I wanted to figure out the correct maths based calculations for adjusting my tongue weight.
I have a trailer that has an axle in a fixed position, so moving the boat is my option.
After deriving the various formulas, I thought that others might find this useful.
There have been many posts about various guidelines and methods for adjusting tongue weight, but I hadn't seen the mathematics anywhere in one place, so I thought that I would add it here.
The salient formula is: d = twm * TD / BW This gives the amount of distance to shift the boat weight to obtain the desired tongue weight change.
'd' is the distance that the boat must be moved to change the tongue weight by the desired amount
'twm' is the amount of tongue weight to be added or removed (moved from/to the wheels)
'TD' is the total distance between the tongue and the wheels
'BW' is the weight of the boat that will be moved to achieve the tongue weight.
If you would like to see the derivation of this and other formulas, see below....
Paul.
Trailer Calculations
A trailer of course is a 'balanced lever'.
Picture of balanced lever model:
<---------------------------------TD-------------------------------->
<---------- x -------------------><------------ y ---------------->
A================CG================B <--- Balanced Lever (trailer)
A = Weight at point A (the Tongue Weight)
B = Weight at point B (the Wheels)
CG = Centre of Gravity
BW = Boat Weight portion of total weight (this is the movable weight)
W = Weight of Trailer and boat
TD = Total distance between A and B (x+y)
General Centre of gravity formulas
Center of Gravity = Total Moments / W
If CG Datum is assumed to be at point A, then
CG = (A *0 + B*TD) / W
CG = B * TD / W
Change in CG due to weight shift (cargo moved),
Wm = Weight moved
d = Distance weight moved
CGm= Distance CG moved
W = Total weight
CGm = Wm * d / W --- (1)
Calculating distance to shift cargo to achieve desired tongue weight
IF one wishes to move/transfer some tongue weight (point A) to the wheels (point B)
1st Calculate what the shift in CG would be for that movement and then calculate how much the boat would need to move to generate that CG shift
IE, CG change due to to tongue weight moved = CG change due to Boat Weight moved
twm = amount of weight to shift from tongue to wheels
bwm = Boat Weight moved
CGtwm = twm * TD / W
(CG movement due to tongue weight movement)
CGbwm = BW * d / W
(CG movement due to boat weight movement)
therefore as we're saying that we will move the boat to achieve the desired CG movement.....
twm * TD / W = BW * d / W
'W' cancels out from both sides leaving
twm * TD = BW * d
Rearrange to get 'd' which is how much we need to move the boat.
d = twm * TD / BW (3) The amount of distance to shift the boat weight to obtain the desired tongue weight change.
Trailer weighing (Lever) formulas
===================^====== <-- ( Balanced Lever)
A (scales) <------- x -------> <-- y -->B
'^' The point to be weighed (Fulcrum)
To determine either tongue or wheels weight, a lever can be used if direct measurement (ie by bathroom scales) is not possible
W = A + B
(i) (Total weight = weight at point A + weight at point B. For this calculation, A and B are the two endpoints of the lever to be used)
A*x = B * y
(ii) Balanced Lever moments,
Weight at point A times the distance to the fulcrum = weight at point B times it's distance from the fulcrum
B=A * x / y
(iii) from (ii)
W = A + (A * x / y)
sub iii into i and then group the 'A' together
W = A(1 + x / y) ---- (2) Can be used for calculating a "Point Weight" using a lever.
If 'y' is made to be 1 foot then the calculation is easy (1+ 'x' feet) times the weight read at point A
I have a trailer that has an axle in a fixed position, so moving the boat is my option.
After deriving the various formulas, I thought that others might find this useful.
There have been many posts about various guidelines and methods for adjusting tongue weight, but I hadn't seen the mathematics anywhere in one place, so I thought that I would add it here.
The salient formula is: d = twm * TD / BW This gives the amount of distance to shift the boat weight to obtain the desired tongue weight change.
'd' is the distance that the boat must be moved to change the tongue weight by the desired amount
'twm' is the amount of tongue weight to be added or removed (moved from/to the wheels)
'TD' is the total distance between the tongue and the wheels
'BW' is the weight of the boat that will be moved to achieve the tongue weight.
If you would like to see the derivation of this and other formulas, see below....
Paul.
Trailer Calculations
A trailer of course is a 'balanced lever'.
Picture of balanced lever model:
<---------------------------------TD-------------------------------->
<---------- x -------------------><------------ y ---------------->
A================CG================B <--- Balanced Lever (trailer)
A = Weight at point A (the Tongue Weight)
B = Weight at point B (the Wheels)
CG = Centre of Gravity
BW = Boat Weight portion of total weight (this is the movable weight)
W = Weight of Trailer and boat
TD = Total distance between A and B (x+y)
General Centre of gravity formulas
Center of Gravity = Total Moments / W
If CG Datum is assumed to be at point A, then
CG = (A *0 + B*TD) / W
CG = B * TD / W
Change in CG due to weight shift (cargo moved),
Wm = Weight moved
d = Distance weight moved
CGm= Distance CG moved
W = Total weight
CGm = Wm * d / W --- (1)
Calculating distance to shift cargo to achieve desired tongue weight
IF one wishes to move/transfer some tongue weight (point A) to the wheels (point B)
1st Calculate what the shift in CG would be for that movement and then calculate how much the boat would need to move to generate that CG shift
IE, CG change due to to tongue weight moved = CG change due to Boat Weight moved
twm = amount of weight to shift from tongue to wheels
bwm = Boat Weight moved
CGtwm = twm * TD / W
(CG movement due to tongue weight movement)
CGbwm = BW * d / W
(CG movement due to boat weight movement)
therefore as we're saying that we will move the boat to achieve the desired CG movement.....
twm * TD / W = BW * d / W
'W' cancels out from both sides leaving
twm * TD = BW * d
Rearrange to get 'd' which is how much we need to move the boat.
d = twm * TD / BW (3) The amount of distance to shift the boat weight to obtain the desired tongue weight change.
Trailer weighing (Lever) formulas
===================^====== <-- ( Balanced Lever)
A (scales) <------- x -------> <-- y -->B
'^' The point to be weighed (Fulcrum)
To determine either tongue or wheels weight, a lever can be used if direct measurement (ie by bathroom scales) is not possible
W = A + B
(i) (Total weight = weight at point A + weight at point B. For this calculation, A and B are the two endpoints of the lever to be used)
A*x = B * y
(ii) Balanced Lever moments,
Weight at point A times the distance to the fulcrum = weight at point B times it's distance from the fulcrum
B=A * x / y
(iii) from (ii)
W = A + (A * x / y)
sub iii into i and then group the 'A' together
W = A(1 + x / y) ---- (2) Can be used for calculating a "Point Weight" using a lever.
If 'y' is made to be 1 foot then the calculation is easy (1+ 'x' feet) times the weight read at point A
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