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Tools for Computing the CP of Model Rocketsby Lynn Kissel, LUNAR# 009A rocket stabilized with fins generally requires that the CP (center of pressure) be located aft of the CG (center of gravity). While it is fairly easy to experimentally locate the prelaunch CG (by finding the point where the prepped rocket "balances" on a knife edge, or by suspending from a string, for example), measurement of the CP is more difficult - a wind tunnel of sufficient quality to measure the CP is a tool that is not usually available to most rocketeers. Fortunately, we have access to programs that let us easily estimate the CP of our creations. We now understand that the CP of the rocket changes with varying angle of attack. The angle of attack is the angle between the centerline of the rocket and the relative wind - the air flow relative to the rocket caused by the motion of the rocket and any movement of the air due to winds or other atmospheric conditions. Generally, it is believed that the CP moves aft as the angle of attack increases, tending to decrease the stability of a rocket as it is buffeted by lateral winds. As a general rule of thumb, model rockets are often designed with the CP 1-2 calibers (body diameters) or more aft of the CG as a safety margin. A rocket is particularly vulnerable to this wind-generated instability as it leaves the launch rod or tower, when its speed is still relatively slow. Depending on relative positions of the CP and CG, the rocket will tend to "weathercock" and fly up wind (if its stable), or it will tend to loop and crash down wind (if its unstable). A good analysis of this subject has been published in the March, 1998 issue of High Power Rocketry ("Wind Caused Instability," by Bob Dahlquist, p. 17). I had a vividly painful experience of wind caused instability on August 10, 1995, when I launched Scorpius (a PML Io, with an added payload section) in an 18 mph wind with a low-thrust F22 "black jack" motor. The disaster, which created my second powdered altimeter-in-a-bag, is described in more detail in "The Phoenix Altimeter"
Fortunately for us, methods exist to allow us to estimate the CP of a rocket for 0-10° and 90° angles of attack. For 90° angle of attack (not a mode wherein most of us want our rockets to be flying), the cardboard cutout method is an effective low-tech approach - a cutout of the lateral (side-ways) outline of the rocket is made and the CG of this cutout is your estimate of the 90° angle of attack CP. Some CP programs can also compute this value numerically. The real breakthrough in designing stable rockets came in 1966. Jim Barrowman, a NASA aerospace engineer developed a series of equations for estimating the small-angle-of-attack CP which have become the basis for most current estimates of the CP used by rocketeers. These equations were subsequently published in 1970 as Centuri TIR-33. This report, which has long been out of print, has been reprinted in the March, 1998 issue of High Power Rocketry ("Centuri TIR-33: Calculating the Center of Pressure of a Model Rocket," by Jim Barrowman, p. 74). It is important to remember that the Barrowman equations make seven assumptions that can severely restrict their validity (near 0° angle of attack; speed much less than speed of sound; smooth air flow; rocket thin and long; nose comes smoothly to point; rocket is axially symmetric; fins are thin flat plates). The Barrowman equations are not valid for non-axially symmetric models (such as boost gliders and the rocket from It! The Terror from Beyond Space shown elsewhere in this issue), and for transonic flights. A number of commercial, shareware and freeware computer programs are now readily available to aid in rocket design. The Rocketry Online web site has pointers to over a dozen programs that can simulate flights, model motors, compute CP/CG and otherwise support rocket design at
Two programs that compute CP/CG have caught my attention. VCP is a free program for Windows-based computers that is great for computing CP based on the Barrowman equations
VCP can support one-, two- or three-stage rockets. One really nice feature is the ability to enter data in mixed units; millimeters here, fractional inches there. VCP automatically converts all your input to the units that you've selected. A quirk (or feature) of VCP is that distances are measured relative to the aft of a component - the main reference point is the aft of the sustainer stage. A graphical display of your input is built up as you go, allowing you to visually check the validity of your input. RockSim 2.0 from Apogee is another interesting program. Although it isn't free, the $35 cost is not too high, and a demo version can be downloaded for free from
RockSim 2.0 claims to be a complete design program, computing not only CP/CG, but it also produces flight simulations, aids design of recovery systems, outputs templates for fin construction, and more. Some particularly nice features of RockSim 2.0 are that it contains an extensive library of predesigned parts, and you can add your own parts to the library. It also has some intelligence about materials - it has default properties for lots of materials such as balsa, basswood, paper, and plastics, so that it can estimate the mass and CG of new custom components based on their dimensions and composition. A graphical display is built up as you add components to your design, allowing for visual verification of your input. RockSim 2.0 utilizes a new "Fossey/RockSim" stability technique that claims to go beyond the Barrowman predictions, which are also computed by the code. I'm not aware of another CP program that claims to go substantially beyond the Barrowman equations. Unfortunately, all the CP programs that I've seen permit the design of only symmetric rockets with 3 or more fins. I'm not sure how well one could compute the CP for highly asymmetric designs (such as the spaceship from It!). The Barrowman equations for fins scale with the number of fins. But, would one get reasonable CP estimates using these equations for 2 or 1 fins? You can watch my flight of It! at the May launch and we'll both learn if it is stable! Copyright © 1998 by LUNAR, All rights reserved. Information date: May 8, 1998 lk |