This thread explains how the MiG-21's spine shape was changed to reduce wave drag at high speeds, improving its performance around Mach 1.2 to 1.6. The PF version with the new spine had less drag and more thrust, making it one of the best MiG-21 variants. The thread also compares it to other jets and discusses how design choices affect speed and aerodynamics.
MiG-21 area rule 🧵
The aerodynamic reason in change from the MiG-21F-13's spine shape to that of the MiG-21PF's is never thoroughly explained in any books on the Fishbed that I know of. That spine was used on MiG-21PFS, PFM & FL too.
Soviet MiG-21F-13 Indian MiG-21FL
The only online publication that I found to discuss this in enough detail is NASA-TM-84647 "Aerodynamic assessment of various supersonic fighter airplanes based on soviet design concepts - M. Leroy Spearman 1983”.
North Korean MiG-21F-13
According to the document, geometric data for the models (MiG-21 Mig-25 etc.) was scarce, and mostly from photos and other sources available at that time. Therefore, one must not consider the results to have excellent accuracy. They do shed some light nonetheless.
Its findings regarding the MiG-21’s wave drag according to supersonic area rule are:
• the MiG-21F-13 model seems to have a sectional area distribution optimized for Mach 1.50
• the MiG-21 model with PF spine seems to have a sectional area distribution optimized for Mach 1.20
•The PF spine seems to give less drag from Mach 1.20 to 1.60 compared to the F-13 one.
So the MiG-21’s spine was modified to the PF’s shape for reasons of supersonic wave drag reduction at M = 1.2 to 1.6, with no wave drag penalty at the higher Mach numbers.
Equally interesting is the fact that the MiG-25 (despite its boxy shape) is better than the MiG-21 in terms of wave drag coefficient beyond Mach 1.60.
You may be wondering, "what do you mean area ruled for Mach 1.5 or 1.2?". Well, if you're familiar only with R. T. Whitcomb's "transonic area rule", in which the sectional area distribution is calculated with plane intercepts at 90° to the velocity vector, then fair point.
With the transonic area rule theory you can only optimize for M = 1. But there is also the "supersonic area rule theory" developed by R. T. Jones and described in NACA-RM-A53H18a "Theory of Wing-Body Drag at Supersonic Speeds - 1953".
In short, the supersonic version extends the transonic one by stating that the plane intercepts should be inclined at the Mach angle of the speed at which you are calculating. For example, at M = 1, the Mach angle is 90° to the velocity vector, at M = 2, it is 30°.
OK, boring stuff over. Back to the Fishbed.
So the MiG-21PF is better area ruled than the MiG-21F-13. It also has the R11F2-300 with 6200 kgf of thrust, rather than the 5750 kgf of the R11F-300. Empty weight increase was not that much, over the F-13. Other than the increased...
..."additive drag" that I discussed at length about in my MiG-21 inlet thread, everything indicates that the MiG-21PF/PFS/PFM/FL variants should be the hottest 21s around. And that's true. Czechoslovak, German, Romanian and many other pilots agree. Some examples:
Afghan MiG-21FL
Bulgarian MiG-21PFM pilot.
Egyptian MiG-21FL pilot in "MiGs in the Middle East, Volume 2" by Tom Cooper, Dr. David Nicolle:
"Notably, Hamid recalled that several early Egyptian MiG-21FL pilots had reported reaching the speed of Mach 2.5 and higher."
Indian MiG-21FL
From "My life with the MiG-21" by Air Commodore Surendra Singh Tyagi, but it's unclear if he is referring FL or the BIS:
"...the aircraft would 'snake' as it went beyond Mach 2.3 but could actually go up to Mach 2.45."
Soviet MiG-21FL at the Domodedovo air parade, 1967.
After the service life of R11F2-300 & R11F2S-300 engines was exhausted, it was permitted to install the R13-300 instead on изделие 76, 94 & 94R (MiG-21PF, PFM & MiG-21R) according to bulletins 21-1109DM-AB & 95/107E. Source:
This means an increase in static, uninstalled thurst from 6200 to 6600 kgf. Making these PF & PFMs the hottest Fishbeds by far.
Soviet MiG-21PFS
The later MiG-21M lost some of that performance due to the extra supersonic drag created by the reshaped spine, but likely also due to the cannon and maybe additional pylon under each wing.
So, let's do a thought experiment. What would a MiG-21 look like in 1970, if the Soviets decided to return to the purely "day-fighter" role & ditched the search radar in the nose? This decision being based on experiences in the Middle East and Vietnam.
Romanian MiG-21PF
In my opinion, it would have the nose of the MiG-21F-13 & spine of the MiG-21PF. There actually existed such an aircraft, the Ye-6T/1 (Ye-66), which had the R11F2-300 and an extended cone travel range for higher Mach numbers.
This hypothetical Fishbed should also have a continuously variable inlet cone program, R13-300 engine, flaps with boundary layer control, cannons (GSh-23 or NR-30) and two hard points under each wing. All of this, by my estimate, together would give an empty weight of about...
5000 kg instead of the 5850kg for the MiG-21BIS or 5610 for the MF.
Soviet MiG-21MF
Shock wave angle as a function of flow Mach number.
Mach 1.7
Mach 2.2
Mach 3.0
Area ruled.
An interesting excerpt from Bill Gunston's MiG-21 book from 1986.
Most likely Artyom Mikoyan lied about the MF's drag being lower than the PF's, in terms of supersonic drag. In terms of subsonic drag, there may indeed be some small advantages to the uniform spine.
MiG-21 area rule 🧵
The aerodynamic reason in change from the MiG-21F-13's spine shape to that of the MiG-21PF's is never thoroughly explained in any books on the Fishbed that I know of. That spine was used on MiG-21PFS, PFM & FL too.
Soviet MiG-21F-13 Indian MiG-21FLThe only online publication that I found to discuss this in enough detail is NASA-TM-84647 "Aerodynamic assessment of various supersonic fighter airplanes based on soviet design concepts - M. Leroy Spearman 1983”.
North Korean MiG-21F-13According to the document, geometric data for the models (MiG-21 Mig-25 etc.) was scarce, and mostly from photos and other sources available at that time. Therefore, one must not consider the results to have excellent accuracy. They do shed some light nonetheless.Its findings regarding the MiG-21’s wave drag according to supersonic area rule are:
• the MiG-21F-13 model seems to have a sectional area distribution optimized for Mach 1.50
• the MiG-21 model with PF spine seems to have a sectional area distribution optimized for Mach 1.20•The PF spine seems to give less drag from Mach 1.20 to 1.60 compared to the F-13 one.
So the MiG-21’s spine was modified to the PF’s shape for reasons of supersonic wave drag reduction at M = 1.2 to 1.6, with no wave drag penalty at the higher Mach numbers.Equally interesting is the fact that the MiG-25 (despite its boxy shape) is better than the MiG-21 in terms of wave drag coefficient beyond Mach 1.60.You may be wondering, "what do you mean area ruled for Mach 1.5 or 1.2?". Well, if you're familiar only with R. T. Whitcomb's "transonic area rule", in which the sectional area distribution is calculated with plane intercepts at 90° to the velocity vector, then fair point.With the transonic area rule theory you can only optimize for M = 1. But there is also the "supersonic area rule theory" developed by R. T. Jones and described in NACA-RM-A53H18a "Theory of Wing-Body Drag at Supersonic Speeds - 1953".In short, the supersonic version extends the transonic one by stating that the plane intercepts should be inclined at the Mach angle of the speed at which you are calculating. For example, at M = 1, the Mach angle is 90° to the velocity vector, at M = 2, it is 30°.OK, boring stuff over. Back to the Fishbed.
So the MiG-21PF is better area ruled than the MiG-21F-13. It also has the R11F2-300 with 6200 kgf of thrust, rather than the 5750 kgf of the R11F-300. Empty weight increase was not that much, over the F-13. Other than the increased......"additive drag" that I discussed at length about in my MiG-21 inlet thread, everything indicates that the MiG-21PF/PFS/PFM/FL variants should be the hottest 21s around. And that's true. Czechoslovak, German, Romanian and many other pilots agree. Some examples:
Afghan MiG-21FLBulgarian MiG-21PFM pilot.Egyptian MiG-21FL pilot in "MiGs in the Middle East, Volume 2" by Tom Cooper, Dr. David Nicolle:
"Notably, Hamid recalled that several early Egyptian MiG-21FL pilots had reported reaching the speed of Mach 2.5 and higher."
Indian MiG-21FLFrom "My life with the MiG-21" by Air Commodore Surendra Singh Tyagi, but it's unclear if he is referring FL or the BIS:
"...the aircraft would 'snake' as it went beyond Mach 2.3 but could actually go up to Mach 2.45."
Soviet MiG-21FL at the Domodedovo air parade, 1967.After the service life of R11F2-300 & R11F2S-300 engines was exhausted, it was permitted to install the R13-300 instead on изделие 76, 94 & 94R (MiG-21PF, PFM & MiG-21R) according to bulletins 21-1109DM-AB & 95/107E. Source:This means an increase in static, uninstalled thurst from 6200 to 6600 kgf. Making these PF & PFMs the hottest Fishbeds by far.
Soviet MiG-21PFSThe later MiG-21M lost some of that performance due to the extra supersonic drag created by the reshaped spine, but likely also due to the cannon and maybe additional pylon under each wing.So, let's do a thought experiment. What would a MiG-21 look like in 1970, if the Soviets decided to return to the purely "day-fighter" role & ditched the search radar in the nose? This decision being based on experiences in the Middle East and Vietnam.
Romanian MiG-21PFIn my opinion, it would have the nose of the MiG-21F-13 & spine of the MiG-21PF. There actually existed such an aircraft, the Ye-6T/1 (Ye-66), which had the R11F2-300 and an extended cone travel range for higher Mach numbers.This hypothetical Fishbed should also have a continuously variable inlet cone program, R13-300 engine, flaps with boundary layer control, cannons (GSh-23 or NR-30) and two hard points under each wing. All of this, by my estimate, together would give an empty weight of about...5000 kg instead of the 5850kg for the MiG-21BIS or 5610 for the MF.
Soviet MiG-21MFShock wave angle as a function of flow Mach number.
Mach 1.7Mach 2.2Mach 3.0Area ruled.An interesting excerpt from Bill Gunston's MiG-21 book from 1986.
Most likely Artyom Mikoyan lied about the MF's drag being lower than the PF's, in terms of supersonic drag. In terms of subsonic drag, there may indeed be some small advantages to the uniform spine.
yes
MiG-21 area rule 🧵
The aerodynamic reason in change from the MiG-21F-13's spine shape to that of the MiG-21PF's is never thoroughly explained in any books on the Fishbed that I know of. That spine was used on MiG-21PFS, PFM & FL too.
Soviet MiG-21F-13 Indian MiG-21FL ... The only online publication that I found to discuss this in enough detail is NASA-TM-84647 "Aerodynamic assessment of various supersonic fighter airplanes based on soviet design concepts - M. Leroy Spearman 1983”.
North Korean MiG-21F-13 ... According to the document, geometric data for the models (MiG-21 Mig-25 etc.) was scarce, and mostly from photos and other sources available at that time. Therefore, one must not consider the results to have excellent accuracy. They do shed some light nonetheless. ... Its findings regarding the MiG-21’s wave drag according to supersonic area rule are:
• the MiG-21F-13 model seems to have a sectional area distribution optimized for Mach 1.50
• the MiG-21 model with PF spine seems to have a sectional area distribution optimized for Mach 1.20 ... •The PF spine seems to give less drag from Mach 1.20 to 1.60 compared to the F-13 one.
So the MiG-21’s spine was modified to the PF’s shape for reasons of supersonic wave drag reduction at M = 1.2 to 1.6, with no wave drag penalty at the higher Mach numbers. ... Equally interesting is the fact that the MiG-25 (despite its boxy shape) is better than the MiG-21 in terms of wave drag coefficient beyond Mach 1.60. ... You may be wondering, "what do you mean area ruled for Mach 1.5 or 1.2?". Well, if you're familiar only with R. T. Whitcomb's "transonic area rule", in which the sectional area distribution is calculated with plane intercepts at 90° to the velocity vector, then fair point. ... With the transonic area rule theory you can only optimize for M = 1. But there is also the "supersonic area rule theory" developed by R. T. Jones and described in NACA-RM-A53H18a "Theory of Wing-Body Drag at Supersonic Speeds - 1953". ... In short, the supersonic version extends the transonic one by stating that the plane intercepts should be inclined at the Mach angle of the speed at which you are calculating. For example, at M = 1, the Mach angle is 90° to the velocity vector, at M = 2, it is 30°. ... OK, boring stuff over. Back to the Fishbed.
So the MiG-21PF is better area ruled than the MiG-21F-13. It also has the R11F2-300 with 6200 kgf of thrust, rather than the 5750 kgf of the R11F-300. Empty weight increase was not that much, over the F-13. Other than the increased... ... ..."additive drag" that I discussed at length about in my MiG-21 inlet thread, everything indicates that the MiG-21PF/PFS/PFM/FL variants should be the hottest 21s around. And that's true. Czechoslovak, German, Romanian and many other pilots agree. Some examples:
Afghan MiG-21FL ... Bulgarian MiG-21PFM pilot. ... Egyptian MiG-21FL pilot in "MiGs in the Middle East, Volume 2" by Tom Cooper, Dr. David Nicolle:
"Notably, Hamid recalled that several early Egyptian MiG-21FL pilots had reported reaching the speed of Mach 2.5 and higher."
Indian MiG-21FL ... From "My life with the MiG-21" by Air Commodore Surendra Singh Tyagi, but it's unclear if he is referring FL or the BIS:
"...the aircraft would 'snake' as it went beyond Mach 2.3 but could actually go up to Mach 2.45."
Soviet MiG-21FL at the Domodedovo air parade, 1967. ... After the service life of R11F2-300 & R11F2S-300 engines was exhausted, it was permitted to install the R13-300 instead on изделие 76, 94 & 94R (MiG-21PF, PFM & MiG-21R) according to bulletins 21-1109DM-AB & 95/107E. Source: ... This means an increase in static, uninstalled thurst from 6200 to 6600 kgf. Making these PF & PFMs the hottest Fishbeds by far.
Soviet MiG-21PFS ... The later MiG-21M lost some of that performance due to the extra supersonic drag created by the reshaped spine, but likely also due to the cannon and maybe additional pylon under each wing. ... So, let's do a thought experiment. What would a MiG-21 look like in 1970, if the Soviets decided to return to the purely "day-fighter" role & ditched the search radar in the nose? This decision being based on experiences in the Middle East and Vietnam.
Romanian MiG-21PF ... In my opinion, it would have the nose of the MiG-21F-13 & spine of the MiG-21PF. There actually existed such an aircraft, the Ye-6T/1 (Ye-66), which had the R11F2-300 and an extended cone travel range for higher Mach numbers. ... This hypothetical Fishbed should also have a continuously variable inlet cone program, R13-300 engine, flaps with boundary layer control, cannons (GSh-23 or NR-30) and two hard points under each wing. All of this, by my estimate, together would give an empty weight of about... ... 5000 kg instead of the 5850kg for the MiG-21BIS or 5610 for the MF.
Soviet MiG-21MF ... Shock wave angle as a function of flow Mach number.
Mach 1.7 ... Mach 2.2 ... Mach 3.0 ... Area ruled. ... An interesting excerpt from Bill Gunston's MiG-21 book from 1986.
Most likely Artyom Mikoyan lied about the MF's drag being lower than the PF's, in terms of supersonic drag. In terms of subsonic drag, there may indeed be some small advantages to the uniform spine.
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