How ICBM Calculate its trajectory?

[YauS]

Modern ICBM are using solid rocket engine which cannot change deltaV. I wonder how it calculate the launch profile to control the target location.

[Bill Phil]

Each ICBM likely has preset targets and trajectories, and for those that don't, there is probably a list of targets and their associated trajectories loaded up into a computer somewhere that can be input into a missile. 

Although I could be very wrong...

[kerbiloid]

2 hours ago, YauS said:

Modern ICBM are using solid rocket

Only American ones and Topol family.
Others are liquid.

2 hours ago, YauS said:

cannot change deltaV

1. The upper stage can be liquid-fueled.
2. The upper stage can cut off the nozzle if required.
3. The upper stage can cut out openings to taint pressure.
4. The upper stage can get into a pose when further acceleration doesn't effect the distance, only flight duration and trajectory curvature.
5. Any combination of 1..4.

Edited January 11, 2018 by kerbiloid

[YauS]

5 minutes ago, kerbiloid said:

Only American ones and Topol family.
Others are liquid.

DF-31/41 is solid.

[kerbiloid]

OK, and one Chinese family.

Edited January 11, 2018 by kerbiloid

[YauS]

4 minutes ago, kerbiloid said:

OK, and one Chinese family.

That's included most of modern ICBM 

[kerbiloid]

1 hour ago, YauS said:

That's included most of modern ICBM 

How many pieces? (Not types)

Edited January 11, 2018 by kerbiloid

[Shadow Wolf56]

@Bill Phil I agree.

 there probably would be some preset equation in the flight computer of our ICBM to calculate the trajectory and launch angle required to hit the target (I have no idea what the formula is).

Not sure if this answer leads to more questions...

Edited January 11, 2018 by Shadow Wolf56

[mikegarrison]

There are two obvious ways to control the point of impact even if the delta-v of the launcher is fixed in advance. 1) You just change the trajectory arc height. 2) You design a re-entry vehicle that has a lot of cross-range maneuvering ability.

[YauS]

2 hours ago, Shadow Wolf56 said:

@Bill Phil I agree.

 there probably would be some preset equation in the flight computer of our ICBM to calculate the trajectory and launch angle required to hit the target (I have no idea what the formula is).

Not sure if this answer leads to more questions...

I had already research some book for this question. Since, most of them provide some equation like this:

which phi is central angle of two point. beta is launch angle.

Also, some adjustments is required.

Edited January 11, 2018 by YauS

[GoSlash27]

Interesting video of the launch sequence:

https://youtu.be/Ygdv1aQnNRY?t=210

They don't talk about it in the video, but stage 3 has vent tubes at the top end that are blown out on command, which extinguishes it. This puts the "bus" within a general chunk of sky. The bus is liquid fueled, and fine- tunes the trajectory to the desired impact point.

Best,
-Slashy

Edited January 11, 2018 by GoSlash27

[wumpus]

Also the trajectory of an ICBM is absurdly high, to make life difficult for any attempt to build an ABM, so simply aiming higher will work well.  But solid motors can (and typically are in at least US ICBMs) be "turned off" by making the nozzle wildly less efficient (blowing the whole nozzle off would be my first guess, but I think they vent before that).

[GoSlash27]

10 minutes ago, wumpus said:

Also the trajectory of an ICBM is absurdly high, to make life difficult for any attempt to build an ABM, so simply aiming higher will work well.  But solid motors can (and typically are in at least US ICBMs) be "turned off" by making the nozzle wildly less efficient (blowing the whole nozzle off would be my first guess, but I think they vent before that).

They actually turn them off by blowing the vent tubes. You would think that this would result in thrust being generated both ways, (or at least I did), but actually it snuffs the SRB out instantly. Thus, the guidance computer has positive control of the final velocity.

Best,

-Slashy

[mikegarrison]

5 hours ago, GoSlash27 said:

Interesting video of the launch sequence:

https://youtu.be/Ygdv1aQnNRY?t=210

They don't talk about it in the video, but stage 3 has vent tubes at the top end that are blown out on command, which extinguishes it. This puts the "bus" within a general chunk of sky. The bus is liquid fueled, and fine- tunes the trajectory to the desired impact point.

Best,
-Slashy

Pretty cold-blooded right there at the end as they blow up an entire city of people and just say "mission accomplished".

[GoSlash27]

1 hour ago, mikegarrison said:

Pretty cold-blooded right there at the end as they blow up an entire city of people and just say "mission accomplished".

True, but that's the mindset they need to have. Otherwise they'd never be able to turn the keys.

Best,
-Slashy

[DerekL1963]

2 hours ago, GoSlash27 said:

They actually turn them off by blowing the vent tubes.

You can turn them off either way - by venting the forward dome or by blowing off the nozzle.  The latter is less well known as the LGM-118 Peacekeeper is the only missile known to have used it operationally.

 

15 hours ago, YauS said:

Modern ICBM are using solid rocket engine which cannot change deltaV. I wonder how it calculate the launch profile to control the target location.

One way, extensively discussed here, is to use thrust termination.  The other is trajectory shaping - for example burning to left for a little bit and then burning to the right to null the velocities and correct the induced error consumes more delta-v than simply burning straight.  This is known a GEMS (Generalized Energy Management Steering), and was used by Trident-I and is used by Trident-II.

This article discusses using GEMS to control speed (and thus range) and has a picture of the resulting trajectory.

[GoSlash27]

On 1/11/2018 at 9:54 AM, mikegarrison said:

Pretty cold-blooded right there at the end as they blow up an entire city of people and just say "mission accomplished".

Also, I should point out a couple details for clarification.

#1, the original launch sequence animation didn't include nuking a city or the words "mission accomplished". #2, ICBMs (or at least American ICBMs) are not tasked with counter- value targets like cities. They are tasked with targets that require precision, like counter-force and command/ control. Thus, this animation isn't quite accurate.

 It does, however, give the general idea of how an ICBM does it's thing.

Here's a less callous version of the same animation:

Spoiler

 

The part that is of interest to us is at 1:29. The 3rd stage thrust termination ports blow out on command, thus giving a precise end to the acceleration in the SRB powered boost phase. This was actually how the energy was managed in the Minuteman I and II. Less accuracy, single larger warhead. Minuteman III brought in the hypergolic MIRV bus, which allowed independent targeting of multiple, smaller warheads on a single ICBM and obviated the need for the thrust termination ports.

Best,
-Slashy

 

Edited January 15, 2018 by GoSlash27

[DerekL1963]

6 hours ago, GoSlash27 said:

The part that is of interest to us is at 1:29. The 3rd stage thrust termination ports blow out on command, thus giving a precise end to the acceleration in the SRB powered boost phase. This was actually how the energy was managed in the Minuteman I and II. Less accuracy, single larger warhead. Minuteman III brought in the hypergolic MIRV bus, which allowed independent targeting of multiple, smaller warheads on a single ICBM and obviated the need for the thrust termination ports.

Nope.  MM-III still has thrust termination ports* because you still have the same problem - how do you reach a target at less than the maximum range of the missile?   Basically, ballistic missiles are designed such that if you burn the final propulsive stage to exhaustion the warhead (or bus) is thrown to the missile's maximum range.  While bus energy can be used to extend the footprint along the range axis, there isn't sufficient energy to extend the range of the bus significantly.  (And any energy expended for range extension isn't available for cross-range expansion.)

*ref: http://ed-thelen.org/Minuteman.pdf pg 89, http://www.au.af.mil/au/awc/space/primer/us_missile_systems.pdf pg 17-9, not to mention the title of the animation you linked to.

Edited January 15, 2018 by DerekL1963

[GoSlash27]

1 hour ago, DerekL1963 said:

MM-III still has thrust termination ports*

DerekL,
 Yeah, it still has them... It just doesn't use them for setting the final trajectory like the previous versions did.

Best,
-Slashy

[DerekL1963]

44 minutes ago, GoSlash27 said:

 Yeah, it still has them... It just doesn't use them for setting the final trajectory like the previous versions did.

Which doesn't mean the same thing as "obviated the need for the thrust termination ports", which you originally wrote.

Just so we're clear here:  Yes, the MM-III has thrust termination ports.  Yes, it uses them to terminate third stage thrust when it has sufficient energy.  No, it doesn't use them to set the final trajectory as that function is now performed by the bus.

All three of these points are illustrated in the video you linked of the MM-III flight sequence.

[GoSlash27]

1 hour ago, DerekL1963 said:

Which doesn't mean the same thing as "obviated the need for the thrust termination ports", which you originally wrote.

Yeah, poor choice of wording on my part.
 

 

1 hour ago, DerekL1963 said:

Just so we're clear here:  Yes, the MM-III has thrust termination ports.  Yes, it uses them to terminate third stage thrust when it has sufficient energy.  No, it doesn't use them to set the final trajectory as that function is now performed by the bus.

All three of these points are illustrated in the video you linked of the MM-III flight sequence.

Agreed.

Best,
-Slashy

[mikegarrison]

General note to all: this has been a really interesting discussion. Thanks to the OP for asking the question.

[p1t1o]

There is something called an "energy management manouver" and many ICBMs and ABMs utilise it. Essentially if the target is sufficiently closer than max range, the rocket will bleed off energy by spiralling. 

Pictured: A THAAD energy management manouvre

 

Another way to manage energy in a solid rocket are special blow-off panels which can instantly "snuff out" a first-stage booster to give a precisely measured amount of impulse.

On another note, when the MX/Posiedon/Peasekeeper ICBM was being developed, they invented a cutting edge inertial navigation platform (GPS cannot be relied upon in wartime for obvious reasons), which was/is considered to be the pinnacle of inertial navigation systems as its accumulated errors, or "drift" (especially over a short time as in an ICBM) are significantly smaller than other sources (such as wind or gravitational anomalies) so making it any more accurate would not have increased the accuracy of the missile.

This is one of the reasons why the gravitational environment of the Earth (its not homogenous/perfectly spherical, differences in density and crustal unevenness etc) is studied so intensely - its good for geo-science but it also happens to be very important for targetting ICBMs.

 

These 3 concepts - advanced intertial navigation, accurate gravity maps and energy management - are some of the most significant ways in which an ICBM is controlled.

Edited January 17, 2018 by p1t1o

[DerekL1963]

23 minutes ago, p1t1o said:

On another note, when the MX/Posiedon/Peasekeeper ICBM was being developed, they invented a cutting edge inertial navigation platform

Nope, the AIRS reference sphere was developed for MX (which was later named Peacekeeper), and has now been installed on Minuteman-III.   Poseidon uses a more conventional gimbal based system.

[kerbiloid]

And here, too. 19 000 parts.
 

Spoiler

43 minutes ago, p1t1o said:

energy management manouvre

When i was a KSP beginner, my rockets also often performed the energy management manouvres.

Spoiler

Btw compare

 

Edited January 17, 2018 by kerbiloid