So today I was a little bit bored, so I decided to bring some numbers into the "thighbands connected to the crotchband" discussion.
First of all I wondered why connecting the chain to the crotch would have any effect at all. While looking at anatomy pictures I realised that the pivotpoint of the leg sits higher than the "lowest" part of the crotch. I modeled this in GeoGebra (https://www.geogebra.org/calculator/hyautmtc) the origin is the pivotpoint of the leg, the point V is some point on the thigh and point A is the point of the crotch D-ring. By using the slider you can see point V pivoting around the origin. d indicates the distance from A to V, in this example in the standing position it is 0.6; In a sitting position however, the distance amounts to 1.07, a 78% increase! The length of the crotch chain is obviously fixed, therefore the extra length needed has to come from somewhere else: the normaly horizontal connection chain is pulled into an angle, supplying the extra length needed, but also pulling the legs together.
Next I wanted to know how big this effect actually is: how far the legs are pulled together is dependent on three factors: 1.) The angle of the legs, with no effect in the standing position and a theoretical maximum at 180° upwards (of course that is physically impossible)
2.) The position of the thighbands: the further down, the smaller the effect. If you increase the radius of the circle in the Geogebra example from one to two and apply the same angle as before the extra needed length is only 28% more than the original length.
3.) The length of the connecting chain.
For the next calculations I'm going to assume that the position of the thighbands is always 15cm below the crotch D-Ring, and that they are unable to slide up the thighs. I'm also only going to be looking into the standing v.s. sitting position. What I'm varying however, is the length of the horizontal connection-chain.
Doing some geometrics I derived formulas for how much the legs are pulled together, depending on the inital chain length. For this I messured how much one point on the thighs "moves away" from the crotch while sitting down. I found, that in this example an extra length of 2.5cm is needed.
I looked at two types of chain styles: first the Upside-down T style and second the tryangle style, where the chain is fed through all three rings in a kind of circle.
I once again graphed my findings in GeoGebra (https://www.geogebra.org/calculator/xgjypuhz). Don't be overwhelmed by the many lines, you can toggle them on/off by clicking on the colored circle next to the function. The x-axis represents the chain length in the standing position, the y-axis how far you would be able to spread your legs in the sitting position. I also created the functions f & g, which represent the shortening of the chain as a percentage. That way both styles can be compared more easily.
First I'd like to draw your attention to the zero points of the function: those are the lengths of chain, that would force the legs completely together when sitting. From there on the curves are rapidly rising the T-style steeper than the triangle style. This is my second finding: the triangle style is much more evil than the T style: With an initial chain length of 10cm the T-style leaves you with 8.66cm when sitting, the triangle style with only 6.09cm. When looking at the percentages you can also see that the T-style is much nicer, leaving you with half your original chain length from 5.7cm upwards, while the triangle style only gives that to you from 8.2cm upwards.
Both styles however become equally unefective at a certain chain length: I defined "uneffective" as the point where both styles let you still spread your legs to 80% the standing distance, which is the case at 8.4cm for T-Style and 16.2cm for triangle style.
What's the takeaway? The argument of "added security" only counts for certain chain lengths. With the right chain length however it is possible to limit how far the legs can be pulled up towards the torso, which is, as I have heard, a way to get rid of the thighbands. To be able to prevent this, is definetly an extra safety benefit.
I hope i could give you some insights into this topic and didn't bore you all to much with all these numbers ;-)
