File:Ratio of Transverse drag to Axial drag in creeping flow for different types of bodies.png

On this graph, we have mainly represented bodies of revolution (circular cylinders, spheroids, double cones formed of two cones united by their base, rectilinear chains of identical spheres). Axisymmetric bodies (square-based prisms) also appear.

We can see this body as a horizontal thin rectangular plate: The transverse movement is then a vertical decantation, the axial movement being a coplanar movement in the larger direction of the plate (for the largest slenderness). For this body without thickness (somewhat immaterial, therefore) the importance of the drag quotient is due to the fact that the transverse drag is a pressure drag whereas the axial drag is only a friction drag. This drag quotient can be compared with that of the same thin rectangular plate in the other two directions (these two directions being coplanar with the thin plate).

The drag ratio of the spheroids is here calculated with the un-simplified formula.

This result of Cox for the double cones is rather little used by the researchers. A double cone is the assembly of two identical cones glued by their base.

The black hollow circular marks draw the Ui prescription for the cylinders. This prescription is written: 2 -2ε + ε ^ 3 + ε ^ 4

The works of Ui and Roger confirm the drag of the cylinders of Cox (of rather great slenderness), but they are valid for Aspect Ratio much weaker.

The irregularities of this curve are probably due to the disparity of the sources used to draw it. For such rectilinear chains of identical spheres, the Aspect Ratio L/D of course corresponds to the number of spheres.

This thin rectangular plate can be viewed as a horizontal plate moving coplanarly in two perpendicular directions. The axial direction corresponds to movements parallel to the largest dimension of the plate of big Aspect Ratio. The transverse direction corresponds to movements parallel to the smallest dimension of the plate of big Aspect Ratio.

The cube, like the sphere, presents a spherical isotropy, that is to say that its drag is the same in all directions. On this graph, cube and sphere are therefore placed on the ordinate 1.

The square-based prisms of Sunada, Ishida, Tokutake, and Okada (in yellow) have a drag ratio quite similar to those of Ui and Roger's cylinders, although the two curves intersect at Aspect Ratio ~ 2.6.

It is often said that this drag ratio is close to 2, but this is true only for bodies of very large Aspect Ratio L / D (it reaches ~ 1.75 only for a circular cylinder or an ellipsoid of Aspect Ratio 1000). This graph gives this same quotient for the most common Aspect Ratio.