I've spent some time solving for the static forces exerted on the receiver with a weight distribution hitch. Note that these measurements are approximate, and that I haven't been able to ensure equal 1/3 distribution of the tongue weight, as I assume in my diagram and calculations. Also, the measurements are specific to my modified hitch and trailer combination.
That said, I solved the attached free body diagram for the torque on the weight distribution arms t(WD) and came up with approximately 11900 in-lbs (just about 1000 ft-lbs) in order to get the distribution of weight on the axles as shown. Assuming that's where it is adjusted, I am able to solve for the moment forces created by the trailer tongue at point R, which is the connection point of the receiver into the Model X. Those forces are the 500# "max" tongue at the ball and the ~1000 ft-lbs of torque from the ball in the opposing direction. They net to -4100 in-lbs, which means approximately 342 ft-lbs of torque in the CCW direction.
So what does that mean relative to the rating of the stock Bosal hitch receiver? Well, the Bosal hitch receiver is stated to support 500lbs of downforce at 8" from the hitch pin. That equates to 500 lbs at approximately 13.5" from my location R, or 562.5 ft-lbs of CCW torque. So, given that my calculations have any merit at all, and noting that they do not include any
dynamic effect, it appears that the WD hitch relieves not only the rear axle, but also the receiver from torque that would normally be applied, allowing for a larger factor of safety around tongue weight fluctuations.
I welcome (and request) any feedback on my calculations, especially if anyone sees something I've done wrong. I recognize I didn't include some of the vertical offsets, but I think the effect is minor in the statics problem. I may revisit and try to tweak it a bit.
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