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Drag coefficients as a function of velocity

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Drag coefficients as a function of velocity

Unread postAuthor: btrettel » Mon Dec 08, 2008 3:47 pm

To help me design a more efficient pneumatic gun I have been doing a little bit of ballistic modeling. The goal is to get a certain range with as little gas consumption as possible.

Let me note immediately that I'm not an aerodynamicist. I am a mechanical engineering student, but I'm only a sophomore. I haven't found basic external ballistics to be exceedingly difficult but it is new to me.

Models of the internal ballistics of a pneumatic gun are rather well developed and I intend to study them later. However, I'm having a difficult time finding information about the drag coefficients of a cylinder and a cylinder with a more aerodynamic nose. I can find drag coefficients for the shapes I'm interested in at different aspect ratios, but I know nothing about the Reynolds number or velocity (which essentially would have the same meaning here) that goes along with those drag coefficients. I've read many times that the drag coefficients vary greatly at low speeds/Reynolds numbers, so I'm unsure how reasonable it would be to use a constant drag coefficient.

For those who might wonder, my current exterior ballistics model makes many assumptions but seems reasonable for what I intend to do. For that reason I doubt this would be useful for other spud gunners. The gun I intend to use this analysis on will be a Nerf gun, so I can make many assumptions that others couldn't make about other projectiles because the center of gravity is so far ahead of the center of pressure. That essentially means the dart will be very stable over the entire trajectory because any deviation in the angle of attack will create a relatively large torque about the center of gravity, pushing the dart back to zero angle of attack.

My model essentially is a system of equations of the force of gravity and drag on a point mass. I reduced the two second order non-linear ODEs to a system of 4 first order non-linear ODEs and used the basic 4th order Runge-Kutta method to approximate the solution. The results seem reasonable for a constant Cd, but I'm sure once I try to fit some actual data to the model I'll notice some problems.

Any specifics or perhaps a description of the trend would be very helpful. At worst I suppose I'll have to figure out how the Cd varies with velocity after the testing I plan to do. Having a decent idea of what to expect can't hurt.
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Re: Drag coefficients as a function of velocity

Unread postAuthor: D_Hall » Mon Dec 08, 2008 9:24 pm

Disclaimer: Once upon a time I used to write ballistic/kinematic codes for the DoD, however, being in the weapons world I don't believe I ever studied anything that was moving at less than Mach 0.3ish. Thus, my experience may be totally irrelevant to the scenario being asked about.

btrettel wrote:However, I'm having a difficult time finding information about the drag coefficients of a cylinder and a cylinder with a more aerodynamic nose.

There is a semi-empiracle code out there called "DATCOM". It was written by the USAF back in the 60s or 70s. By today's standards it's total crap.... But it should do exactly what you're trying to do and it's in the public domain. Look for it. Download it. Learn to use it. And all will be well in this world.... with the caveat that DATCOM was also written in the weapons world and as such it's EXTREME low-end velocity data may be suspect (or it may be just fine; I don't know!).

My model essentially is a system of equations of the force of gravity and drag on a point mass. I reduced the two second order non-linear ODEs to a system of 4 first order non-linear ODEs and used the basic 4th order Runge-Kutta method to approximate the solution. The results seem reasonable for a constant Cd, but I'm sure once I try to fit some actual data to the model I'll notice some problems.

This is one aspect of the modeling community that I always found amusing. Folks would get into heated arguments about whether a Runge Kutta was better than [whatever].... The whole while forgetting that the difference between the numerical methods might yield a 0.5% difference in the final numbers all while their drag data was only good to +/- 5%. Forrest through the trees, anyone?

In ohter words, your methodology is fine. Don't waste anymore time worrying about that.
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Unread postAuthor: btrettel » Mon Dec 08, 2008 9:56 pm

DATCOM sounds interesting. I'll look into it. Thanks. If I find anything interesting or figure out how to work it well I'll be sure to report back here.

I'll definitely compare it against data I measure myself as well to see how reasonable it is at the low speed end of the spectrum. Depending on whether or not I can make highly aerodynamic darts, I wouldn't expect speeds higher than 200 ft/s, so this is well below any actual weapon speeds. This goes back to my earlier problem.

Also, I've emailed some people who mentioned that they worked on Nerf darts with improved aerodynamics and they said they used computer modeling to improve the aerodynamics. This might lead somewhere good.

As for Runge-Kutta vs. others, any higher order method should be fine. Runge-Kutta (the simple 4th order one) converges towards the right answer much faster than the forward Euler method, so that's why I used it. You're right about the errors in the drag data which is why I'm likely not going to switch the method.

I'm actually not very worried about my model. I emailed a former Nerf engineer and she said the model she wrote took the same approach, which is reassuring to someone who barely knows what they're doing.
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Last edited by btrettel on Tue Dec 09, 2008 8:33 pm, edited 1 time in total.

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Unread postAuthor: Hotwired » Mon Dec 08, 2008 10:46 pm

Looks like this is it: http://www.holycows.net/datcom/
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Unread postAuthor: D_Hall » Tue Dec 09, 2008 1:18 am

Close, but not quite.

Digital DATCOM is not the same thing as Missile DATCOM. They're closely related, but they are not the same program.
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Unread postAuthor: btrettel » Tue Dec 09, 2008 8:29 am

Looks like I'll have to settle for Digital DATCOM because I can't find anything more than some discussions about where to get Missile DATCOM. If I'm missing something, please point it out, but as far as I can tell Missile DATCOM is either not available to the public or not available online.

I have found a Yahoo Group of people who use Digital DATCOM so I've asked about finding Missile DATCOM or if Digital DATCOME is a decent replacement: http://tech.groups.yahoo.com/group/digi ... essage/388

Edit: Ah, I think I've found the problem with Missile DATCOM: http://home.coosahs.net/dmarlowe/itar.htm

Edit again: Here's a response:

Ben

You might be able to use Airplane DATCOM (a.k.a. Datcom+), but you are probably dealing with some pretty low Reynolds numbers, and Datcom isn't too accurate down there. I don't know how accurate it is.

Bill


I suppose unless I can figure out where to get Missile DATCOM I'm back to empirical testing I do myself.
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Unread postAuthor: D_Hall » Tue Dec 09, 2008 9:26 am

Yeah, Missile DATCOM is (in theory) an ITAR item and as such it shouldn't be possible to just download, but I *KNOW* I've found it online in the past; it's just been long enough that I don't remember where.
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Unread postAuthor: btrettel » Sat Dec 13, 2008 11:57 am

My university's library finally dug up from storage an old book called "Aerodynamics of Bodies of Revolution", which again was meant for transonic or supersonic projectiles, but it should be helpful at the very least.

The book is available online for those who want to look at it, but it's heavy on the math and whoever scanned it could have used a higher resolution.

...I left this reply box open when I went to pick up the book. The book has a curve for Mach number vs Cd for a blunt cylinder on page 849. Lucky for me the curve seems to be relatively flat until about Mach 0.5. I'm sure the remainder of the book will be helpful in figuring out the basic relationship for other shapes as well as I don't intend to use a blunt cylinder due to the poor aerodynamics.

I'm not completely sure how applicable this data is because Nerf darts seem perform better than the coefficients I've seen reported on the internet predict but the trend probably will be the same.
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