# Derivation of Tail Swing large vehicle

1. Apr 27, 2012

### Probie1

1. The problem statement, all variables and given/known data

I am trying to derive a formula for figuring out the distance the rear of a large truck swings outward when turning a corner. Picture one of thos large moving trucks that you can rent, the back end over hangs the tires by a lot. Now picture it turning a corner and the rear end crossing the center line. That is what I am trying to figure out.

2. Relevant equations

Hypotenuse = sqr (opposite ² + adjacent ²)
Sin = opposite / hypotenuse
Opposite = (.5144) hypotenuse
deg = 180 / (( 2 ) ( pi ) ( rad ))
R [ABC] = A’B’C’
Ts = ((sqr ( A ² + C ² )) – ( E – D )) ( 0.15)

3. The attempt at a solution

Where:
A = adjacent = 500 cm – distance to rear of vehicle
B = hypotenuse = 583.0951895
C = opposite = 300 cm – track width
E = lane width = 600 cm
D = distance from curb = 100 cm
a = 55.7 degrees

Calculate Hypotenuse

Hypotenuse = sqr (opposite ² + adjacent ²)
Hypotenuse = 583.0951859

Verify Hypotenuse

Sin = opposite / hypotenuse
.5144 = 300 / 583.0951895

Opposite = (.5144) hypotenuse
300.00 = (.5144) (583.0951895)

deg = 180 / (( 2 ) ( pi ) ( rad ))
Angle of hypotenuse = 55.7 deg.

Calculate Tail Swing Over Line

R [ABC] = A’B’C’

Ts = ((sqr ( A ² + C ² )) – ( E – D )) ( 0.15)
12.46 = (sqr (300² + 500²)) – ( 600 – 100)
Ts = 12.46 cm

If Ts is negative then Tail Swing will not enter other lane.

Last edited: Apr 27, 2012