I salute you for the amount of time and thought you put into your post. That was a lot of effort you put into helping a complete stranger who may well just be one more knucklehead youngster with silly facial hair and jeans falling off his butt, for all you know.
I did follow the hitch length discussion. Many years ago I came out of school as a mechanical engineer, but instead of using it I joined the Infantry. Not a lot of hard science types in the Infantry. I see your point now re. the "Moment", the product of force and a lever arm, being reduced by the shorter hitch shank. What we might be missing tho is that this applies to all moments that the trailer applies to the truck.
Lets call the rear axle the pivot point, the ball 2' from that pivot point, and my shortened receiver a 10% reduction in lever arm. If the trailer tongue weight is 700lbs then that's 1400ftlbs (2' x 700lbs) of moment applied. There is also 700lbs of "Shear" forces which is the tongue weight itself, neglecting the fact that there's a pivot point.
Lets say the WD hitch tension bars are 2' long and provide 150lbs of total tension, so 300ftlbs of moment. They do not impact shear forces on the system.
Total moment that trailer applies to truck is therefore 1100ftlbs (1400ftlbs - 300ftlbs).
If I understand your point correctly you are saying that that by reducing the shank length by 10% I also reduce my 300ftlbs from the WD hitch. I agree. But I'd point out that shortening the shank length by 10% reduces not just the lever arm for the WD hitch, but also the lever arm that the trailer uses to move the truck around. Therefore the 1400ftlbs is also reduced by 10%. This means that due to shortening the receiver hitch the sum of the moment on the truck is 990ftlbs (10% less than 1100ftlbs), so it's still a net win.
Also, this neglects side to side movement. By shortening the distance to the pivot point by 10% I reduce the ability for trailer sway to move the truck around, therefore the trailer stays more stable when semi's pass.
The discussion above assumes that all forces and lever arms are at 90deg to each other, and in real life they aren't. I had to do it that way or it would get too complicated. Besides, I don't remember how to do cross products in order to make the "not 90deg" math work.
Did I get your point correctly? Did my counter make sense and is it believable?
I did follow the hitch length discussion. Many years ago I came out of school as a mechanical engineer, but instead of using it I joined the Infantry. Not a lot of hard science types in the Infantry. I see your point now re. the "Moment", the product of force and a lever arm, being reduced by the shorter hitch shank. What we might be missing tho is that this applies to all moments that the trailer applies to the truck.
Lets call the rear axle the pivot point, the ball 2' from that pivot point, and my shortened receiver a 10% reduction in lever arm. If the trailer tongue weight is 700lbs then that's 1400ftlbs (2' x 700lbs) of moment applied. There is also 700lbs of "Shear" forces which is the tongue weight itself, neglecting the fact that there's a pivot point.
Lets say the WD hitch tension bars are 2' long and provide 150lbs of total tension, so 300ftlbs of moment. They do not impact shear forces on the system.
Total moment that trailer applies to truck is therefore 1100ftlbs (1400ftlbs - 300ftlbs).
If I understand your point correctly you are saying that that by reducing the shank length by 10% I also reduce my 300ftlbs from the WD hitch. I agree. But I'd point out that shortening the shank length by 10% reduces not just the lever arm for the WD hitch, but also the lever arm that the trailer uses to move the truck around. Therefore the 1400ftlbs is also reduced by 10%. This means that due to shortening the receiver hitch the sum of the moment on the truck is 990ftlbs (10% less than 1100ftlbs), so it's still a net win.
Also, this neglects side to side movement. By shortening the distance to the pivot point by 10% I reduce the ability for trailer sway to move the truck around, therefore the trailer stays more stable when semi's pass.
The discussion above assumes that all forces and lever arms are at 90deg to each other, and in real life they aren't. I had to do it that way or it would get too complicated. Besides, I don't remember how to do cross products in order to make the "not 90deg" math work.
Did I get your point correctly? Did my counter make sense and is it believable?