AIM-54 with plot armor
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Well, at least I’m not the only one who has noticed that.
Sometimes ACM PD HDN captures the enemy further away that is almost flying perpendicular to you, rather than the closer enemy coming at you at supersonic speeds.
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I took some time and did some analysis using data from NASA’s paper
It has test data on Standard Aim54 on page 12, Aim-54C, it shows the missile never exceeds Mach 4, only reached ~3.7, when launched at 45 degree loft and then glide.
On page 11, it discussed weight reduction and its effect on missile performance.
By reducing missile weight by 135lb (equivalent of removing warhead) or only mounting 115lb of research payload, the missile was able to attain Mach 4.3 when launched at same condition.
Removing all payload completely, reducing weight by 250lb (equivalent of removing radar and warhead, only keeping auto pilot to perform preprogrammed/data link flight), the missile was able to achieve Mach 5.
The reasonable guess is, the advertised Mach 4.3 - 5.0 figures are the test flight data of Aim-54 without warhead or radar mounted. Probably done by Hughes/Raytheon to help sell the missile. To achieve this performance, either the ground crew has to swap out the warhead for a smaller one, or it can only be achieved without warhead/radar during testing.
The calculated drag using the data from the paper lines up with what we agreed so far, where Aim-54 suffers significantly from high altitude drag, which MIG_23M also agrees.
Calculating the shape of trajectory
Finding out how high the missile climbed
We knows the Aim-54 in paper climbed at 45 degrees at the start, but we don’t know how Aim-54 is gliding, so we need to know the altitue where missile is gliding at. We can calculate this by finding out the displacement of Aim-54 during climb.
To get the displacement of Aim-54 during climb, we can calculate the area udner the curve during intiial climb. Since the curve is almost linear, we can approximate it by assuming it is a triangle.
Also, since the line doesn’t have significant curvature, it means missile did not suffer excessive drag from pull up to a 45 degree climb.
Speed of sound at 45,000-80,000ft = ~295m/s
v0 = Mach 1.2 = 1.2 * 295 = ~354m/s
v1 = Mach 3.7 = 3.7 * 295 = ~1091m/s
dv = v1 - v0 = 737m/s
dt = 27s
triangle = 737 * 27 / 2 = ~9,950m
rectangle = Mach 1.2 * dt = 354 * 27 = ~9,558m
area = triangle + rectangle = ~19,508m
=> Missile flew ~19,508 meters during 45 deg climb until burn out.
Note: since speed of sound is almost constant when above 40,000ft (Source), thus I will use 295m/s for all calculations.
Using trigonometry, we can calcualte how high it climbed and ground distance traveled when burnout occurred.
19508 * sin(45) = ~13,794m
=> Missile traveled ~13.7km/~45,000ft horizontally when burnout occurred.
=> Missile climbed ~13.7km/~45,000ft vertically when burnout occurred.
=> Missile’s altitude at burn out is around 27500m/90,000ft
Interestingly, this means the missile will reach an altitude of at least 27500m/90,000ft.
Even if missile immdiately level off after burnout, it still needs some time to reduce climb rate to 0.
Thus the maximum altitude reached by the missile is much higher than 27500m/90,000ft
There are some claims that Aim-54 can reach 100,000ft, this paper shows that when Aim-54 is fired with manual lofting of 45 degrees, it will go well above 90,000ft before coming down. Thus adding more credibility to the 100,000ft claim.
Analysis on how far Aim-54 had traveled in supersonic Mach 3 glide
In game, the exaggerated high altitude drag (especially at altitude of Stratosphere) and lofting parameters prevents Aim-54 from gliding at Mach 3+ (885+m/s) above 70,000ft+ for 2 minutes.
From the paper, it shows Aim-54 can perform supersnoic glide at an average speed of Mach 3.2, and it will glide ~113.2km in 2 minutes until it slows down due to drag.
We know in the 204km launch range against BQM-34E scenario, the engagement lasted 158 seconds and the drone flew for ~70km.
If Aim-54 performed 120s of supersonic glide, then it only has 38 seconds for climbing and descend.
From the paper, the acceleration lasted 27 seconds (Rocketdyne Mk47), this means, after the missile exits supersonic glide and dive on the target, it only has 11 seconds to hit the target, i.e. covers a ground distance of 204km.
We know during climb, missile traveled 13.7km horizontally.
13.7 + 113.2 + 70 = 196.9km.
=> When missile exits supersonic glide, it has to fly another 7.1km to hit the drone.
We can calculate the area under the curve between t=147s and t=158s, once again by approximating it as a triangle, plus a rectangle underneath.
v0 = Mach ~2.6 at t=147
v1 = Mach ~1.72 at t=158s
dt = 11s
dv = v0 - v1 = ~259.6m/s
triangle = dv * dt / 2
rectangle = v1 * dt
distance = triangle + rectangle = ~7009.2m
Which is almost 7.1km, this adds up!!!
Find out the maximum glide/dive angle
Since missile travels at supersonic speed and above stratosphere, and missile is not maneuvering significantly, the drag can only increase significantly in two ways:
- Significant increase in drag coefficient as speed changes
- Significant increase in air density due to decrease in altitude (going below stratosphere)
This is known since Paris Gun, object that enters stratosphere has significantly less drag thus improves its range.
=> Aim-54 was able to accelerate during supersonic glide because of this same phenomenon.
=> Thus we can read the graph and estimate when the Aim-54 exited stratosphere.
=> From the graph, we can see that the missile begin significant deceleration aound t=127
Previously, we already calculated the minimum altitude reached by Aim-54, which is 27500m/90,000ft
We know the range covered after burnout: 113.2km + 7km
We also know BQM-34E in the 204km scenario is flying at 50,000ft.
This means the Aim-54 has 12192m/40,000ft to descend before striking BQM-34E
We know tan(angle) = rise / run
Let rise = 12.192km
Let run = 113.2km
=> tan(angle) = 12.192 / 113.2
=> angle = ~6.14deg
Currently Aim-54 in game has loftTargetElevation = -7.75.
I’m not sure if this is the glide slope angle, if it is, then it is fairly accurate.
Find the maximum glide/dive angle to get out of stratosphere
To find the maximum glide/dive angle, we need to know at what altitude the stratosphere ends.
Assuming stratosphere begins at 10,000m (lower stratosphere means missile must glide at higher angle towards ground), the missile must descend 17,500m/~57,400ft instead of 12192m/40,000ft.
=> tan(angle) = 17.5 / 113.2
=> angle = ~8.78deg
This angle is farily small, too.
What these implies is the current trajectory of Aim-54 has some issues but mostly accurate.
One interesting things is, if we average the two angle.
8.78 + 6.14 / 2 = 7.46
This is very close to the value set in “loftTargetElevation”.
If “loftTargetElevation” is indeed the glide slope angle, then this proves that Gaijin really did serious math on Aim-54. In that case, KODO to whoever did this.
Next: check if missile really has excessive drag
Finding out the drag of missile at and after burnout
After burnout, from 27s to 40s, Missile speed dropped from Mach 3.7 to ~Mach 3.4
v0 = 3.7 * 295 = 1091m/s
v1 = 3.4 * 295 = 1003m/s
dv = -88m/s
dt = 13s
a = dv / dt = -88 / 13 = ~6.77m/s^2
empty_mass = 293kg
Force = empty_mass * a = 293 * 6.77 = ~1983N
This means missile is experiencing ~1983N of Net force for deceleration.
This is the upper bound of drag experienced by missile, since we are assuming gravity is completely cancelled out by lift.
If lift does not exist, the missile should be experiencing much greater deceleration, at least greater than 9.8m/s^2
Solving for the drag of missile at and after burnout
From the graph, it is not too unreasonable to deduce that the missile is either following a ballistic trajectory or it actively nose down to enter a glide.
The nose down maneuver likely finishes around t=80s, since that’s when the missile begin to accelerate again due to gravity. This means missile nose down maneuver took 53 seconds to cover 45+ deg, this gives an average rate of ~0.85deg/s
Assuming missile nose down at average rate and starts immediately after burnout, at t=40, the missile should have 45 - 13 * 0.85 = ~33.9 deg pitch.
To simplify calculation, I took the average and assuming missile is at ~39.4 degree nose up attitude during this 13 seconds.
pitch = 39.4
sin(pitch) = 0.6347
cos(pitch) = 0.7727
tan(pitch) = 0.8214
a = 6.77m/s^2
ax = a * cos(pitch) = 5.23m/s^2
ay = a * sin(pitch) = 4.29m/s^2
g = 9.8m/s^2, acting purely on Y-axis
From the diagram, we know:
ay = dragY + g - liftY
Then
=> g = ay + liftY - dragY
=> g - ay = liftY - dragY
Also
ax = dragX + liftX
=> dragX = ax - liftX
Since g and ay are known, let’s fill in numbers.
g - ay = liftY - dragY
=> 9.8 - 4.29 = liftY - dragY
=> 5.51 = liftY - dragY
=> liftY = 5.51 + dragY
Given: dragY / dragX = tan(pitch)
=> dragY = tan(pitch) * dragX
Given: dragX = ax - liftX
=> dragY = tan(pitch) * (ax - liftX)
Given: liftX = liftY * tan(pitch)
=> dragY = tan(pitch) * (ax - liftY * tan(pitch))
Given: liftY = 5.51 + dragY
=> dragY = tan(pttch) * (ax - (5.51 + dragY) * tan(pitch))
Fill in numbers and we get:
dragY = 0.8214 * (5.23 - (5.51 + dragY) * 0.8214)
Now we can solve for dragY by rearranging equations.
dragY = 0.8214 * (5.23 - (4.525914 + dragY * 0.8214))
dragY = 0.8214 * (5.23 - 4.525914 - dragY * 0.8214)
dragY = 0.8214 * (0.704086 - dragY * 0.8214)
dragY = 0.5783362404 - 0.67469796 * dragY
1.67469796 * dragY = 0.5783362404
dragY = 0.5783362404 / 1.67469796
dragY = 0.3453m/s^2
drag = dragY / sin(pitch)
drag = 0.5440m/s^2
This translates to a drag force of ~159.4N, which is whoppingly good.
A rough estimate using 0.47m^2 area and air density of 0.02047 at 28,000m/~91,800ft (Source) yields drag coefficient of ~0.03 when missile is traveling Mach 3+.
Estimating the thrust of Mk47 rocket motor.
The velocity versus time graph in the paper allows us to estimate the Net force at start and end of the burn:
At t=3.33s
dt = 3.33s
v1 = Mach ~1.6
v0 = Mach 1.2
dv = (1.6 - 1.2) * 295 = 118m/s
a = dv / dt = 118 / 3.33 = ~35.4m/s^2
Assuming rocket motor burns its propellant at uniform rate.
t_burn
m0 = 463kg ← full mass
m1 = 293kg ← empty mass when propellants are gone
m_propellant = m0 - m1
Net force = (m0 - m_propellant * dt / t_burn) * a = (463 - 21) * 35.4 = ~15646N
Aim-54 in game currently has thrust of 14350N, we also knows Rocketdyne Mk47 Mod 0 has 13,595N for 27s. This doesn’t match the Net force calculated using the data from NASA paper.
Since this Net force also includes drag force. The actual thrust is higher than Net force.
Even if we triple the propellant consumption.
(463-21*3) * 35.4 = 400 * 35.4 = 14,160N
We still gets 14,160N of thrust, which is still greater than 13,595N.
This suggests either the thrust of Mk47 Mod 0 benefits from increase in altitude when above 45,000ft, or Mk47 Mod 1 had improved thrust in addition to reduced smoke.
Summary
The Aim-54 in game is fairly accurate, except few issues.
- Missile does not climb at 45 degrees after launch, even with 17.5 loftElevation, it is still very slow to pull into a 17.5 degree climb. This causes missile to refuse to climb 10,000m after launch, it nose down too early even if target is very far away
- Missile’s thrust is underestimated at 45,000ft, implementing altitude adjusted thrust may help this.
- Missile’s drag is too much especially above 45,000ft.
Even if only item 1 is fixed, it will improve Aim-54’s experience dramatically and allow it to be uptiered and fight other modern BVRs, and avoid runing the game experience of lower tiered ARB players who are still grinding by bombing.
If Item 3 is fixed in addition to item 1, then it will make Aim-54 competitive in top tier battle.
If all items are fixed, then the work on Aim-54 is done and it becomes a very competitive missile in top tier, the place where it really belongs.
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The NASA paper is not accurate. The top speed numbers and such are far too low.
It is well known that it climbs beyond 100,000 feet when air launched.
The AIM-54A in-game when launched in this configuration reaches the correct peak height and range.
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The AMRAAM can hit past 40nm
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Thr paper LITERALLY states:
Its not accurate info, its based on publicly available info at the time and uses a basic trajectory with zero fin deflection.
Not only is this using basic publicly available info from pre-2006 on the missile, its modelling it like an unguided rocket, and specifies that the use of actual guidance to acheive the desired flight regimes (ie: hypersonic flight regime) should be looked into, along with the fact that “higher fidelity performance analysis should be conducted”
This isnt an accurate paper to compare the AIM-54’s performance to.
Edit: I dont wanna discount all the work you did, i just wanted to point out a very important bit of key information you seemed to have missed when you came to your conclusions, and was tired when i responded.
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Categorically not true, not even slightly.
Which variant? If you are talking about the B then its bullcrap. As I said, no REALISTIC scenario that it can do that. If you are talking about C then yea it can but you need the stars to align for that to happen… All the range in the universe does not matter if the pilot you are shooting at isnt clueless…
Right so you’re referring more to NEZ. Because 120B can quite easily exceed 100km on a non manoeuvring target.
I am not refairing to no escape zone no… I am refairing to a high Pk shot… and also wtf is a km? XD
A kilometre (or kilometer if you’re American), the standard unit used for measuring distance in most of the world.
lmao, I think that one flew past y… Military aviation use the imperial and as such every specification you will find is in fact in nautical miles, knots and feet. You can either follow that or try to convert everything in metric and have a brain aneurism in the process…
Except if you are in Russia… They use Metric for whatever reason…
It is true that pilots use nautical miles and ft. But it is by no means uncommon to find metric used in aircraft / missile engineering (unless of course you’re American).
Anyway going back on topic to you claims about AMRAAM, here’s a firing envelope for AIM-120A, the head on launch range is >80 km.
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Can you spot the error here or do I have to do it for you?
The mixing of nautical miles and km is a little strange (and possibly a mistake - i.e. both units should be km), but the maximum range still aligns with what other sources say, and it comes from declassified MOD report, so is likely trustworthy.
If you are so confident that AMRAAM cannot hit targets at 40 nautical miles care to provide evidence?
Going past the metic and imperial thing, as it was not what I was talking about. Again to clarify, I am talking about EFFECTIVE range, not max range or the no escape range.
To give a very simplified example. In football, a good footballer can score from the center of the field. However this is not a shot that they would ever take in a match for obvious reasons…
So going back to the AMRAAM A/B. Yes you might be able to hit that 40+ nm shot against a target that is not maneuvering and for whatever reason has chosen to cruise at mach 1.4 at 30k feet without a care in the world of whats going on around it.
Or, you do the logical thing, and move much closer and try a shot that would give any pilot with some sort of SA a tough time…
Anyways, do you have any data on the battery life of the A/B ? Because the very limited info I could find suggests under 90 seconds. With the large fins the A/B bleeds a lot of energy thus increasing the TTI (compared to the C). Hence why I was saying that it will run out of battery.
P.S. In your own graph, it says 3G turn at 15nm range. I suppose the target starts a 3G orbit when the missile is at that range ? If so, it kinda proves the point I am trying to make…
The AIM-54 will suffer similar range penalties, so your point is mute.
As it stand the goal is to improve the energy retention so that extreme range shots are possible with the Phoenix.
this is a literal example of effective range? target reacts to the missile with a 3G break and the missile chases.
Cool, but how do you define effective range?
That firing envelope shows the effective range of the AMRAAM against a russian bomber which evades at 3 g shortly before the missile impacts. And it is a realistic scenario (IIRC there was one report noting that the weakest RWRs used by Russia at the time would only detect an AMRAAM’s radar at something like 4 km range).
Obviously the effective range of the missile against a fighter which evades at a higher g, or longer range, or lower altitude would be different.
You can make the effective range of a missile be whatever you want depending on how you define effective range.
Battery life is 80 seconds.
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it does?