Gap Staging Vent Hole Diameters

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lakeroadster

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Is there a recommended size for vent holes when gap staging?

I know the hole diameter should be based on motor size and tube volume, but is there some empirical formula for this or are you folks just swagging it?

I'm designing a 2 stage Red Nova and using (2) 1/4" vent holes in the BT-50H motor tube, with (2) 1/4" vent holes in the outer BT-60 body tube. Largest booster motor will be a D12-0. Think those 1/4" holes are about right?

Red Nova Flutter Dwg Sht 1 of 10 Rev 0.jpgRed Nova Flutter Dwg Sht 5 of 10 Rev 0.jpgRed Nova Flutter Dwg Sht 6 of 10 Rev 0.jpg
 
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David Schwantz

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Hi Lake. I have 3 3/16" holes in mine. Also a D12-0. Your 1/4" holes volume wise should be ok. I ran the 3 holes as one is between each fin. Just think it looks cleaner that way. Good luck.
 

lakeroadster

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Hi Lake. I have 3 3/16" holes in mine. Also a D12-0. Your 1/4" holes volume wise should be ok. I ran the 3 holes as one is between each fin. Just think it looks cleaner that way. Good luck.
Thanks David.

On your example above,
  1. What is the distance from the ejection end of the booster motor to the nozzle of the sustainer motor?
  2. Is the motor tube a BT-50?

I ask because one would think that the calculation for sizing the vent holes should take the total trapped air volume into consideration.

Make sense?
 
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GlenP

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Is there a recommended size for vent holes when gap staging?

I know the hole diameter should be based on motor size and tube volume, but is there some empirical formula for this or are you folks just swagging it?

I'm designing a 2 stage Red Nova and using (2) 1/4" vent holes in the BT-50H motor tube, with (2) 1/4" vent holes in the outer BT-60 body tube. Largest booster motor will be a D12-0. Think those 1/4" holes are about right?

View attachment 491625View attachment 491626View attachment 491627
Do you have a drawing of the sustainer and it’s motor mount when fitted to that booster yet?
 

lakeroadster

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Do you have a drawing of the sustainer and it’s motor mount when fitted to that booster yet?
The sustainer motor fits into the end of the booster motor tube. The motor tube and the outer body tube both have (2) 1/4" dia. holes. There's about 3-1/2" from the booster motor to the sustainer motor.

Red Nova Flutter Dwg Sht 6 of 10 Rev 0.jpg

Red Nova Flutter Dwg Sht 2 of 10 Rev 0.jpg
 

GlenP

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Yeah, that is probably about a long enough gap distance where you need to vent. If they were any closer, like 2" or less for a 24mm booster, I would guess it could get the whole air volume plenty hot to ignite the sustainer, but safer to vent to make sure the booster does not pop itself off before the sustainer lights. Nice pictures!
 

lakeroadster

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Yeah, that is probably about a long enough gap distance where you need to vent. If they were any closer, like 2" or less for a 24mm booster, I would guess it could get the whole air volume plenty hot to ignite the sustainer, but safer to vent to make sure the booster does not pop itself off before the sustainer lights. Nice pictures!
Thanks Glen
 

jqavins

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Your calculations in post #3 confuse me. But before I get into that, the premise of those calculations is incomplete. The purpose of the vent holes is not just to prevent premature separation, but to allow cold air to clear the tube making it possible for the hot air to reach the sustainer motor. For that reason, the holes are often placed even or nearly even with the the sustainer nozzle, with regardless of the distance that is above the booster.

Now to the calculation. The final figure in the upper boxed portion is the volume of tube in the two imches between the motors. The first figure in the lines between the boxes seems to refer to the same thing, but is double the figure above it. Where does this factor of two come from?

V2, the length of tube times vent hole area, doesn't seem to me to represent any physical thing. Where does this come from? Or in other words, why multiply these things (vent hole area and tube length) and what does it mean?

Why 0.001 psi for atmospheric pressure? Shouldn't it be either about 14.5 psia or exactly zero psig? What's "nearly zero" got to do with it?

How did you arrive at the value of P2? Is it somehow from the quantity of gas in the charge? If not, where is said quantity taken into account?
 

BABAR

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Thanks David.

On your example above,
  1. What is the distance from the ejection end of the booster motor to the nozzle of the sustainer motor?
  2. Is the motor tube a BT-50?

I ask because one would think that the calculation for sizing the vent holes should take the total trapped air volume into consideration.

Make sense?

Updated based on input in post #4 by @David Schwantz

View attachment 491695
I will try not to mix up BOOSTER and SUSTAINER here!

I am curious where you get the P2 number “Pressure Increase Due to Booster” as I expect that to depend on differences not just of motor SIZE but also manufacturer (Estes BP motors’ ejection charges often described on this forum as “shotgun” power, presumably much more energetic than the older Quest Motors), diameter of the tubing BETWEEN the booster forward end and the sustainer nozzle (again IMO if you aren’t going minimum diameter you SHOULD extend the mount forward nearly to the nozzle of the SUSTAINER motor) and the length of the tube. For anything less than the shortest gap I expect the residual volume within the motor casing forward of the propellant would be negligible.

Where did you get the 0.018 PSI number?

also, since the model pic I posted, a WAC Corporal on a Tiny Tim booster, has a (for all practical purposes) completely open chamber between the booster and sustainer I think I have demonstrated you cannot make the holes too big.

yes, you COULD make the holes too small, but that begs the question, “who cares?” Meaning just put two Hole punch size holes in for anything other than the longest gaps (over 48”, and to my knowledge nobody but me is currently nutty enough to do this) and call it good. True, if you put the holes in the OUTSIDE (which is your only option on minimum diameter if you have any significant gap) than “too large” a hole does reduce efficiency (max velocity and altitude) by unnecessary drag. However, if your goal is maximum efficiently using black powder motors, first you don’t want to use gap staging, you want the shortest booster you can get away with and do direct staging which needs NO holes. Second, if you are going non-minimum diameter, your best bet is to use a chimney or stuffer extended motor mount to get close to the SUSTAINER nozzle (yup, checked, SUSTAINER, lol), then vent BACKWARD between rings, with holes or notches in rings as large as possible (again, limits are structural integrity of the rings, which I think means you have LOTS of leeway to go large), so again the argument seems moot, make big holes.

my 50+ inch gaps stage used BT-50 outer tube with a 24mm D12-0, I used a BT-20 chimney to duct the gas forward to an 18mm A8-3 mounted in a BT-50 tube. I used three paper punch holes.

@jqavins , I think you mentioned in a post the same idea of using a narrower chimney or stuffer than the actual motor mount, like I did above. I obviously agree with you, as it is what I routinely do. It reduces the VOLUME of dispersal of the ejection charge between motors, hopefully increasing the chance of enough hot gas reaching the SUSTAINER (yes SUSTAINER) nozzle. As well as guiding the gas nearly directly to the nozzle. When I get to gapping over 15 inches I start thinking this way.

for relatively short gaps, again IT MAY NOT MATTER, as the WAC Corporal/Tiny Tim combo works with essentially a wide open space between the motors, but I think when you get beyond say 15 inches you have to start working a bit harder. I do 15 inches of gap using 18mm motors routinely with minimum diameter with no chimney or stuffer, without problems. I punch two regular hole punch holes on each side of the forward end of the BOOSTER, just aft of where the SUSTAINER motor nests.

A caveat, when your ejection charge from one size motor is vented or ducted by a smaller diameter tube, my experience has been HEAT is heavily concentreated on the first few inches just forward of the BOOSTER (yes BOOSTER) motor. I have experienced burn through here, and the bad thing is it is internal so you can’t see it. my experience has been it can happen fast, after only 1 or 2 flights. My routine now is to put rolled up aluminum can glued in here and smear epoxy on the adapter ring to prevent burn through. So far no problems.

for anyone thinking of gapping longer than 6” or so with black powder, you have to consider a serious second problem, booster recovery. Short boosters recovery by tumble classically, I sometimes use horizontal spin up to 18”. Beyond that length (and likely anything over 6” if you DON‘T use horizontal spin) the BOOSTER is likely STILL stable AFTER SEPARATION (not a good thing) and often will come down ballistic, nose first. Not as dangerous to person or vehicles or other property as there is no nose cone, but as you can imagine not so good for the booster (and for those at club launches, earns you a probable stink eye from the LSO!)

anybody interested PM me for ideas on solving this issue for non-electronic black powder extreme long gap staging booster recovery, I have a few solutions, there are likely many more and better ones I haven’t thought of.
 
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lakeroadster

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Nice to see some ideas and questions being tossed about on this. I'll try to answer questions later tonight.

I'm no rocket scientist, my entire concept may be total hogwash.. my goal is to develop some equation to determine vent hole size, determined by actual rocket geometry.
 
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GlenP

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P1V1=P2V2 is Boyle’s law for perfect gas when you don’t change the amount of gas (a closed system) or the temperature. Not sure how you can relate the cold volume of air to the hot volume of air plus burned fuel for venting requirements using a static equation of state like the perfect gas law, it may be more of a dynamic gas problem, like a combustion wave propagating in a shock tube. Experimental trial and error and experience is probably sufficiently useful for LPR hobby rockets when determining vent hole sizes for staging and altimeter uses.

From a mass-flow-rate perspective, you would want to have sufficient total cross-sectional area of the vents so you don't over-throttle the flow. A rough estimate, would be the inside diameter of an 18mm motor if that were your booster engine size, or roughly 13mm dia (0.51"). If you want to have that equivalent area in 4 vent holes, then they each should be about 1/4" diameter. Balance the requirements of venting with structural integrity and try to not make a weak spot in the body tube as well.

diaArea1/4 Area forvent dia
inchin^24 vents in^2inch
0.51​
0.2057​
0.0514​
0.26​
 
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lakeroadster

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Now to the calculation. The final figure in the upper boxed portion is the volume of tube in the two imches between the motors. The first figure in the lines between the boxes seems to refer to the same thing, but is double the figure above it. Where does this factor of two come from?
That's a screw up by me... I fixed it. Thanks.

V2, the length of tube times vent hole area, doesn't seem to me to represent any physical thing. Where does this come from? Or in other words, why multiply these things (vent hole area and tube length) and what does it mean?
The purpose of the calculation is to use the geometry of a rocket that we know works, and develop a calculation to plug data in for a new rocket, and determine what size vent hole is required.

Why 0.001 psi for atmospheric pressure? Shouldn't it be either about 14.5 psia or exactly zero psig? What's "nearly zero" got to do with it?
If I use zero, in the calculation P1 x V1 = P2 x V2, the answer will be zero. So I used a number close to zero.

How did you arrive at the value of P2? Is it somehow from the quantity of gas in the charge? If not, where is said quantity taken into account?
I input a number that would show that (3) 3/16" diameter holes are required. Again, using data from a known successful rocket.
 
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BABAR

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I input a number that would show that (3) 3/16" diameter holes are required. Again, using data from a known successful rocket.
you are calculating the minimum hole size by using data derived from previous hole size?

looks like circular reasoning to me. Your previous data point tells you that three 3/16” holes are at least or greater than the minimum required (Likely the latter.)

great engineering. From a science standpoint, not so much.
 

jqavins

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As to the one question about why didn't I use 0 for P1? P1 x V1 = P2 X V2... plug zero into that equation, and the answer will always be zero.
When the corrsct numbers break your equations, that's a good hint that your equations are wrong. Not always conclusive, but a really good hint.

I'm no rocket scientist, my entire concept may be total hogwash.
Umm, yeah, I'm afraid it looks that way.

you are calculating the minimum hole size by using data derived from previous hole size?

looks like circular reasoning to me. Your previous data point tells you that three 3/16” holes are at least or greater than the minimum required (Likely the latter.)

great engineering. From a science standpoint, not so much.
OK, I get what you're doing here. Start with a known good design, generalize to more designs by some sort of scaling. You might not need the quantity of gas that I asked about if you stay with the same type of engines while scaling, like Estes 18 mm, Estes 24 mm, Q-Jet 18 mm, etc. where you can be comfortable that the gas quantity remains the same. So if 3×3/16 holes works for BT-something and a something-0 engine at whatever inches apart, then lets come up with a formula to compute the required hole area for the same motor type and different dimensions. Is that the idea?

1. That's a fine idea, but I'm with BABAR that I don't think it's necessary.
2. I don't think P1V1=P2V2 is the way to get there. Or if it is, I need a better step by step explanation as to how/why it gets you there.
 
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lakeroadster

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No good deed goes unpunished! Probably not fair to launch pot shots when I don’t have any better ideas. I commend you for your scientific efforts. In any case, your combinations of ingenuity, engineering designs and documentation, and craftsmanship are making you one of the legends on the forum.
Well, shucks.. thanks. :computer:

FWIW: I modified the spreadsheet, basically just taking the geometry of the known rocket that successfully stages, creating a ratio, and using that for the proposed rocket.

Gap Staging Holes Sizing.jpg
 

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