If you look at this picture below, you will notice that the nose portion of the Mig-21 has a unique conical shape which is completely different from the nose of the F-16.
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So what explains the conical design of the nose of the Mig-21?
The nose design of aircraft, like any other part, is a result of optimization in response to a number of factors. The Mikoyan-Gurevich MiG-21 'Fishbed' is a supersonic, second/third generation Soviet fighter/interceptor.
The first jet aircraft to enter serice during the WWII, the Messerschmitt Me 262 'Schwalbe' and Gloster Meteor had twin engines in their wings. In these cases, the nose was designed to carry the cannons, which were the primary armament at the time.
"Messerschmitt Me 262A at the National Museum of the USAF" by USAF museum - http://www.nationalmuseum.af.mil/shared/media/photodb/photos/040820-F-1234P-081.jpg. Licensed under Public Domain via Commons.
"F86Sabre" by Kowloonese at the English language Wikipedia is licensed under CC BY-SA 3.0
The first generation jet fighters, like the F-86 and Mig-15 were subsonic and had engines buried into the fuselage to reduce drag. The nose, again carried the cannons (in case of Mig-25, in the lower fuselage).
However, the second generation jet aircraft were the first operational jets to go supersonic. The Mig-21 was designed in response to a Kremlin specification, which called for Mach 2 level speed (at altitude), while carrying a simple radar and option for future air-to-air missiles.
As the jet engines require airflow to be subsonic at entry, the flow has to be decelerated before reaching the engine. Early in the design (from Ye-50-3), Mig decided to use a conical centerbody for this purpose, as it was decided that the aircraft would be single engined with engine in the fuselage (the engine was supposed to be the Mikulin AM-9B, however, the aircraft ended up using Tumansky R-11).
This nose design decelerated the flow using two oblique shocks and a normal shock, giving improved pressure recovery at high supersonic Mach numbers. The center-body (cone) moved axially according to the Mach number. Also, the center body housed the radar and associated equipment.
The first generation Mig 21s only had a range finder, and the intake diameter had a smaller cone. The following image shows the range finder used in early models of Mig 21.
"Mig21F13web" by Newresid [email protected] - Own work work vector drawig travail personnel dessinn vectoriel. Licensed under CC BY-SA 3.0 via Commons. (Image cropped)
"MiG-21F-13 radar Keski-Suomen ilmailumuseo" by MKFI - Own work. Licensed under Public Domain via Wikimedia Commons.
The photo you've shown are from the later versions (Mig-21 bis from IAF), which had the radars from the "Sapphire" family. To fit the radar antenna into the cone, the cone had to be made bigger, therefore the whole front fuselage had to be redesigned, the diameter of intake got more than 200 mm higher, and the cone itself got longer, wider and moved forwards. The following figure shows the enlarged nose cone section housing the radar. Interestingly, the nose cone seems to be made out of (metal tipped) wood to prevent interference.
"Mig21fishbedHfamilyweb" by Newresid [email protected] - Own work work vector drawing travail personnel dessin vectoriel. Licensed under CC BY-SA 3.0 via Commons. (Image cropped)
Source: toad-design.com
A number of aircraft from that time had conical body inlets, like the British English Electric Lightning.
"Lightning.inflight.arp.750pix" by Arpingstone - Own work. Licensed under Public Domain via Commons.
The F-16, on the other hand, has a simple normal shock diffuser. By the time of F-16, the radars had become bigger and more important (AAMs have become the primary combat weapon, replacing guns), and needed more space in the nose. As a result, the inlets of most of the aircraft had moved to the sides/downwards. The following figure shows the AN/APG-68 radar in F-16.
Source: defenseindustrydaily.com
A lot of early jet aircraft had the intake in the nose. Here's a few more examples:
The cone in the front is required because the Mig-21 is a supersonic aircraft. The cone breaks the shockwave so that the inlet air is sub-sonic. The SR-71 is a very different type of aircraft but you can see that its engines have a very similar style of inlet.
what is the design philosophy behind the shaping of the nose of the Mig-21
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The design philosophy which led away from the nose intake was to fit a powerful radar to the aircraft, which in turn was a consequence of switching from guns to air-to-air missiles as the primary armament of fighter aircraft.
Most designs of the late Forties and early Fifties did not consider powerful radars in individual aircraft, but were based on ground radars and radio communication to direct the aircraft towards their opponents. Much of that strategy was an extrapolation from World War II, where large groups of bombers had to be intercepted.
In the Fifties, the advances in electronics and rocket propulsion made air-to-air missiles possible, and gradually the fighter aircraft found themselves in the role of ground stations, scanning a wide space deeply and directing their missiles to individual targets, just like ground radars had done with fighters in the closing years of World War II. Radar range and performance required a large dish in the nose of the aircraft, and the intake had to move to the sides. In parallel, the increased work load for the individual aircraft resulted in two-seater designs, where the radar system was operated by a dedicated back-seater.
Note that the MiG-21 or the BAC Lightning did have a radar in the nose cone, but this was a very small radar for local orientation and not suitable for detecting targets more than 100 km away and directing guided weapons.
As to why the intake was shaped as it is, please read this answer here on Stack Exchange on the design of supersonic intakes.
North American F-100 Super Sabre (left, picture source). Just like the MiG-21, this was designed to be led from the ground and engage the enemy in visual conditions.
Convair F-106 Delta Dart (right, picture source). This was the first fighter designed to use missiles as a primary weapon. Its radar system was extremely complex, combining on-board with ground assets, for all-weather operation using missiles over long distance, including a nuclear-tipped version for use against big bomber formations.
Just so you don't think that Mikoyan would not try to integrate bigger radars (picture source): The Ye-8 prototype changed the intake to an F-16 style belly intake to make room in the nose for a Sapfir 21 radar, which enabled the MiG-21 to engage targets in all weather conditions and at night. First flight was in April of 1962, but no production followed.
Radar of the Phantom II (right, picture source)
McDonnell-Douglas F-4 Phantom II (left, picture source). Just a decade after the F-100, the nose was designed around a 81cm radar dish and the aircraft gained a dedicated radar operator to engage enemy aircraft without ground support and in all weather conditions. Now, it can be argued that its side intakes were a consequence of using two engines, but the F-106 used a single engine and still had similar side intakes.
Advances in computer control reduce the workload and the size of the aircraft, so the F-16 can be operated by a single person and still carries a radar powerful enough for independent all-weather operation.
It is the intake of the jet engine which gives it that shape, a good number of earlier jet fighter planes did have that configuration. The pointed part is the shock cone for when the plane flies supersonic so that the shock would not mess with the aerodynamics of the plane especially inside the engine.
Image by USAF
A lot of supersonic aircraft of the era had the same kind of intake, the English Electic Lightning off the top of my head:
EE Lightning F6 'XS904 / BQ' by Alan Wilson is licensed under CC BY-SA 2.0
The cone is to slow down the supersonic airflow, so that the air is relatively calm when it goes into the turbine, which ensures a smooth burn. It's in the nose so that the air duct is straight, because, without computer modelling it took a lot of trial and error to design curved air intakes (e.g. in the wings).
To be extremely simple without going into too much technical design theroy.
It allows the engine to breath at high speeds.
You will notice that in front of a high speed fan or a cooler it will be extremely difficult for you to breath, try putting your head out of the car and breath when travelling at 60mph , it will be much more difficult to breath compared to doing the same while travelling at 20mph.
Its the same principle, since you cannot reduce the speed of the aircraft to allow it to breath, the cone acts as a hand in front of your nose at 60mph which will allow you to breath and maintain the speed.
It disrupts the direct flow of the air into the engine and reduces the speed of the air to sub sonic levels which the engine can process.
Fun Fact: The design is already present in nature and was lifted off of the peregrine Falcon.
[Head shot by Keven Law protected under CC BY-SA 2.0]
I'm not an aircraft designer, but I'm pretty sure I've figured out the design philosophy that led to that nose. The aircraft has one engine, which is positioned along the aircraft's central axis. Since it's a jet engine, it needs an intake. The simplest intake design is a straight tube. Due to the positioning of the engine, this puts the intake's inlet right at the nose. As others have mentioned, the cone in the center of the inlet is present in the MiG-21 but not, for example, the F-86 Sabre, because the MiG-21 is a supersonic aircraft, and the F-86 isn't.
The Super 7, an updated J-7, the Chinese MiG-21, had a new nose and intakes. Basically, an F-20 Tigershark grafted onto the fuselage of a J-7 (Grumman were consultants on the project). As such, you can, in effect, see a MiG-21 with a more modern nose.
The inception of forward looking radar created a need for a nosecone on aircraft that already had a centered inlet. As radar size and complexity evolved, so did the requirement of an integral nose cone. This also let to the design of the single or split inlets.
As mentioned above, it's an effective design solution for the placement of an antenna for a fire control radar and supersonic diffuser for a jet intake all in one package which minimizes the frontal cross section of the aircraft, reducing drag. As the BVR SARH and TARH missiles became more ubiquitous as air to air weapons, this necessitated larger and larger antenna for the fire control radar set to increase the range in which the radar could acquire and track targets, forcing the placement of engine intakes elsewhere in the aircraft to maximize available real estate on the nose of the aircraft for for these FCRs.
The nose cone or spike is designed to take supersonic air and slow it down to subsonic so the jet engine can ingest it. The mig-21 spike moves forward and aft based on speed much like the SR-71 ,except they work opposite. The SR-71 spike starts forward and moves aft as the plane goes faster to bring the shockwave inside the inlet. The mig-21 spike starts aft and moves forward to keep the shockwave outside of the inlet as the plane goes faster because it is a external compression inlet. The Convair B-58 Hustler was the same way. Most supersonic planes including the Concorde have external compression inlets which limit their speed to Mach 2. They have the ability to go faster but above Mach 2 it burns way to much fuel to be efficient.
One point not mentioned here, but crucial to this discussion, is the inescapable fact that, all other factors, i.e. sophistication of technology,"Moore's Law", etc., being considered, the effectiveness of a radar, not unlike the lens of a camera, is determined by the sheer physical size of the antenna, with performance actually increasing EXPONENTIALLY(!!!), the greater the diameter. Which is why both the MiG-29, and the Sukhoi Su-27/35 series all have such large, bulbous noses, the better to make up for a deficiency in chip design, and thus general electronic performance and capability. Needless to say, with it being a most basic law of physics, that two objects cannot occupy the same space at the same time, the larger the antenna, and its accompanying radome, the less space available, circumfirentially speaking, for air delivery to the engine, whose needs in this regard, cannot be compromised. Accordingly, and with BOTH(!!) requirements increasing, somebody had to move, and, with the radar antenna having, for obvious reasons, "first dibs" on the nose of the aircraft, the inlets had to "re-locate" to to the flanks. ala, F-102, F-104, F-105, F-106, and F-4, F-111, F-114, F-15, etc., not to mention Migs "23" to "31"! I could say "Lightning" replaced by "Typhoon", or "Mirage" by "Rafale", but you get the point.
