The reason for the note, Frenchy, was because I’d used these terms in my previous post and wanted to ensure (as far as possible) that the meaning was understood.
Ratio is a general (mathematical) term (ie fraction, percentage etc). I was defining how I was using ratio, in this circumstance.
Scale is a ratio relating (usually) measurement on a map/plan/elevation to measurement ‘on the ground’. Again, I was defining how I was using it in this circumstance.
For this discussion, there are 4 measurements : vertical and horizontal on the profile and on the ground (Vp Vg Hp Hg).
I’ve chosen to relate these measurements by the ratio Vp : Hp and the scale Hp : Hg – other combinations would also be sensible (eg as you suggest Hp : Hg and Vp : Vg)
frenchy_84 wrote:The slope of a line is specified as a ratio
The slope or gradient of a line
can be specified as a ratio (V:H) but can also be specified in degrees (or even radians). My point was that to be able to look at profiles and get a sense of the steepness of slopes, you need to have the same ratio (as defined in this context) across the profiles.
The two profiles below are of the same track – but at different ratios. The one on the right looks a lot more manageable !

- scales.JPG (18.87 KiB) Viewed 18783 times