Turbulence - Friend or Foe? |Here's a lot of Aero info, not spread in several threads
 

Rather than sporadically give information in posts... Let me take a moment to explain a few things with respect to aerodynamics, cD and a few terms that go with that.... Basically, I'm about to regurgitate some of the concepts you might learn in a fluid mechanics course (but minimizing the math component)

First, some definitions

Reynolds number: a ratio between the inertial forces (momentum of the working fluid) to viscous forces (property of resistance to shearing) | dependent on: body length, fluid velocity, fluid density, dynamic fluid viscosity, kinematic fluid viscosity.

Frictional Drag: this is the drag between the moving fluid and relativity stationary surface. May be referred to as viscous drag - I'll switch back of forth most likely. This value is dependent/sensitive on the Reynolds number.

Pressure Drag: this is the drag as a result of a pressure drop - wake. Think of that big blast of wind from a semi truck, or the waves generated by a boat. Pressure drag is mildly dependent on the Reynolds number, but generally not sensitive to it. Pressure drag is highly sensitive to body shape.

For both Frictional and Pressure drag.... It's important to note that they are both VERY dependent on fluid viscosity. That is, in inviscid (viscosity = 0) flow, both of drop to 0.

AoA: Angle of attack - draw a line in parallel to fluid flow. Now draw a line from the leading edge of a body to the trailing edge. Measure the angle between these two lines.

Streamlined Body: Drag losses are primarily due to viscous losses. Streamlined bodies of the same thickness are significantly more aerodynamic than a bluff body. Note that a streamlined shape doesn't necessarily mean a streamlined body - at a high AoA, flow separation causes great pressure drops.
Bluff Body: Drag losses at high Reynolds numbers are primarily due to momentum losses - meaning, pressure drop as a result of a wake.

Free Stream: This is the flow that is not impeded by a body.


Boundary Layer: I can spend a lot of time on this, but I'll abridge it... The boundary layer is the fluid directly beside the body. The general profile of the boundary looks something like this:
https://history.nasa.gov/SP-4103/p529.jpg
where the length of the lines represent a velocity vector - the longer the line, the faster the flow. At the point where the fluid meets the body, there is a zero slip condition. That is, at this point the fluid does not move. There are some important implications of this as it applies to differential calculus - but don't worry about that, just understand this concept ;) Below is the shape of the boundary layer (note that the y scale is increased for easier reading):
https://www.cartage.org.lb/en/themes/...s/img00032.gif
Note the several phases of the boundary layer:

1. Laminar
2. Transitional
3. Turbulent

And just for fun - here's a real world example:
https://history.nasa.gov/SP-4103/p530.jpg

Laminar Flow: Fluid "layers" (streamlines) flow over each other in a parallel fashion smoothly over each other.
Transitional Flow: This is more of a mathematical zone as laminar turns into turbulent. I call it mathematical because there are specialized equations that apply to transitional flow only.
Turbulent Flow: The streamlines, instead of slipping over each other, diverge in chaotic eddies. Note that chaotic does not mean random, it "simply" means that it is highly dependent on initial flow conditions - small changes in these conditions create great differences in output.

Please note, there is no critical distinction between laminar, transitional and turbulent flow. The mathematical distinction is almost arbitrary - it's just a number that the community has agreed to use :thumbup:

Okay, I think that just about covers some minimal basics - if I make any knowledge assumptions, please let me know and I'll elaborate :thumbup: :thumbup:

I'm going to talk about bluff bodies for the most part as that's what our cars are (with exceptions - basjoos!).

So lets look at some simple objects and what happens.... A cylinder is a classic example:
https://www.flometrics.com/services/cylinder/cylslo.jpg
So, the flow in the front is generally nice, even and laminar. But downstream, there's some nasty eddies. The large vorticies off of a cylinder have their own natural frequency dependent on fluid velocity and cylinder diameter - coming at regular intervals. These remove energy from the body. The wake of a body typically has this same eddying motion, but not necessarily at a consistent frequency.

This is actually a VERY important phenomena as if this frequency matches the natural frequency of the cylinder (think a street lamp pole), the cylinder will vibrate divergently and without control, eventually self destruct. This is why many light poles, especially in wind prone areas, are tapered. Additionally, power lines may have spoilers and damping mechanisms attached. Even large sky scrapers have vibration control for wind induced motion - one method uses VERY heavy weights (think tons) on the top floor of the building; given a certain wind speed, oil is pumped under the weights so they can move (constrained and attached to the structure by springs)...

How about a sphere?

https://www.princeton.edu/~asmits/Bic...R_combined.GIF

The sphere on the left (a) shows what happens with laminar flow. As soon as the pressure drop becomes significant you get separation, bugger.

So what's the deal with the picture on the right? How did we delay separation? That sphere has a trip wire. What does a trip wire do? It perturbs the boundary layer, a lot. Enough so that nearly the entire boundary layer in contact with the sphere is turbulent.

So how does this change cD? Here's some graphics:
https://www.princeton.edu/~asmits/Bic...oefficient.GIF
cD versus Reynolds #

https://www.princeton.edu/~asmits/Bic...w_patterns.GIF
Points on the graph above correspond to the letters below each case.

"Whoa Whoa Whoa!! Are you telling me cD changes with velocity?"
Yes, yes I am - but don't get too excited as this mainly applies to small objects. cD drops significantly as the Re# increases. BUT, it remains nearly constant for large Re#'s in the laminar region and approaches a constant value after the transitional region. As a car is very wide compared to something like a tennis ball, the Reynolds number is high - very high in fact (on order of 10^6 @ 55mph and 10^5 at ~3mph).


Balls!
Sports balls, believe it or not, have some great design... Smooth balls are not very efficient aerodynamically. This is why golf balls have dimples, tennis balls have fuzz, cricket balls have a stubby seam, baseballs have stitches, American footballs are textured, soccer balls have seams (Everywhere). Okay, some of this is traditional - but it still plays a role.
https://www.princeton.edu/~asmits/Bic.../roughness.GIF
Roughness and cD... Having a bit of roughness induces turbulence. Look at the photo above of the sphere with the trip wire - surface roughness is very similar, in effect, to a trip wire.

This results in a reduction of cD as shown in the above graph (which just so happens to also be in my fluid mechanics book - Fundamentals of Fluid Mechanics produced by John Wiley & Sons :p). Relative roughness is t/D, t being the thickness of "rough" and D being the diameter of a sphere/cylinder. The dashed line on the left is a golf ball.

And on the subject of golf balls... why? The dimples! Why? The dimples act, in effect, like a trip wire. They promote a transition to turbulent flow. By doing so, we get higher skin friction (yet another name for viscous losses). BUT, remember the definition of a bluff body? A golf ball is a sphere - and spheres are bluff bodies. Most of their losses come from the wake - so if we can move the wake further back, we can reduce the wake size and reduce the losses from the wake. It just so happens that by increasing the turbulence, you decrease your drag by reducing where most of the drag is coming from - flow separation (wake).

------
Okay, so what's all of this talk about the benefits of turbulent flow? Turbulence is the most misunderstood concept with regards to aerodynamics, in my opinion. Nature has known for millions of years of the benefits of turbulence. This is why dermal denticles on sharks help lower their cD. Likewise the bumpy tubercles of a whale fin. etc.
https://www.whalepower.com/drupal/fil...mpback_fin.jpg

The key difference between induced turbulence and the turbulence as a result of a shape is the size. Larger eddies, swirls, etc. contain more energy than smaller ones. So if we induce smaller eddies, with a small amount of energy - we move into the turbulent regime without a whole lot of loss that you'd typically associate with the word "turbulence". This will typically be referred to as "energizing the boundary layer." This can happen on a very VERY small scale - the smallest of which is the Kolmogorov micro scale. <-- keep in mind that the mathematic description of turbulence is not solved - we just can't do it, yet :p

Some very notable physicist when asked what they would like to ask God have replied:
Werner Heisenberg: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first."
Horace Lamb: "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic."
^^both of these were mentioned in my lectures :p

--------
Vortex Generators.....
Okay, so I've been building up to this as it has come up a lot recently - trying to give some background before I get to it.

Here's the answer to some straightforward (I hope) questions:
1. Does it increase turbulence?
Yes - the idea is, move the wake back with turbulent flow
2. Does it reduce cD?
The devil's in the details. Properly applied, absolutely yes. Nature has proven this through millions of years of evolutionary change. CFD and tunnel testing too :p
3. wtf counts as a vortex generator?
Almost anything that perturbs flow - from commercially sold tabs to dimples to stiff fuzz (think tennis ball). Vortex Generator does not necessarily refer to one particular product (nor do I endorse any such product).
4. How much improvement?
See #2 - Mitsubishi has published a paper reporting a cD reduction of 6 points (.006) on a Lancer which can be considered significant in the cD world. They used delta wing type vortex generators placed 100mm in front of the predicted separation point:
https://www.primitiveengineering.com/..._effect_vg.jpg
https://www.primitiveengineering.com/...vortex_top.jpg

Note the smaller wake size and how the separation point is further down the rear glass:
https://www.primitiveengineering.com/...ex_gen_cfd.jpg


Whew, freeking long.... Questions/additions? Let me know if I missed a typo too :)

Good read, trebuchet! Thanks for the "scoop" on aerodynamics, lol.

Tubulence - Friend or Foe?

Tubulence. Is this effect brought about by sitting down in the bathtub too fast?

I think it's a term for the bubbles you create while sitting in the bathtub. ;)

Excellent write-up!

I vote to stickify it...

RH77

More the horizontal growth as a result of middle aged spread....

But how embarrassing, a critical spelling error in the title :o

One thing I have to wonder... if vortex generators are so great, why aren't they on the back of the insight, the prius, the UFE-III, the VW 1 litre car, etc. etc? I know length is a constraint, but given the same length, why wouldn't they attempt to drop the rear at a steeper angle and add some VGs, that way they could decrease the size of the wake still further, if it were possible.

Good stuff!
I think I'm seeing a Karmann vortex that's formed at the back of the car in the graphic that's labeled '(a)With VG' while the car '(b)without VG' doesn't show signs of a Karman vortex. Do you see it too? Does it mean anything? Is that a good thing or not?

It would be great if someone had some tuft photos of a prius' rear glass at speed. The Prius hatch is closer to a streamlined shape (as is the 1L and UFE-III). So if the separation point is really far down the glass, or not until a sudden change in body shape (rear cut off), there's more benefit of keeping laminar flow and dealing with skin friction.

I dug around autospeed a little more, and found some more information :p https://www.autospeed.com/cms/A_3061/article.html. They specifically tested the air tab product and they did have promising results - similar, in effect to my tuft testing while behind a semi.

I'm not sure I follow that? Why would that make the wake size smaller? Intuitively, I'm thinking of a steep angled rear end compared to a gently sloping rear end - the steep one has a pretty bad wake issue... Maybe I'm just not understanding what you said?


I do see an obvious downward motion there - but I wouldn't call it a Karman Vortex - a requirement for that would be periodic oscillating eddies - they could be there, it's just hard to tell from one image:
https://www.princeton.edu/~asmits/Bic...w_patterns.GIF
^center image (c)

I think that little downward tail has something to do with the upward curve (compared to photo (b)) and the faster moving flow above it (in yellow - compared to the slower green in (b)). It would be nice to see a few frames to get an idea of the bigger picture there :)

Very nice writeup.

I'm referring to the area of suction behind (the area below boundary layer separation) as "wake". Probably the wrong choice of words.

My understanding is that with the sphere and the trip wire, the trip wire trips the boundary layer into turbulence (energizes it), and as a result, the boundary layer can sustain a steeper angle than the prius-like 17 degrees or so before separating. For the same length car, you might have a more effective boattail that way, since the area of suction would be smaller. i.e. On one hand (prius style), you have a larger area of suction behind the vehicle, and on the more extreme rake + VGs or turbulator tape or whatever you use to trip the boundary layer, you have less area of suction but more energy lost to trip the boundary layer.

Do you get what I'm saying? Think VW beetle but with boundary layer tripping somewhere on top, and a small wing near the very bottom, to get the air leaving in a horizontal direction.

Mighty, I had an interesting conversation with the South East ASME district leader (at least, afterwards - I was told that was his position) - and in speaking with him with respect to HPV fairings, it was recommended (among other things) to explore completely turbulent flow - tripping with some sort of speed bump on the leading edge...

In the next couple months, we'll be modeling that to see what happens - as turbulence is chaotic, there's good chances that it will help, hurt and/or do nothing :p But for us, we're not sure how much of an effect it will have at our relative low velocities :p

On the polar opposite side of things, it was also recommended that we check out deHavilland slots to maintain laminar flow (and provide necessary ventilation). deHavilland slots basically suck air into the foil just before the transition point - I believe this basically "resets" the BL, or at least decreases the thickness.


-----
Any good ideas on how to trip the BL? I was thinking of just experimenting with a triangular shape -like a FedEx Triangle mailer sort of shape. Any suggestions?

Go with some sort of thick tape, and cut it in a zigzag pattern as per here. I'm guessing that a material store will have these sorts of scissors. As to where to find 1mm thick tape, not sure exactly.

I suspect that a lot of hatchbacks where the hatch is roughly 30 degrees or so might conceivably have good airflow with the addition of such turbulator tape. However, I have to wonder why the front windshield wipers aren't tripping the boundary layer. Or maybe the energy they add is too diffuse by the time the air gets to the rear of the car. Or the top of the windshield for that matter.

Thank you for the nice write-up. It's interesting for me to see how N(Re), viscosity, turbulence, etc. apply to aerodynamics. In my field, we mostly think of turbulence in terms of how it affects mixing in a pipe (i.e. flushing out "dead legs") and heat transfer. Also we only care about Newtonian fluids for the most part.

To summarise, it seems like turbulators help when there is unwanted airflow separation. A successfull turbulator is placed a certain distance in front of the point of separation.

Technically - they should be placed just before the transition. So it's correct to say before separation, but it's the zone before separation you're attempting to fix (and thus prevent separation).

This sort of thing can be easily seen in commercial airliner flaps. At full extension, they essentially become multiple airfoils working together as one virtual airfoil. The same thing is seen in rear wings of racecars like F1.

As for a boundary layer trip, I think any shape that does not promote laminar flow over it would be effective. I think the more significant question is the height of the trip from the surface. How thick does the trip layer need to be for best efficiency?

There is obviously a sweet spot where too much depth unnecessarily accelerates more than just boundary layer air. It will remain attached further back, but it ends up being wasted energy. Likewise, too little depth won't accelerate the boundary layer enough and it will detach before the trailing edge.

I suspect there is a formula that can explain this relationship fairly accurately - or at least ballpark a decent starting point based on some general assumptions. Intuitively, I 'get it'. But mathmatically, er....

From what I can see (from the picture of the sphere with boundary layer tripping), there is still a minimum angle that must be maintained or the flow will still separate. i.e., no turbulator is going to help the back of a semi (or similar shape). The boundary layer on the sphere separated at 45 degrees. Note that on the back of the lancer the flow still appears to be separating. (Although that's trusting that the CFD is a true picture, which it isn't necessarily.)

I suspect that this angle will vary depending on how much the boundary layer is energized (turbulator height) and how far back the boundary layer was energized.

All good questions - we intend to investigate :D

I am not aware of equations for such a thing - there very well could be though. The reason, Turbulent flow isn't fully understood (especially in a mathematical sense) - Turbulence is a chaotic system. Complicating things more - we're dealing with curved surfaces :D There are, however, relationships for laminar flow, and fairly accurate equations in the transition zone. But once you get to high Reynolds numbers, small changes drastically change the outcome.



Absolutely right :thumbup: At least, there no research that supports this. Really, a vortex generator fixes an aerodynamic flaw in the design. Think of it as a band aid - the cure being a costly redesign or potentially difficult modification that many/most are not willing to do.


Awesome :thumbup: Are you involved with heat exchanger design? Regurgitating class lectures - turbulence enhances heat transfer (higher Re# = better) - I'm sure you knew that already. As for the "N" - is that a reference to the Nusselt number (I imagine that, and perhaps the prandtl number are used often in your field :) )?

Thinking about it some more... aren't VGs and turbulators separate things? i.e. you'd use VGs if you are generating large vortexes at the corners of the car (e.g. back of a BMW). In something a bit rounder but with a rake of 20 to 45 degrees back, you'd want to trip the boundary layer with a turbulator so as to decrease suction at the back.

And with something like the Lancer, they could have achieved the same thing with a small ridge on the roof of the car somewhere.

Or perhaps a wing like Subaru did with the STi.

That is flatulence. The French use wine corks for this problem.:cool:

There are four articles there...good reading. But with their last test on the Honda Insight...why weren't the airtabs placed up above the rear glass as with the Toyota Prius right above? Separation not expected? Not a fair test...who would expect improvements on an aero tweaked shape?

They need to test something like the green Honda SUV.

https://us1.webpublications.com.au/st.../3060_13lo.jpg

I think it would have made sense for them to evaluate the Insight at significantly higher speeds. But as it was, the whole exercise appeared to be pointless on that car.

As far as "fairness" is concerned... They weren't comparing vehicle to vehicle. They were comparing a concept to another concept. The Prius has a much steeper angle compared to the insight (separation is not expected - as can be seen while driving in the rain). Doing the "wake fill" test on the Prius wouldn't really help if flow has already separated.

As far as the whole "wake fill" idea....

OK, I am sold on the idea of using a turbulator to trip the boundary layer ahead of my hatchback so I don't get held back by suction at highway speeds.

I am going to put a thin zig zagged layer of clear silicone caulk across the roof of my civic hatchback. (I can always scrape 99&#37; of it off later with a razor blade)

The question is, how far should I put the caulk "trip" strip ahead of the hatchback? 100mm like Mitsubishi did?

In Mitsu's test, the VG were placed 100mm ahead of where the airflow separated from the rear glass. Similarly, in the link to the glider modification, the zigzag tape on the wing was placed ahead of the point of separation. The first step is to find where airflow separates from the hatch. I think a good way to determine where flow separates on your car is to do some tuft testing at various speeds.

I did some tuft testing on my car. There's side view pic of my car in my profile for reference. At 60mph flow started to separate at about 2/3 of the way down the rear hatch, or about 6 inches away from the rear deck. The angle of the glass at the point of separation is about 21 degrees. The flow wasn't completely turbulent, the tufts were still pointed downstream, but they wiggled noticeably more than the tufts just upstream.

Now you've got me thinking of using clear silicone caulking to make a zigzag strip!

Edit: oh wait, I just saw your car pic in your profile. It's pretty clear where the air would separate.

DRW- Thanks for the info/help, but my hatch glass is pretty close to vertical. Maybe a 15 degree slope downward (a station wagon would be 0 degrees). So it seems like I need to put the caulk strip on the roof- right?

Its gonna be hard for me to do tuft testing with tufts on the roof unless I can find a volunteer to hang out the window and watch them at 55 mph :D

Ah! I edited my post at the same time you wrote yours!

Erik, the trailing edge of the roof of your car is similar to the Insight. They both have a gently tapered rooflines terminating with a sharp edge. This is done to give the air a definite point to separate from the body. See part one of the vortex article here www.autospeed.com/A_3058/cms/article.html
where they state:

" Cars with a two-box shape (eg hatchbacks and wagons) are always stuck with flow separation at the end of the roof, so creating a larger wake. In those cars, and also at the trailing edge of the boot in three-box cars, the separation should be clean – ie the flow shouldn’t wrap around the end of the roof or the boot lid.


On hatchbacks and wagons, roof extension spoilers achieve this clean separation, as do sedans by means of the sudden transition from horizontal to vertical at the trailing edges of the boot lid."

My interpretation of what that article is saying is that your car already has a nice aero shape at the top of the roof/hatch junction. Sure, it's a large wake, but it has clean separation. VG's might reduce the wake on your car, but it would also make the wake more turbulent.

DRW- Thanks, that was a great article. I am going to try it just to see if ther eis any change in my mileage, but it looks like a Kamm back is the only aero option to help the back end of my car

Have to see the actual data but do those delta wing doodads generate vortices or generate laminar flow?

Gene

Those delta wing doodads are called vortex generators (VG's).

Thanks for the fluids review. Besides vortex generators, will adding heat help trip the boundary layer? If so, do you think exhaust heat could be used to help accomplish this?

You can probably use exhaust flow to do it, in a similar manner to "blown flaps".

It's interesting actually how many vehicles now have a large transverse muffler between the bumper and the gas tank, yes the oval shape probably helps fill the hole, stopping the bumper becoming a drag parachute and cleaning up underbody aerodynamics. There is however potentially a small benefit from them expanding air as it passes over it, when hot, and providing a minute amount of thrust.

By exploiting the Coanda effect, exhaust flow could be made to "drive" a Coanda surface at the underside rear of the vehicle. This would have the benefit of helping clean up rear airflow, while also "sucking" the vehicle to the road somewhat, and should also provide around 15lb of thrust at highway speed.

Air dam
 

When you installed your air dam did you see any increase on the scan gauge?
IF YOU DID HOW much?

green swift

More turbulence links
 

I had done a mini survey on VGs in cleanmpg.com,here, which I'll recap and complement:

Vortex Generators - VGs:

Mitsubishi EVO MR $300
Air Tabs $2.50/ea (+10% MPG CR-V gen-1)
AirFlow Systems $10/25ft (I contacted them on FE and they honestly replied)
Vortekz $20/10pc
Fuel Savers AU$110/9pc (up to 11% savings)

Boundary Layer Energizers etc., not quite VGs:

UC Davis BLEs

Sinha Deturbulator tape (This claims up to 30% MPG increase, still in R&D)
Found in Bman83GL Deturbulator tape topic.

Zig-zag and dimple tape(2,3)

Spoilers
Spoilers (not wings) are used to detach the flow of air from the rear of the car to create a pocket of non-turbulent stagnant air behind the car to finish the air flow like a teardrop (makes a virtual boat tail) and reduce Cd caused by drag from poor rear aerodynamics. Used by modern wedge shaped hatchback cars.

(need references) see Citroen Cx or Toyota Prius.

Other stuff

Aerody.org articles
Wolf-Heinrich Hucho - Aerodynamics of Road Vehicles From Fluid Mechanics to Vehicle Engineering
Recumbents.com
Aerohead's post ecomodder
Car Aerodynamics


Diffuser (read for front/rear impact on underbody drag) and ground effect

Wing and Aerofoil

Maxing out tire pressure

Drag Coefficient - Cd/Cx

Wikipedia listing
Daox CdA listing from ecomodder

Not aero

Driving tips (some usefull A/T tips)
Pulse and glide explained with MPG results

Autospeed articles

As for Autospeed aero articles, I had read a few cool ones (VG experiments, wool tuft testing, airflow test):

Vortex:
https://autospeed.drive.com.au/cms/A_3061/article.html
https://autospeed.drive.com.au/A_3060/cms/article.html
https://www.autospeed.com/A_3059/cms/article.html
https://www.autospeed.com/A_3058/cms/article.html

Aero testing:
https://autospeed.drive.com.au/cms/A_108676/article.html
https://autospeed.drive.com.au/A_108675/cms/article.html
https://autospeed.drive.com.au/A_108674/cms/article.html
https://autospeed.drive.com.au/A_108656/cms/article.html

Aerodynamics:
https://autospeed.drive.com.au/cms/A_107773/article.html
https://www.recumbents.com/car_aerodynamics
https://www.edmunds.com/advice/specia...4/article.html
https://www.ibsinger.com/gallery.htm?...&galleryId=768

Under car airflow (Prius +5MPG):
https://autospeed.drive.com.au/cms/A_2456/article.html
https://autospeed.drive.com.au/cms/A_2455/article.html

Undertrays spoilers and bonnet vents
https://autospeed.drive.com.au/cms/A_2162/article.html
https://autospeed.drive.com.au/cms/A_2160/article.html
https://autospeed.drive.com.au/cms/A_2159/article.html

Wiper blade deflector for noise
https://autospeed.drive.com.au/cms/A_2445/article.html

In F1 cars this method was used in the diffuser. Designers found that the change in gas flow due to changes in engine RPM created balance problems. It was eventually scrapped.

In a regular roadgoing car, I'm not sure there would be enough energy left in the flow (after the muffler) to make much of a difference. Get rid of the muffler, then maybe you might have something (in addition to a headache from the noise).

Yeah, I can see that being a problem, great downforce through a long curve at 10K rpm, but it's time to shift.... annnnnnnnd the back end goes loose.

That's interesting, I mentioned on mpgresearch a while back that it might be possible to use closed cell foam "draft insulating" tape strip to get the same effect. I knew about the effect from a 1970s aeromodeller annual article on use of turbulation strips on model sailplanes. I have 2 points I am going to apply it on Marvin when I get off my butt and get into the aero mods. i) near the back edge of the rear ventilator windows, such that when they are cracked more air will tuck in behind them, and ii) in front of the back light clusters, because modding rear shape there is difficult.

Dam, that's a lot of good info! I'll be reading for weeks.