Why a right hand curve is positive?

In transportation engineering there is the following signage convention  for curves in horizontal alignment design:

  • a right hand curve is considered positive
  • a left hand curve is considered negative

This convention is considered relative to the stationing direction of that alignment.

Horizontal alignment - curve sign convention

Horizontal alignment – curve sign convention

This signage convention is established in the following way (see the figure above):

  • In transportation engineering (roads, railways) the general technical drawing convention is considered – a drawing is read from left to right. The stationing direction of an alignment is generally following this convention. Some exemption from this rule might be accepted. For example, in UK, permanent way or road designs for western England are shown from right to left on a drawing – keeping the geographical location of London, the low chainage end, to the right side of the drawing.
  • within the general conventional setup, a right hand curve will be positioned above the reference line connecting its ends. Conventionally, if the graph is placed above the reference line, its function is considered positive. Due to this, the right hand curve is considered to be defined by a positive radius. Often, the normal cant (for railways) or the superelevation (for roads) applied on this curve is considered to have a (conventional) positive value.
  • The opposite happens to a left hand curve and it will be considered negative.

A similar convention is for the vertical curves. The convex vertical curve (clockwise defined curve) will be considered to have a positive radius – despite the fact that it defines a gradual gradient decrease, a subtraction.

The concave vertical curve (counter clockwise defined curve) will conventionally have a negative radius, even though it defines a gradual gradient increase, a gradient addition.

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