Let me preface this with the statement that the current design of sparrow strainers works. You should not deviate from that design. The following is purely theoretical at this point and is not flight proven.
Here are my observations so far.
At 2 degress AOA, which is about where the Q2 is at high speed cruise, the standard LS! Airfoil produces a Cl of 0.461 and Cd of 0.0191 as shown below
In order to reverse the effect of the elevator deflecting upward in flight, sparrow strainers are installed. As a result, the span that contains the sparrow strainers ends up with an overall NEGATIVE lift coefficient, Cl of -0.333 and almost double the drag of the clean LS1: a Cd of 0.0317 (shown below). The extreme pressure field of the sparrow strainer, because of its high angle relative to the streamlines, actually kills the lift of the LS1 airfoil over the length of span that is occupied by the sparrow strainer. The result is a negative lift coefficient over that portion of the span. So roughly 1/8 of the total canard span (the portion of the span with the sparrow strainer installed) is actually providing negative lift at an AOA of 2 degrees, and is creating lots more drag than it would if there was no sparrow strainer present.
The catch 22 is that we know the sparrow strainer is necessary for the LS1 profile, as we can demonstrate as follows:
If the sparrow strainer is omitted and no stick force is applied (hands off), the elevator portion of the canard will tend to reflex up in flight. But, how much would it reflex up?
Well, it looks like it would reflex up 20 degrees before the pressure field is in equilibrium on top and bottom of the elevator. This would result in the overall “hands off” configuration having a negative Cl = -0.420 over the entire span occupied by the elevator. This would result in a severe “tuck”.
If the elevator portion of the LS1 is redesigned so as to not deflect up or down in flight and to be in trail throughout most of the AOA range, then the a result is shown below. This design should acheive a “hands off” Cl of 0.434 (slightly less than the bare LS1 of 0.461) and a Cd is 0.0198, very slightly higher than the bare LS1. No stick force or sparrow strainer would be required for this elevator profile if it performs as modeled, so the draggy and negative lift portion of the span would not be nescessary.
But what about a different airfoil, such as the the Roncz 1145MS airfoil? R1145MS would result in the same Cl as the modified-elevator LS airfoil, but at a lower Cd of 0.01393. As shown below.
However, the Ronz airfoil, if fitted with an articulated elevator in the Q2 configuration, would tend to see the elevator deflect downward before achieving aerodynamic balance with no springs, stick force or sparrow strainer applied. Equilibrium would be achieved with the elevator deflected downward approximately 2 degrees as shown below. This deflection results in a higher Cl and would require that the overall airfoil be installed 1 degree nose down to the LS1 to perform aerodynamically similar to the LS1 equipped Q2. Doing so, would yield a Cl of 0.458 and Cd of 0.01372 at an AOA of 2 degrees.
So we would mount the Roncz airfoil 1 degree lower angle. If we were to do this on a Q2, then the Cl would be similar to the LS1 airfoil, but the drag would be about 30% lower than the LS1: Cd 0.014 at and AOA of 2 degrees.
Note that none of these models include the effect of a turbulent stall bubble on the trailing edge of the elevator, so the numbers would be slightly different on a flying aircraft.
In summary, we see that the Roncz 1145MS airfoil would probably have been a better choice than the LS1 for a Q2, but it may not have been available at the time the decision of QAC was to go with the LS1. We can also see that the sparrow strainer solves the problem of preventing the LS1 elevator floating up in flight, but at a great drag cost and a reduction in overall canard lift over the span to which the sparrow strainer is applied (roughly 1/8 of the total span of the canard) with the 11.5” sparrow strainer, higher if using the 17.5’ sparrow strainer).
As shown above, it is possible to design a more benign elevator shape for the existing LS1 canard that will solve the problem of the elevator floating up in flight without the need for a sparrow strainer, but this solution is not as efficient with respect to drag as would be use of an entirely new airfoil as was done by John Roncz for the Long EZ.
This is my analysis so far. I will continue to work on this as time permits.