Agreed. The 12 volt 1950 mAh flies the Avistar at a minimum of 33.3 Amps (depending on your planes weight). This is eating a good bit of your motors top Amperage rating. The estimated time the battery will give you is 6/100x1950/33.3 = 3.51 minutes.
If you using ALL of your ESC (full throttle), you might see 6/100x1950/40 = 2.93 minutes.
WARNING: Time estimates herein do not account for the cutoff voltage required by LiPo batteries.

Not to interrupt your already fine work over the last year ... it's fascinating, informative, and useful ... but ...

may I humbly suggest Model Aviation March and April 2005, Selecting Electric Power Systems.

The Avistar:
wspan 59 in.
warea 602 sqin
wght 5 pound (80 ounces)
WINGLOAD (80/602)x144 = 19.14 ounce/sqft

To fly aerobatic, MA suggests between 60-100 watts/pound.
To fly a strong aerobatic plane, MA suggests between 15-25 ounces/sqft.
The aboveMA issues have more detailed information on these important issues.

Simply multiply the Avistar weight times your preference of watts/pound. This gives
a required 'mean' (or average) watts required. For the Avistar, my personal preference
is 5 pounds X 80 watts/pound = 400 watts. This is my 'happy plane' number.

Now select a 'happy battery'. Watts = Amps X Volts. The MA issues will explain
in detail how to do this. Without explaining, although the above posts should have
given you a 'feel' for it by now, I've selected a 4S2P 14.8 volt 4000mAh Thunder Power LiPoly.

Amps = Watts / Volts = 400 / 14.8 = 27.03 Amps required. to keep my 'happy plane' flying at 80 watts/pound.
Time 4S2P 4000 = ( 60 / 1000 X mAH / Amps ) = 60/ 1000 x 4000 / 27.3 = 8.79 min.flight
Time 4S2P 4000 full throttle = 60/1000x4000/40 = 6 minutes (doubtful ... the battery is likely to catch fire).
... the 4S2P likes only 20 Amps continuous ... so, some throttle management is in order ... unless you LIKE fires ...
WARNING: Time estimates herein do not account for the cutoff voltage required by LiPo batteries.

Either a 5S2P 18.5 volt 4000 or an 4S4P 14.8 volt 8000 will increase the flying time. Caveat: these
selections WILL add more weight to the Avistar, thus increasing the Watts above 400 and increasing
the Amps required to keep the plane 'happy' ... so, redo the calculations for either new battery choice
and see if you are happy with the performance.

Time 5S2P 4000 = 10 minutes at 22 Amps.
Time 4S4P 8000 = 15.44 minutes at 31 Amps.
WARNING: Time estimates herein do not account for the cutoff voltage required by LiPo batteries.

I've adjusted the Avistar weight according to Sport Aviators 5 pound (I'm suspicious of this low weight figure, although the 6 pound Graupner Taxi Cup II flies fine with a lot less motor and a lot less battery) flying weight in its online magazine. You WILL, of course, have to weigh your finished Avistar and add the motor wt, mount wt, and battery wt to be sure of the figures.

Last but not least, pick a motor to fit the realities which jump out of calculations such as above.

May I humbly suggest the Model Motors AXI 4120, 70 Amp rating, and the Jeti 40 Amp w BEC controller. It will work witha variety of planes from .25 to .60 ... although the slightly cheaper AXI 2826 (same controller) will work just fine with the Avistar and the 4000 mAh battery (4S4P 8000 is likely to overheat the AXI 2826). I am currently configuring a Hobbico NexSTAR, 6.71 pounds, with the aforementioned configuation and will probably go with the ThunderPower 5S2P 18.5 volt 4000 mAh. Next, however, I plan to do the Avistar ... so I'll be reading this thread as often as possible !!!

In all fairness, I should mention the Hacker C50 series ... they are fine choices for the above situations ... and one each mounted on the fenders of a VolksWagen, should get you to the SuperMarket quicker ... i suggest a 15x8 3 blade prop and a 70 Amp controller.

Thanks !!!

http://www.hobby-lobby.com/brushless_axi.htm
http://www.masportaviator.com/
Bonnie 20
... uses an AXI 2820/10, Jeti 40, and 8 cell NiCad 1700 (too small)
http://www.masportaviator.com/ah.asp?CatID=1&ID=39
http://www.hobby-lobby.com/bonnie.htm
Graupner Taxi Cup II
... this baby has me drooling and the flight videos are superb ... including a somewhat raggedy 'knife edge' ...
... uses an AXI 2826/12, Jeti 40, and a 3S2P 11.1 volt 4200 mAh LiPoly
http://www.hobby-lobby.com/taxicup.htm
The Taxi Cup has a listed flying weight of 6 pounds, thus a WINGLOAD of 23.15 ounces/sqft. This is a bit much for the listed 3S2P. Quite frankly, I would use the same AXI 4120 as above suggested for the AviStar and the NexSTAR ... with at least a 4S2P 4000 mAh.