Bismarck Speed

[Dave Saxton]

Yes, the advantages with using the shortest possible wave length are that it's easier to get suffcient antenna gain and a narrower beam width while using an antenna of practical size.

For example antenna gain is:
G=4 x pie x effective aperture/wave length (squared)

What the effective aperture is depends upon the specific antenna design but it's generally the size of the reflector in wave lengths if its a reflective dish or the like, or its the sum length of the dipoles in wave lengths if it's a dipole array (mattress)

Likewise the bearing resolution is a function of the half power beam width:

HPBW= K x wave length/ D

K is a correction factor and D is the dimesion of the effective aperture. Once again D could be the area of the dish in wave lengths if it's a dish type, or the sum of the dipoles in wave length. A longer wave radar can obtain the same HPBW and therefore the same resolution as shorter wave radar- if you can use a large enough antenna. Of course smaller antennas are needed on ships so the weather attenuation of microwave radars are a worthwhile trade off to get a antenna gain increase and narrow HPBW while using a relatively compact antenna.

There is a weather attenuation of S-band and X band. Indeed the opaque returns of weather was first most noticable when the USN began testing centimetric radar during WWII. A probable example of weather attenuation is the wide variety of ranges of picking up the Scharnhorst at various times at North Cape in slightly different weather conditions. The Belfast's Type 273Q detected the Scharnhorst at about 30km (accounts vary widely though) the first time. The second time the range was only 23.8km. Then later the Duke of York picked up Scharnhorst with its Type-273Q at 42km. Same radar and same target but widely varying results. That's not to say that the variety was soley the result of weather, because there are so many variables. 1.5cm radar never really caught on because it is highly effected by weather, much more so than longer wave lengths.

There is a much smaller differential between the typical range to small targets compared to large targets with shorter wave length as well However, that doesn't mean that a long wave radar can't pickup small objects. The Hohentwiel could pickup submarine periscopes to 6km operating on +/- 54cm, actually better than the performance of most centimetric radar.

Resolution for distance is not effected by wave length.

[Bgile]

Dave,

There is something here that doesn't make sense to me.

When I was in the submarine service, the P-3s and other asw aircraft used Ku band randars to search for submarine periscopes. We were told that that was because Ku band was better at picking up small objects. We got nervous when Ku band signals were strong. X band radars were also dangerous to us, but not quite the same panic level.

You say that isn't so, and I find that confusing to say the least. Submarines made tactical decisions based on that in the 70s when I was doing special operations, and you seem to be saying that was all based on false information.

I was also told in class that the higher the frequency of the radar, the better the resolution, including range resolution. That this was because the pulse leading edge definition was dependent on video bandwidth. Video bandwith is determined by the number of harmonics present in the transmitted signal, and for this reason you get better and better resolution as the radar frequency goes up.

In short, the higher the frequency, the "squarer" the pulse is.

Now I know that sometimes bad information was dissemenated, but this knowlege seemed to work for us.

[Dave Saxton]

The radar cross section of a smaller target is greater with smaller wave length, this is why I said there's less differential in range attainment between large and small targets. This would also explain the use of K band for periscope detection. However, a small wave length is not required to detect small objects. The difference is that there is a much greater differential in the range between detecting a small object like a periscope and large object like a warship when using longer wave lengths.

Range resolution is normally the function of pulse duration. When pulse compression techniques and similar more advanced techniques are in play; then the bandwidth of the IF becomes a factor in the range resolution equation, in addition to the required S/n ratio and the range attainment. However, the amount of bandwidth is a function of the electrical componants making up the circuit. It's not frequency dependent. A lower frequency system can have as much or more bandwidth than a higher frequency system. The British 50cm radars actually had much greater bandwidth than US 3cm radars.

Bandwidth can effect the sharpness of the leading edge of the pulse, depending on the radar design, and that can have effect on range accuracy, rather than range resolution.

[Dave Saxton]

Perhaps I can explain the principle in an easier to understand way.

Distance resolution is a function of the effective pulse duration, regardless of the frequency of the transmitted waves. If radar A has superior range resolution than radar B that is just coincidental to the wave lengths of radar A or radar B. In such case, radar A has a shorter effective pulse duration, by either having a shorter duration of the actual pulse, or by employing pulse compression. Either method requires greater bandwidth of particular componants. Bandwidth is how much information an electrical componant can proccess in a given time period at a given level of gain. Bandwidth is quantified in terms of frequency, but this particular term is unrelated to the operational wave length.

Bandwidth of the doppler filter will effect the resolution of pulse doppler radar, however. It could be that the radar in the 70's was a pulse doppler type as well.

[Bgile]

Perhaps I can explain the principle in an easier to understand way.

Distance resolution is a function of the effective pulse duration, regardless of the frequency of the transmitted waves. If radar A has superior range resolution than radar B that is just coincidental to the wave lengths of radar A or radar B. In such case, radar A has a shorter effective pulse duration, by either having a shorter duration of the actual pulse, or by employing pulse compression. Either method requires greater bandwidth of particular componants. Bandwidth is how much information an electrical componant can proccess in a given time period at a given level of gain. Bandwidth is quantified in terms of frequency, but this particular term is unrelated to the operational wave length.

Bandwidth of the doppler filter will effect the resolution of pulse doppler radar, however. It could be that the radar in the 70's was a pulse doppler type as well.

It's possible, although I don't think so. I think of pulse doppler radars as something designed to pick incoming aircraft or missles out of ground clutter.

[Dave Saxton]

My guess is was a pulse compression radar, especially by the 1970's.

[Herr Nilsson]

It follows from this, that for Bismarck at:

43000 tonnes, 138000 shp = 29 knots
48000 tonnes, 154000 shp = 29 knots
51000 tonnes, 163700 shp = 29 knots

So how does the indisputable 28.4 knots, at 117400 shp, at a displacement of 48,000-49,000 metric tons fit in here?

I wish it were indisputable, but the exact displacement is not given, and recorded draft is inconsistent with ~48000 tonnes.

Maybe it's a stupid question, but why is the recorded draft inconsistent?

[dunmunro]

Maybe it's a stupid question, but why is the recorded draft inconsistent?

The recorded draft was 8.5 meters which equates to aprox 42000 tons. See here for info on draft versus displacement:
http://www.kbismarck.com/genedata.html
The speed recorded is consistent with these speeds:
http://www.bismarck-class.dk/technicall ... inery.html
showing a speed of 29 knots at 43000 tons with 138000 shp.

[Herr Nilsson]

But where is 8.5 m written?

[dunmunro]

But where is 8.5 m written?

Here's the complete data:

A Messprotokoll from 29.10.40 gave the following results:

Water depth 65 m
payload 75%
port shaft 38753 shp at 251,7 rpm
middle shaft 38820 shp at 244,1 rpm
starbord shaft 39837 shp at 252,7 rpm
maximum speed for that day was 28,374 knots
Speed 28.374 knots.
Footnote 2.
Data from the protocol of the speed trials on 2 November 1940. The speed data are based on an average output of 39170 shaft HP (WPS =Wellenpferdestärke)) per screw and 249.5 RPM per screw at a load addition of 75% and a draft of approx. 8.50 m. Other documents are not available. (Authors note. The document does not say if this concerns "AK Fahrt" (Äußerste Kraft), i.e. extreme full-power speed. The source of the speeds of 30.4 kn, 30.6 kn or 30.8 kn given in the current literature, is puzzling. Blohm & Voss states 30.1 kn." From: Schlachtschiff Bismarck: Das Original im Detail, Simon Frey Verlag, 2004, page 008.

[Herr Nilsson]

Ah, OK, I see. But this is wrong. In the speed trial protocol the draft is not stated as a distance between keel and waterline.

Edit:

Here's what you can read there:

29.10.1940

speedtrial29.jpg (16.74 KiB) Viewed 1535 times

[dunmunro]

Here's how google translated the text:

Tiefgang vor der fahrt vorn: 8,5/4; hinten 8,8/4
Tiefgang nach d. fahrt vorn: 8,0/4; hinten 9,0/4;



Draft prior to the ride ahead: 8.5 / 4; rear 8.8 / 4
Draft forward after d. ride: 8.0 / 4; rear 9.0 / 4;

so for the first line I get an average draft of 8.65 metres and for the 2nd line, 8.5 metres.

Is this correct?

[Herr Nilsson]

Once again, it's not in the draft in meters.
Please take a look at the trial protocol from November, 1st:

1.11.1940

speedtrial01.jpg (16.26 KiB) Viewed 1537 times

[dunmunro]

Once again, it's not in the draft in meters.
Please take a look at the trial protocol from November, 1st:

speedtrial01.jpg

OK, so what units/measurements are they using?

[Herr Nilsson]

To be honest I've no idea, there is no unit. Usually there was a zero level let's say 9.5 meters and the +-differences were measured. Maybe you have to devide the numbers by 4 and you have an amount in decimeter. I don't know.
However, you don't need the exact draft, because you can calculate the displacement without it. The test conditions were specified in the M.Dv. 847. IIRC 75% Zuladung means that you have a fully equiped ship, but only the liquids (fuel, water, lubricants, airplane fuel) are reduced by 25%. Simply said the displacement will be between construction displacement and full load.