Calculation of Wing Spars Page: 4 of 13
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If the absolute value of the &gle c a b is greater than -
then Mmax. equals the greate: of the end moments MA and MB.
Formulas (16). and (17) on p.200 (1919) can be combined into
the following formula
Mm = /022 + Og k)
Mmax. -a .w - g . . . . . . . (1)
which may also be obtained from Figs 2. Ustially Mmax. lies so
near the middle of the bay, that we may write
Mm ax = 0 + - g . a " ..... .C)
in agreement with formulas (11), (18) and (20) of my 1919 art-
icle. If a lies in the neighborhood of n, then C must be
calculated. The formula
sec - +
2 - 1
on p.198 (1919) and the table on p.200, for very small safety
factors, lead quickly and accurately to the goal. For a low value
of. we may write:)
C = (MA - MB)
1) Point d (Fig. 2) lies on a circle, whose diameter is a c.
Mr. Ratzersdorfer determines this circle by means of the condi-
tions M = MA for x = 0 and M = MB for x = s. If a varies
only a little from n, then the three points determining the cir-
cle lie nearly in a straight line. I give the calculation the
preference and call the attention of readers, who likewise prefer
to calculate, to two tables:
J. Hrabak, "Praktische Hilfstabellen" (Practical Tables) (Pub-
lished by Teubner in Leipzig). Table V, "Trigonometrische, Linien
von Minute zu Minute, "' also contains the often used secants and
C. Burran, "Tafeln der Functionen Cosinus und sinus mit den
natdrlichen Zahlen als Argument" (G. Reiner, Berlin).
The secant table with the argument P (1919, p.200) also en-
ables the calculation of C2, since
csec - sec
sec2 - 1
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Müller-Breslau, H. Calculation of Wing Spars, report, August 1921; (digital.library.unt.edu/ark:/67531/metadc53634/m1/4/: accessed January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.