AMRAAM G load

[eloise]

above 36,000 feet, 30G, 3.0M, instant turn rate is ~19 deg/s with a radius of 8,730ft. Now the question is can an AMRAAM generate enough lift to do that? An AIM-120B has an empty weight of about 223lb (fuel burned) so 30G is a load of 6690lb (or slg-ft/s^2). The dynamic pressure at 3.0M at 36,000 ft is ~3,000 slg/ft-s^2, this means the missile needs a lifting area of ~2.23 ft^2. This would be the Cl*Aref. Those little fins cant have more than ~0.17ft^2 of area each, say four of them are pulling for a total area of ~0.68ft^2 (based on my own estimation, miniZAP gives 0.697 which may account better for the non-triangular rear fins). This means the combined fins and body would need a Clmax of 3.2 using the miniZAP fin area. If this were true than an AIM-120B would have a "stall speed" of 171 knots at sea level. As such I am skeptical that the Clmax would be so high. The much higher Reynolds numbers of M3 flight could certainly increase the Clmax but I remain skeptical of a value of 3.2. I would need to see more data on missile lift.
Data I have for big-finned Sidewinders indicates a Clmax of 1.3 and a Lifting Area of 1.8 ft^2

with weight of 188 pounds the Sidewinder will have wing loading of around 104 lbs/ft. By comparison F-15C have wingloading of 73 lbs/ft while F-16 has wingloading of 88 lbs/ft , Mig-25 with it's huge size has wingloading of 122 lbs/ft. At burn out the missile will be lighter leading to lower wing loading, If the Mig-25 can fly level at 70-60K ft at speed of mach 2.5, i think there is no reason why AIM-9L would drop like a brick same condition

That being said, however AIM-9L have massive fin-body diameter ratio compared to missiles such as AIM-120, R-77, Meteor ( tiny fin) , these BVR missiles probably turn worse than AIM-9 at high altitude, I kind of wonder why the heck Meteor didn't have a TVC system, It's motor burn all the way to target, and it have tiny fin

[hornetfinn]

Question, don't missiles have a separate motor charge for their boost phase and another one for their Terminal phase?

This makes sense since the hardest maneuvers will be done when the projectile is very close to it's target.

Answer, no. That is why the Meteor being a Ramjet is such a big deal.

Ramjet is a big deal, but there are missiles that have two separate motor charges for boost phase and another one for other part of flight. One example is LFK-NG from MBDA and motor from Bayern-Chemie:

http://www.bayern-chemie.com/dualpulse.htm

SM-3 is another missile with dual-pulse motor:
https://www.orbitalatk.com/defense-systems/missile-products/tsrm/

Btw, LFK-NG might be interesting concept for a new air-to-air missile for F-35. It's somewhat smaller than Brimstone or AGM-169 and has pretty good range (10 km ground launched range), so 4 LFK-NGs should be doable instead of 2 AMRAAMs. It also has LOAL capability, so it should have no trouble being used from internal weapon bays.

[eloise]

So i have decided to measure the wing loading of the AMAARM there may some mistake , but i think it is a decent estimation
AIM-120C have body diameter of 178 mm and total wing span of 445 mm ( 0.445 meters ) http://www.cat-uxo.com/#/aim-120-amraam ... 4588084065
which mean the span of each fin is ( 445-178)/2 = 133.5 mm ( 0.133 meters )
This is AIM-120C fin

here is the fin size relative to the total body

aim-120c.jpg (10.08 KiB) Viewed 21072 times

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 0.133 meters , so the big base is 0.3325 meters , small base is 0.1995 meters
Solve for area :

New Bitmap Image.jpg (20.34 KiB) Viewed 21101 times

we get 0.035 m2 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 is 0.133 meters so the big base is 0.266 meters , small base is 0.0665 meters
solve for area

New Bitmap Image.jpg (21.57 KiB) Viewed 21101 times

we get 0.022 m2 for each frontal fin

to sum up total fin area for AIM-120 is :
0.035*2 + 0.022*2 = 0.114 m2

AIM-120 total weight is 152 kg , The motor assembly weighs 70.3 kg and contains 49 kg of solid propellant. At burn out the AIM-120 will have weight of 103 kg
So the total wing loading of AIM-120 at burn out is 103/0.114 = 903 kg/m2 that is even higher than the Boeing 747 but i guess the AMRAAM can still turn because it can move much faster

[hornetfinn]

i have always thought AIM-120 have boost and sustain motor , with only boost it would be rather shitty at BVR
if we know thrust/drag, Cdo... etc of a missile, i suppose we can even measures it's turn rate at different speed

AIM-120 has a boost and sustain motor which still means it has a single-pulse engine. The rocket motor propels the missile to speed and maintains the speed for some time (total burn time is still something like 7-10 seconds). This is how most current missiles operate. Some SHORAD SAM missiles have true boost only motors as they propel the missile to speed in couple of seconds (huge acceleration) and then the missile just coasts to target. For example VT-1 missile for Crotale NG or missiles for Russian 2S6 Tunguska and Pantsir S1 systems use this kind of missiles. Missiles for these systems have very low drag due to CLOS design (no seeker at all) and thus lose speed very slowly unless maneuvering hard. So they try to minimize the time to target with very high acceleration and average speed.

[eloise]

AIM-120 has a boost and sustain motor which still means it has a single-pulse engine. .

i thought single pulse mean only the motor have fixed amount thrust ? no ?

[hornetfinn]

That being said, however AIM-9L have massive fin-body diameter ratio compared to missiles such as AIM-120, R-77, Meteor ( tiny fin) , these BVR missiles probably turn worse than AIM-9 at high altitude, I kind of wonder why the heck Meteor didn't have a TVC system, It's motor burn all the way to target, and it have tiny fin

I also doubt that fin size is the only thing that affects missile maneuverability even at high altitude. AFAIK, it also depends on missile speed, overall aerodynamic configuration, how much torque is available to turn the fins and how far they can deflect. Large fins also create a lot more drag which means speed slows down quicker after rocket motor burns out and thus missile loses energy to maneuver quicker. AIM-9L has canard control where the actual control surfaces are far forward and newer missiles tend to have tail control system where control surfaces are at the rear end. Tail control system is generally more effective and also need smaller wings for stability but is more complex to implement. Most modern missiles use tail control system. Of course there is also wing control system where large wings are used to control missile flight (R-27, AIM-7 for example) but that's not used much anymore due to making missile rather large due to large wings. I think modern BVR missiles are more maneuverable at high altitude than AIM-9L even with their much smaller wings and fins due to having more effective and powerful control systems.

Very interesting article about missile aerodynamics.
http://goo.gl/BLsmmq

Another interesting one:
https://archive.org/stream/nasa_techdoc_19830009235/19830009235_djvu.txt

[hornetfinn]

AIM-120 has a boost and sustain motor which still means it has a single-pulse engine. .

i thought single pulse mean only the motor have fixed amount thrust ? no ?

Single pulse means that there is a single propellant charge which will burn when ignited. However the amount of thrust is not really fixed and varies during the burn depending on how it is designed. Usually rocket motors are designed to give very high initial thrust which propels the missile quickly to higher speed. Then the rocket motor thrust can be kept quite fixed or it can drop significantly. One variation is that there is fairly constant thrust and no high peak thrust. It depends on propellant properties and how the propellant charge is shaped and designed. However the rocket motor will burn in one event. Dual pulse motors have two separate propellant charges where there can be significant time between burning the charges (like one for boost phase and another for end-game maneuvers).

Single pulse rocket motor thrust works like this:


Interesting source about rocket motors:
http://www.slideshare.net/aticourses/fundamentals-of-rockets-missiles

[sprstdlyscottsmn]

That was some excellent information.

[eloise]

I also doubt that fin size is the only thing that affects missile maneuverability even at high altitude. AFAIK, it also depends on missile speed, overall aerodynamic configuration, how much torque is available to turn the fins and how far they can deflect. Large fins also create a lot more drag which means speed slows down quicker after rocket motor burns out and thus missile loses energy to maneuver quicker. AIM-9L has canard control where the actual control surfaces are far forward and newer missiles tend to have tail control system where control surfaces are at the rear end. Tail control system is generally more effective and also need smaller wings for stability but is more complex to implement. I think modern BVR missiles are more maneuverable at high altitude than AIM-9L even with their much smaller wings and fins due to having more effective and powerful control systems.

in my opinion , most BVR Air to air missile body have quite similar design : a cylinder with pointy nose , in term of speed most of them have top speed around mach 4 , i think you are right that if more torque is available to turn the fins and if the fin can deflect more then it is likely that missile can turn better , however i dont think small missiles like AIM-120 would have more torque than massive one like R-33 , AIM-54 or R-40.
and AIM-9x , R-40 , R-33 , AIM-54 ,Super 530 all use tail control so i dont see any particular advantage of AIM-120 here either
i think the problem of both Meteor and AIM-120 is that their lift area is too small leading massive wing loading

Very interesting article about missile aerodynamics.
http://goo.gl/BLsmmq

Another interesting one:
https://archive.org/stream/nasa_techdoc_19830009235/19830009235_djvu.txt

interesting article with many useful information ,i find this piece very useful

aim-120c.jpg (104.95 KiB) Viewed 20924 times

but to be honest , i dont fully understand some table in there , such as this one :

[hornetfinn]

I found this which seems to have very good and simple explanations about missile aerodynamics:
http://www.aerospaceweb.org/question/weapons/q0158.shtml

Another old but very interesting document about the issue:
http://www.dtic.mil/dtic/tr/fulltext/u2/729009.pdf

Just found this, which seems to contain enormous amount of data on missile aerodynamics...
http://www.dtic.mil/dtic/tr/fulltext/u2/a217480.pdf

I don't think you can draw direct conclusions using wing and fin size about missile maneuverability. While wings and fins increase lift, forward wings can also affect it negatively due to downwash. Older missiles required large wings for stability and while they offered lift, they also negatively affected the control fins in the rear and reduced their effectiveness compared to modern missiles.

Meteor missile has the benefit of having forward thrust available the whole flight. Thus the speed of missile is high in all parts of flight and thus will have a lot of lift available as speed increases lift also (as far as I understand). I think it will have more than enough lift for even very high altitudes.

[hornetfinn]

Some very interesting info about missiles, their aerodynamics and propulsion can be found here:

http://www.okieboat.com/GMM.html

Especially this part:
http://www.okieboat.com/GMM/GMM%203%20and%202%20CHAPTER%203%20Principles%20of%20Missile%20Flight%20and%20Jet%20Propulsion.pdf

[sprstdlyscottsmn]

As I understand it the Meteor does not do Mach 4 all the way to target for long range shots but instead throttles back to Mach 2 in order to extend range.

[eloise]

I found this which seems to have very good and simple explanations about missile aerodynamics:
http://www.aerospaceweb.org/question/weapons/q0158.shtml

Another old but very interesting document about the issue:
http://www.dtic.mil/dtic/tr/fulltext/u2/729009.pdf

Just found this, which seems to contain enormous amount of data on missile aerodynamics...
http://www.dtic.mil/dtic/tr/fulltext/u2/a217480.pdf

I don't think you can draw direct conclusions using wing and fin size about missile maneuverability. While wings and fins increase lift, forward wings can also affect it negatively due to downwash. Older missiles required large wings for stability and while they offered lift, they also negatively affected the control fins in the rear and reduced their effectiveness compared to modern missiles.

Meteor missile has the benefit of having forward thrust available the whole flight. Thus the speed of missile is high in all parts of flight and thus will have a lot of lift available as speed increases lift also (as far as I understand). I think it will have more than enough lift for even very high altitudes.

thanks for these very interesting links, i will have a look at them ( quite long so i havent got chance to read all of them yet ) ,
still in my opinion a missiles is basically similar to a small aircraft that can move very fast , so they both have to obey physic law similarly , while tail control may be able to provide more maneuver than wing control , and at low altitude less wing area equal less drag which will result in longer range and less energy being waste , At high altitude however , missiles still need at least enough lift to at sustain it's altitude and then to turn

lift capabilities can be measured from the following formula:

L = (1/2) d v2 s CL
L = Lift, which must equal the airplane's weight in pounds
d = density of the air. This will change due to altitude. These values can be found in a I.C.A.O. Standard Atmosphere Table.
v = velocity of an aircraft expressed in feet per second
s = the wing area of an aircraft in square feet
CL = Coefficient of lift , which is determined by the type of airfoil and angle of attack.

Let compare 3 missiles AIM-120 , Meteor and the ancient R-40:
AIM-120 weight : 152 kg
Meteor weight : 185 kg
R-40 weight : 461 kg

So basically R-40 is around 2.5 times heavier than Meteor and 3 times heavier than AIM-120
but look at the fin area R-40 have at least like 10-20 times fin area of Meteor and Aim-120




Surely flying faster would help but from the formula, increased speed by 2 times only increase the amount of lift available by 4 times , and i dont think Meteor can fly 2 times faster than R-40 ( of course , there could be a possibility that the intake on Meteor will also contribute to lift , but i think that will only possible if it have intake on two side like the ASMP instead of below the body )

[sprstdlyscottsmn]

The meteor would have a positive angle of attack for flight as it does not seem to have forward fins. The inverted V channel created by the intakes would certainly function in the same manner as the body of the F-14, MiG-29, and Su-27.

[eloise]

The meteor would have a positive angle of attack for flight as it does not seem to have forward fins. The inverted V channel created by the intakes would certainly function in the same manner as the body of the F-14, MiG-29, and Su-27.

Sorry can you explained it with a bit more detail? , why lacking forward fin mean it will fly at an AoA > 0 ? doesn't missile like AIM-132 also lack forward fin? how effective the V channel would be in produce lift compared to normal wing? ( in term of area i mean)

BTW Now thinking about it iam very confused how exactly missiles and aircraft that dont have TVC fly at any AoA rather than 0, let take Meteor for example : wouldn't changing the nose direction will also change the direction of the thrust? ( i know they still can, for example the F-35 but now i don't understand how)