After looking into your slides I have two questions.
1. Therorectically, because the flight is not vertical, I would also need to factor in the tilt angle of the rocket by adjusting the gravitational force as well right? (multiplying gravitational force with the cosine of tilt angle)
2. When calculating for Cd, do I need to also consider the compressibility effects on air density? Thank you.
Phrajphogate:
<< 1. Therorectically, because the flight is not vertical, I would also need to factor in the tilt angle of the rocket by adjusting the gravitational force as well right? (multiplying gravitational force with the cosine of tilt angle) >>
That is correct. You'll find it's a small correction for a nearly vertical flight, but if you have attitude data (pitch angle data) and/or flightpath angle data (based on vertical velocity and horizontal velocity data), then you can include the correction. If you were really arcing over on a trajectory for a lot of the flight, then you'll definitively need pitch attitude and/or flightpath angle measurements, which it sounds like you have.
I've not included the full set of equations here (I posted material previously prepared for the course), but basically, it's the equation of motion for a rocket.
In our Aerospace Vehicle Test Course rockets, we just had axial accelerometers and barometric altimeters. So, the equations presented were just for a straight-up flight. (This assumption is of course shown in the Charts.) We did do a secondary visual check of the flights, "were they basically straight-up?".
As noted previously, if you have a straight-up or nearly straight-up flight, the analysis technique works well. The question for smaller rockets is how small of an instrumentation package is available that has pitch attitude and/or flightpath angle measurements. It sounds like for your O Motor rocket you had the space for an instrumentation unit with the additional measurements. But for backing out CD for small rockets, you really don't need the additional measurements, you just need to measure axial acceleration, and you need to have a straight-up or nearly straight-up flight.
<< 2. When calculating for Cd, do I need to also consider the compressibility effects on air density? Thank you. >>
No. The Drag Equation using the Drag Coefficient (CD) uses the freestream density, the atmospheric density. (See Chart 3; in hindsight I should have added the subscript "infinity" for the atmospheric terms.) So, it is atmospheric density. You'll of course need to vary the atmospheric density with altitude.
Charles E. (Chuck) Rogers
Rogers Aeroscience