What determines the "hang point" and control bar position of a hang glider?
What is the relation between Center of Pressure (C.P.), Aerodynamic Center (A.C.), &quot;hang point&quot; (the point where the flexible &quot;hang strap&quot; connects to the glider, or the point where the &quot;trike&quot; unit is connected to the wing), and the control bar position relative to pilot's body, if the glider is to fly well, meaning that when I lift hands from bar, the glider will not pitch.


a) It is important to note that this is a question about trim, not stability.  We are not asking what will happen to the glider after a disturbance.
b) This answer will address the question in terms of Center of Pressure, not Aerodynamic Center, which simplifies things because we don't have to worry about a pitching moment coefficient.  Note however that the Center of Pressure is not fixed.  In general, the Center of Pressure of the aircraft as a whole moves forward as angle-of-attack is decreased, and moves backwards as angle-of-attack is increased.  (Otherwise the glider would be unstable.)
c) We'll assume that the drag on the pilot's body is negligible, i.e. that the &quot;hang strap&quot; hangs straight down when the pilot is not pulling or pushing on the control bar.
d) In the simple case where the hang strap is connected to the glider right at the CG of the glider, or somewhere along a vertical line passing through the CG of the glider, then in order for the glider to be trimmed to fly hands-off, a line drawn through the Center of Pressure, parallel to the Net Aerodynamic Force vector generated by the glider, must pass through the CG of the glider.  Since the Net Aerodynamic Force vector-- the vector sum of Lift and Drag-- must be vertical in a wings-level steady-state glide, this means that the Center of Pressure must lie somewhere on a vertical line passing through the CG of the glider.
e) In the case where the hang strap is connected to the glider somewhat forward or aft of the CG of the glider, then the following must be true: the torque about the CG created by the G-loading on the pilot's body must exactly counteract the torque about the CG created by the Net Aerodynamic Force acting at the Center of Pressure.  If glider's CG is ahead of the Center of Pressure, then the hang strap must be connected to the glider behind the glider's CG.  If the glider's CG is behind the Center of Pressure, then the hang strap must be connected to the glider ahead of the glider's CG.  Alternatively we could tackle the problem by computing the torques around the Center of Pressure rather than around the glider's CG-- we'd get the same result, because we are free to choose any arbitrary pivot point in torque calculation problem.  We'd just have to remember to adjust the force acting at the CG according to the G-loading, in any case where it is other than one.  Note that in the case where the weight of the glider itself is negligible compared to the weight of the pilot-- which is not a bad approximation for some of the lighter &quot;floater&quot; hang gliders-- this reduces down to the simple statement that the hang strap must be connected to the glider somewhere along a vertical line that passes through the glider's Center of Pressure.  In other words the (center of mass of the) pilot's body must be located somewhere along a vertical line that passes through the glider's Center of Pressure.
f) If your meaning of &quot;if the glider is to fly well&quot; is meant to imply not just that the glider is flying at &quot;trim&quot;, but also that the glider is statically stable in pitch, then we have the added requirement that if the angle-of-attack increases, the Center of Pressure of the whole aircraft must move aft, and if the angle-of-attack decreases, the Center of Pressure of the whole aircraft must move forward.  This is accomplished largely through washout near the wingtips.  The wingtips, being aft of the CG and having a lower incidence than the wing roots, essentially act like the horizontal tail of a more conventional aircraft.
g) Actually, the above comment is only true when the &quot;hang point&quot; is not far below the CG.  If the hang point is well below the CG-- as was the case in some early hang gliders where the hang point was some ways down on the triangular control frame, well below the &quot;keel&quot;-- then &quot;pendulum stability&quot; could in theory keep the glider stable in pitch even if the &quot;Center of Pressure&quot; were completely fixed as angle-of-attack changed, or even if it moved a little bit in the &quot;wrong&quot; direction-- at least at angles-of-attack not higher than the angle-of-attack that yields best L/D.  Example-- angle-of-attack decreases, L/D decreases, Net Aerodynamic Force vector points further aft relative to flight path and also relative to glider, apparent G-load on pilot (opposite in direction to Net Aerodynamic Force vector) points further forward in glider's reference frame, and this changes the direction of the force exerted by the pilot's body on the glider, acting at the hang point (if pilot is flying hands-off the control bar).  Glider tends to pitch up to a higher angle-of-attack.  Note that we've phrased this description in such a way that we need not assume the G-load is 1G, acting purely vertically.  Note also that this effect is further magnified if the Center of Pressure is high above the CG of the glider itself.  And finally, note that we can reach all the same conclusions, at least in the case where the pilot's hands are free of the control bar, if we ignore the direction of the G-load vector and only consider the direction of the Net Aerodynamic Force vector, which acts at the Center of Pressure, so long as we choose the C.G. of the whole system as the pivot point for our torque calculations, calculating the C.G. of the whole system based on the assumption that the pilot's entire mass is concentrated at the &quot;hang point&quot;.


Does hang glider change stability from stable to neutral to unstable when man move his body fore and aft?


Ideally no, at least within the limits of how far the pilot's arms can reach. But in some cases, yes.
Normally in aviation we are concerned with instability when the CG of the system is too far aft.  I'm not aware that this has ever been a problem in actual practice with any flex-wing hang glider.
Some hang gliders can become unstable at high airspeed, so that above a certain airspeed threshold, at progressively higher airspeeds, the pilot must exert progressively less aftwards force on the control bar, or in extreme cases, progressively more forwards force on the control bar, to hold the airspeed constant.  Generally speaking this is caused by flexing of the structure under the aerodynamic load associated with high airspeed.  Certainly if once some threshold airspeed was crossed, the pilot then had to maintain a progressively less forward or further aft body position to hold the airspeed constant at progressively higher airspeeds, that would be clear evidence that the glider was flexing in a way that fundamentally changed its stability characteristics and moved its &quot;Neutral Point&quot;.  And this does in fact happen in some cases.
Keep in mind though that &quot;stability&quot;, even static stability, is somewhat hard to define in hang gliders.  Do we mean that the glider will return to equilibrium after a disturbance if the pilot exerts a constant force with his muscles on the control bar (including the case where the pilot is exerting zero force), or that the glider will return to equilibrium after a disturbance if the pilot exerts whatever force through his arm muscles is required to lock his body in a constant position relative to the glider (in which case the glider and pilot can be treated as a single rigid body)?  Note that changes in the L/D ratio, which change the direction of the net aerodynamic force generated by the glider, and thus the direction of the G-loading acting on the pilot's body, will change how far forward or aft the pilot's body tends to &quot;hang&quot; relative to the control bar when the pilot exerts no muscle force, so these two definitions of stability clearly are not the same.  In some cases involving rather steep dive angles, as angle-of-attack is progressively decreased and airspeed is progressively increased, the pilot may experience a need to exert a progressively less aftwards force or in some cases even progressively stronger forward force (the opposite direction that we really would desire to be the case) on the control bar to keep the glider's airspeed constant, yet the pilot's body position is actually being moved progressively further aft (which is equivalent to moving an aircraft's control stick further forward, and is intuitively consistent with our concept of a stable of aircraft.)  A hang glider pilot would typically describe this as &quot;a loss of normal bar pressure&quot;, yet the relationship between bar position and airspeed may remain &quot;normal&quot;, with the bar having to be placed further aft to reach higher airspeeds.
It's complicated-- some force vector diagrams are really needed to make the point completely clear.  But in short, the relationship between &quot;control stick position&quot; and &quot;control stick pressure&quot; is less straightforward in hang gliders than in most &quot;conventional&quot; aircraft (with unboosted mechanical control linkages).