146 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
When a ship is in flight, it is subject to aerodynamic loading and inertia forces which 
are superposed on the statical load. The aerodynamic forces seem to produce the greatest 
bending moments when the ship is going at an angle of pitch in rectilinear flight, in which 
case the aerodynamic load curve has a marked hump at each end. 
The problem of determining the magnitude and distribution of the dynamic forces is 
outside the scope of this paper; it shall here merely be stated that it forms one of the most 
difficult problems in airship design, because it is not as yet fully cleared up experimentally. 
It is known, however, that unless airships are handled carefully when going at high speed, and 
especially at low altitudes, the dynamic stresses are likely to exceed the statical stresses very 
considerably. This was one of the lessons of the R-38 disaster, which has led to a more com- 
plete study of this branch of the subject. Before that disaster occurred, it was generaily 
thought sufficient to provide for the static forces, the assumption being that the dynamic 
forces would be less serious. 
It is assumed that the forces, to which the ship is subject, are known and that curves of 
shearing force and bending moment are constructed corresponding to the various conditions 
of loading. The problem here to be discussed is how to calculate the stresses in the main 
structure from these data. 
At least two modes of calculations have been used by designers of this craft. One, the 
“method of transverse shears,” described by Mr. E. H. Lewitt in Aeronautics,* consists in 
calculating the tensions in the shear wires due to shearing only and resolving the forces so 
obtained along the longitudinals. By a summation of these forces, beginning from either 
end of the hull, the end load accumulated at any point of the longitudinals in determined. 
The longitudinals are regarded as consisting of rigid bars connected at the joints by friction- 
less hinges and the deflections of the hull are supposed to be wholly due to the stretching of 
the wires. As this method takes no account of the elastic strains and stresses due to bending 
of the ship as a whole, it cannot give a complete solution. 
The other method, referred to as “the method of bending moments,” is based on the 
ordinary formula for bending and gives the longitudinal stresses in the girders, but as ex- 
plained below, the assistance rendered by the wires in taking the longitudinal bending forces 
has been hitherto disregarded. The tension in the wires due to shearing can be determined 
in any panel by considering the effects of shearing in each frame space separately. 
The main purpose of this paper is to show that the bending method is essentially sound, 
and that with certain modifications it is reliable as a means of comparison between the 
strength of different airships. The shear method, on the other hand, in spite of its labori- 
ousness, is incomplete because the elastic elongations and contractions of the girders are neg- 
lected. The relative validity of the two methods has long been a vexed problem, and it is 
evidently of the greatest importance that this fundamental question should be definitely settled. 
It is convenient for the sake of clearness to approach the problem synthetically, build- 
ing up our conception of the complex reactions in an airship from the most elemental cases 
and finally, by combining these, to pass on to the more complete and general case. With 
this in view the author has made a study of a number of simple cases, but unfortunately it was 
impossible to include all of these in the present paper, which is already rather long. 
*Aeronautics, London, Feb. 12, Sept. 9, 1920. 
