Tangent Ogive math?

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McKailas Dad

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I am in the process of (attempting to) making a 4in ogive nose cone, 16.5" long, with a ~5:1 aspect ratio. (I guess that would be a 4.125:1 for a 16.5" length?)

The online calculators I tried were 'dead links'.

I tried the equations from Here, but couldn't figure it out. My math is extremely rusty...(ok, bad)

The 'simplest' equation I could find, that I could understand, was found in a PDF from David Stribling that I forgot where I found!

Radius = d(C2+.25)

Where d=base diameter
C=caliber (or aspect ratio)

Or R=4(17.01+.25)

So R=69.06?

Does that mean I would use a 34.53" 'arm' to draw the radius of my nose cone?

If it were a 5:1...

R=4(25+.25)

So R=101?

Would that be a 101" 'arm' or a 50.5" one?

I hope you understand the question, I'm not even sure I do......

How long of an 'arm' would I need to make to draw the radius for a 4" NC with a 4.125 or 5:1 aspect ratio? (ideal length 16.5")

Thanks (alot...)
 
Pm me your E-mail. I got just what you need. Too large a pdf to post. Design any size, any type cone.

CJ
 
In general, the radius is going to be the length of the "arm" you'd use to trace out the nose shape. For a 4" nosecone with a length of 16.5" you would want to use an arm length of 69.06 inches. You can get the math for this starting with the equation of a circle:

(x-a)^2 + (y-b)^2 = r^2

Where 'a' is the x position of the center of the circle, 'b' is the y position, and 'r' is the radius. You can construct a circle that passes through the points (0,0), (D/2, L), and has a center at (R, 0), where 'D' is the diameter of the nose, 'L' is the length, and 'R' is the radius that you want to solve for (see attached image). This would describe a circle that is tangent to the y axis (a tangent ogive) and has a center on the x axis. The point (D/2, L) represents the tip of the nose where it appears on the circle.

Substituting all that in, you end up with an equation like:

(x-R)^2 + y^2 = R^2

Plugging in the desired point (D/2, L) you can reduce the equation down and solve for the radius R, which would be:

R = 0.25*D + (L^2)/D

So you can just plug in your desired length and diameter and it will generate the proper radius that can be used to sketch out the ogive shape. When you define aspect ratio C = L/D you can see how you end up with the equation you found.

If you want a 5:1 ogive with a diameter of 4" (and therefore L = 20") you would want a radius, and thus arm length, of 101 inches. For the 16.5" long ogive it would be 69.0625 inches.

I hope this helps.

ogive.png
 
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By the way if you download VCP [google it] you just enter the data, and it will print out the desired profile. One of the PDF's is the data from VCP.

Here it is. Does fin marking wraps, transitions fins, the whole she bang & will print out full size profiles of all components. Let me know how you make out.

https://v-serv.com/vcp/
 
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I dunno about you jeff...I've been happy to use the 'TLAR'* method for my nosecones :).
*tlar = that looks about right
rex
 
Jim, thanks for the links/PDFs. Those were some of the ones I ran across and didn't bookmark them.

Unfortunately, the VCP program doesn't work on Vista. Is there a 64bit version? I think there is a way to run 32bit on my 64bit, but I don't have a clue on how to do that, either. :pc: :rolleyes:

Microspeed, thanks for the equations, and helping to make it easier for me to comprehend...

It's times like this that I wish I would have paid more attention (i.e.; not skipped out of class). As much as I don't like math, it sure does come in handy. :eek:

It would be great if someone could come up with (another) online ogive calculator. ;):D
 
Rex R said:
I dunno about you jeff...I've been happy to use the 'TLAR'* method for my nosecones .
*tlar = that looks about right

Yea, yea, I know...

I could simply buy a 4" NC, but I have to make things difficult.

After all the messing around with this project, I'm sure I'll be beyond the ~$30 that would have had one in my hand. I like the Madcow one, here.

Partial reason being I'm working with non-standard BT sizes, AKA 'mailing tubes' (4" Uline). At least I got the tubes for free......
 
The ogive derivation mentioned above is found here.

There is also a spreadsheet there that Ken Payza put together to figure different nose cone shapes....
 
Rocketguy101, I couldn't figure out why your name was so familiar.....

You are David Stribling! (Your PDF was very helpful, thanks!)

Apparently they are blocked out because Yahoo GeoCities "has closed"....?
 
The page is full of empty boxes, why?
The formulas on my original (geocities) webpage were figures. Before geocities shut down the free web pages, I found the jimdo website that said they would convert a geocities page automatically. Right after they converted it, I checked and everything looked great. Unfortunately, I didn't check the figure links, which still pointed to geocities. So, when geocities took the free site down, the broken link boxes appeared. I could not find an easy way to get the figures to appear because jimdo is based on some java or scripted language and makes it nearly impossible to link to a picture that is stored on jimdo. you can basically recode the whole page, but I didn't have time to do all that.

Say what you will about geocities, but it was fairly easy to create a simple html page, load up a bunch of images and point to them.

So, I created the pdf to present the formulas and figures.
 
Not the easiest thing to do, but with these sorts of formulas you cant enter them into Excel and use the chart function to draw the nose cone. Just have to be aware of the fact that your chart needs to be proportioned properly in order for your nose cone to not be distorted.
 
I would like to try to make some type of jig, with a variable length arm for drawing/carving different radius (plural). Again, similar to something I ran across in my Googling that I forgot to bookmark.

I have a tendency to do things that are out of the norm. Why buy a ~$30 nose cone, when I could make my own for twice the price? :rolleyes:

...because then I will know how!


Thanks again for all the help, I really do appreciate it. :eek:
 
Why buy a ~$30 nose cone, when I could make my own for twice the price?... because then I will know how!

Jeff, after you get it figured out, you can show the rest of use how to do it. I have a project on the back burner that requires a homemade nosecone (full-scale Patriot. The nosecone is 44" tall and 16" in diameter.)
 
Guys, I am working on a data pack for a project and I need help figuring out a diameter at a given point on the nose cone . . .

Here are the full-size prototype's dimensions for the nose cone:

It is a 5:1 TANGENT OGIVE ( AEROBEE - 350 )

DIAMETER : 22.0"
LENGTH : 110.0"
RADIUS OF OGIVE : UNKNOWN

I need to know what the diameter of the nose cone is, at a point 6.140" down from the tip . . . That would be 103.860" up from the base.

Any help is greatly appreciated !

Thanks !
 
Guys, I am working on a data pack for a project and I need help figuring out a diameter at a given point on the nose cone . . .

Here are the full-size prototype's dimensions for the nose cone:

It is a 5:1 TANGENT OGIVE ( AEROBEE - 350 )

DIAMETER : 22.0"
LENGTH : 110.0"
RADIUS OF OGIVE : UNKNOWN

I need to know what the diameter of the nose cone is, at a point 6.140" down from the tip . . . That would be 103.860" up from the base.

Any help is greatly appreciated !

Thanks !

get the doc on my ogive nose cone page

equation 1A should give you what you need, 2y will be the diameter at station x. you have d, and C will be L/d
 
A couple years ago I needed an ogive so I plotted it in excel. Just plug in a few values and it plots it for you. You could either scale the graph and print it to whatever dimensions you need and then transfer the curve to your part and cut it out. You could also plot these values or the equation in a CAD program. If you use a 'good' program like Solid Edge, you can upload an entire excel sheet with just the x, y, z values and it'll plot it for you and you can extrude your part, send it to CAM and CNC it. Or whatever you want...

The files are attached.

EDIT: Sounds like rocketguy101 (post above me) has pretty much the same deal. So whatever works for you! :p

View attachment Ogive Transition Equation.xlsx

View attachment Ogive Nose cone.xlsx
 
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