Nope. Blohm & Voss's own register of projects says the P 157 designation was unallocated.
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My dear Dan,
I know you are expert in this field,but their list is not measure,no reason for slip some numbers,just the author
didn't know them or lost their reports,anther example for your list also,there was no P.174 & P.191,but in many
source they are known ?!.
Okay, let's unravel this. We're looking at three lists.
The list on Luft46.com is based on the one which appears on p122-123 of Heinz J. Nowarra's Die Deutsche Luftruestung 1933-1945 Vol. 1. 1993 version. I'll call this the 'Nowarra list'.
I have two wartime lists from T-2 microfilm obtained from NASM: One is handwritten onto printed sheets, with various different handwriting filling it in from P 1 to where it ends at P 208.02. This has no details other than project number, aircraft role and engine type used. I'll call this the 'handwritten list'.
The other list is the printed list I've uploaded a few sections from, which runs from P 1 up to P 212.01 and includes lots of other details including weights, wingspan etc. as you have seen. I'll call this the 'printed list'.
There are certain gaps in common with all three, a handful of instances where the Nowarra list has details the others lack, instances where the handwritten list has more detail and instances where the printed list has detail where the others don't.
There are 40 project numbers where one, two or all three lists have gaps as follows:
P 2 (gap on all three)
P 3 (gap on all three)
P 26 (gap on all three)
P 30 (gap on Nowarra and handwritten list, stats given on printed list)
P 31 (gap on Nowarra and handwritten list, stats given on printed list)
P 32 (gap on Nowarra and handwritten list, stats given on printed list)
P 34 (gap on all three)
P 35 (gap on Nowarra and handwritten list, Landmaschine Lufthansa in printed list)
P 36 (gap on Nowarra and handwritten list, Wassermachine Lufthansa in printed list)
P 87 (gap on all three)
P 91 (gap on all three)
P 93 (gap on Nowarra, ‘Aenderung der Nr. [illegible] P 96, P 103 on handwritten list, gap on printed list)
P 101 ('Zielflugzeug' in Nowarra, gap in both handwritten and printed lists)
P 102 (gap in all three)
P 106 (BV 222 development in Nowarra, ‘222’ with ‘?’ under engines in handwritten list, blank in printed list)
P 107 (BV 222 development in Nowarra, ‘222’ with ‘?’ under engines in handwritten list, blank in printed list)
P 120 (gap on all three)
P 121 (gap on all three)
P 129 ('Jagdeinsitzer' in Nowarra, gap in handwritten and printed lists)
P 130 (gap on all three)
P 132 (gap on all three)
P 133 (gap on all three)
P 136 (gap on all three)
P 137 (gap on all three)
P 139 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 147 ('P 142 als Transporter' in Nowarra and handwritten list, gap in printed list)
P 148 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 149 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 151 (gap on all three)
P 152 (gap on all three)
P 153 (gap on all three)
P 154 (gap on all three)
P 156 (gap on all three)
P 157 (gap on all three)
P 158 (gap on all three)
P 159 (gap on all three)
P 174 ('Gleitbombe' in Nowarra and handwritten list, gap in printed list)
P 182 ('Jagdbomber' in Nowarra, blank in handwritten and printed lists)
P 189 (gap on all three)
P 191 ('Flak-Kreuzer (?)' in Nowarra, unclear on handwritten list but looks like Fernbomber with 8 x BMW 801 to me, blank on printed list)
Eliminating the 23 instances where all three agree, we're left with the following 17 points of disagreement:
P 30 (gap on Nowarra and handwritten list, stats given on printed list)
P 31 (gap on Nowarra and handwritten list, stats given on printed list)
P 32 (gap on Nowarra and handwritten list, stats given on printed list)
P 35 (gap on Nowarra and handwritten list, Landmaschine Lufthansa in printed list)
P 36 (gap on Nowarra and handwritten list, Wassermachine Lufthansa in printed list)
P 93 (gap in Nowarra, ‘Aenderung der Nr. [illegible] P 96, P 103 on handwritten list, gap on printed list)
P 101 ('Zielflugzeug' in Nowarra, gap in both handwritten and printed lists)
P 106 (BV 222 development in Nowarra, ‘222’ with ‘?’ under engines in handwritten list, blank in printed list)
P 107 (BV 222 development in Nowarra, ‘222’ with ‘?’ under engines in handwritten list, blank in printed list)
P 129 ('Jagdeinsitzer' in Nowarra, gap in handwritten and printed lists)
P 139 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 147 ('P 142 als Transporter' in Nowarra and handwritten list, gap in printed list)
P 148 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 149 ('Flugboot' in Nowarra, gap in handwritten and printed lists)
P 174 ('Gleitbombe' in Nowarra and handwritten list, gap in printed list)
P 182 ('Jagdbomber' in Nowarra, blank in handwritten and printed lists)
P 191 ('Flak-Kreuzer (?)' in Nowarra, unclear on handwritten list but looks like Fernbomber with 8 x BMW 801 to me, blank on printed list)
Looking a little more closely at these 17:
P 30 The printed list fails to give a role for this aircraft but gives the engines as 4 x Jumo 206, wing area 125m2 and a starting weight of 17,600kg.
P 31 Again, no role from the printed list but it does give the engine as Jumo 210. No wing area but starting weight was 2450kg.
P 32 No role or engine but wing area was 30m2 and starting weight was 6000kg.
P 35 The printed list gives only 'Landmaschine Lufthansa' with 4 x DB 601 and a top speed of 445km/h at 6000m.
P 36 The printed list gives 'Wassermaschine Lufthansa' with 4 x DB 601 and a top speed of 410km/h at 4000m.
P 93 One of very few instances where the handwritten list differs from Nowarra, this has only a tiny note on it which says ‘Aenderung der Nr. [illegible] P 96, P 103'
P 101 Clearly blank in both period lists. In Nowarra this is given as 'Dasselbe' below the P 100 Zielflugzeug but above the P 102 described as 'Nicht bearbeitet'. My guess would be that it should say 'Nicht bearbeitet' next to P 101 and 'Dasselbe' should be next to P 102 instead. Basically a simple typo.
P 106 The handwritten list has a very faintly pencilled in '222' on this one, with a question mark for the engines. The author clearly wasn't sure about this one.
P 107 The same faint '222' and '?' as P 106.
P 129 This appears to be another typo in Nowarra's list, as with the P 101. The P 130 is 'Nicht bearbeitet' and the P 128 is shown only as '"' from the P 127 Jagdeinsitzer.
P 139 Nowarra just gives this as 'Flugboot' where both period lists are blank. Perhaps some confusion with the Ha 139 - otherwise inexplicable.
P 147 This is blank on the printed list but the handwritten list does clearly have P 147 as 'P 142 als Transporter'.
P 148 Like P 139, Nowarra gives this simply as 'Flugboot' with no other details when both period lists have it as a gap. Inexplicable.
P 149 As with P 148 - Nowarra has no engine or wingspan data - he just gives 'Flugboot' where both period lists have a clear gap.
P 174 The handwritten list very clearly agrees with Nowarra where the printed list is blank - 'Gleitbombe'.
P 182 As with P 101 and P 129, I think this is a typo. It comes at the bottom of a very long list of '"' and probably ought to have been 'Nicht bearbeitet' instead.
P 191 Curiously described by Nowarra as 'Flak-Kreuzer (?) 8 x BMW 801'. It is pretty unclear on the handwritten list, but it looks to me more like 'Fernbomber 8 x BMW 801'.
I would conclude that the Nowarra list is based on the T-2 captured 'handwritten list' but with a few basic inaccuracies where the information hasn't been transcribed correctly. The 'handwritten list' itself is, as noted, in a number of different hands and gets visibly scrappier as it gets towards the end. I would guess that this was the ongoing company list, which stopped being updated after the P 208.02. The printed list is much more useful because it includes lots more technical detail but it does exclude more projects than the handwritten list. This might be because the files had been lost, as you suppose. Perhaps it was intended to replace the scrappy handwritten list and was produced as work was being carried out on the P 208.02 in the autumn of 1944. The fact remains, however, that Blohm & Voss clearly did not use every number they could have used for their projects. At least 23 went unused and we will probably never know why. And P 157 was among them.