Catenary shape of a towed underwater cable

[xtamx]

Hello,

I'm designing a towed underwater vehicle (towfish) and I am having trouble with determining cable tension at the length of the cable at given depths and speeds.

I have estimates of vehicle drag at speeds up to 4 m/s and the vehicle weight in water is known. Its really just the effect of the cable on the whole system and the eventual steady state shape it will take. I've attached a diagram of the forces for reference.

Does anyone know of any simple methods for estimating this? At this point the project is very preliminary and I would not need any detailed simulations or anything. Just the steady state shape.

 

[phinds]

Your title suggest that you believe the cable shape to be a catenary, but that shape is held by a chain/string/whatever, that is held at two ends and subject to gravity. Even in steady-state, your cable is not under those conditions.

 

[xtamx]

All of the literature that I have looked at for towfish designs have used catenary descriptions of the cables. They also have a catenary shape with mooring cables/chains. I've done a bit of mooring analysis in school but the equations are a bit different since in that case the cable weight per length is much higher than the cable drag per length so the drag is neglected. Drag is dominant in my case though as the diameter is much smaller.

 

[SteamKing]

All of the literature that I have looked at for towfish designs have used catenary descriptions of the cables. They also have a catenary shape with mooring cables/chains. I've done a bit of mooring analysis in school but the equations are a bit different since in that case the cable weight per length is much higher than the cable drag per length so the drag is neglected. Drag is dominant in my case though as the diameter is much smaller.

You don't have a simple catenary shape like you find in most introductory mechanics books: you have a complex, 3-D shape develop as the cable is towed thru the water with the towfish attached. These types of problems are important because of the increasing need to perform underwater surveys using towed instruments, so some research effort has been expended in analyzing what happens to towed cables.

These articles may give you some ideas, but the general case is usually analyzed with computer software nowadays:

http://dspace.mit.edu/bitstream/handle/1721.1/18539/Triantafyllou-1994-Calculation.pdf

ftp://dns.soest.hawaii.edu/bhowe/outgoing/IEEEOES_2013/papers/130503-135.pdf

 

[xtamx]

That looks pretty good. It's a bit involved for a project that may or may not go ahead. Definitely useful if it does though, thanks.

I'm really hoping to find a simple quick calculation of cable length and tension at the top and bottom but the more I look into it the less I think its possible. Just ballpark estimates would do.

 

[256bits]

Your diagram has the curve of the cable going the wrong way. The attachment to the vehicle should be nearly horizontal and curve upwards to the support ship.

If you need just a first-ballpark calculation, disregard the weight of the vehicle and cable, and assume a nearly vertical cable, and constant speed. Then use the drag force on the vehicle as the tension on the cable at that point, neglecting the vehicle weight. Moving up the cable, the tension increases due to the drag on the cable itself, to a maximum at the ship connection. That gives you a bare minimum in tension.

Next, add in the weight of the vehicle and cable.
Next, add in some acceleration to change speeds.

Of course, these do not take into account the catenary shape of the cable yet, and the different drag produced on that shape, but you might be able to work that in somehow with different drag parameters on the cable.

This of course is only for one way direction of the support ship, with no pattern zig-zag or otherwise, which would produce dynamic loading of some sort.

See
http://www.rov.org/rov_design_drag.cfm
as a simple example.
Note that when they write V2 they mean V squared.

 

[olivermsun]

Your diagram has the curve of the cable going the wrong way. The attachment to the vehicle should be nearly horizontal and curve upwards to the support ship.

Are you sure about this? It is not what I think of happening when the fish acts as (or includes) a depressor,but maybe I am misunderstanding your description.

 

[256bits]

Are you sure about this? It is not what I think of happening when the fish acts as (or includes) a depressor,but maybe I am misunderstanding your description.

You would be correct, and thanks for pointing that out, even without the depressor.
Explanation - drag/weight ratio would affect the curve OP asked for a preliminary, but there is much more to the problem after that.

In response to your post, some more reading for the OP.
http://scholar.lib.vt.edu/theses/available/etd-06172005-114444/unrestricted/AmyThesis.pdf