doug: had to introduce etown/north hardin into the equation huh?
for those that have no idea what I am talking about... seems doug man graduated from etown high in 73 as I was graduating from north hardin 12 mile sup the road... and I did take intro to chem/physics as a freshman where i got an A... but that was like 36 years ago.....ouch.... there was a fierce rivalry between etwon and north hardin back then...
anyway there seems to be a 3rd case where all the forces must equal 0, ie boost gliders during the boost phase...
if Me = FeXe <--thrust x moment arm length
if Mw = Fw x moment arm length where Fw - wing force
if Mt = Ft x moment arm length. where Ft = tail force
if Mp = Fp x moment arm length where Fp is pod force
then Mtotal = Me+Mw+Mt+Mp = 0 for the glider to more or less go straight up...
In reality equlibrium is probably NOT really possible but is at a small enough magnitude such that it becomes a side force and the BG boost is a shallow arc........
during the coast phase Mtotal = Mw+Mt+Mp = 0
when a BG boost straight up(or in a shallow arc), the wing lift,stab lift, motor thrust and Pop Drag forces must be in balance. During motor thrusting, tehrefor, the BG probably is in an equilibroiu condition with the wing ooperating at a near-zero lift or slightly negative anagle of attack to produce minmal lift during boost. After motor burnout, the BG is again probably at an equlibium condition with the wing at a slightly higher angle of attack where its lift force offsets the pod drag/stabilzer lift forces.
this is why you see BG's go into opposite shallow arcs during boost and coast phase. (the infamous S curve) The closer you are to the equlibrium condition ( ie forces and moments balance) the less will be the arc , ie the S curve will be more flat therefore the trajectory is straighter which is good. You want to keep the BG during both boost and cast with a small trajectory "cone'" , preferbaly -5 to say +5 as lift and drag are both reduced by boosting and coasting at smaller anagles of attack to true vertical.