General Report on Tunny
11D Page 12
By choosing suitable patterns for psis and motors it can always be arranged (and after March 1942 nearly always was arranged) that ab was as nearly as possible ½ in each impulse.
(e) Dottage.
The dottage (d) is defined as the number of dots in the pattern of μ37.
Then proportion of dots in μ37 = d/37. This proportion will be unchanged by the extension of μ37 by μ61.
Therefore proportion of dots in BM = d/37
But proportion of crosses in limitation = ½ (approx)
Therefore proportion of dots in TM = d/74
Therefore a = proportion of crosses in TM = 
The ΔΨ1 pattern must therefore be constructed with the nearest even number to 
crosses (and so on).
For SZ 40 with no limitation the calculation is slightly different and left to the reader.
(f) Values of a, b, d.
In known wheel patterns (for SZ 42A and SZ 42B)
d varies from 14 to 28
a varies from .81 to .62
b varies from .62 to .81 so that psi extensions occur from 2/5 to 4/5 of the time.
(Wheel characteristics are discussed more fully in Chapter
22)
11D HOW TUNNY IS USED.
(a) Fish Links.
Tunny machines worked in pairs, and each pair formed a link which was given (by us) the name of a fish e.g. in May, 1944:
JELLYFISH connected STRAUSSBERG exchange (near BERLIN), with HEERESGRUPPE D and WEST at PARIS.
WHITING connected KOENIGSBERG exchange with HEERESGRUPPE NORD at RIGA
The units to which links were connected remained pretty stable, but the position first of the army groups and later of the exchanges became increasingly mobile after the invasion. This aspect of Tunny is discussed in 11E
It is obvious that two Tunny machines transmitting to each other must generate identical key streams and must therefore
(i) have the same pattern of dots and crosses round their wheels
(ii) have the patterns set in the same position at the start of each transmission. After this the motors and limitation will act identically at both ends and the machines should always be in step, their motion being synchronised by electrical signals transmitted before and after each teleprinter letter.
Different sets of wheel patterns (GRUNDSCHLUESSEL) and different
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