Drag penalty for having a shallow rear window angle, and using spoiler to re-attach ?

[freebeard]

When contemplating The Template, keep in mind that the cross section is half-circular. So the taper in plan is twice the taper in elevation. In theory the wake approaches zero, and your blue line would have a negligible width.

aerohead doesn't mind if you capitalize his handle, but it grinds my gears (....just a little bit. ).

[tomi_k]

Wman455 : thanks for the comments and pics.

Correct and understood, that pressure influences perpendicular to the surface... Pics I made was purely to illustrate what I was trying to explain earlier (and did the pics fairly quickly). And yes, I am in midst of doing my own measurements but wanted to check over here if someone has info how pressure changes on the rear of the car impacts to drag / fuel economy, especially cases which I tried to describe (shallower rear angle, yet still attached flow -> spoiler impact to pressures / drag / fuel economy?


So based on your pressure measurements as mods on your spoiler impacted to the rear window / area surface pressures, did that help on fuel economy? And if did how much?

[Vman455]

Originally Posted by tomi_k

So based on your pressure measurements as mods on your spoiler impacted to the rear window / area surface pressures, did that help on fuel economy? And if did how much?

That's impossible to give an exact number either way, even though you see so many people try to do that on the internet; there's too much variability in the real world and I don't have access to a laboratory or wind tunnel (and unfortunately, the Prius has an electronic throttle so I can't use throttle-stop testing to see if it might be reducing the overall drag). The only thing I can say is: I ran a statistical analysis of the 6 months of tank fills prior to fitting the spoiler and the 6 months after fitting it when I took a stats course last year, and there was significant evidence to conclude (with 95% confidence) that the mean fuel economy per tank was greater after the spoiler was installed. That suggests it is helping, but there's always a possibility it's something else.

Keep in mind that just because it appears to be helping my car does not guarantee it will help yours; you will have to test your design yourself and find out.

[tomi_k]

Thanks, Vman455 ! Totally understood. I am not looking direct association to my vehicle, just trying to get what type of improvements people doing mods are generally achieving with spoilers (if any) and magnitude of them (like 0.1%, 1%, 10% etc.)... And if I have understood correctly, e.g. using your spoiler as an example, the wake area increased a bit but gained pressure reduction on larger rear window area and then based on experiments, sounded like drag reduction happened based on your measurements and analysis. Earlier Aerohead indicated regarding the wake area, that's it's not the area but the pressure... in what magnitude, i have no idea nor data and that's what I try to understand....

Specifically related to spoiler, I am build one with adjustment of height and angle and planning to run series of tests to see what happens on my vehicle. My questions earlier were (and still are) something what I am curious to understand as if there is clear evidence that rear window / area pressures or change of them with help of a spoiler (or a wing) targeting to reduce overall drag can NOT be achieved due to basic aerodynamics, then it gives me some kind of baseline that IF I do not see improvements on results, then I have some idea why that's not happening. I have read few books, articles and searched info about overall drag reduction of road vehicles (not interested to increase downforce at the moment). Then run into spoilers / wings which put me thinking while targeting to reduce wake area drastically, would it be possible to "tweak" the airflow over the rear window area with spoilers while reducing overall drag.
I am just trying to form an generic idea how rear window / area angle vs. overall drag vs. wake area is behaving and how they correlate / associate.

If I would ask that what happens putting a 10sq.ft. flat plate on top of my vehicle and nobody would be saying that it does increase drag, don't do it and if I couldn't figure that out using any generic theories - I would not have much other options than head out and test it... lol.

[aerohead]

Originally Posted by tomi_k

Thanks, Aerohead & Freebeard ! Just trying to get my head around the topic what matters the most... and learning. And thanks for being patient to respond (probably basic and silly questions) but gotta start from somewhere....

<Quote>
* Flow reattaches on top of the spoiler, and captures a locked-vortex against the body, as high as the spoiler.
</Quote>

From drag perspective, the air flow before the spoiler what happens for the overall drag if

a) flow on front of the spoiler is attached? If flow is attached, is the spoiler directed air flow direction reducing the drag (i.e. surface pressure direction (at the end) -> without spoiler the surface pressure is against the direction of vehicle movement vs. with spoiler the surface pressure is in same direction of vehicle movement)?
b) flow on front of the spoiler is not attached -> and creates a "air bubble" (turbulent)... is this what causes overall drag increase if wake increase is not necessary the dominant factor?

According one of Hucho's document (see picture attached), if I understood correctly, regardless of attached or separated airflow, when the critical angle of rear portion of the shape is exceeded, overall drag will increase. Unfortunately, I found this information a bit too late but glad I found it.

The other attached picture is an illustration of what I am trying to understand... If Hucho's document info is correct and valid... is there a way to recover "penalty of overall drag" caused by exceeded rear slanted angle as it sounds like increased drag is evident regardless what type of flow over the rear shape one has and/or and if wake area is reduced?

1) Your first image is of the Ahmed body, which is on stilts and lacks wheel drag as we know it, so it's information is conditional from the get-go.
2) This Ahmed body's aft-body constitutes 21.5% of overall body length.
3) Cds associated for different rear slope angles on this model are accurate only for 21.5% aft-bodies, and without wheels.
4) The drag minimum, for a rear slope angle occurs at a 9-degree angle ( Cd 0.2298 )
5) The overall drag minimum ( depicted ), occurs at 25-degrees rear slope, 10-degree diffuser, and 10-degrees boat-tailing, with three counter-attacking vortices in three different planes.
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6) Your second image is from Hucho et al.'s SAE Paper 760185, Figure 24.
7) They're demonstrating how the VW can experience either a 'fastback' wake, or a 'squareback wake', based upon solely the rear slope angle.
8) The figure also depicts the 'vortex-drag' spike, between 26.5-degrees and 33.5-degrees, where 'bi-stable' flow ( both fastback and squareback can cycle back and forwards ) exists.
9) On this Volkswagen, the percentage of aft-body-to-total body length is not provided. ( the VW Golf/Rabbit was 16.4% )
10) So, as with the Ahmed body, drag values are only valid for the aft-body percentage shown.
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11) That said, if one made the mistake of doing a rear slope of, say, 28.5-degrees, you could add a rear spoiler, of which a straight-edge, laid across the top of the spoiler, to the rear of the car indicated below 26.5-degrees, to kill the vortex.
12) The spoiler would create the 'locked-vortex', with the swirling air captured in front of it, and laminar flow skipping over the vortex.
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13) If you add a spoiler to a rear slope which already has attached flow, you re-accelerate the flow to a higher velocity, which lowers the pressure at the very top of the spoiler, increasing the size of the wake, while lowering base pressure, increasing pressure drag, and overall drag.
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14) The 'template' is derived from a streamlined body of revolution of Cd 0.04. As a 'half-body', it's Cd 0.08. Adding modest wheels pushes it up to Cd 0.13. Full-coverage wheel fairings drops it back to Cd 0.10, with 'knife-edges.'
15) Since it's not uncommon for an aero modification involving compound curves to run to 800-man-hours ( for instance a bedcover ), fabrication time, I've limited the maximum rear slope angle on the 'template' to 21-22-degrees.( you don't want to do an 800-hour project 'twice' if you don't have to ).
At these 'angles' flow separation is impossible.
16) Volkswagen's lowest drag body reported so far, is the 1981 VW Flow-Body, long-tail, Cd 0.14, with a maximum rear slope of 21.5-degrees. Approximately Cd 0.105 with full wheel fairings. I don't have the plan-view of this car with me, but knowledge of it is important to the context of this shape's performance.
17) Volkswagen's lowest drag, running vehicle, the XL1, just happens to be a near-exact-match to the aft-body of the 'template, type-C.'
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17) There are lower drag bodies which have already been explored. Hucho shows half a dozen or so.
None of them that I've seen have the facility for forward, outward vision for the driver. They'd be okay for ( and have been used for ) a mileage marathon or solar car, but I can't see how one could operate them on public roads.

[aerohead]

Years ago, I graphically analyzed Hucho's 2nd-Edition Figure 4.59, which comes from SAE Paper 810185, by Buchheim et al..
I've done a linear interpolation between the 27% aft-body and 36% aft-body, tested and reported in Figure 4.59.
An 18-degree drag minimum aft-body rear slope angle occurs, approximately, with a 32% aft-body, @ Cd 0.436.
Should a spoiler be added to the contour:
* the wake area would be increased
* flow separating at the top of the added spoiler, would be more horizontal, directed 'away' from the wake
* the flow would be at a higher velocity
* the flow would be at a lower static pressure
* communicating this lower pressure into the wake could lower base pressure
* increasing pressure drag
* increasing overall drag
* at normal posted speed limits, any reduced rear lift might be statistically meaningless
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The 1969 Dodge Charger Daytona, with a 41.7% aft-body, exhibited its lowest drag with the roof rolling into a backlight angle of 18-degrees. The presence of the reflexed boot ( trunklid ) created a departure angle of 15.5-degrees, for an indicated Cd 0.270.
The same roof, rolling into a constant 12-degee backlight and 'fastback' came in at Cd 0.275. The trailing edge of the 'fastback' actually delivers the flow 'above' the streamlined pathway, both increasing wake area, plus re-accelerating the flow.

[tomi_k]

Originally Posted by aerohead

Years ago, I graphically analyzed Hucho's 2nd-Edition Figure 4.59, which comes from SAE Paper 810185, by Buchheim et al..
I've done a linear interpolation between the 27% aft-body and 36% aft-body, tested and reported in Figure 4.59.

Aerohead : What figure in the 810185 you are referring into?

[aerohead]

Originally Posted by tomi_k

Aerohead : What figure in the 810185 you are referring into?

Sorry, I kept with Hucho's Figure numbering from his book, and did not cite Buchheim's figure.
The figure has two vehicles stacked to the left, the upper depicts a fastback wake, the lower, a squareback wake.
The table to the right gives delta-Cd along the left margin, and angles ascending from zero to 90-degrees, left to right.
Five different aft-body proportions are listed, 9%, 18%, 27%, 36%, and 45%.
From the five curves the drag minimum 'buckets' are leaping off the page.
13.3-degrees, 15.3-degrees, 17.4-degrees, 18.5-degrees, and 22.5-degrees, respectively.
I won't be back until next Wednesday, but I'll snag that number.

[tomi_k]

Aerohead, thanks ! I think you are referring into Figure 14, on page 10 in the SAE 810185 (Fig, 14 - Influence of rear end slope inclination angle on drag coefficient).

My vehicle (pickup truck) has L0 / L -ratio of 0.3441 (without a tail extension) and L0 / L of 0.4087 (with the tail extension) as of today. For L0, I use trucks bed length (without and with the tail extension).

<quote>
I've done a linear interpolation between the 27% aft-body and 36% aft-body, tested and reported in Figure 4.59.
</quote>

So you interpolated that range, tested it and results fall into the interpolated line, correct?

[aerohead]

Originally Posted by tomi_k

Aerohead, thanks ! I think you are referring into Figure 14, on page 10 in the SAE 810185 (Fig, 14 - Influence of rear end slope inclination angle on drag coefficient).

My vehicle (pickup truck) has L0 / L -ratio of 0.3441 (without a tail extension) and L0 / L of 0.4087 (with the tail extension) as of today. For L0, I use trucks bed length (without and with the tail extension).

<quote>
I've done a linear interpolation between the 27% aft-body and 36% aft-body, tested and reported in Figure 4.59.
</quote>

So you interpolated that range, tested it and results fall into the interpolated line, correct?

Sorry, I should have been more specific.
It was Buchheim and his associates which did the testing, with their results tabulated in the graphic.
As a first ( and only ) approximation, as if the drag varied monotonically, I just did the simple interpolation, positioning the 18-degrees between the upper and lower known values, as a percentage of the spread between the two values. A 'ballpark' figure.
And these values are for a very crude model, with no roof curvature. Where the downslope angle begins, that's the beginning of the aft-body, in elevation view. FIAT's model had 25-degrees tumblehome as a 'Standard.' Buchheim made no mention of any other conditions.
If your pickup has roof camber, looking from the side, then wherever the roof 'peak' is situated, this location constitutes the 'beginning' of it's aft-body.
If your were going to build a bedcover with a curved top, you'd want to take off from where the trucks cab leaves off, then extend out from there, respecting the cab's roof peak.
You'd need an absolutely flat surface to park on, and you'd want around 300-pounds ( 136-kg ) in the front seats to 'settle' the suspension.
We need to know how much aft-body length you already have for the cab, then add either of your two lengths to that.
And the height from the ground to the roof peak ( with the ballast ). We could design from that if we had to.