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Rectangular intakes have more corners which might increase subsonic pressure losses and would weigh larger than a pitot (Semi-circular) type intake. Are the designer drivers solely based on supersonic pressure loss improvement? Or for area-ruling? Am I missing something here?

F 16 has a pitot (Semi-circular) type intake whereas JAS 39 Gripen has a rectangular one. I wonder why.

Edit: The question is in reference to a fighter aircraft intake which employ fuselage buried engine configuration in-contrast to wing mounted or externally integrated engines. Fighter aircraft intakes are more complex when compared to simple cowl-lip configurations designed for larger commercial engines. Intake shape,size,location are function of wide variety of parameters, so something must be influencing the intake entry cross section of a fighter aircraft configuration.

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    $\begingroup$ Possible duplicate of Why do turbofan engines have a circular or oval shape instead a square shape? $\endgroup$
    – user14897
    Jun 27, 2018 at 16:09
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    $\begingroup$ @ymb1: While I agree that this is a dupe, the answers to the original question might not be sufficient. $\endgroup$ Jun 27, 2018 at 16:25
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    $\begingroup$ A reminder: if you have answers, however partial, please post them in the answer field. $\endgroup$
    – Federico
    Jun 27, 2018 at 16:49

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Are the design drivers solely based on supersonic pressure loss improvement?

Yes. And sometimes a few more considerations need to be taken into account.

We have covered the reason for intake shapes well on this site, but the details must be collected from several answers. In a nutshell: Higher flight Mach numbers need more elaborate and heavier intakes in order to convert the kinetic energy of the flow into pressure. A pitot intake is light and simple, but a poor choice for speeds in excess of Mach 1.6.

Rectangular intakes are normally chosen in order to make internal, moveable ramps possible which create a cascade of shocks in order to slow down the flow as efficiently as possible. Such designs are typical for Mach 2 aircraft (think Concorde, F-14, F-15, XB-70). Another way would be a central intake with a moveable spike, but those had to make way for big radar arrays in more modern designs. The JAS-39 intake is a little special: It sits next to the fully moveable canards, and those need a vertical wall in order to minimise the gap between canard root and fuselage/intake structure. Yes, a round intake would be slightly lighter, but is impossible due to the situation of the canards.

Detail of JAS-39 canard

Detail of JAS-39 canard, taken from this picture.

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Another reason is stealth - the shapes can be selected to minimize radar return. See the F22 and F35 leading edge shapes for example.

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From what I could find, the rectangular geometry of fighter aircraft intakes is due to the fact that the intakes incorporate sharper inlet lips in order to decelerate airflow to subsonic speeds to avoid supersonic performance losses from shock waves. There are some aircraft such as the MiG-21 and SR-71 which use adjustable inlet cones in order to be able to cruise at higher speeds without significant performance losses. According to Wikipedia, the MiG-21's inlet cone allows the creation of two shock waves, both of which are aimed at the inlet lips.

As for the F-16's semi-circular inlet, I'm not sure why that is the case. I couldn't quite find any helpful info.

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You have the right idea when you discuss area rule (Coke bottle) shape and pressure/compressibility. A classic example of the area rule shape for supersonic flight is the T-38/AT-38 and it's big brother the F-5. A large part of the limitation on the T-38's flight envelope is the air entering the engine. I have flown it up to Mach 1.3 which it can do reliably, however to go beyond that up to M 1.5 requires a very narrow range of temperature and pressure altitude due to the susceptibility to engine compressor stall and flameouts above 1.3 , due in large part to the supersonic airflow entering the intakes. The F-16, mentioned above, not only has a semi-circular (shark's mouth) intake, but also a large curve inside the intake (like a slide at a kid's park, slopes up as you enter the intake) and there are actually two flavors of intake for the Viper depending on the engine (the smallmouth and largemouth intake), the very long version of which is here: https://arc.aiaa.org/doi/abs/10.2514/3.22758?journalCode=jpp

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