Re: Intercept Algorithms and V1.

On Mar 25, 7:57 am, "Ken S. Tucker" <dynam...@xxxxxxxxxxxx> wrote:
We wrote a computer SIM using an inbound subsonic
cruise missile (500 mph) with no evasion ability vs a
2000 mph piloted interceptor, (none stealthy).
The Interceptor had realistic fuel, g-turn limits and
acceleration, but unguided missiles/cannon.

I was surprised how difficult it was to master the
Interception Algorithm.

I bet you didn't attempt a Kalman filter?

The classic intercept course for a missile is:
1 Pursuit course. (Whereby the seeker head locks on to the target and
aligns itself with it and the control algorithm then attempts to
align the missile flight path with the seeker; this leads to a sort of
hyperbolic flight path.)

2 P/N or Proportional Navigation. (Whereby the seeker head locks on
to the target and the control algorithm then measures the angular
rate of change of target with reference to ‘inertial space’ (using
rate gyros) and then establishes a missile heading such that the
seeker head has a zero angular rate unchanging angle this eventually
leads to the missile flying a straight line intercept course so long
as the target doesn't manoeuvre.

P/N is generally superior, German WW2 missile researchers settled on
pursuit course for AAM and P/N for SAM as optimal solution.
(Reference Fritz Trenkle “German Guidance Systems”)

(These were second generation autonomous homing seekers designed to
replace first generation MCLOS guidance or they were termaninal
systems for the bigger SAMs eg “Hambur” and “Madrid”. They were
mainly infra-red but also active radar based and were in some cases
intended for both AAM and SAM but with different intercept
algorithms). I think this pattern is more or less the same today.

I suspect for a fighter intercept a P/N will work quite well for
passing instructions from a GCI (ground control intercept) to the
missile.


The GCI operator would immediately turn the interceptor direct towards
the target. The next radar sweep 10 to 20 seconds later the GCI
operator instead of giving the new heading would draw a baseline
between the interceptors last and present position and measure the
targets relative angular rate to this baseline and tell the
interceptor pilot a new heading which would be direct towards the
target plus the relative angular target rate per radar sweep. Within
3-4 sweeps the interceptor and target will be on a collision course.


Solving a set of parametric simultaneously equations should be
possible: AAA predictors did it regularly.

A Head on intercept and shoot would require radar and computer control
and would be best mounted on a Mosquito though no such device existed
AFAIKT.

The Oberon Eule blind fire system that the Luftwaffe was hoping to
develop might have been able to do this.

I mention this because there
has been discussions about B2 interceptions and others.

So I thought a look at some historical, here,http://en.wikipedia.org/wiki/V-1_flying_bomb
for some reality feed-back.

What we found with the SIM is how much an early warning
is important to line up the interception.

V1's increased in speed as their motors were improved both due to
design changes but mostly through production quality issues. In
addition some with reduced warheads had both considerably greater
range and greater speed again. Some V1’s were tracked at 420mph the
worst at 240mph.

As fuel was reduced their speed increased as well. Average speed
was just over 360mph though it increased. This sounds less than a
fighter such as the 400+ mph fighters of the day but was generally
faster than a Mk.IX Spitifre.LF since this was at low altitude well
below the optimal speed of the interceptor and difficult even for
Tempests and Griffon Spitifires with 100/150 fuel.

Note that V1's soon after their introduction developed the ability to
fly 'dog leg' courses (ie second in flight course change on top of
that made just after launch). This is because by straight line back
tracking of radar tracks and triangulating the path of several
missiles it was possible to discern the launch site location of V1's
without the dog leg feature.

If V1 had of been equiped with the FuG 101a radar altimeter (in use
from 1940) they could have used sea skimming to hide in sea clutter or
flown so low that they would have stayed hidden from many more AAA
guns. Since they came in at several thousand feet rather than seal
level the warning radars were still looking skywards rather than down
into clutter.


The V1 was a very low level flying machine, making radar
detection difficult. In the V1 link is mention of a Wellington
"AEWC", that I rather think was a smoke-screen to cover
the real reports that came from the ground intel near the
launch sites, because look-down radar from a flying a/c
was quite advanced.

The Wellingtons worked reasonably well over water. The frequencies
need to be chosen well to avoid absorption by water and wave tops.
The antenna was a massive end fire array ‘yagi’ that looked like a
sword fishes nose. (the aninal not the biplane)


((I recommend not arguing Science, Technology and Intel
with liberal arts historians, a scientist can be an excellent
historian, but historian's do not understand scientist's)).

There are a few good technical Historians around, unfortunately their
work is little covered; this is unfortunate as I find their work is
actually quite readable for the average person. Louise Browns Radar
History of WW2 is quite good in that it reasonably covers both sides.

Much of the technical history indeed the actual history of WW2 is
severely distorted by the technical illiteracy or disaffinity of non
technically inclined Historians. The other is a failure or simply
laziness in not checking German or Japanese sources to see what really
was going on in the other side.

Another issue is over reliance on allied intel reports which in many
cases are inaccurate due to the nature of such reports (being a work
in progress based on limited knowledge) and thus rather out of context
yet are taken as the be all and end all. They should be cross checked
with interviews or documents on the German side and finally there is
the distortion from the 1950s when it was customary to disparage the
loosers.



Intel Theory:
At the moment the V1 was launched a brief encrypted
radio signal was transmitted and RAF scrambled, but
the Nazi's would figure it was the AEWC that did the
detection, so ULTRA protected the real Intel source with
the Wellington hoax.

ULTRA seldom worked that fast, though its theoretically conceivable
that it could on a good get a excellent crib or operator mistake and
find the settings for the day and them make those available certainly
it was seldom unlikely to be fast enough to work in the 20-30 minute
flight of a V1 and then you have the problem of sifting through the
data of 1 million enigma machines.

In good circumstances it could work in a few hours since once a
particular message in a particular code group had been 'cracked' the
code settings were available for the rest of the day (or at least a
few hours) for other messages.

As a side note: In the first quarter of 1944 the German Army
introduced “unkehrwalz D” or “reflector d”. This was completely
rewireable and eventually Bletchely park started to loose the ability
to decrypt certain code groups in the field and was likely to loose
the lot for at least 1 mayvw 2 years.. It allowed all letters to be
jumbled. Unfortunately for the German Army because they were able to
introduce it only slowly unkehrwalze D coexisted and communicated with
machines within code groups that were not so equipped and since the
same settings for the other rotors were used and messages coexisted it
was possible to reconstruct the “unkehrwalze D” wirings on the basis
of known rotor settings and messages from machines that not yet been
given the unit. In fact all the mistakes this slow roll out caused
actually improved code breaking for a while. Of course the Fi.103 V1
was a Luftwaffe show and they had the slackest code drill of all.
Another procedural change was an instruction for code machine
operators to add a advance the rotors manually in a certain pattern
during long messages. This destroyed long cribs which were needed to
reconstruct rotors or reflectors.

Bletchley park was probably going to go blind for about 18 months on
the Army codes. Naval enigma was supposed to go from a 4 rotor
system (3 rotating 1 stationary) to a 5 rotor system which I suspect
would have had a similar effect.


Our experience with the Interception Algorithm (IA)
was flying directly at a 400 mph V1 at 450 mph had
a closing speed of 850 mph, hard to shoot it, likely
miss, and then a 180 bleeding turn was required with
only 50 mph to catch up to it after that.

Most importantly ‘play’ in 3 dimensions.

1 Why not just patrol, let the ground controller set a course
intercept predicted flight path of the drone and then align the two
flight paths of the interceptor with the flight path of the drone
(flying in the same direction) then wait for the missile to pass below
and then accelerate and dive down upon it.

Ground controllers had a lot of neuro fuzzy ability but the idea of a
head on intercept followed by an aggressive turn into a classic
pursuit at the same altitude doesn’t make sense to me: it places quite
a few demands on human ability. Diving in some way is essential.

2 Alternatively run a right angle to the predicted flight path of the
V1 then turn into it head on into it but flying 7000ft or more above
it (ie 10000ft) As you pass over perform a split-S (roll 180 then
pull back for an inverted half loop until you have reversed course):
you are now on the tail of the V1 with enough energy advantage to fly
pursuit at over 500 mph.

3 Alternatively run an constant angle intercept on a virtual target a
few miles ahead or aside of the target so that you can aligne with its
course or do the split-s manoeuvre.

4 (I think this is what they actually did) run a constant angle
intercept from the frontal sector at about 4000ft higher altitude when
the V1 is sighted switch to a classic pursuit path diving turn into a
tail chase.

The ability to climb to harbour or buildup potential energy (as
altitude) may be more critical than low level speed since this energy
can be coverted to burst speed, I this is why even lowly Spitfires
IX’s that were generally slightly slower could in fact intercept V1’s
but had a climb rate equal to tempests AFAIKT and could perform
intercepts.


We found the IA was to come from the side but that
takes time to set-up, then move parallel to flip or disrupt
it.
Ken

They key here is vertical manoivering.


.

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