Ideal car rear roofline angle and shape for low drag?

What is ideal rear roofline(rear window and trunk) angle and shape(straight line, curve ..etc) for lower drag?
Keep in mind if you increase angle, you reduce butt area / wake, but induce low pressure at rear window/trunk , if you decrease angle you increase butt/wake but increase pressure at rear window/trunk.

Here's a partial answer from Aerodynamics of Road Vehicles 4th Edition, edited by Wolf-Heinrich Hucho:

The book has a lot more in Section 4.4.5. Details of the transition from roof to back, and from side to back have significant effect on the drag. That book is the standard reference for any person interested in vehicle aerodynamic drag. It's also easy to understand, and I highly recommend it. This is apparently the current (5th) edition of this book: https://www.amazon.com/dp/0768079772/?tag=pfamazon01-20

A real world example of the effect of adding an aerodynamic topper to a pickup truck is here: https://ecomodder.com/forum/showthread.php/modding-06-gmc-canyon-17070.html.

If you want to study the aerodynamics of an existing car, this book by Julian Edgar is excellent: https://www.amazon.com/dp/1787112837/?tag=pfamazon01-20.

From my site, this is the effect of the rear roofline treatment in order of importance:


Each design adds approximately 0.01 to the drag coefficient ##C_d##. For example, the hatchback with ##\theta## = 25°-35° (design #6) adds approx. 0.06 to ##C_d##.

From the same page, you can find one of the sources for this (Theory of ground vehicles, 2nd ed., J.Y. Wong, 1993, p. 179):

jrmichler said:

Here's a partial answer from Aerodynamics of Road Vehicles 4th Edition, edited by Wolf-Heinrich Hucho:
View attachment 316946
The book has a lot more in Section 4.4.5. Details of the transition from roof to back, and from side to back have significant effect on the drag. That book is the standard reference for any person interested in vehicle aerodynamic drag. It's also easy to understand, and I highly recommend it. This is apparently the current (5th) edition of this book: https://www.amazon.com/dp/0768079772/?tag=pfamazon01-20

A real world example of the effect of adding an aerodynamic topper to a pickup truck is here: https://ecomodder.com/forum/showthread.php/modding-06-gmc-canyon-17070.html.

If you want to study the aerodynamics of an existing car, this book by Julian Edgar is excellent: https://www.amazon.com/dp/1787112837/?tag=pfamazon01-20.

What is delta Cd, why Cd has minus and plus sign, can you describe this graph?

jack action said:

From my site, this is the effect of the rear roofline treatment in order of importance:

View attachment 316947​

Each design adds approximately 0.01 to the drag coefficient ##C_d##. For example, the hatchback with ##\theta## = 25°-35° (design #6) adds approx. 0.06 to ##C_d##.

From the same page, you can find one of the sources for this (Theory of ground vehicles, 2nd ed., J.Y. Wong, 1993, p. 179):

View attachment 316948​

I think design 5 has highiest drag, round edge cause low pressure point here.
If better look modern cars have sharp edges at side and top where air leave car,you must avoiding low pressure peak.


Also I think in hatchback where flow separate from back, rear window angle don't change nothing, because flow is allways separated, if angle is 40° or 80° is the same...

What is book description with second graph?

jrmichler said:

A real world example of the effect of adding an aerodynamic topper to a pickup truck is here: https://ecomodder.com/forum/showthread.php/modding-06-gmc-canyon-17070.html.

I skimmed that thread: you were looking at LEDs in 2011? You are ahead of the curve!

jrmichler said:

Here's a partial answer from Aerodynamics of Road Vehicles 4th Edition, edited by Wolf-Heinrich Hucho:
View attachment 316946

Why Cd is negative, can you explain what this graph show

You really need to read the entire section in Hucho to properly understand it. There are other graphs in there, and text explaining everything. That book is necessary if you are truly interested in the subject, although there might be other vehicle aerodynamics books that are as good. If you are not interested enough to buy a copy, borrow one from a library.

That graph is based on a simplified model. The more detailed information in the book also discusses the effect of important design details at the side corners.

You need to spend time studying the graph. First, look at the horizontal axis. It's the angle ##\phi##, which starts at zero. When ##\phi## is zero, the model is a simple squareback. The various lines in the graph represent different lengths of the rear taper. Those lengths are expressed as a ratio to the overall length as shown in the top part of the sketch and in the block set inside the graph.

A taper angle of zero is a simple squareback, and has an overall ##C_D## of whatever it is. The vertical axis is the change of the ##C_D## from that baseline ##C_D##.

jrmichler said:

A taper angle of zero is a simple squareback, and has an overall ##C_D## of whatever it is. The vertical axis is the change of the ##C_D## from that baseline ##C_D##.

Now is clear.
Inerestly for some high AoA angles for lines 0.09 and 0.18,drag even worse than squareback.

So longer the rear=better (0.45 line), at 20° "AoA" Cd start rise, probably flow separation start.

Does flow separation induce low pressure or high pressure at the rear window+trunk compare to attached flow?

Attacehd flow is faster so this mean low pressure, hmm but we don't wont to have low pressure here,
goal is to increase pressure at the back of car as much as possible ...?

So we can deliberately stall rear window/trunk to decrease drag of car?

Jurgen M said:

Does flow separation induce low pressure or high pressure at the rear window+trunk compare to attached flow?

Flow separation creates a low pressure zone that is pulling the car backward.

Jurgen M said:

Attacehd flow is faster so this mean low pressure, hmm but we don't wont to have low pressure here,
goal is to increase pressure at the back of car as much as possible ...?

So we can deliberately stall rear window/trunk to decrease drag of car?

You are mixing two concepts: Lift and drag.

With lift, you speed up the flow on one side of a vehicle to reduce its static pressure, and this creates a net force perpendicular to the flow that pulls the vehicle on the high-speed flow side.

With drag, you have to imagine the vehicle moving instantly in the surrounding air which, for an instant, compresses the air in front of it (high pressure zone) and leaves an empty spot of vacuum behind it (low pressure zone). This creates a net force parallel to the flow that pulls the vehicle backward. Of course, nature hates emptiness, so the surrounding air will try to fill the rear end vacuum as fast as possible, leading to chaotic turbulences.

So with drag, the objective is to reduce this rear end low pressure by forcing the flow to follow the contour of the vehicle, thus no flow separation, no turbulences, and no low pressure pulling backward. You just want to "split" the air as you go in, not "break it apart".

If there is flow separation behind the vehicle (behind the rear bumper), it acts on the vertical area of the rear end, but it has no horizontal surfaces to act upon so it doesn't affect the lift/downforce of the vehicle.

But if the flow separation is on the upper surface of the vehicle (behind the rear window, over the trunk, for example), the low pressure zone will act on the vertical surface (of the rear window), but also on the horizontal surface (of the trunk) and increase the lift at the rear end of the vehicle.

jack action said:

Flow separation creates a low pressure zone that is pulling the car backward.

Yes you are right, here at 5:40 we can see how pressure drop when flow separation starts..
(But how then F-duct system reduce drag at F1 car if stalling the wing reduce pressure at back side of rear wing?)

Jurgen M said:

But how then F-duct system reduce drag at F1 car if stalling the wing reduce pressure at back side of rear wing?

I don't know the system, but it seems the duct as a whole is blocking the flow to the rear wing, thus the wing is in the turbulence behind the duct, which is not good. At higher speeds, they divert part of the duct flow to go straight through, effectively reducing the duct frontal area and creating a more laminar flow for the wing. But I might be mistaken.

jack action said:

I don't know the system, but it seems the duct as a whole is blocking the flow to the rear wing, thus the wing is in the turbulence behind the duct, which is not good. At higher speeds, they divert part of the duct flow to go straight through, effectively reducing the duct frontal area and creating a more laminar flow for the wing. But I might be mistaken.

Here is some explanation how this looks like:
https://formula1techandart.wordpress.com/2010/12/14/mc-laren’s-innovative-rear-wing-system-f-duct/

https://www.formula1-dictionary.net/f_duct.html

I see now.

First, you should accept that creating lift will most likely create drag because there is no free lunch. Therefore, by reducing lift, you should expect the drag to drop.

The drawings in your post show the streamline going upwards, ending with a simple arrow. I highly doubt that this is what actually happens, especially at high speeds. The streamlines must come back down and that will be turbulent. By creating the extra turbulence, you are effectively altering the top wing shape by thickening it. The middle streamlines are therefore diverted to a more horizontal flow - themselves pushing down on the lower streamlines and pulling the top ones down - thus less turbulence overall is needed to bring back the entire flow horizontal. This decreases the pressure drop, leading to less downforce and less drag.

In the following images, do you see how the shape of the turbulent flow tends to create another horizontal "drop shape" to bring back the streamlines horizontally?


If you would create turbulence in the middle of the wing, it would pull the top streamlines down, leading to a smaller "drop shape", close to the wing shape. We call that reattaching the flow. Here are other examples:

@jack action Thanks for answer.