e***@yahoo.com.au
2006-04-20 15:33:39 UTC
Walter Dornberger, the young Artillery officer along with Werner von
Braun is credited with being the main driving force behind The EMW A4
(i.e. V2) ballistic missile development in Germany during the second
world war.
In 1942 he claimed that at "Reichs Mark" RM40,000 that the V2
rocket was a cheaper way of delivering explosives than a two engine
Luftwaffe bomber that cost RM1,500,000 to build and train the crew for
but lasted an average of only 6 missions over Britain. Post war
analysis suggests that the V2 cost RM120,000 but this was probably
likely to fall to RM50,000 and possibly even RM28,000. This would have
brought the cost down to similar levels to that of the complicated
BMW801 fuel injected engine used in the Fw 190 fighter.
Many of the claims of the cost of the V2 program fail to note that
major programs such as the Ju 88 for the Germans and the B-24 or B-17
program for the US had similar cost levels when both research and
development, production, factory costs, airfield defense costs and
operation are considered. It is one thing to count the unit cost of a
B-26 or B-24 and quite another to factor in air and ground crew
training costs, fuel, bombs, ammunition, research and development,
maintaining of navigation aids and air seas rescue, airfield
development and protection, administration etc. When the V2 program
is counted as being 2 billon Reichmarks these anciliary operation costs
are factored in however they are generally not when compared to a
conventional bomber. When compared 'apples to apples' its
economics are comparable to a conventional bomber. Part of the reason
may be just straight repetition of 'passed down wisdom" part is a
desire to discredit the Nazi regime. In part it may have been Albert
Speer who while an ardent rocket supporter wanted a scapegoat to
salvage the reputation of competence he cultivated.
A V2 on Dornbergers figures alone could deliver 30 or 12 missiles at
the same cost of RM1,500,000 as compared to equipping a crew of 3-4
with a two engine bomber and hoping that it and its crew would last 30
missions unscathed. Production quantities of 1500 V2 missiles per
month were considered feasible by the Penemunde development Team. The
quantities of 5500 month demanded by Hitler required using of impressed
labour. (Eg it was agreed to take some 1500 skilled French workers
were taken prisoner to relieve production bottlenecks)
Incidently actual production costs of a Ju 88 were about RM400,000 in
1939 and only about RM200,000 in 1941. The Germany industry learned
mass production on this aircraft and generally it took 2 years to gets
costs down. A B-24 cost $296 000 each (RM750,000, compared to $224 000
(RM 600,000) for the B-17.
In his 1948 Autobiography "Crusade In Europe" Dwight Eisenhower is
credited with saying that had the V2 been available in quantity 6
months earlier (than its September deployment) Overlord would probably
have been canceled. (overlord was the 6 June 1944 D-day invasion).
After investigation I find this quite believable. Dwight Eisenhower,
as head of the overlord invasion, is quite a credible source.
On the other hand the detractors of the V2 claim it was colossally
expensive, inaccurate (claiming inaccuracies of 17km or miles in some
accounts) and that when compared to an allied bomber, that it was
militarily ineffective and that it was a pure terror weapon. (All of
these have been said about strategic bombing incidentally). It is
noted that proportionally that Germany supposedly invested as much into
the V2 program as the US invested into the Manhattan Nuclear Bomb
project. (I actually question those figures)
What then are the factors that would have determined V2 effectiveness?
I will cover 4 areas.
1 Timing. Could the V2 have been ready earlier; could it have
improved? What would the effect of the weapon being available months
prior to D-day.
2 Accuracy. What did it achieve, what was the effect and what was
possible.
3 Cost effectiveness in the light of the above.
4 Accuracy compared to conventional bombing.
The V2's operational deployment was delayed by a number of factors.
These factors also prevented the weapon from maturing in accuracy and
reliability earlier in its deployment.
1 Hitler's reluctance. Max Valier who was an engineer fascinted in
rocketetry and known to Hitler from the early nazi days in Munich..
Valier had died in a Rocket explosion. Hitler regarded the missile in
the same way he regarded Zeppelins: dangerous, explosive and therefor
unusable. He was quite understandably not impressed. Hitler believed
in the Vril, an intelligent life force that protected the earth. He
imagined or rather dreamed of the V2 damaging the earth protective
mantle (more or less correct as modern studies have shown but also an
exaggeration). Hitler was silent, awkward and unresponsive upon
visiting Penemunde development facility and the opinions he expressed
were influenced by the above. That was March 1939.
As a result V2 development was restricted by lack of full high level
support. Apart from retarding the deployment one outcome may have been
that development of advanced forms radio guidance systems for the V2
was restricted (the experts were needed for radar and radio navigation
development) so the engineers had to emphasise a simple 'inertial'
system that relied on a gyroscopic accelerometer. A radio beacon
system was deployed in the latter stages of the V2s operational life
that apparently improved accuracy (by a factor of 5-10) in perhaps 25%
of late war launches but even this system was improvised and
underdeveloped compared to what was needed. (Note: inertial guidance
quickly outperformed radio based systems in all but applications with
very close transmitters).
Another delay was a Heinrich Himmler power play as the system began
showing promise. Dornberger and von Braun were both arrested for what
amounts to sabotage so as to intimidate them into taking V2 development
into Himmlers Schutz Staffel SS weapons program. The charge arose out
of relatively innocuous discussions and comments by von Braun and
Dornberger that they were ultimately developing space travel for post
war use rather than developing weapons and was intended to intimidate
them into leaving the Army and joining the SS. The arrests came at a
critical phase of V2 testing.
The V2 could have been available considerably earlier.
The targeting error claimed by Walter Dornberger and the German
guidance experts (including F Mueller who designed the original V2
system) that eventually became US citizens and worked at the Redstone
Arsenal at Huntington was a CEP of 4.5 kilometers or 2.8 miles for the
LEV-3 guidance system. It's a realistic figure that ignores gross
malfunctions.
CEP or "Circular Error Probability" is the radius of a circle in
which 50% of all munitions will fall. In the case of a Gausian
distribution (Rayleigh in 2 dimensions) of those falling outside the
CEP radius some 43% will be outside one CEP radius but within two while
7% will be outside two but within 3.. Within the CEP radius there will
be a clustering towards the aim point but it is not by much; the
distribution is almost random.
Probability of weapon falling within <r = 1-exp-1(r2/(1.414*CEP2))
(I'll tabulate these later). If the standard deviation is known
instead of the CEP then the 1.414 factor above is changed to a 2 and
the CEP is replaced by the standard deviation.
However the actual results were slightly less: British counter
intelligence had captured German agents in Britain and turned them. As
the Germans were too afraid of risking Arado 234 Jet reconnaissance
aircraft over Britain so for post strike reconnaissance analysis they
had to rely on their agents. Although the repeatability of the V2
LEV-3 guidance system may have been 4.5km there appear to have been
local factors such as gravitation, coreolis effects not fully accounted
for.
The British were selectively feeding the Germans impact points that
correlated with a correct time of impact but a selective impact points
in wrong position for the time of that impact to gradually move the V2
impact point out of London. Compensating for the British deception
brings a CEP of less than 6km not the 17km often mentioned. V2
'reliability' eventually achieved 80%-90% at its peak though it
languished as low as 43% at for some time. Many gross V2 misses were
due to guidance system malfunction; for instance a gyroscope
instability or failure that would to produce almost complete loss of
control on one axis. It is a matter of philosophy as to whether these
are included in evaluating CEP (many ended up in the sea or
countryside) but because they were so large and there were a
significant number of them they, along with 'double cross' tend to
totally distort the realistically achievable CEP.
For comparison; in WWII, a B-17 with the Norden Bomb sight had a 3,300'
(1000m) circular error probability (CEP), which by reason of energy
distribution means to absolutely guarantee a target kill a drop of
9,000 (500lb?) bombs from 1,000 bombers was needed...which put more
than 10,000 airmen at risk. In Korea, an F-84F had a 1,000' CEP, which
means to absolutely guarantee a target kill a to drop of 1,100 bombs
from 550 fighters put 550 airmen at risk. In SEA, an F-4 had a 400'
CEP, which means to absolutely guarantee a target kill a drop of 176
bombs from 30 fighters put 60 airmen at risk.
In accuracy and collateral damage high altitude bombing was not much
better in accuracy than the V2 and for the B-29 operating at is full
ceiling with 100mph cross winds at different heights it may have been
worse.
Within a few years missiles with guidance systems based on the V2's
SG-66 (an expeimental replacement for the LEV-3 generally used) but
using the same principles (eg the US Armies Redstone missile of the
1950s that was substnatially built by von Brauns team achieved a CEP
300 yards). These inertially guided missiles using much the same type
of system as the V2 would be exhibiting better accuracy than WW2
bombers and accuracy as good as the bombers of the day. (F-84F CEP 300
yards)
A Soviet SCUD-A with a crude early V2 style of boost phase only
'inertial' guidance system has a CEP of 3km at 300km. (It was
designed for nuclear use). A slightly latter model SCUD-B using a
refined but similar boost phase fully inertial system has a CEP of 450m
at 300km. (A Modern SCUD-D achieves 50m by adding in a terminal system
based on scene correlation; the SCUD's reputation for inaccuracy
comes from non authentic non Soviet extended range versions).
Pn(<r) = 1-exp-1(r^2/ (1.414*(CEP)^2))
In the following tables I've chosen 400 missiles as an launch rate
against a target. With production rates of 1500-5500 per month firings
of several times this rate per month were feasible. Imagine
CEP 4.5km, 400 missiles launched this CEP corresponds to the LEV-3
system.
r meters probability nos of missiles, nos of
hits
4000 0.428097089 400 171.2388
2000 0.130377882 400 52.15115
1000 0.034321318 400 13.72853
500 0.008693027 400 3.477211
250 0.002180377 400 0.872151
125 0.000545541 400 0.218216
62.5 0.000136413 400 0.054565
31.25 3.4105E-05 400 0.013642
15.625 8.52636E-06 400 0.003411
7.8125 2.1316E-06 400 0.000853
CEP 2km 400 missiles launched this correspond to the reported accuracy
of the Leitstrahl system.
r meters probability nos of missiles, nos of
hits
4000 0.940919497 400 376.3678
2000 0.506983964 400 202.7936
1000 0.162055487 400 64.82219
500 0.043238226 400 17.29529
250 0.010989383 400 4.395753
125 0.002758741 400 1.103496
62.5 0.0006904 400 0.27616
31.25 0.000172645 400 0.069058
15.625 4.3164E-05 400 0.017266
7.8125 1.07912E-05 400 0.004316
CEP 1km, 400 missiles launched, this corresponds to an imagined
improved V2 guidance system perhaps the SG-66 that was undergoing
testing with improved gyroscope bearings. A CEP of 1km corresponds to
Norden accuracy when aimed from high altitude.
r meters probability nos of missiles, nos of hits
2000 0.940919497 400 376.3678
1000 0.506983964 400 202.7936
500 0.162055487 400 64.82219
250 0.043238226 400 17.29529
125 0.010989383 400 4.395753
62.5 0.002758741 400 1.103496
31.25 0.0006904 400 0.27616
15.625 0.000172645 400 0.069058
7.8125 4.3164E-05 400 0.017266
3.90625 1.07912E-05 400 0.004316
CEP 300m, 400 missiles launched. (CEP of a 1952 redstone missile)
r probability nos of missiles, nos of hits
range prob nos launch nos of hits
600 0.940919497 400 376.3678
300 0.506983964 400 202.7936
150 0.162055487 400 64.82219
75 0.043238226 400 17.29529
37.5 0.010989383 400 4.395753
18.75 0.002758741 400 1.103496
9.375 0.0006904 400 0.27616
4.6875 0.000172645 400 0.069058
2.34375 4.3164E-05 400 0.017266
1.17187 1.07912E-05 400 0.004316
As can be seen with a CEP of 4km the V2's ability to destroy a
specific target is not great unless a great many launches (about 1
months total production). It would however be capable of causing great
damage to a large factory, steel works, power station, dock area or oil
refinery and if its CEP could be brought down to less than 1km it would
be quite effective. Ultimately shear numbers will have the desired
effect. A V1 hit within 300 meters could kill a man standing in the
open and would send someone flying through the air. The crater
photographs I've seen look about 30m in diameter and 30m deep. Truly
massive.
With an putative improved CEP of 1km (essentially that of a Norden
operating at high altitude) It becomes quite menacing to specific
targets in small launch salvos. On the basis of papers and research
and the calibre of person doing the development I believe this degree
of accuracy would have been achievable by the Germans within one year.
The standard guidance system of the V2 was the LEV-3 which consisted of
a pair of gyroscopes to control missile attitude and a gyroscopic
accelerometer capable of providing acceleration, speed and distance
information to initiate the tilt over of the missile and terminate
motor cutoff. Once motor cutoff had been achieved the missile was
purely ballistic. Since only two gyroscopes were used it was necessary
to launch the missile from a rotating platform to align it with the
target. One vertical gyroscope controlled roll and yaw of the missile
while another horizontal unit controlled pitch. A single "PIGA"
(Pendulating Integrating Gyroscopic Accelerometer) was aligned with the
thrust axis. The PIGA was called the MMIA (Mueller Mechanical
Integrating Accelerometer) by the Germans in honour of Fritz Mueller.
Charles Stark Draper recognised the brilliance of the instrument and it
was redubed the PIGA. It is used in the Minuteman, MX and late model
trident missiles for guidance where it achieved 0.5m accuracy over an
interconintental ICBM flight (the 100m CEP was caused by other errors)
A more advanced system was the SG-66, which mounted several
accelerometers on a stable platform controlled by 3 gyroscopes and had
for instance an accelerometer to compensate for cross range errors.
This was test flown only a few times before the end of the war but was
expected to control accuracy considerably. It formed the basis of
both the Redstone and SCUD guidance.
A "Leitstrahl" guidance system that used a radio guidance beam was
also in use and apparently improved accuracy by a factor of 5-10
(particularly over short ranges) according to some sources. (in
reality its was somewhat better over short ranges). It was kept very
secret due to the possibility that the signals might be detected and be
used to discover the launch sites. It is credited with a CEP 2km by
some sources. Ironically it was never detected and never jamed.
The Soviet SCUD-B achieved a CEP of 450m at 300km using inertial
systems that guided the missile for the fist 60 seconds of flight. The
Redstone Arsenal missile (essentially von Brauns team including Fritz
Mueller the inventor of the gyroscopic accelerometer) with an influx of
American engineers) achieved an improvement of accuracy by a factor of
10 over the V2 from 2.8 miles (4.5km) to 270m (300 yards) at
considerably greater ranges.
It might be supposed that the Germans using an electronic beam method
could eventualy have achieved similar accuracies as the Soviets
achieved in the 1950s using an guidence and control system active for
only the first 60 seconds of fligh. (450m at 300km and about 600m at
400km). Such a system was being planed. (I believe the code name may
have been 'Viktoria'.) It would have used the Doppler principle
to provide accurate velocity and range information to the missiles and
tightly controlled beams to maintain the missile on the correct path
free from cross winds during the first 80 seconds of boosted flight.
A PIGA or Pendulating Integrating Gyroscopic Acceleromer was called
MMIG (Mueller Mechanical Integrating Accelerometer) by the Germans in
honour of F Mueller its inventor. It consisted of a gyroscope spinning
at a precise speed but mounted on a rotating pedestal so that it was
free to rotate or 'precess' about the another orthogonal axis. A
pendulum was mounted along so that it would unbalance the gyro as the
mass was accelerated. As the pendulum 'falls' it would cause the
gyro to 'precess' about its pedestal at a rate proportional to the
acceleration and the rpm of the gyro. A sensor (or switch contact in
the V2) activates a torque motor to rotate the pedestal in the opposite
direction so as to maintain pendulum position by forcing it to precess
in the opposite direction.. It was found that electrical contacts
worked much better than potentiometers on the accelerometer and that
they were suprisiningly precise.
In the V2 this torqueing of the precesional axis rotated a gear system
that operated electrical contacts to initiate the various sequences at
the exact speed.. A V2 would take-off and within 4 seconds would begin
its tilt over to 49 degrees (always the same angle) at a rate of about
3 degrees/second. After 20 seconds the missile was supersonic and at
95% the thrust of the motor would be reduced from 25 tons to 8 tons in
preperation for 'brenschluss' (burn termination) since the
shutdown sequence took 2.5 seconds and this added to much missile
error. The two 'strapdown' gyroscopes of the V2 used
potentiometers as position pickoff. A mechanism rotated the body of
the potentiometer to obtain the 3 degree/second tiltover. The DC
potentiometers voltages were amplified by an electronic DC amplifier
and proportional integral derivative style controller that worked by
converting DC voltages to AC, amplifying them and then converting back
to DC where they would be used to operate electrohydraulic servo valves
that controlled the tail fins.
Several improvements were being planed.
1 A 3 Axis stable platform LEV-3. Apart from not needing a rotating
launch platform and maintaining the main thrust axis accelerometer in a
stable alignment this had lateral accelerometers to control cross range
errors produced by cross winds. The LEV-3 was actually test flown
several times and formed the basis of all post war ballistic missile
developments in the USA and USSR.
2 Integrator on main accelerometer. The output of the "PIGA" in
terms of number of revolutions was actually speed. It was intended to
integrate this mechanically with a 'ball and disk integrator' (as
used in bomb sights) to produce a distance flown. This would be used a
solve an equation that determined rocket cut off (Brennschluss) that
more accurately factored in distance as well as speed. This system was
implemented on Redstone and was known as delta t control.
3 Fluid bearings. A large source of gyroscope and accelerometer error
was due to bearing resistence and vibration. Kreisel Garraete, the
company at which Mueller worked experimented with the use of
pressurised water fluid bearings. Post war missiles tended to
initially use compressed air and later went to a refrigerant gas style
liquid because of the problem of compressed air storage and then
disturbing influence aircompressors had for long periods of opperation.
Water was simply corrosive.
The Redstone missile essentialy had the above guidence system with the
refinement of highly accurate accelerometers, gyroscopes and a system
for levelling the platoform prior to launch.
Below find a few references:
http://www.v2rocket.com/start/deployment/mobileoperations.html
(webmasters note: It is generally believed that the A4/V2 was not an
effective weapon because it was not accurate enough to hit an exact
target. While pinpoint accuracy was not associated with the V2, it was
much more accurate than generally reported. Not every batterie received
or installed the Leitstrahl-Guide Beam apparatus, which, was crucial to
the greater accuracy of the weapon. In the later stages of the war the
accuracy improved greatly, sometimes to within meters of the target.)
http://www.usafe.af.mil/iraqifree/FAQ's.htm
In WWII, a B-17 with the Norden Bomb Site had a 3,300' circular error
of probability (CEP), which means to absolutely guarantee a target kill
you had to drop 9,000 bombs from 1,000 bombers...which put more than
10,000 airmen at risk. In Korea, an F-84F had a 1,000' CEP, which means
to absolutely guarantee a target kill you had to drop 1,100 bombs from
550 fighters...which put 550 airmen at risk. In SEA, an F-4 had a 400'
CEP, which means to absolutely guarantee a target kill you had to drop
176 bombs from 30 fighters...which put 60 airmen at risk.
http://www.ww2guide.com/bombs.shtml
In the fall of 1944, only seven per cent of all bombs dropped by the
Eighth Air Force hit within 1,000ft of their aim point; even a
fighter-bomber in a 40 degree dive releasing a bomb at 7,000 ft could
have a circular error (CEP) of as much as 1,000 ft. It took 108 B-17
bombers, crewed by 1,080 airmen, dropping 648 bombs to guarantee a 96
per cent chance of getting just two hits inside a 400 by 500 ft area (a
German power-generation plant.)
VOL. 4, NO. 3 J. GUIDANCE AND CONTROL MAY-JUNE 1981
History of Key Technologies AIAA 81-4120
1981 Developments in the Field of Automatic
Guidance and Control of Rockets
Walter Haeussermann
The Bendix Corporation, Huntsville, Ala.
AIAA 2001-4288
The Pendulous Integrating Gyroscope
Accelerometer (RIGA) from the V-2 to
Trident D5, the Strategic Instrument of Choice
R.E. Hopkins
The Charles Stark Draper Laboratory, Inc.
Cambridge, MA
Dr. Fritz K. Mueller, Dr. Walter Haeussermann
Huntsville, AL
999999999
http://forum-der-wehrmacht.de/index.php?s=cd28569eb4bf6047766be16f45d1e628&showtopic=10964
Von der Me 109 weiß ich, dass ein flugfähiges Exemplar etwa 500.000
Euro kostet / wert ist.
Im Krieg lag der Preis bei etwa 50.000 Reichsmark.
Below are costs of various German Weapons in Reichs Mark.
00000
Pz.Kpfw. I Ausf. B ca. 38.000,- ohne Waffen
Pz.Kpfw. II Ausf. b 52.640,- -
Pz.Kpfw. II Ausf. F 49.228,- ohne Waffen
15cm. s.I.G. auf Fgst. Pz.Kpfw. II (Sf.) 53.000,- -
Pz.Kpfw. III Ausf. M 103.163,- ohne Funkausrüstung
Pz.Kpfw. IV Ausf. G 115.962,- mit 7,5cm KwK 40 L/43
Pz.Kpfw. Panther 117.100,- frühe Version, ohne Waffen
Pz.Kpfw. Tiger Ausf. E 250.800,- ohne Waffen u. Funkausrüstung
Pz.Kpfw. Tiger Ausf. E 299.800,- voll ausgerüstet
Pz.Kpfw. Tiger I Ausf. E 645.000,- Exportpreis für Japan
Pz.Kpfw. Tiger II Ausf. B 321.500,- -
Sd.Kfz. 222 23.420,- ohne Funkausrüstung
Sd.Kfz. 232 57.290,- ohne Funkausrüstung
Sd.Kfz. 6 30.000,- -
Sd.Kfz. 7 36.000,- -
Sd.Kfz. 8 46.000,- -
Sd.Kfz. 9 75.000,- (später 60.000) -
http://www.nexusboard.de/showthread.php?siteid=332&threadid=198491&nx=ca459e2818269ce73574416be37b0e43
Hallo,
ich habe einmal die Preisliste aus "Achtung Panzer" kopiert:
In Englishe
Prices of selected models.
Model: Price in Reichsmarks (RM):
Volkswagen Käfer (VW Beetle) 990
Opel Kadett 2100
DKW Meisterklasse 2350
Ford Taunus 2870
Adler Triumph Junior 2950
Sd.Kfz.6 30000
Sd.Kfz.7 36000
Sd.Kfz.8 46000
Sd.Kfz.9 60000
Sd.Kfz.10 15000
Sd.Kfz.11 22000
PzKpfw II Ausf a 52640 with armament
PzKpfw II Ausf B 38000 w/o armament
PzKpfw II Ausf F 49228 w/o armament / 52728 with armament
Sturmpanzer II Bison 53000 with armament
PzKpfw III Ausf M 96183 w/o armament / 103163 w/o radio
Stug III Ausf G 82500 with armament & radio
PzKpfw IV Ausf F2 115962 with armament & radio
75mm KwK 37 L/24 8000
75mm StuK 37 L/24 9150
75mm StuK 40 L/43 12500
75mm KwK 42 L/70 12000
PzKpfw VI Tiger 250800 w/o armament & radio / 299800 with armament &
radio
PzKpfw VI Tiger II 321500 with armament & radio
Braun is credited with being the main driving force behind The EMW A4
(i.e. V2) ballistic missile development in Germany during the second
world war.
In 1942 he claimed that at "Reichs Mark" RM40,000 that the V2
rocket was a cheaper way of delivering explosives than a two engine
Luftwaffe bomber that cost RM1,500,000 to build and train the crew for
but lasted an average of only 6 missions over Britain. Post war
analysis suggests that the V2 cost RM120,000 but this was probably
likely to fall to RM50,000 and possibly even RM28,000. This would have
brought the cost down to similar levels to that of the complicated
BMW801 fuel injected engine used in the Fw 190 fighter.
Many of the claims of the cost of the V2 program fail to note that
major programs such as the Ju 88 for the Germans and the B-24 or B-17
program for the US had similar cost levels when both research and
development, production, factory costs, airfield defense costs and
operation are considered. It is one thing to count the unit cost of a
B-26 or B-24 and quite another to factor in air and ground crew
training costs, fuel, bombs, ammunition, research and development,
maintaining of navigation aids and air seas rescue, airfield
development and protection, administration etc. When the V2 program
is counted as being 2 billon Reichmarks these anciliary operation costs
are factored in however they are generally not when compared to a
conventional bomber. When compared 'apples to apples' its
economics are comparable to a conventional bomber. Part of the reason
may be just straight repetition of 'passed down wisdom" part is a
desire to discredit the Nazi regime. In part it may have been Albert
Speer who while an ardent rocket supporter wanted a scapegoat to
salvage the reputation of competence he cultivated.
A V2 on Dornbergers figures alone could deliver 30 or 12 missiles at
the same cost of RM1,500,000 as compared to equipping a crew of 3-4
with a two engine bomber and hoping that it and its crew would last 30
missions unscathed. Production quantities of 1500 V2 missiles per
month were considered feasible by the Penemunde development Team. The
quantities of 5500 month demanded by Hitler required using of impressed
labour. (Eg it was agreed to take some 1500 skilled French workers
were taken prisoner to relieve production bottlenecks)
Incidently actual production costs of a Ju 88 were about RM400,000 in
1939 and only about RM200,000 in 1941. The Germany industry learned
mass production on this aircraft and generally it took 2 years to gets
costs down. A B-24 cost $296 000 each (RM750,000, compared to $224 000
(RM 600,000) for the B-17.
In his 1948 Autobiography "Crusade In Europe" Dwight Eisenhower is
credited with saying that had the V2 been available in quantity 6
months earlier (than its September deployment) Overlord would probably
have been canceled. (overlord was the 6 June 1944 D-day invasion).
After investigation I find this quite believable. Dwight Eisenhower,
as head of the overlord invasion, is quite a credible source.
On the other hand the detractors of the V2 claim it was colossally
expensive, inaccurate (claiming inaccuracies of 17km or miles in some
accounts) and that when compared to an allied bomber, that it was
militarily ineffective and that it was a pure terror weapon. (All of
these have been said about strategic bombing incidentally). It is
noted that proportionally that Germany supposedly invested as much into
the V2 program as the US invested into the Manhattan Nuclear Bomb
project. (I actually question those figures)
What then are the factors that would have determined V2 effectiveness?
I will cover 4 areas.
1 Timing. Could the V2 have been ready earlier; could it have
improved? What would the effect of the weapon being available months
prior to D-day.
2 Accuracy. What did it achieve, what was the effect and what was
possible.
3 Cost effectiveness in the light of the above.
4 Accuracy compared to conventional bombing.
The V2's operational deployment was delayed by a number of factors.
These factors also prevented the weapon from maturing in accuracy and
reliability earlier in its deployment.
1 Hitler's reluctance. Max Valier who was an engineer fascinted in
rocketetry and known to Hitler from the early nazi days in Munich..
Valier had died in a Rocket explosion. Hitler regarded the missile in
the same way he regarded Zeppelins: dangerous, explosive and therefor
unusable. He was quite understandably not impressed. Hitler believed
in the Vril, an intelligent life force that protected the earth. He
imagined or rather dreamed of the V2 damaging the earth protective
mantle (more or less correct as modern studies have shown but also an
exaggeration). Hitler was silent, awkward and unresponsive upon
visiting Penemunde development facility and the opinions he expressed
were influenced by the above. That was March 1939.
As a result V2 development was restricted by lack of full high level
support. Apart from retarding the deployment one outcome may have been
that development of advanced forms radio guidance systems for the V2
was restricted (the experts were needed for radar and radio navigation
development) so the engineers had to emphasise a simple 'inertial'
system that relied on a gyroscopic accelerometer. A radio beacon
system was deployed in the latter stages of the V2s operational life
that apparently improved accuracy (by a factor of 5-10) in perhaps 25%
of late war launches but even this system was improvised and
underdeveloped compared to what was needed. (Note: inertial guidance
quickly outperformed radio based systems in all but applications with
very close transmitters).
Another delay was a Heinrich Himmler power play as the system began
showing promise. Dornberger and von Braun were both arrested for what
amounts to sabotage so as to intimidate them into taking V2 development
into Himmlers Schutz Staffel SS weapons program. The charge arose out
of relatively innocuous discussions and comments by von Braun and
Dornberger that they were ultimately developing space travel for post
war use rather than developing weapons and was intended to intimidate
them into leaving the Army and joining the SS. The arrests came at a
critical phase of V2 testing.
The V2 could have been available considerably earlier.
The targeting error claimed by Walter Dornberger and the German
guidance experts (including F Mueller who designed the original V2
system) that eventually became US citizens and worked at the Redstone
Arsenal at Huntington was a CEP of 4.5 kilometers or 2.8 miles for the
LEV-3 guidance system. It's a realistic figure that ignores gross
malfunctions.
CEP or "Circular Error Probability" is the radius of a circle in
which 50% of all munitions will fall. In the case of a Gausian
distribution (Rayleigh in 2 dimensions) of those falling outside the
CEP radius some 43% will be outside one CEP radius but within two while
7% will be outside two but within 3.. Within the CEP radius there will
be a clustering towards the aim point but it is not by much; the
distribution is almost random.
Probability of weapon falling within <r = 1-exp-1(r2/(1.414*CEP2))
(I'll tabulate these later). If the standard deviation is known
instead of the CEP then the 1.414 factor above is changed to a 2 and
the CEP is replaced by the standard deviation.
However the actual results were slightly less: British counter
intelligence had captured German agents in Britain and turned them. As
the Germans were too afraid of risking Arado 234 Jet reconnaissance
aircraft over Britain so for post strike reconnaissance analysis they
had to rely on their agents. Although the repeatability of the V2
LEV-3 guidance system may have been 4.5km there appear to have been
local factors such as gravitation, coreolis effects not fully accounted
for.
The British were selectively feeding the Germans impact points that
correlated with a correct time of impact but a selective impact points
in wrong position for the time of that impact to gradually move the V2
impact point out of London. Compensating for the British deception
brings a CEP of less than 6km not the 17km often mentioned. V2
'reliability' eventually achieved 80%-90% at its peak though it
languished as low as 43% at for some time. Many gross V2 misses were
due to guidance system malfunction; for instance a gyroscope
instability or failure that would to produce almost complete loss of
control on one axis. It is a matter of philosophy as to whether these
are included in evaluating CEP (many ended up in the sea or
countryside) but because they were so large and there were a
significant number of them they, along with 'double cross' tend to
totally distort the realistically achievable CEP.
For comparison; in WWII, a B-17 with the Norden Bomb sight had a 3,300'
(1000m) circular error probability (CEP), which by reason of energy
distribution means to absolutely guarantee a target kill a drop of
9,000 (500lb?) bombs from 1,000 bombers was needed...which put more
than 10,000 airmen at risk. In Korea, an F-84F had a 1,000' CEP, which
means to absolutely guarantee a target kill a to drop of 1,100 bombs
from 550 fighters put 550 airmen at risk. In SEA, an F-4 had a 400'
CEP, which means to absolutely guarantee a target kill a drop of 176
bombs from 30 fighters put 60 airmen at risk.
In accuracy and collateral damage high altitude bombing was not much
better in accuracy than the V2 and for the B-29 operating at is full
ceiling with 100mph cross winds at different heights it may have been
worse.
Within a few years missiles with guidance systems based on the V2's
SG-66 (an expeimental replacement for the LEV-3 generally used) but
using the same principles (eg the US Armies Redstone missile of the
1950s that was substnatially built by von Brauns team achieved a CEP
300 yards). These inertially guided missiles using much the same type
of system as the V2 would be exhibiting better accuracy than WW2
bombers and accuracy as good as the bombers of the day. (F-84F CEP 300
yards)
A Soviet SCUD-A with a crude early V2 style of boost phase only
'inertial' guidance system has a CEP of 3km at 300km. (It was
designed for nuclear use). A slightly latter model SCUD-B using a
refined but similar boost phase fully inertial system has a CEP of 450m
at 300km. (A Modern SCUD-D achieves 50m by adding in a terminal system
based on scene correlation; the SCUD's reputation for inaccuracy
comes from non authentic non Soviet extended range versions).
Pn(<r) = 1-exp-1(r^2/ (1.414*(CEP)^2))
In the following tables I've chosen 400 missiles as an launch rate
against a target. With production rates of 1500-5500 per month firings
of several times this rate per month were feasible. Imagine
CEP 4.5km, 400 missiles launched this CEP corresponds to the LEV-3
system.
r meters probability nos of missiles, nos of
hits
4000 0.428097089 400 171.2388
2000 0.130377882 400 52.15115
1000 0.034321318 400 13.72853
500 0.008693027 400 3.477211
250 0.002180377 400 0.872151
125 0.000545541 400 0.218216
62.5 0.000136413 400 0.054565
31.25 3.4105E-05 400 0.013642
15.625 8.52636E-06 400 0.003411
7.8125 2.1316E-06 400 0.000853
CEP 2km 400 missiles launched this correspond to the reported accuracy
of the Leitstrahl system.
r meters probability nos of missiles, nos of
hits
4000 0.940919497 400 376.3678
2000 0.506983964 400 202.7936
1000 0.162055487 400 64.82219
500 0.043238226 400 17.29529
250 0.010989383 400 4.395753
125 0.002758741 400 1.103496
62.5 0.0006904 400 0.27616
31.25 0.000172645 400 0.069058
15.625 4.3164E-05 400 0.017266
7.8125 1.07912E-05 400 0.004316
CEP 1km, 400 missiles launched, this corresponds to an imagined
improved V2 guidance system perhaps the SG-66 that was undergoing
testing with improved gyroscope bearings. A CEP of 1km corresponds to
Norden accuracy when aimed from high altitude.
r meters probability nos of missiles, nos of hits
2000 0.940919497 400 376.3678
1000 0.506983964 400 202.7936
500 0.162055487 400 64.82219
250 0.043238226 400 17.29529
125 0.010989383 400 4.395753
62.5 0.002758741 400 1.103496
31.25 0.0006904 400 0.27616
15.625 0.000172645 400 0.069058
7.8125 4.3164E-05 400 0.017266
3.90625 1.07912E-05 400 0.004316
CEP 300m, 400 missiles launched. (CEP of a 1952 redstone missile)
r probability nos of missiles, nos of hits
range prob nos launch nos of hits
600 0.940919497 400 376.3678
300 0.506983964 400 202.7936
150 0.162055487 400 64.82219
75 0.043238226 400 17.29529
37.5 0.010989383 400 4.395753
18.75 0.002758741 400 1.103496
9.375 0.0006904 400 0.27616
4.6875 0.000172645 400 0.069058
2.34375 4.3164E-05 400 0.017266
1.17187 1.07912E-05 400 0.004316
As can be seen with a CEP of 4km the V2's ability to destroy a
specific target is not great unless a great many launches (about 1
months total production). It would however be capable of causing great
damage to a large factory, steel works, power station, dock area or oil
refinery and if its CEP could be brought down to less than 1km it would
be quite effective. Ultimately shear numbers will have the desired
effect. A V1 hit within 300 meters could kill a man standing in the
open and would send someone flying through the air. The crater
photographs I've seen look about 30m in diameter and 30m deep. Truly
massive.
With an putative improved CEP of 1km (essentially that of a Norden
operating at high altitude) It becomes quite menacing to specific
targets in small launch salvos. On the basis of papers and research
and the calibre of person doing the development I believe this degree
of accuracy would have been achievable by the Germans within one year.
The standard guidance system of the V2 was the LEV-3 which consisted of
a pair of gyroscopes to control missile attitude and a gyroscopic
accelerometer capable of providing acceleration, speed and distance
information to initiate the tilt over of the missile and terminate
motor cutoff. Once motor cutoff had been achieved the missile was
purely ballistic. Since only two gyroscopes were used it was necessary
to launch the missile from a rotating platform to align it with the
target. One vertical gyroscope controlled roll and yaw of the missile
while another horizontal unit controlled pitch. A single "PIGA"
(Pendulating Integrating Gyroscopic Accelerometer) was aligned with the
thrust axis. The PIGA was called the MMIA (Mueller Mechanical
Integrating Accelerometer) by the Germans in honour of Fritz Mueller.
Charles Stark Draper recognised the brilliance of the instrument and it
was redubed the PIGA. It is used in the Minuteman, MX and late model
trident missiles for guidance where it achieved 0.5m accuracy over an
interconintental ICBM flight (the 100m CEP was caused by other errors)
A more advanced system was the SG-66, which mounted several
accelerometers on a stable platform controlled by 3 gyroscopes and had
for instance an accelerometer to compensate for cross range errors.
This was test flown only a few times before the end of the war but was
expected to control accuracy considerably. It formed the basis of
both the Redstone and SCUD guidance.
A "Leitstrahl" guidance system that used a radio guidance beam was
also in use and apparently improved accuracy by a factor of 5-10
(particularly over short ranges) according to some sources. (in
reality its was somewhat better over short ranges). It was kept very
secret due to the possibility that the signals might be detected and be
used to discover the launch sites. It is credited with a CEP 2km by
some sources. Ironically it was never detected and never jamed.
The Soviet SCUD-B achieved a CEP of 450m at 300km using inertial
systems that guided the missile for the fist 60 seconds of flight. The
Redstone Arsenal missile (essentially von Brauns team including Fritz
Mueller the inventor of the gyroscopic accelerometer) with an influx of
American engineers) achieved an improvement of accuracy by a factor of
10 over the V2 from 2.8 miles (4.5km) to 270m (300 yards) at
considerably greater ranges.
It might be supposed that the Germans using an electronic beam method
could eventualy have achieved similar accuracies as the Soviets
achieved in the 1950s using an guidence and control system active for
only the first 60 seconds of fligh. (450m at 300km and about 600m at
400km). Such a system was being planed. (I believe the code name may
have been 'Viktoria'.) It would have used the Doppler principle
to provide accurate velocity and range information to the missiles and
tightly controlled beams to maintain the missile on the correct path
free from cross winds during the first 80 seconds of boosted flight.
A PIGA or Pendulating Integrating Gyroscopic Acceleromer was called
MMIG (Mueller Mechanical Integrating Accelerometer) by the Germans in
honour of F Mueller its inventor. It consisted of a gyroscope spinning
at a precise speed but mounted on a rotating pedestal so that it was
free to rotate or 'precess' about the another orthogonal axis. A
pendulum was mounted along so that it would unbalance the gyro as the
mass was accelerated. As the pendulum 'falls' it would cause the
gyro to 'precess' about its pedestal at a rate proportional to the
acceleration and the rpm of the gyro. A sensor (or switch contact in
the V2) activates a torque motor to rotate the pedestal in the opposite
direction so as to maintain pendulum position by forcing it to precess
in the opposite direction.. It was found that electrical contacts
worked much better than potentiometers on the accelerometer and that
they were suprisiningly precise.
In the V2 this torqueing of the precesional axis rotated a gear system
that operated electrical contacts to initiate the various sequences at
the exact speed.. A V2 would take-off and within 4 seconds would begin
its tilt over to 49 degrees (always the same angle) at a rate of about
3 degrees/second. After 20 seconds the missile was supersonic and at
95% the thrust of the motor would be reduced from 25 tons to 8 tons in
preperation for 'brenschluss' (burn termination) since the
shutdown sequence took 2.5 seconds and this added to much missile
error. The two 'strapdown' gyroscopes of the V2 used
potentiometers as position pickoff. A mechanism rotated the body of
the potentiometer to obtain the 3 degree/second tiltover. The DC
potentiometers voltages were amplified by an electronic DC amplifier
and proportional integral derivative style controller that worked by
converting DC voltages to AC, amplifying them and then converting back
to DC where they would be used to operate electrohydraulic servo valves
that controlled the tail fins.
Several improvements were being planed.
1 A 3 Axis stable platform LEV-3. Apart from not needing a rotating
launch platform and maintaining the main thrust axis accelerometer in a
stable alignment this had lateral accelerometers to control cross range
errors produced by cross winds. The LEV-3 was actually test flown
several times and formed the basis of all post war ballistic missile
developments in the USA and USSR.
2 Integrator on main accelerometer. The output of the "PIGA" in
terms of number of revolutions was actually speed. It was intended to
integrate this mechanically with a 'ball and disk integrator' (as
used in bomb sights) to produce a distance flown. This would be used a
solve an equation that determined rocket cut off (Brennschluss) that
more accurately factored in distance as well as speed. This system was
implemented on Redstone and was known as delta t control.
3 Fluid bearings. A large source of gyroscope and accelerometer error
was due to bearing resistence and vibration. Kreisel Garraete, the
company at which Mueller worked experimented with the use of
pressurised water fluid bearings. Post war missiles tended to
initially use compressed air and later went to a refrigerant gas style
liquid because of the problem of compressed air storage and then
disturbing influence aircompressors had for long periods of opperation.
Water was simply corrosive.
The Redstone missile essentialy had the above guidence system with the
refinement of highly accurate accelerometers, gyroscopes and a system
for levelling the platoform prior to launch.
Below find a few references:
http://www.v2rocket.com/start/deployment/mobileoperations.html
(webmasters note: It is generally believed that the A4/V2 was not an
effective weapon because it was not accurate enough to hit an exact
target. While pinpoint accuracy was not associated with the V2, it was
much more accurate than generally reported. Not every batterie received
or installed the Leitstrahl-Guide Beam apparatus, which, was crucial to
the greater accuracy of the weapon. In the later stages of the war the
accuracy improved greatly, sometimes to within meters of the target.)
http://www.usafe.af.mil/iraqifree/FAQ's.htm
In WWII, a B-17 with the Norden Bomb Site had a 3,300' circular error
of probability (CEP), which means to absolutely guarantee a target kill
you had to drop 9,000 bombs from 1,000 bombers...which put more than
10,000 airmen at risk. In Korea, an F-84F had a 1,000' CEP, which means
to absolutely guarantee a target kill you had to drop 1,100 bombs from
550 fighters...which put 550 airmen at risk. In SEA, an F-4 had a 400'
CEP, which means to absolutely guarantee a target kill you had to drop
176 bombs from 30 fighters...which put 60 airmen at risk.
http://www.ww2guide.com/bombs.shtml
In the fall of 1944, only seven per cent of all bombs dropped by the
Eighth Air Force hit within 1,000ft of their aim point; even a
fighter-bomber in a 40 degree dive releasing a bomb at 7,000 ft could
have a circular error (CEP) of as much as 1,000 ft. It took 108 B-17
bombers, crewed by 1,080 airmen, dropping 648 bombs to guarantee a 96
per cent chance of getting just two hits inside a 400 by 500 ft area (a
German power-generation plant.)
VOL. 4, NO. 3 J. GUIDANCE AND CONTROL MAY-JUNE 1981
History of Key Technologies AIAA 81-4120
1981 Developments in the Field of Automatic
Guidance and Control of Rockets
Walter Haeussermann
The Bendix Corporation, Huntsville, Ala.
AIAA 2001-4288
The Pendulous Integrating Gyroscope
Accelerometer (RIGA) from the V-2 to
Trident D5, the Strategic Instrument of Choice
R.E. Hopkins
The Charles Stark Draper Laboratory, Inc.
Cambridge, MA
Dr. Fritz K. Mueller, Dr. Walter Haeussermann
Huntsville, AL
999999999
http://forum-der-wehrmacht.de/index.php?s=cd28569eb4bf6047766be16f45d1e628&showtopic=10964
Von der Me 109 weiß ich, dass ein flugfähiges Exemplar etwa 500.000
Euro kostet / wert ist.
Im Krieg lag der Preis bei etwa 50.000 Reichsmark.
Below are costs of various German Weapons in Reichs Mark.
00000
Pz.Kpfw. I Ausf. B ca. 38.000,- ohne Waffen
Pz.Kpfw. II Ausf. b 52.640,- -
Pz.Kpfw. II Ausf. F 49.228,- ohne Waffen
15cm. s.I.G. auf Fgst. Pz.Kpfw. II (Sf.) 53.000,- -
Pz.Kpfw. III Ausf. M 103.163,- ohne Funkausrüstung
Pz.Kpfw. IV Ausf. G 115.962,- mit 7,5cm KwK 40 L/43
Pz.Kpfw. Panther 117.100,- frühe Version, ohne Waffen
Pz.Kpfw. Tiger Ausf. E 250.800,- ohne Waffen u. Funkausrüstung
Pz.Kpfw. Tiger Ausf. E 299.800,- voll ausgerüstet
Pz.Kpfw. Tiger I Ausf. E 645.000,- Exportpreis für Japan
Pz.Kpfw. Tiger II Ausf. B 321.500,- -
Sd.Kfz. 222 23.420,- ohne Funkausrüstung
Sd.Kfz. 232 57.290,- ohne Funkausrüstung
Sd.Kfz. 6 30.000,- -
Sd.Kfz. 7 36.000,- -
Sd.Kfz. 8 46.000,- -
Sd.Kfz. 9 75.000,- (später 60.000) -
http://www.nexusboard.de/showthread.php?siteid=332&threadid=198491&nx=ca459e2818269ce73574416be37b0e43
Hallo,
ich habe einmal die Preisliste aus "Achtung Panzer" kopiert:
In Englishe
Prices of selected models.
Model: Price in Reichsmarks (RM):
Volkswagen Käfer (VW Beetle) 990
Opel Kadett 2100
DKW Meisterklasse 2350
Ford Taunus 2870
Adler Triumph Junior 2950
Sd.Kfz.6 30000
Sd.Kfz.7 36000
Sd.Kfz.8 46000
Sd.Kfz.9 60000
Sd.Kfz.10 15000
Sd.Kfz.11 22000
PzKpfw II Ausf a 52640 with armament
PzKpfw II Ausf B 38000 w/o armament
PzKpfw II Ausf F 49228 w/o armament / 52728 with armament
Sturmpanzer II Bison 53000 with armament
PzKpfw III Ausf M 96183 w/o armament / 103163 w/o radio
Stug III Ausf G 82500 with armament & radio
PzKpfw IV Ausf F2 115962 with armament & radio
75mm KwK 37 L/24 8000
75mm StuK 37 L/24 9150
75mm StuK 40 L/43 12500
75mm KwK 42 L/70 12000
PzKpfw VI Tiger 250800 w/o armament & radio / 299800 with armament &
radio
PzKpfw VI Tiger II 321500 with armament & radio