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Drag penalty for having a shallow rear window angle, and using spoiler to re-attach ?
I was wondering if you guys could post a chart showing the aero penalty for having to use a spoiler / trunk ( boot ) to re-attach the airflow when the rear window angle is not steep enough.
I have seen a couple of cars that had exceptional Cd figures despite having too shallow a curve to the rear window. The cars usually re-attach the air flow at the trunk/boot, or by using a spoiler. Thanks. |
Something like this truck here that had a .315 Cd.
http://highperformancetrucks.com/gal...serialNumber=2 I was surprised to see some - open bed - GM truck studies even dipping into the .20s ( .28 - .29 ) That's a lot of turbulent air flowing back there. |
Additional spoilers
I had to remove 15-images from the above post.I'm adding more here
http://i1271.photobucket.com/albums/...ntitled5-4.jpg http://i1271.photobucket.com/albums/...ntitled3-5.jpg http://i1271.photobucket.com/albums/...d2/06-2829.jpg http://i1271.photobucket.com/albums/...d2/06-2827.jpg http://i1271.photobucket.com/albums/...d2/06-2818.jpg http://i1271.photobucket.com/albums/...d2/06-2817.jpg http://i1271.photobucket.com/albums/...d2/06-2815.jpg http://i1271.photobucket.com/albums/...ad2/06-286.jpg http://i1271.photobucket.com/albums/...Untitled16.jpg http://i1271.photobucket.com/albums/...Untitled15.jpg http://i1271.photobucket.com/albums/...ntitled3-2.jpg http://i1271.photobucket.com/albums/...d2/06-1316.jpg http://i1271.photobucket.com/albums/...2/06-133-1.jpg http://i1271.photobucket.com/albums/...ad2/06-131.jpg http://i1271.photobucket.com/albums/...d2/Scan102.jpg |
Wow. That was an awesome post.
Thanks Aerohead ! |
0.315
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The original half-tonneau was only good for an 8% drag reduction on the C-10 pickup.We don't know for sure what its effect to the GMC was. We do know that the rear has reattached flow and that it captures a vortex in there.Here's the GMC (bottom) http://i1271.photobucket.com/albums/...ead2/5-175.jpg Here's a link to an article about the 1986 Pontiac Grand Prix 2+2 with its aeroback rear treatment for NASCAR slaying which illustrates one car's different 'attitude' to the air Homologation Hotness - 1986 Pontiac 2+2 | Hemmings Motor News |
So apparently, the drag was actually better on a rear window angle of 18* versus 12* ? ( .270 versus . 275 )
( From the Charger Daytona on the second image section ) Is that due to being just outside the template ? |
Daytona
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Chrysler referred to a 12-degree slope as a 'fastback,' but it includes zero curvature,is not incorporated into the cars body,and would cause an 'overshoot' jet,with the downwash actually interfering with the pressure recovery of the ideal contour,degrading the drag. These notchbacks have the most complex flow of all body types.They do provide nice rear vision,they're lighter,and the trunks are easy to use,hence their popularity in everyday driving. In Kamm's last official assignment for the Battelle Institute,he discarded the Audi's notchback,and went directly for his Fachsenfeld/Kamm signature K-form roof.http://i1271.photobucket.com/albums/...ntitled7-2.jpg For lower drag,you'd just provide the elongation which Hucho has been pushing since the early 80s. |
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As we all know, the stock '68 - '70 Charger had buttresses on the sides of the rear glass. http://i1170.photobucket.com/albums/...0/DSC00348.jpg |
The buttress area was "filled-in" ala' Daytona 500 models:
http://www.mopardealer.com/_borders/...n71daytona.jpg |
Not quite the case you're after, but one that does point out the value in getting the rear shape correct.
A Pontiac Solstice Convertible has a Cd of .44 or .45 with the top up (hard to find "real" numbers). The Coupe version is 10% better, say about .41 (again VERY hard to find good numbers). http://1-photos.ebizautos.com/used-2...5630-1-640.jpg Top up side view doesn't really show what it's like: http://www.skyroadster.com/forums/at...k_solstice.jpg http://media.ed.edmunds-media.com/po..._oem_1_500.jpg I've been told the airflow never reattaches on the convertible, but that the tail on the coupe is just high enough to get some reattachment. (Note that they both use the same door glass, rear fenders, tailllights, and rear bumper/fascia.) |
Solstice
I believe that the first year model was reported at Cd 0.45.Then Cd 0.44 for the following year(s).
It's an exquisite example of an aft-body drag penalty.Thanks! |
In context of the this thread - Assuming e.g that rear window angle is 18degree at the maximum (lets say a fastback type rear end shape) and flow over the rear window is attached without a spoiler (not a wing). With a spoiler and still assuming that flow over the rear window and the spoiler is attached, can the spoiler reduce the drag caused by 18degree rear window?
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18-degrees
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* On a simple prismatic body, with simple angles and no curvature, optimum backlight angle is a function of the percentage of the length of the aft-body, compared to the overall length of the vehicle, expressed as a ratio. * On complex bodies, where curvature is used, the optimum backlight angle will also be a function of the percentage of aft-body. * Some cars, designed for maximum interior useful volume, won't have any appreciable backlight angle at all, they'll just be vertical. * In order to anticipate some hypothetical, we really need to specify a few more details of the body proportions. * It's best to just pick a specific vehicle, and one in which blueprints are available, depicting all surfaces and proportions as they appear in reality. -------------------------------------------------------------------------------------- * And we need to be very careful how we use the term 'attached flow'. ------------------------------------------------------------------------------------- A few specific vehicles: * Volkswagen's 2013 XL1, Cd 0.189, rear downslope angle = 17-degrees maximum. * GM's 1996 EV1 rear slope maximum = 20-degrees, then reflexed to 18-degrees, and continued to reflex as low as 14-degrees at the trailing edge. * GM's 1993 Impact land speed record car's boat tail extension, relaxed the rear reflex to only 10-degrees at the trailing edge, for Cd 0.137. * Ford's 1985 Cd 0.137, Probe-V concept had a maximum 11.5-degrees. * GM's 1987 Cd 0.089 Sunraycer rear slope angle never exceeded 17.5-degrees. * HONDA's Cd 0.10, 1993 Dream solar racer's maximum rear slope was 11-degrees. ------------------------------------------------------------------------------------- I'll bring Rolf Buchheim's prismatic drag table next Wednesday. It may contain some data for an 18-degree backlight. |
Thanks for the respond, Aerohead.
The 18degree was a reference which I gathered from some of the Hucho's article and seems that the rear angle (whole rear end portion) somewhere between 15-18degree seems to be the maximum / critical angle before major drag increase (if the angle is made shallower)... What I try to understand is that can a spoiler be used at the end rear end shape to reduce drag? Ex. if the rear end shape maximum angle is e.g. 18degree and one installs a spoiler at the end in a way that airflow over the spoiler is "attached", impact to wake is minimal but air flow pressure on front of the spoiler (in larger area) would be changed from negative to positive pressure. If these conditions would be met in a same vehicle, would that lead to reduced drag? Or is this too general description? E.g. if the rear end angle is made, lets say maximum of 22degree (reduced wake area), so the rear end shape exceeds the critical angle.... But installing the spoiler in away that the tip of the spoiler would still form "artificial" angle of 18degrees or less (from tip of the spoiler to earlier point of the shape, tangent point), and the flow would remain still attached over the spoiler, flow pressure would be changed from negative to positive - would this lead overall reduction of drag? Ultimately I try to understand that if "wake area" is bad and that would be minimized by creating the rear end shape which has shallower angle than e.g. 18degree, would (any) spoiler shape / angle / size be able to recover drag penalty caused by the angle which exceeds so called "critical angle" (somewhere between 15-18degrees)... |
18-degree and spoiler
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* If flow was attached at 18-degrees you'd have pressure regain, and when flow finally separated at the end of the body, the wake would at as high a pressure as you'd obtain. * The 'size' of the wake is not as important as it's pressure. * If the flow was separated at 18-degrees, it would be the job of the spoiler to do exactly as you describe. * Flow reattaches on top of the spoiler, and captures a locked-vortex against the body, as high as the spoiler. * Allowing slower, higher pressure to act against the upper rear surface, killing lift, while allowing slower, higher pressure air in the wake, reducing pressure drag, the major component of drag. * If you know the streamline path over the existing profile, then it's just a matter of placing the top of the spoiler where the optimum profile ought to be. * HOT ROD Magazine's Chevy Camaro Bonneville land speed record car does exactly this. |
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Consider also the Gurney flap or wickerbill. Quote:
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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? |
Re: your second picture--
Pressure always acts normal to a surface. The arrows in the lower image are not correct. A spoiler affects flow upstream because pressure is transmitted through air (fluid) at ~340 m/s. Fitting a spoiler may increase pressure as far upstream as the roof, as I found on my Prius with a small lip spoiler: https://ecomodder.com/forum/member-v...no-spoiler.jpg Gauge pressures with no lip spoiler https://ecomodder.com/forum/member-v...02-spoiler.jpg Gauge pressures with lip spoiler https://ecomodder.com/forum/member-v...difference.jpg Difference https://ecomodder.com/forum/member-v...927-132853.jpg Lip spoiler for reference Les than $100 worth of equipment and a couple hours and you can measure yourself and find out what a spoiler does on your car. |
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. :)). |
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? |
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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. |
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. |
considering your images
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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. ------------------------------------------------------------------------------------ 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. -------------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------------- 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. -------------------------------------------------------------------------------------- 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.' -------------------------------------------------------------------------------------- 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. |
an 18-degree example
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 ------------------------------------------------------------------------------------- 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. |
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figure
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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. |
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? |
tested and reported
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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. |
Thanks, Aerohead! I didn't see indication of a roof camber to be included into aft-body ration in the SAE 810185 but now when you mentioned, it makes sense.
Without roof camber : * L0 / L -ratio of 0.3441 (without a tail extension) * L0 / L of 0.4087 (with the tail extension) With roof camber: * L0 / L -ratio of 0.5234 (without the tail extension) * L0 / L of 0.5704 (with the tail extension) According the SAE 810185, it implies that larger aft-body ratios has chance achieving lower drag coefficients. I have a sideview profile of the truck roof (from the windshield to the rear window) which then continues to the end of the bed and beyond. The roof peak seemed to be fairly front of the cabin (towards windshield) which increases the aft-body ratios. I have a cardboard template from the top of the windshield all the way down to the end of the bed and beyond where I fitted the sideview profile. |
2 Attachment(s)
An attempt to questimate what happens DeltaCd (min.) vs. slope angle (at min DeltaCd). with aft-body -ratio beyond of 0.45....
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aft-body ratio
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Brett's Aerolid measured a delta-Cd= 0.067 reduction. Brett's boat tail was good for delta-Cd 0.031 drag reduction. With both, Aerostealth, who bought one of each, was able to achieve Cybertruck's drag coefficient in 2014. In Feysal Ahmed's Master's Thesis, he was able to see a delta- 19% Cd with his 3-D type aeroshell. From the two trips to the wind tunnel with the T-100, with the 'cleanest' configuration, and allowing for the blockage ratio comparison model, there's a strong probability that the truck measured as low as Cd 0.17 ( as a 'camera' truck ), if measured at the A2 Wind Tunnel ( which I hope to validate when I go there ). Whatever you do, you're not going to see any truly remarkable drag reduction until you put some boat-tailing on the truck. The virtually 'slab-sides' of pickup beds preclude any meaningful pressure recovery along the sides, relying solely on the 'roof' for all the heavy lifting.:( |
' Re: your second picture'
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image
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------------------------------------------------------------------------------------- Ah, never mind, I just found it at #19 permalink! I never clicked on the second image, and missed the red arrows you were referring to. Oh the difference a mouse-click will make! |
if flow is attached
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2) flow would be increasingly decelerating over the length of the entire roof, aft of the roof apex. 3) local static pressure would be increasingly rising, in proportion to the local velocity, as the flow moved rearwards. 4) when flow reached the end of the body and detached, it would be the 'slowest' and 'highest' pressure, having recovered pressure the entire length of the roof. 5) there would be no separated wake, just a thick turbulent boundary layer sloughing off the body. ------------------------------------------------------------------------------------- 6) the addition of a rear spoiler would introduce an obstacle in the flow path, requiring the flow to re-accelerate to a higher velocity around the larger cross-section, and at lower local static pressure. 7) the local separation line would move to the periphery of the spoiler. 8) a turbulent wake would be introduced. 9) direct downforce would be introduced. 10) at the expense of lower base pressure 11) higher pressure drag. 12) higher overall drag. |
drag penalty comparison ( sort of )
I dredged up a couple of cars which share similar curved-roof length percentages.
The Ford / Merkur-Scorpio 2-door, and VW 2000. Both have around 38% aft-body, Cd 0.33, and Cd 0.25, respectively. -------------------------------------------------------------------------------------- *The Ford starts with a 25-degree fastback ( as measured from the horizontal ). * The 'notchback' shelf / step is added, relaxing the rear slope to 19.5-degrees. * A lower rear spoiler is added, increasing height and length, relaxing the slope angle further, to 16.4-degrees. * Finally, the upper wing is added, creating a 14-degree slope angle off the backlight within an inch of the 'fast' template, and Cd 0.33. -------------------------------------------------------------------------------------- * Volkswagen just goes for the throat, with a simple non-porous fastback, of 14-degrees downslope angle, with a perfect match to Wolfgang Klemperer's Cd 0.15 Basic Body contour of 1922, coming in at Cd 0.25, 70.4 - inches ( 1,788mm) short of Klemperer's long-tail total length. ------------------------------------------------------------------------------------- * Klemperer's tail reaches a maximum rear slope angle of 24.5-degrees, exceeding Mair's recommended 22-degrees at 89% tail length. This appears to be the same contour Toyota has chosen for all their Prius variants, since the Gen-II. Which, on the Prius, also happens to match Mair's transition region to 22-degrees rear slope. |
Aerohead : I guess you figured out that I posted those pictures with the arrows which also had a mistake regarding the arrows not pointing perpendicular to the roof line, apologies for that.
I just did it quickly to try to simplify my questions what I tried to figure out regarding what happens at the end with a spoiler, how spoiler acts in terms of drag, how overall airflow "sees" the spoiler and what is impact of that to overall drag vs. the roof angles. Thanks for detailed responses on this matter - much appreciated. |
When the target is 22 degrees, in plan that's 44 degrees --close enough to 45.
In my experiment with Zeppelin-izing a Beetle I established a 45 degree bulkhead and found where the gentlest curve to reach it was. https://ecomodder.com/forum/member-f...7-100-0623.jpg The solid bulkhead is where a boat tail without the reflex curve would terminate. The open bulkhead is at the original bumper location. I think terminating in a vertical line instead of a low point would impart directional stability. I guess I've never posted the picture, but I established that a Studebaker Starlight-style V-shaped window would not impair rear vision. Cooling would be through the front of the rear fenders. Oversize like Tatra to allow either side to work in a crosswind. |
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