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Discussion Starter · #1 · (Edited)
I was reminded again of this recently talking to a friend about the Spey casting book he is working on. I know I have referenced this on here on multiple occasions in the past as the solution to many sink tip questions, but James Havstad published a paper on sink rates of lines in 1979 that can be found here:


that contains on the last page a simple approximate (the actual fluid mechanics is more complicated) equation for the true sink rate of a tip or line in terms of its diameter and density. The actual equation is

U = 37.5 (S-1)^0.563 D^0.689

where U is the sink rate in ips, S is the specific gravity of the section of the line or tip (the ratio of the density of the line to the density of the water it is in) in question, and D is the diameter in inches. For those that may be unfamiliar with this use of the carrot symbol (^) in this context this just means “to the power of”. These can be computed using any calculator with more than the most basic functions, though you may have to find a key you have not used much before. But S and D can be determined by anyone with a ruler, a scale, and a micrometer. So for example if you have a box full of unidentified sink tips you can use this formula to figure out the sink rates.

The equation is a first order approximation, but is accurate to %1 for lines and tips.

One of the “problems” is that different companies use different methods to determine the labeled sink rates and so those rates cannot be reliably compared across brands. The other, related issue is that the actual sink rates on the label are not strictly correct, and tend to overestimate the sink rates of a real line. The latter issue may not be that practically important since the way tips are used tends to be more like shifting gears in a manual transmission, which you do by going up and down according to need and not typically with reference to the precise gear ratios.

The Havstad equation provides a reliable way to calculate the sink rate of any tip, or section of line. If the companies that make sink tips would simply post the Havstad sink rates then all of them could be put on the same footing and compared. That is exactly what he proposed in the paper referenced above. But companies are probably more concerned, in general, with marketing considerations. If they then determine a sink rate using a certain method and it comes out to be a number that sells, even if the method is inaccurate, they are covered. They probably feel off the hook on accuracy considerations. They will rightly point out that their competition is using similar methods so they have no choice, etc.

Anyway, this is the answer to a lot of questions about tips.
 

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Discussion Starter · #3 · (Edited)
Someone should throw casting angle, sink time, and water velocity into that equation to make it pragmatic.
I fully get that this level of analysis can make a lot of people on here wax ironic, but if you are serious - as you appear to be - then that HAS already been done in detail, as I have reported on here in the past several times. The follow up work to that article is also catalogued at the site above where the 1979 reprint is posted. The other articles and results posted there, primarily by one of the creators of the site above Tom Keelin, who is an engineer, cover the treatment of things like the effect of the water speed and other factors, including the temperature and salinity of the water, and the shape of the line on hang down. There is even a built in depth calculator there, and multiple tables that can be used to answer practical questions. It is all there somewhere if you poke around, especially in Tom’s published papers, though the site is not organized super clearly - more along the lines of an exuberant discussion of certain practical questions with lots of cross links. Kind of like what a lot of sites looked like at the very beginning of the internet age, and exactly like a lot of people’s first attempt at a web site. :)

I focused on the Havstad paper before only because it answers the specific questions of how different sink tips compare to each other in spite of what the labels might say. The sink DEPTH is the most practical question above, and is proportional to the sink rate and length of the tip or section of line. That is dealt with in detail at the Fly Fishing Research website (Fly Fishing Research) if you are actually interested. But I do get that it is way TMI for most people.

Like I said in the previous post, the WAY the basic physics is used practically is more akin to driving a stick shift - by feel rather than numbers - but knowing the precise, rigorous analysis has been done can be useful, if only to combat the occasional misinformation about these issues that sometimes gets posted.
 
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