Vanished wrote:
http://academic.brooklyn.cuny.edu/physics/sobel/Phys1/eqm.html
As D2 changes (say moving from pin to jacks) the sum of the moments still needs to be 0... F1 (weight on tires) does not change, only the F2 increases assuming the CG is in front of back wheels..
Using the link for nomenclature
If like you suggest F1 and D1 are fixed, and the moments about A are 0, then as D2 varies F2 inversely varies. In fact, if you make D2 the same as D1, then F2 would have to equal F1 for moments to remain zero. However this ignores one other thing we do know. The sum of ALL forces and moments must be zero. There are no forces in the X direction but there are in the Y direction. We also know the weight A does not change. We know F1 + F2 must always equal A in order for the forces to add to zero. So if F2 increases, F1 must decrease because the total weight of the trailer did not change and there are no other outside forces.
You have 2 unknowns, F1 and F2. You need 2 equations to solve for 2 unknowns.
For those interested,:) consider the following
Sum forces in Y
F1 + F2 - A = 0 or F1 + F2 = A
Sum Moments about a point = 0 (we will use A)
-F1D1 + F2D2 = 0 or F2D2 = F1D1
For simplicity sake lets say A = 15,000lbs. So F1 + F2 = 15,000, but you don't know exactly how much F1 or F2 is. That is where the moment equation comes in
F1D1 = F2D2 or F1 = F2(D2/D1) So F1 will always be a factor of F2 and depends on the ratio of D2/D1.
For exercise sake lets say
Axle to COG D1=5
COG to Pin D2 = 20
So F1(5) = F2(20), F1 = (20/5)F2, F1 = 4F2
Now go back to F1 + F2 = 15000
since F1=4F2, 4F2 + F2 = 15000, 5F2 = 15000, F2 = 3000 (pin)
and then F1 + F2 = 15000 so F1 = 15000-F2, F1 = 12000 (axles)
So what happens if we change D2?
If say the landing gear is 5 feet closer than the pin,
D2 = 15
Then D2/D1 will be (15/5) so F1 = 3F2
We know A stays the same, so
F1 + F2 =15000, 3F2 + F2 = 15,000, 4F2 = 15000, F2 = 3750 (landing gear)
F1 + 3750 = 15000, F1 = 11,250 (axle)
So by making D2 shorter, F2 increased and F1 decreased, but not by a significant amount. But if you keep moving the support closer, when D2 is the same as D1, then F1 will be the same as F2, each half of the trailer weight A
