Not all that inexplicably - this is the type of problem I love to give my freshman physics students.
The tension in the ridgeline is dependent on angle, so if we assume the tension is going to make a difference in the way the hammock "feels", you're just plain not going to be able to avoid this problem altogether.
Let's make a simple physics problem, shall we?
If we model the hammock as a simplified situation, with two weights (the two ends of the hammock) suspended by two lines, and a ridgeline between them, we can capture all the essential physics by looking at half of the problem (the forces on the other side will simply be the mirror).
So, the forces acting on the mass m will be the sum of
T1,
T2, and the force due to gravity, m
g. Furthermore, since the mass is stationary and not accelerating, we know the sum of forces acting on it is zero.
Let's break that down into components. We'll assume up and left is positive, and down and right is negative.
In the horizontal direction:
-T1 sin θ + T2 = 0, or T2 = T1 sin θ
In the vertical direction:
T1 cos θ - mg = 0, or T1 cos θ = mg
Putting it all together, T2 = (mg/cos θ) *sin θ, or T2 = mg tan θ
So, even in this incredibly simplified drawing, the tension in the ridgeline depends on the angle at which the hammock is suspended. Since we've already demonstrated that changing the tension in the ridgeline changes the "feel" of the hammock, no matter what you do to the suspension, the angle at which the hammock is hung will affect its feel.
It will just affect it MUCH LESS than it would without a ridgeline, since without a ridgeline the sag would be determined COMPLETELY by the suspension angle, and not mostly by the ridgeline with a slight variation depending on how tight the ridgeline is.
Now as far as WHY the amount of tension in the ridgeline affects the feel of the lay in the hammock - that's a bit more complicated, and you really have to start thinking about how the hammock fabric lies, and what changing the forces on each end of the hammock will do to the feel of it. That's a much more complicated problem, and I am definitely NOT in the mood to attempt to write up a solution
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