Derivation of Tail Swing large vehicle

In summary, the conversation discusses the process of deriving a formula to calculate the distance that the rear of a large truck swings outward when turning a corner. The necessary equations and variables are provided, and the solution is calculated to be 12.46 cm. It is also noted that if the result is negative, the tail swing will not enter the other lane.
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Homework Statement



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.



Homework 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)




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.
 
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The Distance the Rear of a Large Truck will Swing Outward when Turning a Corner is 12.46 cm.
 

What is "Derivation of Tail Swing large vehicle"?

"Derivation of Tail Swing large vehicle" is a scientific concept that explains the movement of the rear end (or tail) of a large vehicle while making turns or navigating narrow spaces. It takes into account factors such as the vehicle's size, shape, and wheelbase to determine how much space is needed for the tail end to safely swing out.

Why is it important to understand the derivation of tail swing for large vehicles?

Understanding the derivation of tail swing for large vehicles is important for several reasons. First, it helps ensure the safe operation of these vehicles, as tail swing can pose a hazard to people and objects in its path. Second, it can aid in the design and construction of roads, parking lots, and other spaces to accommodate large vehicles. Lastly, it can improve the efficiency and accuracy of computer simulations used in transportation planning and traffic management.

What factors affect the derivation of tail swing for large vehicles?

Several factors can influence the derivation of tail swing for large vehicles. Some of the most significant ones include the size and shape of the vehicle, the length of its wheelbase, the angle of the turn being made, and the speed at which the vehicle is traveling. Additionally, external factors such as road conditions and weather can also play a role.

How can the derivation of tail swing for large vehicles be calculated?

There are several mathematical models and equations that can be used to calculate the derivation of tail swing for large vehicles. These models take into account the various factors mentioned above and provide estimates of the amount of space needed for the tail end to swing out. Some models also incorporate real-world data from physical experiments or computer simulations to improve their accuracy.

Are there any safety precautions that drivers should take regarding tail swing for large vehicles?

Yes, there are several safety precautions that drivers of large vehicles should take to minimize the risk of tail swing accidents. These include being aware of the vehicle's size and shape and how it affects its turning ability, making wider turns when possible, and being cautious when navigating narrow spaces. Additionally, drivers should be familiar with the specific tail swing characteristics of their vehicle and adjust their driving accordingly.

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