rocket flight pitch and yaw prediction

huangyhg

rocket flight pitch and yaw prediction
background;
of the sugar shot to space project (see sugarshot.org) which is an amateur project expected to fly to 67 miles altitude, we (the payload team and our outside analysts) are attempting to apply some analysis for the sake of  predicting the flight path 'on the fly', and analytically, as a prediction.  to this end, i seek your help in coming up with a justifiable (proof-worthy) approach to the problem.
the rocket;
vertically-bound rocket flight, 27 feet tall, 1100 lbs,
(900 lbs solid fuel) with no guidance whatsoever except fixed fin-induced rotation attempting 4 turns per second.
due to the consumption of fuel, the center of gravity will move forward for 9 seconds, remain constant for a short period, then move aft-wards - all the while the vehicle configuration does not change (no parts are dropped) but the wieght of the fuel is given up, of course.  hypersonic
flight (mach 5+) is expected briefly.  
  
the problem;
  we (myself as payload team lead, and the outside analysts) take it that a vertically-bound rocket flight, with no guidance whatsoever except fixed fin-induced rotation (roll - but we call it spin), would upon liftoff be pointed 'perfectly' vertically, yet have the tendency to fly along a roughly 'parabolic' path.   
   what we need is a way to predict what would be normal or expected for this parabola.  
   presently we have three different possible ways of viewing the problem.  
a  my personal favorite is the simple view.. that the wind will be blowing say 4 miles per hour (of course its not constant), and this will cause the flight axis to veer from vertical and is not so hard to calculate - based on fairly simple physics.  so 'prediction' involves knowing
what winds to expect at altitudes for the unknown launch location.
b  another view is that even if launched vertically in still air, the flight path will be predictably parabolic.  but i differ.. in the next, c..
c like 'b' above, with the same moving 'center of gravity' and stationary 'center of pressure', even with no wind the parabolic flight path would be a matter of statistical distributions of possible flight paths, with a most likely path (with the highest probability of occurance).
for myself, i want foremost to get it right, but also to convince the guys who want to use the 'b' approach that it's not possible, and that 'c' is too messy, and that 'a'
is most likely arguably true as it 'stands to reason'.
so it's your turn.. please advise us on what approach makes the most sense.  one of our goals is to convince the faa that we know exactly what to expect for possible flight paths, and particularly what window we can operate in without terminating the flight.   
to reiterate, the problem is one of, for a solid fuel rocket, launched vertically, what 'parabolic' flight path could be calculated on what basis?
i know this is a 'sketchy' problem, all the more reason to ask you guys.. so thanks much for reading, i look forward to your insights and feedback.
geoff
  

      
my apologies for the title, of course we are talking about 'flight trajectory' for a vertically-bound flight.
this something that you can run on rocksim:
hi there, from my experience with ballistics you going to find that the rocket will follow its 'parabolic' curve but as the centre of mass changes the point along the rocket that is following the curve directly will change (like the pivot point of the rocket if you like). some thing tells me that the heavier part of the rocket will circle tightest to the 'true path' and deviate less (although i could be wrong). which to my mind will result in the nose circling very tightly at the start of the flight with the back following on a slightly wider curve (resulting in a fairly true path) however when the cm drops back the nose will follow a wider path and will become a lot more succeptible to being blown off course.
i say this from test results with firearms rounds with different combinations of light weight polymer tips, heavy bases and hollow bases etc
some of this may apply to a lesser degree as the rocket has constant propulsion during flight rather than a dropping momentum but it may help your calculations.
i had perfect balance, symetry and aim at launch the rocket would go straight up and straight down, except for wind factors. any other deviations from vertical will result in your parabolic path. i would guess that your biggest problem will be getting the rocket going exactly vertically at lift-off. fin/spin stabilization does not begin to work until you have a fairly high speed so guide rails are usually used to launch a rocket. most amateur rockets i've seen will make a quick angle change as they leave the guide rails and then go straight when the fins take over control. any vibration in the rail mechanism can cause big errors.
a couple of points ...
i take it that guidance is different to stabilisation, which i think you need.
i wonder how you could convince the faa that you can predict where an unguided rocket is going to land.  i suspect that if you can do this, then the military will want to know, and probably declare your work secret, and then the industrial complex which provides the military with all sorts of guided missiles will come knocking, and all that'll be left is this thread, and a new urban legend.
anyways, good luck
while this may already have been considered, why not just use gyroscopes to prevent the unstable swinging?
mike
even gyroscopes could be viewed as a guidance component and also wieght is a big issue. we are avoiding guidance components, to fit regs.  mike makes a good point too that 'unstable swinging' is possible - we have yet to analyze our instabilities (center of gravity moves forward substantially).
**    presuming stable powered flight, i suspect the predictable changes in attitude will result from all horizontal accelerations due to wind.  for example, as the rocket rises another hundred yards, the wind may change say x.x mph - depending on where the center of gravity is at that moment, such and such attitude rotation could be calculated as resulting from accelerations induced by such wind.  i understand this view may be far too simplistic, and would appreciate your feedback. **
  thanks for the apogeerockets sim links.  we have to do our own calculations though.. we will get thrust from sim programs, but we ought to stick to our own analysis whereever possible.  
  as a general rule, we avoid any and all active stabilisation and guidance control, since we are going for enough waivers as is.
   presently i favor the view i proposed above between the asterisks **.  
geoff

           
      
  
   
the apogee website contains lots of information about stability, since model rockets are completely unguided.  you need to read those articles pertaining to stability and the location of the center of pressure, relative to center of mass.
ttfn
also, note that solid rockets leave behind slag (metal oxide) residues, and these may (depending on where the molten slag puddles form) shift the radial position of the c.g.  this phenomenon has happened with spin-stabilized spacecraft upper stage boosters (e.g. apogee kick motors).