172 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
In actual airships there are rather large irregularities in the distribution of the material, 
especially in the lower part of the hull where the effect of the keel must be considered, and 
the discrepancy between the results obtained by the two methods may be very great. En- 
gineers may reasonably feel that the existence of such discrepancies casts doubt upon the 
validity of both methods of analysis, and some amplification of Professor Hovgaard’s expla- 
nation of the reasons for the discrepancy seems to be called for. 
In a steel ship structure, distortion by shear, either transversely or longitudinally, is so 
small as to be negligible; and in consequence of the very small distortion by longitudinal 
shear, plane sections remain almost perfectly plane, regardless of the ordinary shearing and 
bending forces applied to the structure, and the ordinary bending formula is therefore ap- 
plicable to a high order of accuracy, in spite of structural irregularities. The hull of a rigid 
airship may appear to be structurally more regular than the average steel ship, but, as Pro- 
fessor Hovgaard points out, it is extremely limber in shear, owing to the shearing forces being 
transmitted through the hull by very light steel wires. In transverse shear, the deflection of 
a rigid airship is usually several times as large as the deflection by bending; but it is longitu- 
dinal shearing deflections which most interfere with the applicability of the bending theory 
to the solution of the problem of longitudinal strength. 
The bending theory requires that plane sections remain plane; or, in other words, the 
longitudinal strain of the members must vary in a definite manner. In a rigid airship the 
stresses, and consequently the strains in the longitudinals, are due to the forces applied by the 
shear wires at the joints; and it follows that unless the cross-sectional areas of the wires are 
proportioned in a certain definite manner to the forces to be transmitted, the movements of the 
joints and the strains in the members will not be such as to maintain plane sections, and the 
stresses will therefore not be in accordance with the ordinary theory of bending. 
Professor Hovgaard uses some examples of irregular structures to show that the method 
of shears gives erroneous results. He might have carried the examples further and shown 
the inadequacy of the bending theory to account for the stresses. The truth must always 
lie somewhere between the results given by the two methods and will, in general, be nearer to 
the bending than to the shear theory. 
Exact solutions of the problem by the Principle of Least Work or by deflections have 
proved impracticable. Twenty simultaneous equations were required for the solution of the 
comparatively simple case of four bays of an hexagonal-braced tubular structure having 
one of the six longitudinal members three times as large as each of the others so as to simu- 
late the effect of the keel of a rigid airship. Probably the ultimate method of calculation will 
involve the use of correction factors, determined by experience and experiment, for convert- 
ing the actual areas of the longitudinal members into effective areas. The effective areas 
will then be used in computing the moment of inertia of the cross-sections of the hull, and 
in finding the total end load taken by each member. 
CoMMANDER LAND:—As a result of the various accidents which have happened to rigid 
airships, and in view of the fact that we are going ahead with the ZR-1, it was deemed de- 
sirable and advisable to requisition a committee of outside tethnical experts to go over the 
complete work that has been done by the Bureau of Aeronautics on ZR-1 primarily, and also 
on the work which is being done by the Bureau of Aeronautics generally on lighter 
than air design. 
This committee has done a splendid amount of hard and strenuous work, and I believe 
