Aligning elements

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1). Eight sided cylinder (with 5 sections) as the original object - and you want to make it into a 16 sided cylinder. Select all radial edges and connect them (if done in one go, you'll have to dissolve the end face junk :))
2). Press V to convert to vert mode (scale radial won't do anything with edges like this)
3). Apply Vert | Scale -> Radial -> Y -> 108.239 %. This will place the newly created verts in their correct places.
4-5). Before and after views of the cylinder end face.

Scaling Factors:

3 to 6 sections: 200 %
4 to 8                141.421 %                           (141.42135624)
5 to 10              123.607 %                           (123.60679775)
6 to 12              115.470 %                           (115.47005384)
7 to 14              110.992 %                           (110.99162642)
8 to 16              108.239 %                           (108.23922003)

16 to 32            101.959 %                           (101.95911582)

Using Inflate (RMB option, especially) can also be used (to excellent effect) for getting stray (or new) geometry onto true circular paths - but (and it's a big 'but', imo) - it can only be used a 'plane at a time' - as it's really placing verts onto a spherical surface.
Using Inflate in this manner on a complex cylindrical object then becomes quite messy - imo.
The method used here can also be used on objects that don't have a constant cross-section - eg sphere / cone etc.

(Use more accurate figures as necessary - precision will be affected if factors are too approximate, of course :) )

Whether you'll have any use / interest in the above is up to you, but I find these, together with Inflate and Flatten (as mentioned) quite useful for aligning stuff - perhaps because I mess up on a regular basis and need a wide range of such options :)

Expression used - if you need other factors

{1 + [(1 - Sin A) / Sin A] } * 100 

A (half the internal angle at the periphery of the polygon) is given by

A = (180 - 360 / N) / 2         (N = number of sides of the original poly)
Truing-up elements - using Scale -> Radial -> 0%

Say you have a scenario where geometry has got messed up and you need to re-establish a straight line of edges (or verts). Whilst this can also be done using 2 Flatten ops (along 2 axes in separate goes), the following method might be quicker - especially in a non-orthogonal situation like this.
1). A cylinder where some of the axial edges have been messed around with - and need to be sorted out. Select the first group of edges to be 'straightened'.
2). We need to define the axis (or line) to which the 'wobblies' are to be straightened - since I've (deliberately) rotated the basic object away from the main axes in all 3 planes - this 'straighten' axis will have to be explicitly defined.
Apply Edge | Scale -> Choose MMB option - Pick axis for Radial Scale. Using LMB, select the vert at one end of the 'wobblies' - Wings will display the vector axis - here shown in yellow, coming out from the top vert.
3). Selecting the vert on the lower end of the 'wobblies' alters the vector axis to the correct position - passing through both verts - again shown in yellow (Note that the origin of this vector is halfway between the verts used to define it - this can be important sometimes - although not in this case)
4). Execute Scale | Radial with RMB and drag to 0% - constrain with shift. This will re-align all selected geometry to the chosen axis, because it is scaling  (reducing) to zero all the relevant offset distances of the appropriate verts from the vector axis.

The vector axis (in this case) could just as easily been defined by other methods -
Clicking on the end face (if you're sure it's a true axial plane) and transferring its origin to the desired position.
Selecting one of the existing (true) axial edges and transferring the origin.
Either of these methods would be better employed if you're unsure about the integrity of the 2 verts at either end of the 'wobblies'

If the object in question IS orthogonal - things are then much simpler - just choose an axis for your Scale | Radial  -> X,Y or Z operation and transfer the origin via RMB option.

Whilst a cylinder has been used here to demo the method - it can, of course, be tried in any situation (and with any type of geom) that requires a similar result?
Introducing and aligning new geometry to a cylinder.

If you sometimes have the need to increase the complexity of a cylindrical-based object - when it's inconvenient to 'start over' as it were - then the following might be of use.