In the days after NH launched, a frequent topic was: "How fast will NH escape the Solar System?" I made a number of crude estimates, but only now do I think I have a really decent answer.
Here goes--please feel free to check my figures. All have been rounded to the nearest tenth:
The NH website lists the (I'm assuming) relative velocity of the spacecraft and Pluto at encounter will be 13.9 km/s. I realized that by using Pluto's velocity at that time, I could work backward and calculate the spacecraft's.
I used Orbits 3.0 (a very old but useful solar system program) to find Pluto's velocity on July 15, 2015: 5.6 km/s. I then plugged this number into the Pythagorean Theorem, assuming that simple vector geometry would work:
x^2 + 5.6^2 = 13.9^2
X^2 + 31.4 = 193.2
X^2 = 161.8
x = 12.7 km/s
This speed works out to about 2.7 AUs per year at encounter. If my final assumption is correct--that the velocity will change very little once the spacecraft is past Pluto--then NH will definitively beat the Pioneers, at 2.6 AUs per year for 10 and 2.4 for 11, but will never catch up to the Voyagers.
See Heavens Above (they've just added NH):
http://www.heavens-above.com/solar-escape.asp