Missile energy (split)

[mvsgas]

25 054 532 it is

I know it will get way more complicate than my little brain can handle, but what do I have to loose? Better than the typical "this aircraft is better that that one" conversation

[marcos]

I get 25 054 532 Joule.

 

½ * 136 * 607²

 

½ * 136 * 368 449

 

136 * 184 224,5

 

25 054 532

The initial energy will also be determined by initial altitude vs altitude of target, i.e. the potential energy over the potential energy of the target.

 

E.g. at 20000m launch altitude with target at sea level:

 

136*10*20000 = 27,200,000J

 

Initial energy = KE + PE + CE (Chemical Energy) = 25,054,532 + 27,200,000 + CE = 52,254,532J + CE

 

Assuming 50kg of hydrazine propellant with suitable oxidizer:

 

CE = 50*19,410,000 = 970,500,000J

 

So

 

Initial Energy = ~1023MJ (1,023,000,000J)

[mvsgas]

Can we just think of a non maneuvering target at the same speed and altitude?

[marcos]

Yes. In that case the PE term is zero.

 

The speed the missile reaches will be given by:

 

{2*[(Initial Energy) - (The integral of the work done in overcoming drag with respect to velocity)]}/mass

 

The integral of the work done in overcoming drag is basically derived from:

 

W=Fs (Work done = Force*Distance)

 

where Force = Drag = 0.5 * Cd (Drag Coefficient) * Density * drag cross-sectional area * V^2

 

But Cd is also a function of V, since velocity will determine the relative impact of induced drag, pressure drag, skin friction drag and wave drag on the overall drag at anyone time. And Cd-tot is comprised of:

 

f(Cd-tot, V) = f(Cd-induced, V) + f(Cd-skin-friction, V) + f(Cd-pressure drag, V) + f(Cd-wave drag, V)

 

So:

 

The integral of the work done in overcoming drag with respect to velocity = The integral from initial speed to final speed of 0.5 * [f(Cd-induced, V) + f(Cd-skin-friction, V) + f(Cd-pressure drag, V) + f(Cd-wave drag, V)] * f(density, V) * drag cross-sectional area * V^2 * V*t (Distance) dV

 

*Note - density is also affected by mach number, with significant effect above M=0.4.

 

But of course you don't know your final speed yet, so congratulations, you have a differential equation to solve after you've determined the functions that relate the various different drag coefficients to velocity that is.

Edited August 12, 2012 by marcos

[combatace]

There is some more calculations to it. As the rocket motor ignites the fuel starts burning and missiles starts getting lighter, so less thrust is required to push it further. Considering 136Kg missiles one needs to know the empty mass of the missile without the propellant, and also rate of burning of fuel to understand the acceleration within the time of ignition and burn-out.

Again the acceleration will not just be affected by the density of air but the shape of the missile, AIM-120C has its fins chopped off because the chopped off portion was creating more drag then generating lift and providing control.

As missile accelerates the shock cone will go thinner and it acceleration will be affected if any portion of the fin is in or out of shock cone at higher altitude or lower.

[marcos]

Indeed. I find that a good CFD package and a supercomputer usually comes in handy around about now.

 

I think the changing mass of the missile would be included in the function that yields the induced drag component of the all-up drag coefficient. As the missile becomes lighter, the lift required for level flight will reduce, and the induced drag will therefore reduce and so the induced drag coefficient will also reduce.

 

Oh hang on, you're right, I'm dividing by mass too, missed that. Assuming the rocket motor has a consistent burn rate, I think we could look at using an average mass simply given by [start mass + (start mass - end mass)/2]

 

Looking on the bright side, at least it's a rocket motor and not a ramjet where the changing shock pattern and pressure losses in the intake as the ramps move about will affect the problem and the thrust at any given speed.

 

The shock cone issue will be covered within the function for the wave drag coefficient, which as you rightly hint at, is a function of altitude, or more specifically air density, as well as velocity, since mach number changes with altitude even at constant velocity.

Edited August 12, 2012 by marcos

[mvsgas]

Thanks for bearing with me, since it will take me a long time to understand this.

So initial energy the very instant the rocket motor start to push or move the missile, before it evens leaves the missiles rail, is;

1,023,000,000J

next will be the Jules before the very instant before the rocket motor stops, right?

 

Can we just calculate the energy at that point , the very instant before motor stops, and later subtract energy loss due to friction, drag, etc is that possible?

Edited August 12, 2012 by mvsgas

[EtherealN]

Well, tbh, all you really need to understand is that the motor is not sufficient to push the missile to it's aerodynamic/structural limits. (Except possibly at sea level where the air is just too damn dense.)

 

Proving this with theoretical examples though is extremely difficult, since it would require a huge amount of information that we simply don't have. (Even if the maths was simple, which it isn't, we could easily fabricate theoretical examples where the missile is or isn't limited by it's motor, and neither would inform us of actual, real world, operational missiles.) So to my mind, we've been informed by people that work with these and probably have access to lots of fun documents we don't (and that they, for obvious reasons, cannot share).

Edited August 12, 2012 by EtherealN

[marcos]

Thanks for bearing with me, since it will take me a long time to understand this.

So initial energy the very instant the rocket motor start to push or move the missile, before it evens leaves the missiles rail, is;

1,023,000,000J

next will be the Jules before the very instant before the rocket motor stops, right?

That will be the start energy 'roughly' but you have to realise that most of that is in the chemical bonds in the propellant.

 

When the rocket motor stops, the remaining energy will be the KE, with the rest of the initial energy having been spent overcoming drag.

 

Looking at it this way, an accelerating missile needs energy first and foremost to balance the drag. That will keep it going at a steady speed. It then needs extra energy to convert to KE during acceleration.

 

So at evey point in flight, there is a Wdrag=F.ds element (where F=drag), which is the energy required to do the work in overcoming the instantaneous drag and continue to move the missile forward at a constant speed over the next small part of distance. Then the missile needs extra energy to do the work necessary to accelerate the missile over the next small portion of distance, Wacceleration=Resultant Force.ds.

 

So at any instant you have:

 

Work Done = Wdrag + Wacceleration (wok done to overcome drag + work done to accelerate)

 

In terms of Newton's 2nd Law:

 

Missile Thrust = Drag + Resultant Force

 

OR

 

Missile Thrust - Drag = Resultant Force

 

Bear in mind that the conversion of stored chemical energy to useful work will not be 100% efficient though.

[mvsgas]

Well, tbh, all you really need to understand is that the motor is not sufficient to push the missile to it's aerodynamic/structural limits. (Except possibly at sea level where the air is just too damn dense.)

 

Proving this with theoretical examples though is extremely difficult, since it would require a huge amount of information that we simply don't have. (Even if the maths was simple, which it isn't, we could easily fabricate theoretical examples where the missile is or isn't limited by it's motor, and neither would inform us of actual, real world, operational missiles.) So to my mind, we've been informed by people that work with these and probably have access to lots of fun documents we don't (and that they, for obvious reasons, cannot share).

 

 

I conceded to that idea before this even started, I simply was looking to see it in the numbers. Not trying to disprove nor challenge. I just figure it would be interesting to talk about it. Like I said before, I think is better than the typical "this is better than that" or "this is wrong because my third causing, neighbor, high school friend said so" typical thread

[marcos]

Well, tbh, all you really need to understand is that the motor is not sufficient to push the missile to it's aerodynamic/structural limits. (Except possibly at sea level where the air is just too damn dense.)

 

Proving this with theoretical examples though is extremely difficult, since it would require a huge amount of information that we simply don't have. (Even if the maths was simple, which it isn't, we could easily fabricate theoretical examples where the missile is or isn't limited by it's motor, and neither would inform us of actual, real world, operational missiles.) So to my mind, we've been informed by people that work with these and probably have access to lots of fun documents we don't (and that they, for obvious reasons, cannot share).

It's worth bearing in mind that the Apollo 13 cabin was doing almost Mach 40 on re-entry and many ICBMs are going way faster than Mach 4-5 when they leave the atmosphere. Even experimental cruise missiles have been tested at Mach 7.

 

I honestly don't know where the structural limits of an AIM-120 lie, but I don't see any problems with launch from a conventional aircraft. Maybe if it was launched from an X-43 there might be a problem.

 

I think the real answer lies in the fact that all missiles are tested and qualified for every launch platform. So no, there won't be a problem in combat.

Edited August 12, 2012 by marcos

[mvsgas]

Lets not talk about specific missiles, we don't have the info and if we are guessing, might as well just make up the whole missile.

I just like the science behind it

[marcos]

Of course it is possible that the missile stops acceleration at a given speed through control. Not possible with solid fuel though.

Edited August 12, 2012 by marcos

[GGTharos]

Actually we can talk about specific missiles, such as the AIM-9L for which we do indeed have information.

 

Lets not talk about specific missiles, we don't have the info and if we are guessing, might as well just make up the whole missile.

I just like the science behind it

[marcos]

Do we know what speed its structure will fail at though? The specific energy of its rocket fuel, conversion efficient, amount? Drag-velocity relationships?

[GGTharos]

No, all we have is a lateral g-limit of 40g as far as structural failure goes. Failure due to excessive speed was not even considered in the particular study available, as all launches are made from 0.9M. On the other hand, there are means of simulating the ballistic capabilities of the AIM-9L pretty closely, and I really don't think that it would have any issues with a high speed launch.

[combatace]

Well if we consider specific missiles then R-33 is a typical example. While in development its designers faced the problem of overheating due to friction resulting in component damage.

There are no specifics out about R-37 but it will be interesting as it is said to have speed of mach 7.

Sea skimming missile brahmos is also a typical example flying on mach 3 at sea level.

[winz]

All you need is thrust of the missile engine, engine burn-time, weight and the drag equation for any given speed.

You then compose an acceleration equation, run it throug a defined integral and that will yield the theoretical maximal speed the missile can achieve with that engine. Then we can take guesses if missile would survive such speed.

 

Well, in theory, I still havne't got my morning coffee, so I might be totally wrong :D

[SgtPappy]

I suppose if you really wanted to be accurate you'd have to model the loss in weight as a function of time due to the rocket fuel being burned up with another integral, but this is more important with longer-ranged missiles like the R-27E series or the AIM-54 and R-33.

 

You might have to divide the problem into supersonic and then subsonic regimes too since the C_d and C_l values are likely to vary dramatically for some missiles between the regimes. Thankfully, there are computer programs for that.

[GGTharos]

It doesn't. It's in the same class as the R-33 and AIM-54. You need to launch these at Mach 2 to get them to cruise at mach 5. Launching them at mach 3 won't get'em to mach 6, let alone 7.

 

Other than that though, yep, thermal problems are real, but not new.

 

There are no specifics out about R-37 but it will be interesting as it is said to have speed of mach 7.

[marcos]

Some sources say Mach 6 but most sources seem to suggest it's been dropped.

 

These are the only pictures around for it:

 

http://www.airwar.ru/enc_e/fighter/mig31bm.html

 

Edited August 13, 2012 by marcos

[GGTharos]

Mach 6 or close to mach 6 would make sense if launched from the 31 while it's going balls-to-the-wall :)

 

Last I heard about the R-37 it was being tested prior to IOC. I think it was cancelled once before though.

[WildBillKelsoe]

my head hurts!!!

[marcos]

Mach 6 or close to mach 6 would make sense if launched from the 31 while it's going balls-to-the-wall :)

 

Last I heard about the R-37 it was being tested prior to IOC. I think it was cancelled once before though.

Who knows. All I have are internet sources, which can occasionally be wrong.:smilewink:

 

Wiki mentions something about a rocket booster on one version that supposedly gives a range of 400km but that's wiki.

Edited August 13, 2012 by marcos