BurnSim Exit Diameter question...

[Tad]

Maybe it's a simple answer but I can't seem to figure it out. If I have calculated my appropriate nozzle throat size for a proper KN range based on my bates grain set-up, and I obtain the proper exit diameter from BurnSim, how do I calculate the distance from throat to nozzle end (exit diameter)? I say this because I am making my own nozzles using an epoxied cone of paper. By changing the diameter of the paper (say 6 inch diameter cut to center radius) I fold it into the proper exit diameter but obviously the length from throat to exit varies based on the diameter of the circle being folded. I can have any diameter needed in order to obtain the proper distance. I just would like to know how do I determine the proper distance from nozzle throat to exit.
Hope that wasn't confusing.
Thanks.

 

[3stoogesrocketry]

4 to 1 expansion at a 30 degree angle will get you going.

 

[Tad]

So, when it says, "Expansion Ratio: 4.94", is that a 4.94 to 1 expansion at 30 degree angle?

 

[prfesser]

If I understand correctly, you are looking for the distance A:


The half-angle of the exit cone is 15 degrees. The distance O is 1/2 * (exit dia - throat dia)

tan(15) = O / A, so A = O / tan(15) or A = [1/2 * (exit dia - throat dia)] / tan(15)

Yes, a 4.94 to 1 expansion at 30 deg whole-angle.

Best -- Terry

 

[Tad]

If I understand correctly, you are looking for the distance A:
View attachment 441085

The half-angle of the exit cone is 15 degrees. The distance O is 1/2 * (exit dia - throat dia)

tan(15) = O / A, so A = O / tan(15) or A = [1/2 * (exit dia - throat dia)] / tan(15)

Yes, a 4.94 to 1 expansion at 30 deg whole-angle.

Best -- Terry

Thank you so much, Terry for the equation. If my throat diameter is .5625" and my nozzle exit diameter is 1.25", did I do my math correctly with A = 1.283 inches?

 

[prfesser]

Thank you so much, Terry for the equation. If my throat diameter is .5625" and my nozzle exit diameter is 1.25", did I do my math correctly with A = 1.283 inches?

That's what I get too. Well done!

 

[Tad]

That's what I get too. Well done!

Awesome! Thank you so much, professor



So, last question. The 4.94 to 1 expansion ratio. How do I use that info? Does that mean that if I needed to have a nozzle that is longer than 1.283 inches, I use the (roughly) 5:1 at 30 degrees ratio to expand the nozzle length for a longer nozzle? Or is the 1.283 inch length the most efficient length for the nozzle throat I chose. Just don't know how to use or incorporate the 4.94 to 1 expansion ratio. Thank you so much for your kind attention.

 

[prfesser]

As I point out in ECP, the expansion ratio is non-critical. The difference between perfect expansion at atmospheric pressure (say, 5:1 for a particular propellant at a particular pressure) and a slightly lower or higher expansion ration (4:1 or 6:1 under the same conditions) doesn't affect much beyond Isp, and even that isn't affected very much. Perhaps 1-2%. Other concerns are far more important.

 

[Tad]

As I point out in ECP, the expansion ratio is non-critical. The difference between perfect expansion at atmospheric pressure (say, 5:1 for a particular propellant at a particular pressure) and a slightly lower or higher expansion ration (4:1 or 6:1 under the same conditions) doesn't affect much beyond Isp, and even that isn't affected very much. Perhaps 1-2%. Other concerns are far more important.

Very well. thank you once again.

Have a great weekend.