In November 2019, Samantha James of Carwow published a very interesting article titled “Best-looking cars of the last decade.” What made it more interesting yet is that their review applied golden ratio analysis techniques used for human faces to the front end view of automobiles. Headlights became eyes. Emblems became noses. Grills became mouths. Makes good sense, right? I’ve been showing the golden ratio in human faces since the late 1990s. London plastic surgeon Dr. Julian Silva is recognized for giving a golden ratio score of famous celebrity faces, as shown below left. Carwow used a very similar approach, as shown on the right:
Carwow is UK company that helps consumers to make choosing and buying their perfect car easy and enjoyable. Stefanie Finch of their PR agency, Propellernet.co.uk, contacted me on behalf of Carwow to ask if I’d be interested in covering their story on this site. I of course said “YES!” She and the Carwow team were kind enough to provide me with the inside story on what they did, and answered my many questions to understand and validate their study.
Now here’s the spoiler. Of 626 cars analyzed, Carwow identified the best-looking car of the last decade to be the 2016 Smart ForTwo Cabrio:
To be completely honest, of all the cars I’ve ever seen in my life, this car would probably strike me as being in the bottom 10% when it comes to good-looking cars. So how did it score so high? Does the golden ratio work when it comes to cars? Time to investigate!
How could the 2016 Smart ForTwo Cabrio be the best looking car of the past decade?
As it turns out, the methodology used by Carwow was very impressive. It was thoughtful and creative, and their research and analysis was very detailed and exhaustive. I’ve reviewed facial studies by major universities on the presence of golden ratios in the human face whose methods didn’t even begin to compare to those used Carwow’s Mat Watson and team. Here’s what they did:
Identify 14 key, common markers that appear in the frontal design of a car:
- Windshield – Top Left / Top Center / Top Right
- Wing Mirror Midpoint – Left / Right
- Headlight Midpoint – Left / Right
- Grill – Left / Center / Right
- Logo/Emblem
- Body Bottom – Left / Center / Right
They then:
- Computed the ratios between every possible permutation of those points. Note that taking 3 points with 14 to pick from results in 364 combinations and 2,184 permutations!
- Identified the most significant 50 ratios found in these 2,184 sets of points, as ranked by their conformity to the Golden Ratio.
- Averaged these same 50 ratios for each car to get the car’s score for conformity to the Golden Ratio
- Converted that to a score between 0 and 100.
Carwow said that the ratio between 0 and 100 was built to give a scale of conformity. They used an average of the ratios and then calculated how close that was to the golden ratio as an absolute number.
Carwow also used a min-max scaling methodology between the ratio furthest from the golden ratio and the ratio closest to the golden ratio. This provided a theoretical limit of how close to golden ratio conformity the cars could get. This was then applied to the average of all the 50 ratios for all 626 cars. In practicality, these two measures were almost the same thing, but they wanted to use their actual measurements to keep things feeling ‘fairer’. The score for first place SmartForTwo Cabrio was a 98.83% conformity to the golden ratio.
A great methodology, so why the questionable results?
I must compliment Mat and the Carwow team on doing such an exhaustive evaluation of car “facial marker” possibilities, and for identifying the ratios in their body of evidence that most closely aligned with the golden ratio in then doing their assessment. Many university studies of the human face by major universities and industry professionals might have produced much better results if such rigor had been applied.
Still, I was puzzled as to how a car that I found to be so visually unappealing could have been the best-looking car of the past decade.
I did some research to find the best looking cars as judged by other major automotive magazines, including Car and Driver, AutoGuide and US News.
Among them, I found three cars that were recognized by both Car and Driver and AutoGuide for their styling and beauty. I found that these great looking cars all rated below #200 in the Carwow rankings:
- Lexus LC – Ranked #214 by Carwow with a score of 96.50%
- Alfa Romeo Giulia – Ranked #240 by Carwow with a score of 96.20%
- Infiniti Q60 – Ranked #224 by Carwow with a score of 96.38%
I also asked Carwow’s project lead, Mat Watson, for his personal favorites, which were:
- Peugeot 508 – Ranked #123 by Carwow
- Aston Martin Vantage – Ranked #554 by Carwow
- Range Rover Velar – Ranked #270 by Carwow
I asked, “Ignoring the analysis for a second, and just going on feelings, how would you rate the beauty of each of your top 3 cars against the Carwow top three, simply using a 1-10 scale, where 10 is the highest?”
Iain Reid, Carwow’s site editor, provided his rankings:
- Peugeot 508 – 8/10 by Ian, but only #123 by Carwow
- Aston Martin Vantage – 9/10 by Ian, but only #554 by Carwow
- Range Rover Velar – 9/10 by Ian, but only #270 by Carwow
- Smart Fortwo Cabrio – 2/10 by Ian, but #1 by Carwow
- Volkswagen Up – 4/10 by Ian, but #2 by Carwow
- Vauxhall Mokka – 2/10 by Ian, but #3 by Carwow
There continued to be a clear disconnect here. I asked why their personal tastes didn’t align with the Golden Ratio results, and the Carwow team shared this perspective with me:
“For many people, it’s impossible to ignore the whole chassis of the car, or dismiss the beauty of the individual features within the headlights, the hood ornaments or bumper details. When determining the beauty of something, humans take in a much wider view, noticing all the smaller design details that get lost in a pure ratio/distance analysis. Furthermore, other non-design factors evoke an emotional reaction into how someone responds to a car’s aesthetic. For example the noise they imagine the engine makes, how they imagine the leather seats might feel or smell like, or the thrill of adrenaline they might feel at opening up into 6th gear on an open coastal road. It’s these extra imagined layers of emotion that influence people’s perception of a car’s beauty – whilst your brain might not read the face of a Smart Car as being ugly or ill-designed, the model doesn’t evoke those powerful stirs of emotion in the way Aston Martin or Range Rover does.”
I agree that there are more factors in a car’s beauty that its front view. It seemed though that we should be able to make a reasonably consistent assessment of a car’s visual appeal and “beauty” without smelling the leather or hearing its engine roar.
The Golden Ratio – Beautiful or Ugly?
So it was very clear that the cars that Carwow identified as being closest to the golden ratio in their key markers were in fact rather ugly cars, when judged by the Carwow team’s natural instincts as car buffs and automotive professionals. Conversely, the cars that this team thought to be the most beautiful ranked surprising low on the Carwow list.
So is this proof that the golden ratio has no real correlation to beauty?
Fortunately, having studied this topic for over twenty years, I was able to identify the problem. While Carwow’s methodology was very ingenious and rigorous, one of their most fundamental assumptions had a fatal flaw.
The Carwow team assumed that any golden ratio relationship between two line segments formed by three of their markers would emulate the golden ratio relationships found in nature and in the design arts. This, however, simply isn’t the case. The golden ratio, by the very definition provided by Euclid in 300 BC, is based on this:
“A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser.”
This concept is illustrated below:
This same division of a straight line at this one special golden ratio point appears in the proportions of the human face:
Auto manufacturers have used this technique in the design of their logos:
Aston Martin applied this same golden ratio concept to the design of their 2014 Rapide-S and DB9 models:
This same division of a straight line into segments in golden ratio proportion also appears in the geometry of a five-pointed star. Note that multiple golden ratio proportions appear here – in the black to blue lines, the blue to red lines, and the red to green lines:
There’s certainly a beauty in the face, the logos, the Aston Martins and the five-pointed star.
Suppose, however, that I took these golden ratio segments of the star and rearranged them into something very different:
The lines are all the same. The arrangement is still symmetrical, just like the front end of a car would be. All the same golden ratio relationships exist between the lines, but the beauty that was there is now gone. As you can imagine, a beautiful face could also be rearranged and distorted to keep certain golden ratio relationships intact, but the face would no longer be beautiful either. These golden ratios are no longer discernible by the human eye, especially when placed among the 364 possible combinations of lines.
Golden Ratio design is all about visual aesthetics, not just mathematics.
Unfortunately, this type of visual distortion is pretty much what Carwow did in taking their measurements and then doing their ratings. They did the math, and did it very well, but they missed the the very critical fundamental concept that the beauty associated with golden ratio is based on dividing a straight line at the one very unique point that gives it the familiar and pleasing aesthetic that we see in nature, geometry and the arts. The beauty that comes from the golden ratio is not based on just a jumble of lines with mathematical ratios in their relative lengths that happen to come close to 1.618.
To illustrate the point, here’s another set of lines from the original five-pointed star whose golden ratio relationships have been distorted. The blue lines are 95% of their original size, the red are 90% and the green are 85%.
Using Carwow’s scoring methodology, this set of lines above would have a much lower correlation to the golden ratio and should thus be not nearly as attractive as the jumbled version of the star above. That’s clearly though not the case. This star is still more appealing because the lines better represent the concept of dividing a line at its golden ratio point. That is likely why cars that were in fact designed with better aesthetics produced lower conformity scores than the cars that were really quite unattractive.
Reverse engineering the golden ratio data and proving the concept.
I reverse engineered the methodology of Carwow’s results and confirmed with them that I’d done it correctly. From this, I found that if we look at the 50 markers that produced the highest correlation to golden ratios for the Smart ForTwo Cabrio, we find 23 relationships that are with 0.02 of the golden ratio:
The two images below illustrate the actual configuration of each of the above 23 “golden ratio” markers above, with a different color for each set of two lines that they identified as being a “golden ratio:”
For the 23 Smart ForTwo Cabrio markers whose golden ratios varied by less than 0.02 from the golden ratio, only ONE was in a straight line. This was the Grill Center – Emblem Center – Windshield Center measure, with its two permutations appearing twice in the list above.
Golden ratios, yes, but not perceptible by the human eye.
This means that all of the rest of the data points that drove the Smart ForTwo Cabrio to the #1 position in Carwow’s list were actually based on measures of markers that were visually confusing by being at odd angles to one another and not forming a straight line. As such, the lines formed by these markers would have had no real visual impact on the human perception of golden ratios in the car’s design. There was thus no reason to rank the cars as beautiful based on the measurements used by the Carwow team. That, I truly believe, is why there was no correlation between what everyone perceived as being beautiful and what their “golden ratio measurement” rankings said.
Great efforts don’t always produce great results, but we still win by learning.
Despite my findings on the lack of validity in the methodology and the results of the Carwow beauty rankings, I want to compliment the entire Carwow team on their ingenuity on coming up with this approach, and their very hard work in the exhaustive measurements and calculations that they performed.
Perhaps by applying the concepts I’ve described above, they could rerun the numbers and find out which cars really come closest to golden ratio proportions based on the visually perceptible division of a straight line into its golden ratio proportions, as we see in the beauty of a human face.
Applying the Golden Ratio in design.
What if we were to to apply traditional golden ratio design techniques to analyzing the beauty of car design? Mat might find that his personal favorite, the Peugot 508, has more golden ratios than the Carwow team realized that explain some of its beauty, as illustrated below:
I would like to thank the Carwow team for so generously sharing their research, time and perspectives with me.
I’d be happy to consult with the Carwow team in approaching this initiative with a more traditional and classic use of the golden ratio. I am happy to make the same offer to any parties who are interested in studying appearances of the golden ratio and its relationship to human perceptions of beauty and aesthetics. Golden ratio analysis isn’t difficult in concept, but it does require a depth of experience and knowledge of its appearances and applications to prevent the analysis from leading to the wrong conclusions.