CP calculation disparity

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Sanjivino

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Hi,

I have just recently started building model rockets from scratch. They are small low power rockets.

When I measure the Centre of Presure for a rocket with the Barowman equation [I got a free Excel based software from the Internet], the CP is quite close to the tail of the rocket. For the same rocket, with the Cardbaord Silhouette method the CP is found a couple of centimeters forwards. In other words for the same model rocket the calculated CP is a few centimeters aft of the cardboard method.

Could some please explain why I am getting this disarity and which method should I rely on for the small rockets.

Thanks.

Sanjivino
 
I have found using software is usually easiest. There are paid for and free one. Keep in mind as well the equations we use make a number of assumptions about the rocket and how it will fly.
 
The cardboard cutout should not be used. It is only interesting from a historical perspective, and of little to no practical use compared to Barrowman.
 
+1 on the Apogee Peak of Flight Newsletter linked above, that explains it well.

To summarize very briefly here: the two methods are based on different assumptions. Barrowman equations are based on the rocket flying nose first into the wind, at zero-deg angle of attack. The cardboard method is based on the rocket flying sideways to the wind, at 90-deg angle of attack. The cardboard method is more conservative, if you use that to determine the balance point of your model, yes it will be a stable design, but more stable than is needed, i.e. it may require you to add weight that you don't really need to the nose, which might not be so important just for fun recreational non-contest flying, but as a consequence it also may tend to weathervane into the wind much more than desired.
 
I was trying to think of a situation where the added nose weight required by the cardboard method might be a big issue for the recreational scratch builder: say you are already at the weight limit of a particular engine size at a given engine-mount/body-tube diameter. The cardboard CP location may tell you that nose weight is needed, but if you add that weight, then you won't be fast enough at the end of the launch rod for safe/stable flight due to the added weight. So, if you are already at the max weight limit for a 18mm C-size motor, then the overly conservative cardboard method may tell you that you are stuck with either an unstable or too heavy design, erroneously. So, adding some weight as prescribed with that method might not just be a matter of degraded max altitude performance.
 
The cardboard cutout should not be used. It is only interesting from a historical perspective, and of little to no practical use compared to Barrowman.

While your comment above can be true for most of the typical HPR or smaller 3F&NC model rockets, your reasoning is totally incorrect when speaking of airframes that do not fit symmetic simple outlines. The cardboard cutout method is still a very useful CP-CG working method with asymmetic PMC and Odd-Roc building where the typical shapes do not fit within the Barrowman confines.

To more accurately answer the OP question concerning why the two methods come up with different locations. The Barrowman equations give a more mathmatically correct location based on the combination of all generally symmetric areodynamic charactistics of the vehicles parts.
To be sure the Cardboard cutout method gives a very conservative estimate of the LCP (Lateral Center of Pressure) based on the outline configuration of the vehicle Assuming 90 angle of attach. The Method can be used in all forms of rocketry to this day AS A Starting POINT to establish a good CG for the model to insure stable flight based on its balance point LCP. The Cardboard Cutout method is generally used in conjunction with a Swing test to ensure the proper CG 1 to 1.5caliber Static margin location.
 
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+1 on the Apogee Peak of Flight Newsletter linked above, that explains it well.

To summarize very briefly here: the two methods are based on different assumptions. Barrowman equations are based on the rocket flying nose first into the wind, at zero-deg angle of attack. The cardboard method is based on the rocket flying sideways to the wind, at 90-deg angle of attack. The cardboard method is more conservative, if you use that to determine the balance point of your model, yes it will be a stable design, but more stable than is needed, i.e. it may require you to add weight that you don't really need to the nose, which might not be so important just for fun recreational non-contest flying, but as a consequence it also may tend to weathervane into the wind much more than desired.

This is a good explanation.

These are two different methods, so they're going to indicate two different points. The cardboard cutout method is actually the center of lateral area, which coincides with the CP in the worst-case scenario, that being, at a 90 degree angle of attack to the direction of flight (IOW, rocket nose pointing 90 degrees to the direction of flight, or "flying sideways"). In reality, you should never see such an enormous angle of attack, and since CP is a FLUID point, NOT a FIXED point (it moves around based on the angle of attack, the airspeed, air density, and a lot of other factors in flight) technically speaking this is the furthest forward the CP should move in flight, because a 90 degree angle of attack is the "worst possible scenario" (and will move the CP the furthest forward). IOW, the *real* CP should always be BEHIND where the cardboard cutout method indicates... SO, if the rocket has at least a 1 caliber stability (one body diameter between the actual measured CG and the cardboard cutout CP, it should (theoretically at least) always be stable.

Now, the Barrowman equations are just ONE way to calculate the CP... they rely on certain simplifying 'assumptions' that might not apply to the rocket design, especially when it gets more complex and deviates from the "3FNC" designs... The Barrowman equations are the starting point for all the other methods, which then use their own specific assumptions and "refinements" to "more accurately" figure out the CP (more closely estimate it). The RockSim method (in the RockSim simulation program) makes certain refinements and different assumptions and methods to determine the CP; one can see this by switching between the three methods (cardboard cutout/center of lateral area, Barrowman method, RockSim method) and comparing the calculated CP points from each. The Barrowman and Rocksim methods are usually pretty darn close to each other, depending on how 'different' the rocket design is from the "3FNC" type rocket shapes assumed in the Barrowman equations.

It's good to compare methods.. if you have the tools available to you, avail yourself of them. CP is something that can never *quite* be nailed down to 100% accuracy anyway, since it moves around depending on the dynamics of the rocket in flight. That's why regardless of what method you use, they are all still basically, at heart, approximations.

Later! OL JR :)
 
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