question on center of pressure

[rocketsonly]

Hey. I'm currently working on a science fair project at my school dealing with how fin shapes effect the rocket's stability/height. Everything is going to be controlled as close as possible (stability calibers, temperature, wind speed, etc.). So I just finished calculating all my fin shapes which are regular geometric shapes (semi cirle, equilaterial triangle, square, semi hexagon). Here are the fin root chords for each type:

semi circle - 6.88 cm
equilateral trangle - 4.066
square - 3.0152
semi hexagon - 7.848

I can give the other lengths if you all want any. But why do these chord length vary by so much?! They all have the same exact (actually, with in .001 cm) CP distance from nose cone!

Thanks,
Matthew

 

[slim_t]

That's a very good question.
If I figured everything correctly based on your dimensions, the semicircle and semihexagon are close to twice the size of the triangle and square. If this is correct, I don't know how the CP would be the same, unless you have reached a point where making the fins larger just doesn't change anything much.
Have you checked the results of a smaller semicircle?
Try one close to half it's current size and see if it moves your CP.

When you post again, give us some details of the rocket itself.
I'm sure others will jump in on this soon, so we'll get it figured out somehow.

Some shapes can use their surface area more efficiently than others. For instance, fins that are swept back could be smaller than fins that are swept forward and still have the same effect, because of the leverage they have on the rocket.

But the shapes your looking at should be able to have very similar sizes and have the same CP, but they will have significant differences in the amount of drag induced on the rocket, thus affecting height and speed.

Tim

 

[rocketsonly]

Yea, I just checked all the dimensions for the fins again. When reducing the size of a semi hexagon and semi circle the CP moves dramatically. So according to the Barrowman Equations, the CP still remains the same although a set of fins is almost doubled those of another set of fins.

About the rocket. (note, all measurements are in cm)
Tube diameter - 4.158 cm (BT-60)
Tube length - 48.35
Nose cone length - 6.35 (orgive, very similiar, if not exact, to nose found on Estes Baby Bertha)

The rear ends of the four fins are flush with the end of the tube. Once I have made all the fins produce the same CP on the body, I will play around with some weights in order to make the CG and overall weight of the rocket the same on each rocket (yes, it will take a while). I don't know the exact weight of the rocket, but pretty much it's all the standard components (body tube, engine mounts, etc.), but with a PerfectFlite recording only altimeter near the top of the rocket, placed inside a centered BT-20/engine tube. The fins will be made of 1/8 inch balsa wood, I should have used 1/16 instead , too late to buy more wood. Nose is also made of balsa wood. Body tube won't be painted. Hmm.. I believe that's it. Let me know if you all would like anymore information!

Thanks,
Matthew

 

[slim_t]

This really doesn't make any sense to me yet.
If you look at the triangle and the semihexagon:
The semihexagon is nearly 3x the size of the triangle, and the triangle will fit inside the semihexagon.
So if you started with the semihexagon and then trimmed material away until you got the triangle, how could the Cp stay the same?

Anyone?

Tim

I've got to go play with rocksim now.

 

[rocketsonly]

Yea, I thought something was wrong when I did the equations. So I did it countless times more to make sure everything was right, I even made sure all the formulas were right in the Microsoft Excel calculator thing guy made online! PLEASE HELP!
-Matthew

 

[Elbmod]

surely its the area of the shapes you should be considering not individual lengths.

IIRC the CP is the position where the turning force caused by air moving over the rocket is balanced. Beacuase the fins have larger areas than the NC it tends to be more rearward. I suggect you calculate areasof the shapes and compare them.

 

[rocketsonly]

Okay, here's what happens when you calculate the surface area of each fin.

Semi circle - 18.588 cm2
Equilateral triangle - 7.159
Square - 9.091
Semi hexagon - 20.002

Now, that's when you only find the lateral area of one side, double it and you will find the complete lateral area for each fin.

Semi circle - 37.176
Equilateral triangle - 14.318
Square - 18.182
Semi hexagon - 40.004

Any ideas?

Thanks,
Matthew

 

[Elbmod]

are the fins in the same place on the rocket i.e. same distance from nose cone to leading edge of the fins?

 

[rocketsonly]

Hey! Smart thinking! That might be the reason, I'll check it out in a few minutes. But no, all the fins have their rear end flush with the bottom of the body tube. Since each fin has a differentfin root chord, their leading edge is at a different distance from the nose cone. I'll let you guys know what happens when I move the larger fins up a little!
-Matthew

 

[slim_t]

OK, I think I know what's going on.
The size of your body tube is very large relative to the size of the fins.
Even though you increase the fins size, it is a very small change to the overall area of the whole rocket.
Your CP should change, but it may be so small a change that you won't see it unless you carry your decimal place out alot farther.
You can try that easily if your using Excel.

I tried an exagerated case in Rocksim, and looked at the triangle versus the hexagon, and the CP did change, but it was only a fraction of an inch.

I think if you were to increase all the fins sizes to where they had a more significant change on the total area of the rocket, you would notice a change.

Still, what your dealing with as far as shape changing the stability of a rocket, it all boils down to surface area and the leverage that surface area has on the rocket.

I hope I didn't make things worse.

Draw all your parts to scale and you'll see what I'm talking about.

Tim

 

[Elbmod]

Ok I've been having a play with rocksim and just knocked up two models one with equilateral and one with ellipsoidal fins using your measurements...


the ellipsoidal fin yields data CG 17.708, CP 46.500
the equilateral fin yields data CG 15.867 CP 38.233

clearly if I continue on I'm going to get other results too but I thought the idea was to give the position of CP in the same place in which case the measurements are all nuts.

I think you need to check your calculations

 

[Elbmod]

oh! just had another thought...

CP is all about moments (turning forces) and so a small area a long way from the body tube could have as big an effect as a large area close to the body tube ( think of how you balance a see-saw with an elephant and a baby - elephant near pivot and baby a looooong way away)

You are probably also seeing an artifact of this process and a good reason why simulaiton programs are so useful!

 

[rocketsonly]

I just finished building my rockets, and will test them all today with A8-3 motors. I'll let you all know what happens...
-Matthew

 

[Elbmod]

don't forget the pictures...

 

[rocketsonly]

Okay, so I launched the semi circle fins and semi hexagon fins with A8-3 engines, at the lowest angle the launcher would permit because of very strong winds. Everything deployed perfectly, but I didn't dar to launch the smaller fins on the other two rockets. Especially on such a windy day like that! I'll get pictures up soon.
-Matthew

 

[slim_t]

Have you ever used Rocksim?
You can get the demo version free, and it lets you design rockets, but not save the files.
It would probably help alot with your experiment since you can do flight simulations to determine a predicted altitude.
A good experiment would be to measure the actual altitudes of your rockets and compare it to Rocksims calculations.

Just a suggestion.

Tim

 

[rocketsonly]

Okay thanks, I'll take a look at it.
-Matthew

 

[rocketsonly]

Pictures coming up soon! Please wait!
-Matthew