Calculating ring or circumference projection into a gap.

[satamax]

Here's a copy of what i explaned to Allen Lumley at permies. And thought it could be usefull to keep it here for newbs.

Ring projection, the projection of the tube's wall into the barrel gap.

I mean, the theoretical surface of the wall of the exhaust tube as if it was completely inserted in the barrel up to the heat riser, comprised between outer shell of the heat riser, and the barrel.

For example, you have a flue or exhaust tube of 6"

That's a perimeter of 6"x 3.1415926 or so that's 18.84 inches.

Multiplied by the gap let say 2" = 37.69²

Heat riser CSA of a 6 incher 28.27

28.27² x 1.5 =42.41² So a gap of 2 inches with a 6 inch exhaust tube isn't good enough.

42, 41/ 18.84= 2" 1/4 so the gap needs to be at least 2.1/4 to have a ring projection of 42,41 square inches necessary for good performance.

If you aim for 3 times the CSA,

You could reverse it this way

2 inch gap

28,27²x3 = 84.82² /2 = 42,41/3.1415926 = 13.49 inches in diameter for the "transition area"


Allen, that's it, the theoretical surface of the projection of a perimeter into a gap, = ring projection to me.

And that has to be at the absolute minimum 1.5 times the CSA. Would it be on top of the riser or at the side of the barrel for the transition area. Up to 3times the csa for the transition area which seems to be the "safe" number. For the top of the riser, even several feet can be done no prob, so it's a minimum we're looking at, not maximum. That 3 times figure arose, i think because it was a convenient number for newbs.

At 4 times CSA, you get to the lower limit for bell's . Well, let me explain, a bell has to have a horizontal cross sectional area of at least 4 times the CSA to work at all. There's no upper limit, exept the ISA.

So again, that brings us back to that 3 times the CSA for that transition area, otherwise it might start acting as a bell if bigger.

A little side note; for example, heat riser's gap can't be smaller than that 1.5 times CSA, because of the laminar flow effect. The gases at the inside corner of the "elbow" where they exit the heat riser and turn; are completely stalling, and each layer goes a little faster as they're more distant form a surface. Thus creating turbulences and reduction in pression, which in turn slow down the flow. The top of the barrel stalls the gases too, due again to friction. The top of a heat riser can be made better, being rounded outwards, , like a rounded funnel. (trumpet bell) That means that the ring projection is bigger too (and helps the transition of the flow from one direction to another) . The absolute contrary of what everybody does

I suspect that the whole sheebang of a rocket could be tuned to a certain note, due to the hemoltz resonances. (at the top of the heat riser, enlarging it as i have described, would drop the note down)

Well, i'm going astray, due to previous life experience

Hope this can be of some use.

[photoman290]

i know metric is not used in america but it makes those sort of calculations a lot easier. just do all the calc in metric then convert the result to imperial.

[satamax]

Nov 5, 2014 5:36:11 GMT -8 photoman290 said:

i know metric is not used in america but it makes those sort of calculations a lot easier. just do all the calc in metric then convert the result to imperial.

Well, i went from metric to imperial already once, for the guys to understand at permies. But you're welcome to redo them in metric again, to post here

Btw, the calcs are exactly the same, would they be metric or imperial! And also, you'll notice that i use imperial decimal most of the time, not imperial fractional. Which get on my nerves! Blady fourths eighths sixteenths, thirtysecondths and sixtyfourths. As long as the horendous base of twelve doesn't get involved, as it used with old english money! Farthings and all that. At least, the american were already decimal at the time for their money And they're slowly turning metric

[photoman290]

at least we are not trying to send a space probe anywhere i tend to use both metric and imperial depending on what it is i am trying to do."can i have 8 foot of 4x2 please" sounds much better than "can i have 2.4 metres of 100x50mm ". but i am old enough to been taught imperial measurements, before this new fangled metric stuff came in.

[satamax]

Well, can i have four metres of rafter is as easy Or 5x10 (cm)

[satamax]

Well, quoting myself from another post, to try to make things clearer.

The "barrel gap" is the empty space between heat riser and barrel.

You have to understand that the gases change direction when they exit the heat riser to enter the barrel, and when they exit the barrel to enter the flue.

Hence the 1.5 times the CSA. Or cross sectional area of the heat riser.

So, in the example above, you have the perimeter of the exhaust or flue pipe in the side of the barrel. and between the edge of that pipe, and the nearest object causing a restriction; in this case the heat riser. You have a "gap". The narrowest point, is usually the projection of the flue tube lip, to the heat riser. So for calculating, it's easy, you take the circumference of the flue tube, multiplied by the empty space between heat riser and the tube's edge. Or the barrel, since the tube's edge should be flush with the barrel. This will give you a surface of "gap", an empty space where the gases can flow.

That surface should be at least 1.5 times the surface or cross sectional area (CSA) of the insides of the heat riser.

Here you have six inches diameter, so the surface is 28.27 square inches.

Circumference of the flue pipe is 6 x PI, 18.84 inches. multiplied by the gap, in the example above, i used a arbitrarily determined 2 inches gap. You get 37.69 square inches, which is too small, compared to the theoretical 1.5 times heat riser's CSA of 42.41.

You have two ways to increase the "gap's" surface. Either increasing the gap, which i did, at 2.1/4; or you can enlarge the flue pipe entering the barrel. And you will reduce your diameter further down the flue tube.

Let's say, you use 8 inches, remember that the heat riser is still six inches.

8xPI, 25.13 inches circumference. Multiplied by a two inch gap. 50.26 square inches. Good to go, as it surpasses the 42.41 square inches previously determined as being the smallest gap's surface required.

Get it?