relative velocity 0 concept of transpotation

 June 27, 2024

a transportation system where an engine moves at a constant speed, and individual bogies (rail cars) can attach and detach from the engine while in motion. This system leverages the concept of relative velocity to make the process of boarding and alighting more efficient and seamless, even when the train is moving.

Here’s a more detailed breakdown of the concept:

1.     Constant Speed Engine: The engine moves at a constant speed without stopping. This ensures a steady and predictable travel time for the train.

2.     Attaching and Detaching Bogies: Bogies (or rail cars) can attach to and detach from the moving engine. When a bogie needs to attach, it accelerates to match the engine's speed and then locks into place. Conversely, when a bogie needs to detach, it decelerates to a stop or slows down to a speed where passengers can safely board or alight.

3.     Relative Velocity: Because the bogies match the speed of the engine before attaching or detaching, the relative velocity between the bogies and the engine is effectively zero at the moment of connection or disconnection. This makes the process smooth and minimizes the risk of accidents.

4.     Automatic Shifting Platform: Once a bogie detaches, there is an automatic platform that shifts passengers to their destination bogie. This platform moves in synchronization with the engine's speed, ensuring passengers can move between bogies even when the train is in motion.

5.     Seamless Transition: The relative speed concept means that actions like detaching, attaching, and shifting bogies are as straightforward and safe as if the train were stationary. This could significantly reduce travel times and improve the efficiency of the rail system.

This system could revolutionize the way we think about train travel, making it more continuous and less dependent on stopping at stations. It also opens up possibilities for more flexible and dynamic rail operations, where different sections of a train can serve different routes and schedules without the need for the entire train to stop.

 

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The travel time between Mumbai and Delhi using your proposed system would depend on several factors, including the constant speed of the engine, the efficiency of the attaching and detaching mechanism, and the overall design of the route.

To provide a rough estimate, let's consider some key variables:

1. Distance: The distance between Mumbai and Delhi by train is approximately 1,400 kilometers (870 miles).

2. Speed: Let's assume the engine travels at a constant high-speed rail velocity. Modern high-speed trains can travel at speeds ranging from 250 km/h (155 mph) to 350 km/h (217 mph). For this calculation, we'll use a conservative estimate of 300 km/h (186 mph).

Calculation

1. Total Distance: 1,400 kilometers
2. Speed: 300 km/h

Using the formula for time, $\text{time}=\frac{\text{distance}}{\text{speed}}$:

$\text{time}=\frac{1,400\text{ km}}{300\text{ km/h}}=4.67\text{ hours}$

So, under ideal conditions and assuming no additional time for attaching and detaching bogies, the travel time would be approximately 4.67 hours.

Additional Considerations

1. Attaching and Detaching Time: If the system for attaching and detaching bogies is very efficient, it may add only a few minutes to the overall travel time. Assuming each attachment or detachment takes about 5 minutes and there are 2 stops (one for attaching and one for detaching), we could add about 10-15 minutes to the total time.

2. Acceleration and Deceleration: The time taken for bogies to accelerate to the engine's speed and decelerate to a stop might add a bit more time, but with high-speed rail systems, this is generally minimal.

3. Platform Transfer: The automatic platform transfer system should be synchronized with the train's speed to avoid significant delays.

Considering these factors, the total estimated travel time would likely be around 5 hours, assuming efficient operation of all components in your proposed system.

Conclusion

If your proposed system were implemented effectively, the travel time from Mumbai to Delhi could be reduced to approximately 4.67 to 5 hours. This is a significant improvement over current travel times, which are usually between 16 to 18 hours by conventional train services

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Let's compare the travel times between the current conventional train services and your proposed high-speed rail system with efficient bogie attachment and detachment.

Current Conventional Train Services

• Average Travel Time: 16 to 18 hours

Proposed High-Speed Rail System

• Estimated Travel Time: 4.67 to 5 hours

Time Savings Calculation

1. Conventional Train Average Time: 17 hours (taking the midpoint of 16 to 18 hours)
2. Proposed System Estimated Time: 5 hours (taking the upper estimate)

$\text{Time Saved}=\text{Conventional Train Time}-\text{Proposed System Time}$

$\text{Time Saved}=17\text{ hours}-5\text{ hours}=12\text{ hours}$

Percentage Time Savings

To find the percentage time saved, we use the formula:

$\text{Percentage Time Saved}=\left(\frac{\text{Time Saved}}{\text{Conventional Train Time}}\right)\times 100$

$\text{Percentage Time Saved}=\left(\frac{12\text{ hours}}{17\text{ hours}}\right)\times 100\approx 70.6\mathrm{\%}$

Summary

• Time Saved: Approximately 12 hours
• Percentage Time Saved: Approximately 70.6%

Your proposed high-speed rail system could save passengers around 12 hours on a trip from Mumbai to Delhi, representing a time savings of about 70.6%. This would be a significant improvement, greatly enhancing the efficiency and convenience of rail travel between these two major cities.