This wasn't conceptual.. wasn't built because they did not have the funding. Go read the detailed article about it on global defense
and as for your length claim.
the S-56 was the carrier variant.
S-54 vital statistics
DIMENSIONS:
Wingspan 9.08 m (29 ft 9 1/2 in)
Length overall
12.30 m (40 ft 4 in)
Height overall 4.47 m (14 ft 8 in)
WEIGHTS AND LOADINGS:
Weight empty, equipped 4,790 kg (10,560 lb)
Max T-O weight 9,410 kg (20,745 lb)
Max landing weight 7,130 kg (15,718 lb)
Max wing loading 356.2 kg/m2 (72.94 lb/sq ft)
Max power loading 154.75 kg/kN (1.52 Ib/lb st)
PERFORMANCE (estimated):
Max level speed:
at height Mach 1.55 (890 knots / 1,650 km/h / 1,025 mph)
at S/L Mach 0.98 (645 knots / 1,200 km/h / 745 mph)
T-O speed 98 knots (180 km/h 112 mph)
Landing speed 92 knots (I7O km/h 106 mph)
Service ceiling 18,000 m (59,050 ft)
T-O run 380 m (1,250 ft)
Landing run 500 m (1,640 ft)
Range with max fuel
at S/L 440 nm (820 km/510 miles)
at height 1,080 nm (2,000 km/1,240 miles)
G-limits +9/-3
for comparision here is the Gripen
# Length: 14.1 m (46 ft 3 in)
# Wingspan: 8.4 m (27 ft 7 in)
# Height: 4.5 m (14 ft 9 in)
# Wing area: 30.0 m² (323 ft²
# Empty weight: 5,700 kg (14,600 lb)
# Loaded weight: 8,500 kg (18,700 lb)
# Max takeoff weight: 14,000 kg (31,000 lb)
# Powerplant: 1× Volvo Aero RM12 afterburning turbofan
* Dry thrust: 54 kN (12,100 lbf)
* Thrust with afterburner: 80.5 kN (18,100 lbf)
And the JF-17
# Length: 14.0 m [46] (45.9 ft)
# Wingspan: 9.45 m (including 2 wingtip missiles) [46] (31 ft)
# Height: 4.77 m (15 ft 8 in)
# Wing area: 24.4 m² [46] (263 ft²
# Empty weight: 6,411 kg [47] (14,134 lb)
# Loaded weight: 9,100 kg including 2× wing-tip mounted air-to-air missiles [48] [49] (20,062 lb)
# Max takeoff weight: 12,700 kg [48] (28,000 lb)
# Powerplant: 1× Klimov RD-93 turbofan [50]
* Dry thrust: 49.4 kN [51] [52] (11,106 lbf)
* Thrust with afterburner: 84.4 kN [53] [54] (18,973 lbf)
(shamelessly taken off Wikipedia )
It wasn't built because nobody funded it.. That doesn't make it aerodynamically impossible OR a failure. If that was the case that you judge an aircraft just by whether someone flew it or not, then a lot of brilliant designs which were wind tunnel tested are failures..
and.. finally.. If there was such the issue with canards..then are the swedes or the Europeans nuts to build those jets? The advent of computer assisted flight is precisely the reason that canards(and other unstable dynamics) are now used in aircraft. The Distortion is handled by both using clever aerodynamics and redundant flight computers which make the necessary corrections to the control surfaces to ensure the aircraft does not .
The canards also contribute to the extreme maneuverability these fighters exhibit. Whether they contribute to the RCS is also managed by flight computer which in the case of the eurofighter ensure that the canards are always in the optimal position to ensure a lower RCS.
Which bring us to the original idea of why you cant use twin tails and canards on the same jet.. I see no.. SCIENTIFIC proof that it cannot be done. Or wasn't done because it was aerodynamically impossible. There were a lot of reason many aircraft failed to leave the drawing or model stage, quite a few because simply nobody wanted them at that time.
This particular jet wasn't built as the Sukhoi company has its own internal competition by the larger siblings of this one. So when you could buy a 27 or 30 for a marginally higher price and get a better performing aircraft in terms of range and speed.
So.. ipso facto, while you are correct in saying that nothing in production exists using this configuration. It does not belittle the concept or the design philosophy as inherently flawed. Canards and Twin tails are both used TOGETHER as moving control surfaces in much lighter, slower and faster aircraft than the ones I mention. And so this particular part of your post which I question "its aerodynamically Impossible for a small plane to have both twin tail and canards at a same time." still stands for me an unsubstantiated claim. Cheers