AIM-120 turn rate at 60k feet

[garrya]

So someone over F-16 made an estimation of maximum turn rate AIM-120 could make at 60k feet when motor burn out

His conclusion is that AIM-120 can make an instantaneous 21g turn at 60k feet, is his estimation acceptable? or too inaccurate?

 

 

http://www.f-16.net/forum/viewtopic.php?f=38&t=28234&start=60

 

https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiz9IHp3f_JAhXHzxQKHd5wDA0QFggfMAA&url=http%3A%2F%2Fforums.eagle.ru%2Fattachment.php%3Fattachmentid%3D104165%26d%3D1410108839&usg=AFQjCNGFKcbFJS70VyYzQtfsNm7ISTmEYw&sig2=V6uoQDAnuLrZ85rFtlcQAw&bvm=bv.110151844,d.d24

 

 

 

 

 

AIM-120C-5 have body diameter of 180 mm and total wing span of 482 mm ( 0.482 meters ) which mean the span of each fin is ( 482-180)/2 = 151 mm ( 0.151 meters )

This is AIM-120C fin

 

here is the fin size relative to the total body

 

The photos shows that Aim-120's fin have trapezoid shape ,

For the rear fin : the big base length is around 2.5 times the height

the small base length is around 1.5 times the height

the height (wing span ) as we measured earlier is around 0.151 meters , so the big base is 0.3775 meters , small base is 0.2265 meters

Solve for area we have 0.046 square meters for each rear fin

 

 

For the frontal fin : the big base length is around 2 times the height

the small base length is around 0.5 times the height ,the height (wing span ) as we measured earlier is around 0.151 meters so the big base is 0.302 meters , small base is 0.0755 meters

Solve for area we have 0.029 square meters for each frontal fin

 

we have total of 4 frontal fins and 4 rear fins so total fin area on aim-120 is :

0.046*4 + 0.029*4 = 0.3 m2 ( this number is 3 times bigger than my estimation earlier in this thread because before I only estimate area of horizontal fin and ignore vertical fins )

 

For missiles body i put picture of Aim-120 into paint and use the ruler app to calculate the ratio between the cone length and total missiles length

the pointy part of the cone accounted for 1/9.4 of total missiles length , so the cone length is 388 mm ( 0.388 meters ), missiles length is 3262 mm ( 3.262 meters )

missiles have diameter of 180 mm so the radius of the base is 90 mm ( 0.09 meters )

solved for area ( put number in formula )we have :

lateral surface area of Aim-120 body is : 1.84 square meters

lateral surface area of Aim-120 pointy nose cone is : 0.11 square meters

 

So the total wetted area of aim-120 is 1.84 + 0.11 + 0.3*2 = 2.55 square meters

 

 

 

According to the model graph in pdf file

At altitude of 5 km they estimated the CL value for wetted area of Aim-120 to be 0.11 at AoA of 30 degree and speed of 1200 m/s

Also from the graph when altitude rise by 15 km the CL value at same AoA reduced by around 10%

From data above it safe to assumed at altitude of 60-65K feet ( 19-20 km ) , speed of 1200 m/s and AoA of 30 degree then CL value for wetted area of Aim-120 is around 0.099 - 0.1

 

put everything estimation value above into equation

Air density at 60K ft = 0.12 kg / m3

AIM-120 total weight is 152 kg , 52 kg of solid propellant so at burn out aim-120 weight will be 100 kg

at 60K feet speed of sound is 293 m/s

let say aim-120 max speed at burn out is mach 4

CL value at AoA of 30 degree , 60K feet = 0.1

total wetted area of aim-120 is 1.84 + 0.11 + 0.3*2 = 2.55 square meters

 

Lift = 1/2 * rho * v^2 * S * CL

at maximum instantaneous G turn then lift must be equal weight* acceleration so :

100*10*( G-load ) = 1/2* 0.12* (293*4 )^2 * (2.55)* 0.1

G-load = 21 G

 

 

thrust is 16771 N

lift equal thus*sin (AoA )

the lift from thrust when missiles fly at AoA of 5 degrees = 1461 Newtons

the lift from thrust when missiles fly at AoA of 10 degrees = 2912 Newtons

the lift from thrust when missiles fly at AoA of 15 degrees = 4340 Newtons

the lift from thrust when missiles fly at AoA of 20 degrees = 5736 Newtons

the lift from thrust when missiles fly at AoA of 25 degrees = 7087 Newtons

the lift from thrust when missiles fly at AoA of 30 degrees = 8385.5 Newtons

Edited December 31, 2015 by garrya

[garrya]

Bonus questions can anyone please translate or explain this graph ?

[GGTharos]

Looks like flight envelope of mig 25

[garrya]

Looks like flight envelope of mig 25

 

yes it is, but i don't understand Russian so i don't know what they write in it

Btw, how can Mig-25, Mig-31 fly much higher and faster than Su-27, F-15, Mirage IV?

[GGTharos]

Different type of engine designed to operate up there. Turbofans probably wouldn't be very happy in such thin air, though NASA had flown their f-15 to M2.7 ... Don't recall the altitude.

 

Anyway regarding the graph, looks like flight envelopes for a bunch of different payloads.

 

Can't make out too much more than that :-)

[garrya]

Different type of engine designed to operate up there. Turbofans probably wouldn't be very happy in such thin air

 

but D-30F6 on mig-31 is a turbofan engine, and with very high bypass value too ( similar to F-135)

[GGTharos]

Like I said, NASA got their F-15 up there, but I'm also pretty certain that they modified the engines. :-)