After 3 days of nothing done, some pressure vessel calculations, Day 13

After being busy and not being able to do much, I've done some calculations on the pressure vessel capabilities.

Brass 360 (the alloy I think I'm using) has a yield strength of about 45000 psi, and an ultimate tensile strength of 58000 psi. We assume a typical ASME factor of safety of 4. In the cross-section, the threads will be about 19.5mm in diameter, in a block of metal with a square cross-section of 1.5 inches on a side, leaving us with walls about 9.3mm thick at the thinnest. That means the wall thickness is roughly the same as the radius of the whole, meaning that, if we abuse the thin-walled pressure vessel equations, we can get roughly 10000psi internal pressure. Of course, thin-walled pressure vessel assumptions only work if the wall is roughly one tenth the radius, so in our case, we can make a very conservative estimate (remember, this is on top of the factor of safety) that 1000psi should be safe, at least in cross-section. And even that is an order of magnitude higher than we expect, so we will likely have a factor of safety of at least 100 if we carried out all the necessary calculations (and you include the ultimate strength). So this allows us to possibly survive a hard-start even if we start using liquid fuels, and also gives us some margin for changing of the properties with increased temperature.

Found out spark plug is larger than expected, Day 9

So, I cut a piece of wood roughly as big as I expect my igniter to be (1.5"x1.5"x3"), then after talking to a guy named Michael, I thought I ought to check my spark plug, and I found that it's 3 or 4 mm larger in diameter than I expected, which actually means I can make the chamber shorter (which is good and gives me more of a chance of being able to use the drill press for it).

Another thing I learned is that I probably will want to use the lathe for the rocket igniter, although I still will most likely use the drill press since I know how to use it.

Tomorrow, I will update the CAD drawing and will show a picture of the piece of wood I am going to use as a mock-up.

Also, I will calculate the pressure vessel strength of the combustion chamber. Maybe not tomorrow, though.

Nothing done, Day 8

Nothing done for the rocket igniter today, but tomorrow I hope to go to the Hack Factory again with the goal of looking around and finding some more orifices. Also, I will try to cut a block of wood to try making a better mock-up of the igniter.

Fitting pictures, Day 7

As promised, here are the pictures of the two orifices I plan on maybe using:

I may have to use different ones, but these are the two I have to work with right now (I can get more of each kind).

In the meantime, I'm learning a real CAD program, Alibre.

Propane flowrate, Day 5 & 6, a little late

For propane:

The formula for subsonic mass flow rate through an orifice is:

http://en.wikipedia.org/wiki/Orifice_plate#Calculation_of_expansion_factor

mdot is mass flowrate (kg/s)

C is the orifice flow coefficient (unitless), .61-.9 (we pick .7)

A₂ is cross-section area of orifice (m^2), ((.0265 in)^2) * pi = 1.42334131*10^-6 m^2

ρ₁ is upstream gas density (kg/m^3), ~11 kg/m^3

P₁ is upstream gas pressure (Pa or N/m^2), 80 psi = 551580 Pa

P₂ is downstream gas density (Pa or N/m^2), 60 psi = 413685 Pa

k is the ratio of specific heats (dimensionless), 1.127 (for propane at room temp)

http://www.google.com/search?q=.7*(.0265in)^2*pi*sqrt(2*11kg/m^3*80psi*(1.127/(1.127-1))*((60/80)^(2/1.127)-(60/80)^((2.127)/1.127))) = 0.00143057116  kg / s

So, the mass flowrate for propane will be about 1.4 grams per second, about the same as for the air flowrate (except we are operating the propane at a lower pressure). This means I'm going to have to have a much different orifice size for the propane versus the air, since the propane should only be about 4% of the total mixture by volume.

It's after midnight, and I didn't get to show pictures of the existing orifices for air and propane. I'll do that Monday sometime.

Orifice sizes, redo CAD drawing for right dimensions, Day 4

Well, I didn't get the chance to calculate the orifice size last night, but I have done it today.

The formula for subsonic mass flow rate through an orifice is:

http://en.wikipedia.org/wiki/Orifice_plate#Calculation_of_expansion_factor
mdot is mass flowrate (kg/s)
C is the orifice flow coefficient (unitless), .61-.9 (we pick .7)
A₂ is cross-section area of orifice (m^2), ((.0265 in)^2) * pi = 1.42334131*10^-6 m^2
ρ₁ is upstream gas density (kg/m^3), 7.2 kg/m^3
P₁ is upstream gas pressure (Pa or N/m^2), 90 psi = 620528 Pa
P₂ is downstream gas density (Pa or N/m^2), 60 psi = 413685 Pa
k is the ratio of specific heats (dimensionless), 1.4 (for air at room temp)
http://www.google.com/search?q=.7*(.0265in)^2*pi*sqrt(2*7.2kg/m^3*90psi*(1.4/(1.4-1))*((2/3)^(2/1.4)-(2/3)^((2.4)/1.4))) = 0.00137946227 kg / s
So, the mass flowrate for air will be about 1.4 grams per second. A little more than that will be the total, since we have to add propane (which is going to be ~4% by volume). I should add that this is with using one of my existing orifices for the air. I may choose to use a larger (existing) orifice for air and use this smaller orifice for propane, but honestly I'm too tired right now to calculate any further tonight.

I also realized today that my chamber will be about 16.5 mm in diameter (not 18mm), since the recommended drill size for a 18mm diameter with 1.5mm threads tap is 16.5mm (or 21/23") according to this: http://www.carbidedepot.com/formulas-tap-metric.htm

That forced me to redo my CAD drawing. I also decided to make it not as thick to go with a cuboid of 1.5"x1.5"x2.75" instead of 2"x2"x3" in order to save a little on material costs. This will allow me to use bronze for about the same price if that turns out to be easier to drill. Bronze reported works better than stainless with liquid oxygen, though of course we're nowhere near liquid oxygen right now. You can't tell much difference in this picture, though. I've also started to learn how to program OpenSCAD, which is a CAD program which doesn't have a WYSIWYG interface, but instead allows you to model with a kind of programming language. This would make it pretty easy to change parameters automatically or with a formula, which may be handy in the future, though it's sort of limited, now. Reminds me of POV-Ray, which I used to use a lot "back in the day."

This weekend, I will try to nail down the orifice size for the propane side and trade my orifice options. I'll also take pictures of the orifices and possibly (if I have time) try making a mock-up of the rocket igniter using wood (allowing me to actually use the tools I will need to use for the metal one, allowing me to check clearances, etc).

CAD drawing of simple rocket igniter, Day 3

So, here is a CAD drawing of my rocket igniter. The small grid spaces are one millimeter on a side. It will be machined out of a block of metal (most likely stainless, maybe steel or brass) using a drill press. I don't know how I'm going to do the nozzle, yet, though.

The top will be threaded for my 18 mm spark plug, and the two holes, one on each side, will be threaded for my orifices (the size of which I haven't calculated, yet... should finish that up tonight). I may also just drill the orifices directly in the metal, though I'll still have to thread holes for attaching the propellant hoses to them.