Effects of Vehicle Shape on Aerodynamic Characteristics

[Piwoslaw]

As we all know, improving the airflow over one part of a vehicle often effects how air flows over other parts. For example, the hood and windshield angles determine how the air flows over the roof and sides.

The following comes from Piechna's book. I haven't seen the original work (cited below), so I don't have the full data. I give only what Piechna wrote.

Asago and Takagi ([1]) systematically tested the shape of a sedan, changing 10 different elements of the body. They planned the experiments in such a way that the number of tests could be reduced from 3^10 to only 81. Each of those 81 tests was performed twice.

The tests were conducted on a 1:5 scale model in a wind tunnel. The following elements were tested:

1. Narrowing the body at the front and rear,
2. Side window angle (22° and 30°),
3. Length of front bumper,
4. Angle of grille (0°, 12.5°, 25°),
5. Angle of hood/bonnet (5°, 7°, 9°),
6. Angle of windshield (25°, 30°, 35°),
7. Angle of rear window (30°, 35°, 40°, 45°, 50°),
8. Inward angling of rear pillar,
9. Angle of trunk/boot (4°, 8°, 12°),
10. Geometry of rear spoiler.

The effect of each of these elements on the drag coefficient was tested, then the propotional change in Cx (Cd) was calculated. Here is an ordering of those effects:

1. 46.5% - Angle of hood/bonnet (element #5)
2. 17.0% - Angle of grille (element #4)
3. 11.7% - Narrowing the body at the front and rear (element #1)
4. 11.5% - Angle of rear window (element #7)
5. 3.9% - Inward angling of rear pillar (element #8)
6. 1.9% - Relationship between rear window angle and spoiler
7. 1.7% - Relationship between windshield and rear window angles

As the above list shows, the hood/bonnet angle has the largest effect on the drag coefficient Cx of a sedan shaped vehicle. Increasing it from 5° to 9° reduced Cd from 0.52 to 0.47.

Changing the rear window angle from 30° to 40° increased Cx from 0.47-0.485 (depends on windshield angle) to 0.51.

Here is a drawing of how the drag coefficient Cx depends on windshield and rear window angles (Y-axis is Cx, X-axis is windshield angle, curve 1 has rear window angle of 30°, curve 2 has rear window angle of 35°):

The lift force is mostly effected by:

• Rear spoiler arrangement (element #10)
• Angle of trunk/boot (element #9)
• Angle of rear window (element #7)

Adding a spoiler decreased the lift coefficient Cz from 0.51-0.52 to 0.43-0.42.

A flatter trunk/boot cover (4°) with spoilers gave lower lift coefficient values (0.38-0.39) than a 12° cover (0.45).

The lateral force (with inclination gamma = 10°) is mostly effected by:

• Angle of rear window (element #7)
• Angle of trunk/boot (element #9)
• Angle of grille (element #4)

Increasing the rear window angle from 30° to 40° increased the lateral force coefficient Cy from 0.42 to 0.49. Increasing the hood/bonnet angle from 5° to 9° increased Cy from 0.44 to 0.47.

The coefficient of angular (swerving?) momentum Cm is effected by:

• Angle of grille (element #4)
• Angle of rear window (element #7)

Increasing grille angle from 0° (vertical) to 25° increased Cm from 0.132 to 0.159. Increasing the rear window angle causes Cm to decrease.

The optimal geometry to obtain the lowest aerodynamic drag (Cx = 0.435) is as follows:

• extended front bumper,
• swept back grille (25° from vertical),
• steep hood/bonnet angle (9°),
• moderate side window angle (22°),
• pronounced narrowing of body both front and rear,
• rear pillars angled inwards,
• flatter windshield angle (25°),
• almost flat trunk/boot (4°).

The optimum for lowest lift is slightly different (shorter front bumper, vertical grille, steep rear window - 40°).

As mentioned earlier, this is only a review from Piechna's book. If anyone has access to Asago and Takagi's work, please post more info here.


[1] Asago T., Takagi M., Use of a Designed Experiment for Systematically Testing the Effects of Vehicle Shape on Aerodynamic Characteristics, JSAE Review, No.2, April 1987, pp.26-33.

[PaleMelanesian]

Really? I'm amazed that the hood angle has that much effect.

[Arragonis]

I am going to take time to look at this vs Helga, especially that second list.

[aerohead]

Originally Posted by Piwoslaw

As we all know, improving the airflow over one part of a vehicle often effects how air flows over other parts. For example, the hood and windshield angles determine how the air flows over the roof and sides.

The following comes from Piechna's book. I haven't seen the original work (cited below), so I don't have the full data. I give only what Piechna wrote.

Asago and Takagi ([1]) systematically tested the shape of a sedan, changing 10 different elements of the body. They planned the experiments in such a way that the number of tests could be reduced from 3^10 to only 81. Each of those 81 tests was performed twice.

The tests were conducted on a 1:5 scale model in a wind tunnel. The following elements were tested:

1. Narrowing the body at the front and rear,
2. Side window angle (22° and 30°),
3. Length of front bumper,
4. Angle of grille (0°, 12.5°, 25°),
5. Angle of hood/bonnet (5°, 7°, 9°),
6. Angle of windshield (25°, 30°, 35°),
7. Angle of rear window (30°, 35°, 40°, 45°, 50°),
8. Inward angling of rear pillar,
9. Angle of trunk/boot (4°, 8°, 12°),
10. Geometry of rear spoiler.

The effect of each of these elements on the drag coefficient was tested, then the propotional change in Cx (Cd) was calculated. Here is an ordering of those effects:

1. 46.5% - Angle of hood/bonnet (element #5)
2. 17.0% - Angle of grille (element #4)
3. 11.7% - Narrowing the body at the front and rear (element #1)
4. 11.5% - Angle of rear window (element #7)
5. 3.9% - Inward angling of rear pillar (element #8)
6. 1.9% - Relationship between rear window angle and spoiler
7. 1.7% - Relationship between windshield and rear window angles

As the above list shows, the hood/bonnet angle has the largest effect on the drag coefficient Cx of a sedan shaped vehicle. Increasing it from 5° to 9° reduced Cd from 0.52 to 0.47.

Changing the rear window angle from 30° to 40° increased Cx from 0.47-0.485 (depends on windshield angle) to 0.51.

Here is a drawing of how the drag coefficient Cx depends on windshield and rear window angles (Y-axis is Cx, X-axis is windshield angle, curve 1 has rear window angle of 30°, curve 2 has rear window angle of 35°):

The lift force is mostly effected by:

• Rear spoiler arrangement (element #10)
• Angle of trunk/boot (element #9)
• Angle of rear window (element #7)

Adding a spoiler decreased the lift coefficient Cz from 0.51-0.52 to 0.43-0.42.

A flatter trunk/boot cover (4°) with spoilers gave lower lift coefficient values (0.38-0.39) than a 12° cover (0.45).

The lateral force (with inclination gamma = 10°) is mostly effected by:

• Angle of rear window (element #7)
• Angle of trunk/boot (element #9)
• Angle of grille (element #4)

Increasing the rear window angle from 30° to 40° increased the lateral force coefficient Cy from 0.42 to 0.49. Increasing the hood/bonnet angle from 5° to 9° increased Cy from 0.44 to 0.47.

The coefficient of angular (swerving?) momentum Cm is effected by:

• Angle of grille (element #4)
• Angle of rear window (element #7)

Increasing grille angle from 0° (vertical) to 25° increased Cm from 0.132 to 0.159. Increasing the rear window angle causes Cm to decrease.

The optimal geometry to obtain the lowest aerodynamic drag (Cx = 0.435) is as follows:

• extended front bumper,
• swept back grille (25° from vertical),
• steep hood/bonnet angle (9°),
• moderate side window angle (22°),
• pronounced narrowing of body both front and rear,
• rear pillars angled inwards,
• flatter windshield angle (25°),
• almost flat trunk/boot (4°).

The optimum for lowest lift is slightly different (shorter front bumper, vertical grille, steep rear window - 40°).

As mentioned earlier, this is only a review from Piechna's book. If anyone has access to Asago and Takagi's work, please post more info here.


[1] Asago T., Takagi M., Use of a Designed Experiment for Systematically Testing the Effects of Vehicle Shape on Aerodynamic Characteristics, JSAE Review, No.2, April 1987, pp.26-33.

I have that work or a similar SAE report at home.All this is in Hucho's book.Hucho did similar testing when at VW in the early 1970s.
Most modern generic cars have embraced the best of these findings to obtain the mpg they enjoy.
In my Sticky on Mod-Data I believe I touch on all these themes.

[Cd]

I wonder if the grille had rounded edges in this test.

[Delmar]

Thanks for posting this... for me, this is good encouragement for my project of making a custom fiberglass hood, which will have a steeper angle than the existing stock hood... Yes one of my many lofty projects planned for the year
encouragement never the less...

[Piwoslaw]

Thanks, Aerohead. I've never had Hucho's work in my hands, so I wasn't aware that he covered this.

[aerohead]

Originally Posted by Piwoslaw

Thanks, Aerohead. I've never had Hucho's work in my hands, so I wasn't aware that he covered this.

I've not yet dug in to find the paper,but I'm thinking it is circa mid-1980s.
It's kind of a rehash of R.G.S.White's work at MIRA in England,published in 1969.( A Method of Estimating Automobile Drag Coeffiients,SAE Paper# 69018 )
White took a wind tunnel model and ran it through 44 physical body change iterations to qualify the lowest drag capability for 9 major body categories.
If you combined the best of each category,the 'recipe' could yield a car body with Cd as low as 0.24.Not bad for 1969.I'm pretty certain that HONDA used White's work to help create their 178 mpg P-100 in 1972.
There is an image of his table in the Phil Knox's Aerodynamic Photos Album somewhere.

[aerohead]

Piwoslaw,I located the material I was thinking about.
The work Hucho cites in his book comes from the work of G.W.Carr of the Motor Industry Research Institute (MIRA),England,who submitted work from the mid-1960s,into the latter 1970s.This material is virtually identical in scope to your material.
I also have SAE Paper # 860211,by Alfons M. Gilhaus and Volker E.Renn of Ford Werke AG,K'o'ln,Germany which duplicates the work of Carr and your source.
It's funny how researchers appear to operate in a vacuum.

[Arragonis]

Did these guys work in this at all ?



Precursor to the Sierra ?