Spar Location

The location of the spar in the wing is important to reduce the twisting forces on it and help to keep the weight down. The obvious location is at the centre of pressure for the aerofoil.

Wortmann FX 63-137 at 0 degrees (XFLR5)

This works at one angle of attack but as soon at this angle changes, so does the centre of pressure.

Wortmann FX 63-137 at 3.5 degrees (XFLR5)

Where is the centre of pressure? How do you find out where the centre of pressure is? First you need to know the coefficient of moment, normally referred to as the  pitching moment, moment, CM for the section. This is about constant up to near stall. It is defined as :-

I won’t give the derivation but an alternative definition is:definition  is:-

This can be rearranged to give the position of the centre of pressure

Where c is the chord of the wing Cl is the lift coefficient Cm is the pitching coefficient M is the total pitching force S is the area of the wing V is the velocity of the wing xcp is the position of the centre of presure as a fraction of the chord x1/4 is the quarter chord position ρ is the density of air 

What effect does this have on the spar? We can find the centre of pressure, now we want to know the twisting force this will produce on the spar. This depends on the lift and the distance from the centre of pressure to the spar, more  particularly the centre of a spar with a circular cross-section. If these coincide the twisting force is zero but otherwise it is the

distance from the spar to the centre of pressure multiplied by the lift.

Twisting force on spar from wing FX 63-137

How can the twisting force be reduced? An aerofoil with a smaller coefficient of moment, C m can be used like the Lissaman 7669 or the wing chord could be reduced. Reducing the wing chord would also have the effect of reducing the wing area, increasing the flying speed and possibly increasing the  power requirement although reducing the wing area is likely to either reduce the weight of the secondary structure. (Ribs, leading and trailing edge, wing covering) or result in a better wing shape that will reduce drag and increase the lift coefficient.

So where does the spar go? Well, my suggestion is near  the centre of pressure at the angle you expect to be flying at. While it would be nice if you could fly your HPA at a constant angle this is not going to happen.

FX 63-137 at 2.5 degrees C L of 1.1(XFLR5)

Slightly forward of the anticipated centre of pressure allows for increased angle of incidence and the centre of pressure moving forwards and any twisting is likely to result in wash out which is what you want in the wing . It also allows for flying at increased angle of incidence as a result of trying to reduce power. Placing the spar as low in the wing as possible will also help to reduce the twisting forces.