I believe it's possible, and have written an Excel program to do it. Note that this method analyzes single-axis accelerometer data alone to produce two-dimensional trajectories. It does not use altimeter data to find the vertical component of velocity.Inertial data can be reconciled with altimeter data after the fact, however, and facilities (Graphs, statistics, and optimization) are provided for that purpose.
The program is called OVAA.xls. It is available free of charge in the PC downloads section of
See description below.
-Larry Curcio
OVAA.XLS VERSION 2.0 Copyright 5 August 2006 Larry Curcio
WHAT IT DOES OVAA stands for Off-Vertical Accelerometer Analysis. It exploits the observation that accelerometer data are unaffected by gravity. (See explanation below.) Thus, to a good approximation, accelerometer data measure the sum of thrust and drag accelerations along the longitudinal axis of the rocket. Vertical accelerometer analyzers plug these readings into a 1-dimensional trajectory simulator to produce a rendering of the trajectory, based on the assumption that the rocket's ascent is entirely vertical. OVAA plugs the readings into a two-dimensional trajectory simulator to cover off-vertical flights. For vertical flights, OVAA is entirely equivalent to a one-dimensional accelerometer analysis program.
OVAA.xls is a Visual Basic macro application in Microsoft Excel=99. It takes advantage of the Excel's spreadsheet, graphing, and optimizing facilities to provide a versatile environment for trajectory analysis. OVAA.xls is specifically designed for flight computers that take simultaneous inertial and barometric readings.
OVAA.xls has the following functions:
1) Finds altitude, throw distance, velocity, acceleration at each point; 2) Temperature-corrects barometric data; 3) Extracts thrust/time tables from inertial data; 4) Extracts drag coefficient/speed tables; 5) Evaluates goodness of fit between inertial and barometric altitudes; 6) Can find the launch angle that yields the best such fit 7) Provides a low-pass filter utility to reduce noise in Cd curves; and 8) Has a scratch area for ad-hoc computations and graphs.OVAA.xls provides the following graphs:
1) Inertial and Barometric Altitudes v Time during ascent 2) Inertial Altitude v Throw Distance during ascent 3) Velocity v Time during ascent 4) Acceleration v Time during ascent 5) Inertial - Barometric Altitude v Time during ascent 6) Thrust v Time 7) Drag Coefficient v SpeedDISCLAIMER No warranty of any kind is made for this program or the underlying OVAA method. Indeed, at this writing, the method is not substantiated by any formal research. The author takes no responsibility for its use. Decisions made on the basis of its output are made at the risk or the user alone. Off-vertical flights are also made at the risk of the user.
This program is intended for post-flight analysis, and not in-flight control. The underlying method may have control applications, but the author takes no responsibility for experiments based on such applications.
This program is not intended for use with rockets that are illegally constructed, transported, stored, or flown.
The author takes no responsibility for copies of this software that may be infected with viruses. Again, this program is used at the sole risk of the user.
CONTACT INFORMATION At this writing, OVAA analysis is brand new. I have precious little data to work with, and would appreciate hearing from you and sharing yours. I can be reached at
snipped-for-privacy@verizon.net
Two-dimensional analysis of single-axis data represents a new technology that can potentially extend the usefulness of existing products. Even though better technologies are emerging, the existing technologies are still substantially less expensive.
The development of such new technology is potentially advantageous to flight computer manufacturers, but the advantage is contingent upon established validity, and validity must be founded on data. For this reason, I am asking manufacturers of flight instrumentation to collect and share off-vertical data with me and with others.
Thanks and regards,
-Larry Curcio