cars is 30, i.e 255/30/20 which would give you a tire height of 26.02"

I didn't realize the S4 and SQ5 could have a different Final Drive Ratio and tires. I redid the numbers with the correct S4 ratio and tires. The results are almost identical (of by 1%). Not surprising as Audi changed the drive ratio to match the tire diameter proportionally. Makes sense.

-------- Tire Diam / Final Drive Ratio
SQ5 -- 91.216 / 3.2 = 28.51
S4 --- 81.744 / 2.85 = 28.68

Good to see how this works. Six months from now, I probably won't remember any of it. I'll just enjoy the ride.

[OverBoosted]

This is on a dyno, but I do agree with you in any other case. I believe you might be correct in that the top end is higher though - I think the TCU is limiting it to an extent.

Confirmed today 1st-4th are accurate based on the gear chart i provided. Performed the test in manual mode and let the car up shift at 6500, 1st 37 mph, 2nd 55, 3rd 82 and 4th 104. Still curious about those that have tested on a dyno only reaching low ~190, is this a limit by the tcu or speedometer error?

[spindlewood]

Confirmed today 1st-4th are accurate based on the gear chart i provided. Performed the test in manual mode and let the car up shift at 6500, 1st 37 mph, 2nd 55, 3rd 82 and 4th 104. Still curious about those that have tested on a dyno only reaching low ~190, is this a limit by the tcu or speedometer error?

It makes sense that the original numbers fit since mph isn't tied to torque output. I've removed the losses from impacting mph and it agrees with your numbers.

I would guess top mph is being limited by the power loss from friction and wind drag on top of drive train losses.

[Kondax]

Confirmed today 1st-4th are accurate based on the gear chart i provided. Performed the test in manual mode and let the car up shift at 6500, 1st 37 mph, 2nd 55, 3rd 82 and 4th 104. Still curious about those that have tested on a dyno only reaching low ~190, is this a limit by the tcu or speedometer error?

I believe it's the TCU limiting it, that's interesting to know

[spindlewood]

I believe it's the TCU limiting it, that's interesting to know

Do you think Audi is limiting speed based on liability or for some other reason? I didn't catch that it maxed out on a dyno.

What is the max speed comparable models have hit?

[Kondax]

Do you think Audi is limiting speed based on liability or for some other reason? I didn't catch that it maxed out on a dyno.

What is the max speed comparable models have hit?

Apparently the gearbox goes into a "limp" mode once you hit 190-something. Can't say why, probably a safety reason.