__Aircraft religious caricatures__

by: X.Toff, Oct.25+Dec.26 2004

Jean Barbaud (http://lt.macfly.free.fr ou http://jeanbarbaud.blogspot.com/),

Rob Henderson (http://www.caricatureaircraftpictures.com/),

Pat Cherry (http://blackheartart.com),

Thomas Troestler (http://www.desinaero.fr.st),

we were facing a mystery:

I finally found an answer trying to create mathematical caricatures with computer (Corel Draw software), without the artistic talent of these great Masters. Very surprisingly, my explanation is religious:

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The step-by-step way to these explanations, and much more, are featured in my "Virtual Mustangs" ("Mustangs Virtuels" in French), a 185-pages book including a complete English translation, 30 artistic caricatures and 500 Mustangs invented by dreamers.

Getting (for free) the printable files of the book "Virtual Mustangs":Downloading explanations here |

ADDITION Oct.27th 2004:

Well, the principle is that God is (or would be) the highest perfection, so a

But what is a

Well, to find the good shape, mathematical perfect calculations may help, you just need to find a figure to optimize. Obviously, the major numbers to define a rectangle are the ratios Big-side/Short-side or Short-side/Big-side.

Which one of these 2 ratios, and to which value (1.01 to 1000 are possible for the first, 0.01 to 0.99 for the second)? One of our forefathers then said he has found THE unique answer: the perfect rectangle is an horizontal rectangle A which is a

Mathematicians took it easy: G=1+(1/G) thus G²=G+1 thus G²-G-1=0 thus G=

The other (mathematically true) answer to the same equation (before the sqrt: + replaced by -) being negative, impossible for a ratio of lengths, G above is the only answer, God's answer concluded the official Church...

In the modern society, the everyday-used rectangle was not mainly the shape of architects (rooms, windows) but the shape of paper sheets (before TV and computer screens became available). English/American schools and companies seem to hesitate between 8.5"x11" or 12" or 14" (ratio 1.29 or 1.41 or 1.65) while continental European countries seem to use a single one, called A4 (8.27"x11,69", ratio 1.41). Is this another rectangle being a

The basic principle was choosing a 1m² sheet of paper, called A1, of perfect shape to find. As this is too big for everyday use, it was fold in 2 and cut (into a A2 sheet), and the idea was there: Big-side/Short-side of A2 = Big side/Short-side of A1, precisely, without a reference to a square basis anymore, a kind of perfect rectangle from just a

Once more, mathematicians took it easy: the ratio long/short A comes from L/S=S/(L/2) thus L²/S²=2 thus L/S=sqrt(2)=1.414...

With LxS=1m², this gives A1, then folding (in 2) 4 times, that gave A4 of 1/(4)² m².

Knowing that, why have I chosen the church G=1.62 rather then the paper A=1.41? The answer is simple:

- I agree that usually an aircraft has port/starboard symmetry (not always: for asymmetric aircraft, have fun with my site http://cmeunier.chez-alice.fr/asym_dahu_aeroUK.htm). So the

- Working on a

ADDITION Nov.7th 2004:

The new generations may laugh at these complicated figures of the past, when choosing dimensions was not handled by everyone in a democratic way; now, it is clear that - no matter if you choose 640/480 pixels, or 800/600, 1024/768, 1152/864, 1280/960, 1600/1200, 2400/1800 - all comes from the very simple shape 4/3, without crazy square root, and the ideal ratio is 4/3=

ADDITION Oct.28th 2004:

Tonight I made a nightmare: I was in a hall of Justice, and severely condemned - thrice guilty.

1- It is stupid to ask whether 1.41 should be the length/span ratio or span/length ratio : the folding clearly occurs at the middle of the big side, so the centerline is there, and this is automatically 1.41=span/length (closer to a wide U-2 than to a long X-15) = length/half-span. And for the P-51 VTOL with folding on the wing, it

2- When you come into a church, you move forward in a long holy alley, and the sides are not important. So the church rectangle, drawn on a paper on a table in front of you is vertical, not horizontal. And about aircraft: after the tail-sitter foolish dead-end, it is now admitted that the principle of flight requires of course an horizontal wing, so you are not allowed to turn "nose up" your golden baby plane: the tail-to-nose

3- Flying machines cannot exist, young Gallileo! Are there flying machines in the holy Bible? No! So you

ADDITION Jan.19th 2013:

More than 60 more Mustang caricatures, of artists or myself, are featured at the beginning of my site updating the book: http://www.kristofmeunier.fr/Suite_Mustangs_V.htm

ADDITION Sep.19th 2019:

On a (French) site of mine: http://www.kristofmeunier.fr/nombdor0.htm I have explained that the Golden number provides no beauty. I may show it here with aircraft profiles.

1/ Filling a golden rectangle by increasing the fin height is decreasing beauty instead of increasing it:

2/ Even with spiral golden effect, the result is not a special beauty: