Here we will go over some aspects of how the three COUGAR GPS receivers performed on the SIERRA payload with repect to the position solution and some other GPS related parameters. (The other reason to have GPS on all three payloads is to get accurate timing synchronization, which we won't deal with here.)
(Each plot can be obtained as a *.pdf file by clicking on it or "saving target as".)
First we have a map of Alaska and both the nominal and actual trajectories flown. On each curve we have points marked for the 600km (altitude) upleg, apogee, and the 600km downleg. The Actual flown trajectory, taken from the GPS data on the aft subpayload, is plotted as the blue curve. We have also taken bothe trajectories and "mapped" the position down along the IGRF magnetic field to an altitude of 100km. These are the magenta and red curves, for the nominal and actual trajectories, respectively.
This is just a close up of the previous plot.
Next is the altitude of the the SIERRA payloads as a function of flight time.
One thing to notice is that since the altitude is
hundreds of km, it is not possible to tell the difference between the three payloads
(zero to about 1km) on
this scale.
So we have to zoom in at apogee: Note that the Black, Blue and Red traces correspond to the
Cornell Cougar Receiver, the Green is the radar altitude data, the grey is the WFF sponsored
GPS Receiver on the main payload, and the gold is the differentially corrected WFF solution.
Now, in making these measurements of position, it is necessary to determine the amount of error we should expect. Since the U.S. govt. shut down Selective Availabilty (check out the effects of this [ SA Deactivated ]), we can be much more accurate. As we see below, the error is around 5 meters or so, found by looking at the noise in comparing differences between payload positions when they haven't separated yet:
Also in considering the error, we should look at the number of GPS satellites that we tracked and the Dilution of Precision. The next plot shows this, and we see that we pick up a couple satellites (which are below the horizon while we are on the ground) by the time we get into main part of the flight. And our DOP also imporves when we get airborne.
To get a better idea of the relative altitudes of the three payloads at any time during the flight we can plot the difference between the aft and the other two payloads. Thus, below we can see that the aft payload was the lowest, and the forward payload was the highest during the flight.
Next we can look at the area between the payloads by looking at the angle (theta= the angle aft-main-fwd) and the distances between the payloads:
Now the final thing we can attempt to do with the basic GPS data is try and determine
the ejection speed and direction of both subpayloads with respect to the main payload.
We wanted to do this to determine if the ejection speed was close to what we expected
and if the direction was what we planned. Something very important to remember in all
these velocity calculations is the error of about 5m that we showed above. That means our
velocity estimates have considerable error margins and these calculations are just to get
an idea. Once the attitude solution is determined we will have directions much more
accurately. Also, we are looking at the relative velocities here, which are
only a couple m/s, whereas the velocity of the payloads is on the order of 1.4km/s, so
again, this is only preliminary.
Here is the determination of the seperation speed.
Finally, we compare the pointing coordinates that we determine using the GPS velocity to that which we planned on (nominal values).
There are even more things we can do with the GPS positioning data. We can determine where the payloads are with respect to the IGRF magnetic field plane (since or objective was to have them seperate in the B-Plane). We can also display positions relative to the Center of Mass and in different (and useful) coordinate systems. If you are interested in these plots go to: [ 3D and Magnetic reference Plots ] or [ WonderCube 3D visualizaton tool. ]