A more accurate Volumetric Metering Equation (check my work)

[auxiliary]

Hi Hybrid Spudders,

I have been dissatisfied with the current approaches to calculating the correct amount of fuel for hybrids using volumetric metering. One, because they don't account for the volume of the meter itself, and two because they don't account for the volume of the dead space between the pump check valve and isolation valve. I worked it out myself and got an equation that is giving me some numbers that make sense.

If you are interested, try playing around with it and if possible, I'd be delighted if you could double check my work for soundness. I typed up the problem in Word and exported it to PDF the snipped it into jpegs so the formatting isn't awful.

[jackssmirkingrevenge]

Very well presented, better than this hodge podge of ideas.

Have you thought of making an excel sheet where you can just punch in the relevant parameters and have it automatically calculated?

[auxiliary]

I admit I hadn't thought of that! I made one just now very easily, but I was thinking it would be great to have a calculator that also works for manometric metering and syringe metering too. Also with different fuels as well. I'm not sure how to attach my quick Excel calculator here though. Before moving forward with anything I was hoping to get it vetted a bit. Perhaps if someone has an operational hybrid that uses volumetric metering they could test this out?

A note about volumes...

For smaller hybrids (for which the above equation is suited for) it is difficult to measure volumes of inside fittings geometrically. So I suggest an approach using water. Weigh your chamber/meter/fittings-with-dead-space on a gram scale. Write down the mass. Then fill the volume with water. Weight it again. Subract the two mass readings and you've got the mass of enclosed water. Use the density of water 1.0g/mL to convert to volume.

This ^^^ approach worked great for my smaller combustion cannons with small fuel meters. Also, if the ball valves used have a large internal volume inside the ball that is significant you can use my diagram to tell which valves should be considered as which volumes as denoted by the colors red, green, or blue.

[jackssmirkingrevenge]

I'm not sure how to attach my quick Excel calculator here though.

Did you try the uploader? IIRC it allows Excel files.

I used the water method to determine the dead space volume of my shock pump, with the tiny chambers I was working with not taking into account even though it was 1.5mL would have thrown the calculations right off.

[auxiliary]

I tried using the uploader, but I got this message in red text that it does not support .xlsx files. I'm glad you mentioned that about your shock pump! It makes me feel the value of what I put my energy into.

[D_Hall]

I wasn't aware that there was another way to do it volumetrically.

That said, for bonus points you may want to go ahead and include an altitude correction for your calculations. In other words, pressure gauges often read pressure differentials rather than absolute pressures and this can itself result in inaccuracies for systems such as that you propose. The reason being that such tend to assume that 14.7 psi is ambient pressure, but ambient pressure can vary quite a bit. It's more like 13.5 psi as I sit here typing this and I'm not at a particularly high altitude.

In any event, making altitude corrections isn't difficult so if you're really trying to do it right, I'd include such.

[auxiliary]

Thanks for that advice D_Hall. I think you're right, afterall if I'm accounting for the itty bitty stuff, the altitude is a significant factor as well. I just gotta figure out how to work that into the equation...

The most obvious effect that altitude will have is there is less concentration of oxygen in the air for a given volume, so that would necessitate reducing the pressure in the propane meter.

But there is another effect as well that I'm not sure how to deal with that you mentioned with gauges. When we get a gauge and hold it up we see it just reads 0 psi. I wonder, for most gauges, if you add even 1psi more it will read 1psi? Or is there a fudge factor in there so that the needle will only rise if it senses more than say 5psi or so? I feel like that this variance in pressure gauge behavior is another big factor and that might not be so easy to handle without getting expensive sensitive ones.

There's probably a limit to which equations like mine are helpful unless accurate equipment is available. But I think that dealing with the dead space issue with just some math is a good start.

[D_Hall]

The best way to deal with ambient pressure corrections is to start with a gauge that reads in absolute pressure. They're out there, but they're less common. Still, they make the math so much easier.

And yes, you're right. There's only so much that you can do unless you want to invest in accurate equipment. FWIW, the gauges I installed on VERA were about $1200 *each*. While damned few people are going to be able to do that, the old saying of "aim little, miss little" probably applies here.

[jackssmirkingrevenge]

I've never used manometric metering personally, it's always been volumetric though of course my hybrid forays have always had relatively small chambers.

You'd need a rather oversized syringe for larger caliber launchers, but is that such a weird idea?



Yes, yes it is... but I figure still less complex to make and with no need for expensive gauges.

[mark.f]

I think with normal "purging" of your meter and air systems with propane (or air) respectively, and a good design like SB15's "air-through-meter" design solves most of these problems. Dead space in the pump is something to take into account for smaller launchers. Good points, all of them.

[auxiliary]

Mark - What you said about "air through meter" designs got me thinking! What I like about that idea is that I need only one ball valve and the procedure of operation would be shorter. One drawback I can think of is that there is more wasted fuel. But after calculating it, it's really not that much. So decided to go with that design!

I've started this hybrid project a few weeks or so ago and the parts came in and now I've got something together. I'm waiting on a 14mm spark plug that's coming in the mail that will thread into the adapter on the back of the 1/2 tee. It's got a hand pump I made that goes to 120psi pretty easy. In case you're interested I included the volume diagram and final equation for this air-through meter design which takes into account the volume of the meter.

[mark.f]

I'm having a hard time sussing out your derivation for that equation, do you mind posting it? I've put up my math here a long time ago, if you want to check it out, although I don't take into account dead volume of the pump/etc.

[auxiliary]

I tried plugging is some test numbers into your Pm equation (the second one down) and I was getting slightly different results. It might be hard to figure out this discrepancy because we took different approaches. I used partial pressures and did not account for atmospheric pressure because it was on both sides of the equation. But I want to look into this further to see if I'm making an incorrect assumption here, because it might be that I suspect. And you're approach uses mix number... Just to be clear n=1 (1x) means a regular old combustion right? For now here are my calcs worked out. I adapted it to use the same variable notation as you I believe.

[mark.f]

I think the discrepancies between our numbers boils down to using "mix numbers" in mine, which doesn't scale perfectly with the numbers you would get using a preignition pressure of 10 atmospheres vs. a "10x mix", etc. It might possibly be time to rewrite my page!

[auxiliary]

I got a chance to test my numbers and I found out that I was leaving out a Patm in there. I fueled up my hybrid as per the original equation above and no ignition. Then I tried the version that accounts for the additional atmoshpere of air already in the chamber and it worked! I just couldn't wrap my head around this simple addition for some reason (or subraction? ) so I just had to test it out. Anyway the equation that worked for me is this: