Delta-v obtained from Titan by the Cassini spacecraft; just how much of a "gas tank" was it?

Question

In the video Cassini at Titan: A World Unveiled after about 01:56 Linda Spilker, Cassini Project Scientist, Jet Propulsion Laboratory says:

Not only was Titan fascinating in its own right, a moon the size of the planet Mercury, it was also Cassini’s “gas tank”. It allowed us to change the shape and orientation of the orbit in order to explore the poles of Saturn and the rings and all of the icy moons, by carrying a lot less fuel than we would have to have carried otherwise.

It gave us the energy to go all the way across the rings, and fly between the gap; between the rings and the planet.

Immediately following that, Jonathan Lunine, Cassini Titan Scientist, Cornell University says:

Because of these flyby’s of Titan, using Titan as a gravitational slingshot…

And so many of the remarkable discoveries that have been made by Cassini, for example mapping the composition of the plume of Enceladus, would not have been possible without Titan there.

We could not have gotten to these places, without using Titan.

Question: Is there a way to estimate the total delta-v that Titan contributed to the mission? Or, starting from Cassini's initial orbit, or since it's orbit dropped to say 250,000 km or so, estimate the fraction of all delta-v from then until EOM that was contributed by maneuvers using Titan?

GIF:

above: Teaser GIF to get you to enjoy the real thing here (since even the low-res version is larger than the stackexchange imgur's limit of 2 MB oops! MiB)

Related questions and further info on this crazy ride called the "ball of yarn":

• Flying fuel tanks! Which deep-space spacecraft had the largest fuel mass fraction? Images showing that Cassini actually looks like a giant tank, decorated with instruments and a dish. I got a value of 56% for the fraction of Cassini's mass that was fuel. This answer demonstrates an enormous amount of research and finds several spacecraft that had an even larger fuel mass fraction!
• What force is bringing Cassini down into Saturn's atmosphere in another 145 days; drag, or…?
• Unravelling Cassini's “ball of yarn” orbit around Saturn, tabulation of propulsive maneuvers?
• Why would Cassini need to reach 64 degrees inclination before “threading the needle”?

Answer 1

I downloaded the ~170 SPK reconstructed trajectory kernels (at Saturn) from the NAIF node of PDS and searched for instances where Cassini was within Titan's sphere of influence (~43,000 km).

Note that this construct actually excludes the third Titan flyby from the tally (T-C, Huygens probe entry; 60,000 km, blame the Italians) for a total of 126 considered flybys.

I quantified each flyby by 4 metrics (using standard hyperbolic trajectory assumptions):

• $v_{\infty}$
• periapsis distance of flyby
• flyby deflection angle ($\delta = 2 \nu$ in Wikipedia nomenclature)
• flyby $\Delta V$ (calculated with equation from a question of mine)

(Personal work)

The total $\Delta V$ of all 126 Titan flybys was 89.4 km/s.

This is corroborated by this NASA source (that I found AFTER completing all of this work :))):

By mission’s end, Cassini achieved a delta-v of about 200,000 miles per hour (about 90,000 meters per second) from Titan flybys — roughly 37 times what it could ever have achieved by propellant alone.

Therefore Titan contributed ~97.4% of all "delta V" (while at Saturn).

Cassini-Titan "Ball of (broken) Yarn":

(Personal Work, Titan base image source (Astropedia) -> MATLAB "Copper" color map)

J2000 frame, this is not where Cassini flew over Titan relative to surface features, just a neat animation :)