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So, I'm trying to build a model engine, and I've run into a minor hiccup: the nozzle I had planned is not large enough - it would look small and weird. I need to scale it up.



That's not a huge problem, per se: I only need to build one "petal" and then recast it x times. I also have the benefit of being able to heat the first cast in hot water, give it a curve, and then recast that instead, so the petals will have a normal nozzle shape instead of being flat. it actually will look better.

The problem I ran into is I only want to do this once, and I am absolutely terrible at math. Since this is model related and we have some smart guys here, I am just gonna ask here for help (sorry I'm not vomiting blood, shopping for a PC, or trying to get scale off a bathtub ayyy).

If my petals are shaped like this:



And I'm using a PVC cap, which has an outside diameter about 10CM, how large do A and B need to be on my engine? Lets assume I am going to use 5 petals. I don't really know how to account for how long they should be when they are going to be curved.

I'm a little confused. Do you want the engine to be 10CM, or are you just cutting the material?

You also might want to have this moved into P&M for better answers.




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Are... are you making a Lightning???

Ok, I'm sure I was unclear. Sorry.

If you look at that PVC cap I circled, that's what I am going to be attaching those nozzle petals to. I am going to make 5 of them, and they attach at the flat part labelled B.

I wrapped a tape around the cap, marked it where the tape met, and measured it. It's about 10cm exactly.

If I have 5 of these petals, then I assume the bottoms (B) need to be roughly 2cm, right? I don't know how to get the dimensions for the rest though.

 daedalus wrote:
... are you making a Lightning???

no spoilers!

Oh. Okay. That does make more sense. I'm gonna give this a shot and hopefully someone else can come along behind me and doublecheck my work. Regardless, before you start cutting, I'd take some spare cardstock, cut out the patterns on it, and then just kinda try to fold it together and see what happens.

Have any idea what the distance of a perpendicular line between segment A and segment B is? That is to say, per the orientation of your diagram, the "height" of the petal? Ultimately, I think that's the missing piece before we can give you the length of A.

For reference, it's about 1.5cm on the GW lightning (not that you're making one), but the engine on it looks like the OD is about 8 cm, though mine is assembled and behaving, so I don't want to try to hard to wrap the measuring tape around it.

You need to know the radius which "A" has to fit around as well, because obviously A depends on how much the petals collapse.

For B, if I assume you want B to rest tangent to the circle, then B is equal to....

B = 2*tan(360/(2*number of sides))*radius

You can use the same formula for A, you just need to know the radius.

The way that equation works, given I'm too lazy to draw a diagram, if you draw lines from the centre of the circle to the points of the polygon formed by the petals then the angle between those lines = 360/number of sides. If you take one of the pizza slices formed by those lines, draw another line from the centre of the circle to the centre of B in your drawing (ie. the centre of one of the polygon edges) the half-pizza slice you're left with forms a right angle triangle.

The length of 1 edge of that triangle is the radius of the circle, hence the length of the other edge (the one that isn't the hypotenuse) is = tan(theta)*radius where theta is the half angle of your pizza slice, which we already determined was 360/number of sides, so halve that and put it back in the other formula you get triangle side = tan(360/(2*number of sides))*radius.

Then B = twice that because to form that right angle triangle, you cut the pizza slice triangle in half through the centre of B, thus...

B = 2*tan(360/(2*number of sides))*radius

That will assume the petal sits around the tangent of the circle, if you need an offset due to the thickness of the material or simply for a different design, just change the radius of the circle.

EDIT: And obviously if using 360/number of sides, make sure your calculator is in degree mode, if you want to use the calculator in radian mode swap 360 for 2*pi.

Crap, that's a good point. I presumed that the petals were going to be touching, but they wouldn't necessarily.

FWIW, not a Lightning. No, don't have to be touching. And will definitely rough it out with some cardstock first.

I haven't decided on the length of the petals, but for the sake of this argument, let's say it will be about 3cm long.

Thanks again, both of you!

Well, without more precise specs, it's harder to give you a more precise solution.

I made a thing with A = 1.75 cm, B = 2 cm, and the "height" = 1.875 cm

Here is a picture of it compared to an Avenger exhaust:






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Personally, I think it's a little short for the diameter of the engine. Checking out the proportions of both the lightning and the avenger, they really don't have much of a sharp angle to the pedals though, so you either have to have a less pronounced angle, or you have to have stubbier petals.

Thanks for mocking that up! You're right, they do look stubby - I'm going to have to make them longer.