JBarca wrote:
Hi Ed, Welcome to the discussion! When you came up with 1,000# per chain load, what are the assumptions surrounding this?
John, I don't know how Ed did it, but here is my approach to defining the relationship between tension and load transfer.
First we need to define some dimensions and variables. Let:
a = tow vehicle wheelbase
b = ball overhang (longitudinal distance from TV rear axle to ball)
c = distance from ball to mid-point between the TT's axles
d = perpendicular distance from Andersen chain to center of ball (reported by Andersen owner to be 6.5")
TW = tongue weight
LTT = load transferred to TT's axles
LF1 = load removed from TV's front axle due to TW without WD applied
LF2 = load transferred to TV's front axle when WD is activated
T = Andersen chain tension per chain
M = moment (torque) generated by Andersen chain tension (total for 2 chains)
then (assuming zero pitch-axis rotational friction between ball and coupler)
M = 2*d*T
LTT = M/c = 2*d*T/c
LF2 = LTT*(b+c)/a = 2*d*T*(b+c)/(a*c)
also
LF1 = TW*b/a
If we want to restore a load equal to some percentage (call it FALR) of that which was removed from the front axle, we have:
LF2 = LF1*FALR/100, or 2*d*T*(b+c)/(a*c) = FALR*TW*b/(a*100)
solving for chain tension (per chain) gives
T = FALR*TW*b*c/{2*d*(b+c)*100}
for example, if: b=60", c=200", d=6.5", TW=600#, and you want to restore 50% of the load removed (FALR=50)
T = 50*600*60*200/(2*6.5*260*100) = 1065# per chain
Ron