Calculation of Viscous Drag in Incompressible Flows

Performance of non-rigid airships operating in the neutral buoyancy condition

“…. (7) This second graph includes a plot of the numerical prediction * made by Cebeci et al (21) and Hoerner's volumetric drag coefficient approximation (12) , airship can be treated as a rigid body of revolution, although in reality it will have some compliance and elasticity, as well as being slightly asymmetric. In preliminary design studies, the drag coefficient of such a body (at zero incidence and at low subsonic Mach numbers) is usually approximated by a relation of the form, C DS ≅ C f Γ shape , where Γ shape is a geometric factor typically a function of fineness ratio, L/d, and C f is the overall skin friction of a flat plate with the same length, L, at zero incidence (8)(9) ⋅ For smooth bodies, in the subsonic flow regime of interest, C f is well-approximated (10) by the Prandtl-Schlicting Formula (11) ;…”

“…Cornish & Boatwater (18) , ordinary; ▲ Cornish & Boatwater (18) , cleaned-up; ---------Cebeci et al (21) , L/d = 4⋅2; ----Goodyear (6)…”

“…setting A = 0 was pessimistic), but for Re L > 10 8 the area of the laminar region near the nose stagnation point would be relatively small, resulting in a minor correction. For example, in order to model the flow over the ZS2G-1 airship, Cebeci and Bradshaw (20) and Cebeci et al (21) assumed transition at x/L = 0⋅05 for 0⋅93 × 10 8 < Re L < 1⋅88 × 10 8 .…”

On the Problem of Shaping an Axisymmetric Body to Obtain Low Drag at Large Reynolds Numbers

“…Because the straightforward calculation of drag by integration of surface pressur,, and skin friction turns out to be inaccurate [1], the drag of a body must be obtained by considering the deficit of momentum far downstream in the wake. The basic analysis, which is given in [2], is merely outlined here.…”