Rule of thumb
Justathought:
My rule of thumb requires 3 steps:
D=(R x A) x 0,018
where
D=Distance on the arc
R=Radius (Distance from Fix)
A=Angle
x 0,018 can easily be resolved: multiply by 2, subtract 10% from the result and divide this result by 100.
Example:
You are flying on the 15 DME arc for 60 degrees:
a) 15 x 60 = 900
b) (900 x 2) - 10% = 1620
c) 1620 : 100 = 16,2NM
Correct distance travelled is 15,708 NM. The error is always 3,13% on the high side, which is acceptable (at least to me).
Hope that answers your question.