From my simple understanding of the transverse wave energy transfer through the junction of two different mediums the transfer coefficient at the interface depends on the mechanical impedance of the two types of lines. As given in this summary on transverse waves
http://imageshack.com/a/img923/989/GY7Irk.jpg
An example of the wave transmission down a rope with two different linear mass densities is shown here: on YouTube
He does not say how he joined the two rope sections, but I wonder if it would have made a much of a difference in his experiment since the length of that junction would have been so short compared to the length of the transverse wave he was using?
The same consideration applies to our fly line to leader junction. Since that junction overlap distance is so short compared to the length of the wave traveling down the line will it have much of an effect on the energy transfer? The relative linear mass density of the line and leader will be important to the energy transfer as given by the transfer coefficient above, but will the type of connection by itself have much of an effect on the relative smoothness loop layout?
Maybe some high speed videos of the propagation of the loop as it goes through the line/ leader junction would show how different types of junctions affect that transfer. Obviously the design of the taper in the leader will have an effect on the layout of the fly, but the taper used in the leader is another complicated matter that I was surprised did not come up in the recent discussion with line expert Bruce Richards. For this topic the impact of the leader design will not relevant since the same leader was used in all the tests.
I thought it might be interesting to compare the transfer from a line to a leader where the only variable was the type of connection used to join the two. Three popular types of connections were used in this series of experiments. My personal favorite is Dave Whiltlock’s Zap-a-Gap connection where the end of the leader is “welded” to the inside of the fly line.
There are a number of sites on the web that show how to make this really slick (no pun intended) connection. Mr. Whitlock says he has never had one of these junctions fail, but I have had the leader pull out from the line when applying a lot of tension in the leader to straighten it. So buyer beware of using this elegant connection for big fish.
The second connection used was standard 5 turn nail knot where I did not bother to run the end of the leader through the end of the line to make a smoother junction that is less likely to get hung up on the top guide.
The third was the much maligned loop to loop connection where the loops were made by whipping a short folded back section either the line or the leader to make the loops.
I thought I could do the tests by taking videos of the loop against a dark background to see how smoothly the wave went through the three different types of junctions. However that was easier said than done as I found the leader had no problem in going through the relatively wide DN loops that I produced in casting. There was really nothing to see using the Whitlock connection going through this loop as shown below. The black mark on the end of the line marks the junction in this video and you can see it goes through the loop with amazing smoothness.

Consequently after trying different approaches I found the most demanding loop could be produced by hauling a length of line on a piece of tar paper on the ground. This produced a very small loop (approximately 11 cm diameter) and had the added bonus that the path of the junction stayed within the close up frame of view of the camera. For dimensioning purposes the markers on the tape are 20 cm apart.
So in no particular order here is the transition I observed with the three junction types.
Connection #1

Connection #2

Connection #3

I would be interested so see if most people can see a difference that the junctions made on the transfer. Which video do you think is associated with each junction type? Can you pick out the one that was produced with the loop to loop connection?
The video for these comparisons are on vimeo at url=https://vimeo.com/154426156 if you are interested in being able to pause the playback. I blackened the end of the fly line with a marker to delineate the junction point in these videos.
Gordy
P.S. added on Feb. 15, 2016
Since Paul was the only one brave enough to hazard a guess on which connection was which I assume the consensus opinion is that the connection type had little or no effect on how the loop rolled out.
For the record:
Connection #1 was the loop to loop
Connection #2 was the Whitlock splice
Connection #3 was the 5 turn nail knot