# Calculating Fluid Dynamic Forces on a Towing Cable

1. Apr 20, 2013

### Imurphy

I am trying to develop a calculator to approximate the depth of a trolling rig used by fisherman, which is typically a lead weight with a hook (jighead), attached to a single plastic/rubber shad body (bucktail example). The other typical rig is a jig/shad setup with an array of unweighted shad bodies running radially from a single weighted lure (umbrella rig). There is some empirical studies already which are a good reference, but they are difficult to use when there are any deviations.

I'm trying to use some basic physics formulations without getting into naiver-stokes, flexibility/vibration considerations, etc., to get an accuracy around +/- 7.5% depth.

To solve this problem I'm breaking it down into:

Depth=(L*sin(θ)-Hrod)

Where L is the line length, Hrod is the height of the rod (start of line) above the water level and θ is the angle with respect to the water level.

θ=invtan (Fy/Fx)

Where Fy is the sum of forces in the y direction (weight - buoyancy), and Fx is the drag forces.

It is trivial to get Fy for just the lure, and approximating the drag as a lead sphere is also pretty easy. I may be able to solve for Cd of these lures from the data I have. Although the tail of the shad body oscillates, we should be able to add in a drag/weight/buoyancy for any N shad bodies with some accuracy. With these considerations we get a constant angle independent of line length. The next step is to approximate the weight and drag of the line to add in the decrease in θ as line length increases. This is where it gets tricky. I started off trying to approximate the line as a rigid cylinder but the issue is that the area used to find drag length of line in the water for buoyancy are both dependent of the angle θ. Is there a simple way to iterate this to get the steady state angle that I'm not thinking of? Or can anyone explain to me how to properly find the forces on the line that will add to the total system?

I found this Thesis, but unfortunately I'm not a fluids guy so its hard to get much usefulness from it.

Also, can anyone see anything I may be overlooking with the problem?

Thanks to anyone willing to help, I've been slowly looking into this problems for at least a year.

2. Apr 24, 2013

### stewartcs

Can you provide a diagram of what you're trying to figure out? I'm not clear on what you want to know. It seems you are asking how to calculate the depth of the "rig" on the end of a cable/line that is being dragged through the water; is that correct?

CS

3. Apr 25, 2013

### Imurphy

Diagram Attached. Hope that helps. I'm looking for Fy,line and Fx,line from Fluid forces, for solving for the Depth of the rig/lure. I'm right now trying to approximate viscous drag and form drag on the line. As you can image, these forces increase as more line is in the water, which typically reduces angle θ. The angle is used to calculate the drag so there arises a paradigm. I was attempting to supply a predetermined angle (say for L=50' theta is 30 and L=100' theta is 20 degrees) to solve for the fluid forces but there are obviously some accuracy issues with that.

Thanks,
Imurphy

#### Attached Files:

• ###### Trolling Depth Image.jpg
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Last edited: Apr 25, 2013
4. May 5, 2013

### Simon Bridge

Could it be related to this thread?

OP cites "intellectual property concerns" as a reason to be cagey about details.
What is the IP policy for PF?