"Myring" submersible shape?

[pmudesign]

I'm hoping someone here can help. I'm involved in designing a small submersible and I frequently see references to the "Myring" hull shape which is often used in torpedo designs. Does anyone have any links to where I might learn more about this shape and how to reproduce it?

Also, what NACA foil would be recommended for such a craft that cruises at roughly 5 knots (fin aspect ratio to be about 2:1).

Thanks very much.

[Stumble]

I think you are refering to the paper written by D.F. Myring, “A theoretical study of body drag in subcritical axisymmetric flow” Aeronautical Quarterly, 27(3), pp.186-194 August 1976. I don't even know what the title means, but if you need it I am sure you can check a library.

[pmudesign]

Thanks Stumble, that's the reference I see a lot of other designers using. Unfortunately the magazine's been out of print for a long time and we don't have any technical libraries here, I was hoping there might be a reprint or overview someplace on the internet. I've searched and searched and haven't found anything so far.

On the other question, any NACA foil recommendations?

[Guest625101138]

I do not recall Myring being referred to in literature I have looked at for underwater hull forms but I found a reference linked below. The name that often comes up is Bruce Carmichael and his laminar flow hull.

If you are aiming to minimise the drag and the components can be placed to fit the particular shape then a fineness ratio of around 8 works out to be optimum for deep water operation. If it is going to operate closer to the surface than 3 diameters then fineness will be greater to get minimum drag because wave production becomes significant.

Fineness of 8 will translate to a 12% NACA. I do not think the Carmichael hull offers a huge advantage in practice but I have not looked carefully at it. The bow section of the Carmichael hull is very close to the shape of a NACA 16 series foil designed for zero lift but the tail is oddly pinched.

There are papers around on AUV design that compare different shapes. Many end up going for cylinders with nose cones and tail cones as these give flexibility in the payload.

This link shows the Carmichael hull shape:
http://www.ise.bc.ca/design_HullForm.html
Given the work to produce the shape I feel it will be the lowest drag option if you can get good surface finish and maintain control to keep stable motion.

This paper references Myring and it covers turbulent flow so probably more realistic than laminar flow:
http://www.focus-offshore.com/Docs/S&BINTRE.pdf
The hull based on Myring work looks like the best performer in 1991. But be a little wary because prop design can have a huge impact on performance.

There are many YouTube videos on human power subs and these will give you good insight into the most efficient forms. They are achieving around the speed you nominate. If you look through what wins each year you will start to get an idea of what works best. The common theme is around the 8 fineness and high aspect props for efficiency.

Rick W

[Guest625101138]

I had a look at the latest HPS winner I could find. Omer5 won in 2007. I have attached an image. They cracked 8 knots in this boat. That is impressive for a craft of its size and power level. Remember these are full of water and the pilot has to pump his legs in water - a tough ask.

Rick W

[JacobH]

Myring's Equations for nose & tail curves.

Transcription Note: I went a little overboard with the parentheses just to be sure. Crosschecking tool: Curly brackets were only used for containing numerators and denominators.

Nose Curve:
r(x) = (1/2)*d*[ 1 - ( {x+aoffset-a}/{a} ) ^2 ] ^(1/n)

Tail Curve:
r(x) = (1/2)*d - [ ( {3*d}/{2*c^2} ) - ( {tan(theta)}/{c} ) ] * [ (x-a-b+aoffset)^2 ] + [ ( {d}/{c^3} ) - ( {tan(theta)}/{c^2} ) ] * [ (x-a-b+aoffset)^3 ]

Where:
a = length of nosecone (linear)
aoffset = offset from tip of nose cone (linear)
b = length of constant-diameter midbody (linear)
c = length of tailcone (linear) (Ed. note: without truncaton, if any)
d = diameter of midbody (linear)
r(x) = offset at station "x" (linear)
theta = angle of departure (radians)
x = distance from tip (linear)
n = sharpness of entry factor (unitless)
and all linear distances are in the same unit

Myring curves are described using the notation "a/b/n/theta/0.5*d", however the author does not seem to follow this convention in the following sentence.

Ed notes:
1) Positive values will make for a more bulbous tip. I had aoffset=0 for the project I was on.
2) For "n", Gomariz uses 55. I used 2, and got a very nice curve. I plotted n=55 and the resulting curve was much more blunt than their depiction. This must be highly reliant on aspect ratio of the vehicle as a whole, so you should experiment to find a satisfactory number.
2) The figure shows c_offset (tail truncation), but the value is not used in either equation. To truncate, just ignore any offsets smaller than the radius you wish to leave open. Guess-and-checking of c and theta will yield better departure shapes for your design constraint.
3) On my model, the tail curve ended up changing concavity at the end (d = 3, c = 12, theta = 15 degrees). This seems to happen if c =< d*2 (observed by toying with 'd' in Excel). So for short tails, Myring profiles may not be the most suitable. The nose curve does not seem to have this problem. If you do have a short tail, consider using an egg-shape (the oblong half, not the near-constant-radiused half); that won me the lowest drag in a college assignment (where the requirements were d = 4 and c=<12. The egg shape worked better than NACA curves in my testing using Cosmos FloWorks).
4) If you put this into MS Excel and graph it, you may see hard spots due to how it draws. However, if you draft the offsets (either manually or in a software such as Solidworks), you will see that the curve is better than Excel portrays.
5) When laying the nosecone curve in Solidworks, I made the end tangent to a line parallel with the centerline to ensure that the nose-midbody joint was smooth. Additionally, I added a perpendicular relation between the spline and the centerline. This changed the shape from pointed to rounded.
6) Initially, I had accidently dropped the cubing factor at the end of the tail equation. The curve looked good, except that it crossed the centerline before the end of the tailcone.
7) I do not know where this was published; the document was sent to me.


These were obtained from this secondary source:
Title: Autonomous vehicle development for vertical submarine observation
Authors: S. Gomáriz, J. Prat, A. Arbos, O. Pallares C. Viñolo
Source: SARTI Research Group. Department of Electronic Engineering.
Technical University of Catalonia.
Avda. Victor Balaguer s/n. 08800
Vilanova i la Geltrú. Barcelona. Spain.
Contact:Tel.: +34 938967781
email : spartacus.gomariz@upc.edu
Pages: 1,2
Primary Reference: D. F. Myring. “A theoretical study of body drag in subcritical axisymmetric flow”. Aeronautical Quarterly, 27(3):186–94, August
1976. 14, 15, 43