The documents we've linked to say this about nominal distance:

If a task distance is less than Nominal Distance, the day will be
probably devalued.

Nominal Distance should be set to the expected “normal” task distance for the
competition site.

In most cases what I have experienced is that the nominal distance
is set quite a bit shorter than what the historical record would indicate should
be the "normal" task distance. For example, at the recent hang gliding worlds
the nominal distance was set at 80 kilometers (that is the value that one of the
GAP authors wanted). I wanted a value of 120 km. The shortest task was 127
kilometers. The average task was 186 km. The nominal distances seems to have
been set about 100 km too short. We'll see about this soon enough.

The day would be devalued by reducing the Distance Validity. Distance validity
is determined by a ratio of areas (we've seen this before). Let's look into it.
This is the picture that the GAP authors paint:

The Distance Validity is just the comparison of the area under Actual distance
flown curve versus the area under the Nominal lines, ignoring the area below the
minimum distance.

Let's look at a nominal curve for a 100 km task, with a nominal 20% at goal, a
nominal distance of 60 km, and a 5 km minimal distance:

We can determine the area under the curve and above the minimal distance by
adding up the areas shown by the three colors. The area is as follows:

(Gnom/100 * (Dmax-Dnom))/2 + (1 - Gnom/100) * (Dnom - Dmin) / 2 + Gnom/100 * (Dnom-Dmin)

Gnom = the nominal percentage of pilots in goal (set by the meet director), 20%
in this case.

Dmax = the maximum distance flown, in this case to goal at 100 km.

Dnom = the nominal distance chosen by the meet director, 60 km

Dmin = the minimum distance for the meet, chosen by the meet director, 5 km.

Doing a little algebraic manipulation we get the area to be:

(1 + Gnom/100) * (Dnom - Dmin) / 2 + Gnom/100 * (Dmax-Dnom)/2

Multiply this times the number of pilot who flew, Nfly.

To get the Distance Validity, divide the actual total distance flown by those
pilots who flew further than the minimum distance minus the portion of that
distance that was the minimum distance by the value we just figured out above.

So how far do pilots on average have to fly to get full validity:

The pilots who fly further than the minimum distance have to fly on average 48
km to make the day have complete Distance Validity (equal to 1) in this case,
with the nominal distance equal to 60 km and the goal equal to 100 km with one
pilot at least making goal (and assuming all pilots make at least the minimal
distance). So the full validity distance is less than the nominal distance.

Can we determine for a range of values of Gnom, Dmax (goal distance), Dmin, Dnom,
what the average pilot's distance will have to be for full distance validity?
Sure. And I'll show you how in the next article on Nominal Distance.