A Question about CP/CG
 

The following question was asked on RMR the other day:

I always forget? CP needs to be ahead of the CG? or vice versa?

The rule is, the CG needs to be between 1 and 2 body diameters, HIGHER (toward the nose cone) than the CP, Center of Pressure.

The center of mass (what we often also call the center of gravity, or CG) of an object is an imaginary point around which the mass of the object is balanced. This is where you could literally balance the rocket on your outstretched finger. Gravity affects the object the same way it would affect a single "point mass" at this same location, which simplifies quite a few physics problems. Another "feature" of the CG is that, if an unsupported object were to rotate, it would do so around the CG. This is the property that concerns us....

Similarly, you can think of the Center of Pressure, or CP, as the imaginary point at which all of the aerodynamic forces on the object are balanced.

Now, with just these two definitions, it's easy to see what we want to happen with our rockets.

If our rocket starts out traveling forward, the forces pushing on the CP of the rocket will be pushing backwards (drag will be trying to slow the rocket down, for instance).

Imagine a stick representing the rocket. Now, mount the stick on a pivot, so it can rotate. The pivot represents the CG. In flight, the rocket starts to wander off course (rotate the stick a bit). Now, if you push in a backwards direction on one place on the stick, what is the result in the following circumstances?

1) You push backwards at a point ahead of the pivot
2) You push backwards at the pivot
3) You push backwards at a point behind the pivot
 

If it helps you visualize it better, imaging having a toothpick hanging below the stick at the CP as you hold the stick by the pivot and slowly lower the toothpick into a river.

If the CP is ahead of the CG, the stick will pivot around backwards (unstable). If the CP is exactly at the CG, the stick might pivot, or it might not, or it might just wiggle around randomly as the current buffets it (neutral stability). If the CP is behind the CG, it will drag the stick back into a straight line with the current if it is disturbed (stable).

Another point to remember is, as your motor burns its fuel, the CG moves toward the nose, making the rocket more stable. This is why some unstable rockets stabilize in flight. Hope the rocket is pointing up when it does stabilize. WARNING: If you are flying a hybrid powered rocket, the CG moves BACKWARD (towards the CP) so you need to do your pre-flight CG check with an empty tank and a used fuel slug.

Your CG can be determined by balancing the rocket on your finger, or by suspending a loop of cord or light rope from the ceiling and balancing the rocket on it.

Your CP can be determined one of three ways:

• draw and cut out an exact scale flat image (like what you would see in a photograph) of your rocket and balance it on a ruler edge. This suggestion comes from the pre-Barrowman days.
• Measure every aspect of your rocket and manually work out the Barrowman calculations. This suggestion comes from the pre-computer days.
• (The easiest) Buy a copy of RockSim from Apogee Components and "build" your rocket there.

I have an Aerotech HV Arcas, which has a 2.6" diameter airframe. With the rocket loaded and ready to go to the pad, the CG should be between 2.6"-5.2" ahead (higher) of the CP.

If your CG is closer than 1 body diameter (or worse, CP/CG is inverted) your rocket will fly in every direction but up, presenting a danger to everybody in range. I saw a rocket like this once clear the rod, did a 270 degree turn and run along around the ground until burnout. This is NOT how you get the crowd to do the wave.

If your CG is greater than 2 diameters above your CP, then your rocket is OVERSTABLE. Egg-lofting rockets (especially the double egg lofters) are tremendously overstable. Camera rockets are also notoriously overstable. But the negative transitions inherent in these rocket designs compensate for the overstable condition. But for most 3FNC's, being overstable means if you have any wind at lift off, the rocket will turn itself heavily into the wind, going ballistic (or even horizontal) instead of vertical. This always results in you taking a long walk to recover.

If you do need to add nose weight, you need to do this carefully. The best way to do this is to make a loop of cord that you can balance the rocket with. Mark on the rocket the area where the CG needs to be (again, 1 to 2 body diameters ahead of the CP). Prepare the rocket normally for flight, including engine, wadding, parachute, etc., then suspend the rocket from the loop and find the CG. Tape one side of a sandwich baggie to the tip of the nose cone. Add a little weight, rebalance the rocket. Repeat until the CG is about 75% of the way to the 2 diameter limit. The reason for this is when you actually put the weight in the nose cone, the CG will move back (remember, right now it's hanging off the tip of the nose cone). Also remember that the adhesive you will use to keep the weight up there will also affect the CG by its own weight as well. As far as what to use for weight, there are many different mediums to choose from. You can shove modelers clay into the nose cone (roll it into a snake before inserting it into the nose cone), or drop heavy items in and cover them with expanding foam or epoxy. I have seen lead shot, sand and even small nuts and screws as the weight. NOTE: When adding epoxy into the nose cone, it is highly recommended that you hold the nose cone in a bucket of water during the process. Epoxy gets hot during the curing process and can melt/deform the nose cone.

.