Getting the truck over the crossing

[pope]

Homework Statement

Independent study question by a non-engineer and with no background in physics. There is no practical application for this problem. I have heard a stop sign can increase the danger at certain RR crossings by increasing the time the truck is exposed to the tracks. Trying to determine the number of seconds it takes to get a 65-foot trailer truck to completely clear a RR crossing from a full stop.

Taking assumptions from AASHTO Green Book: the truck is 65 feet long. It will travel over the crossing in first gear. It accelerates 1.47 ft/s2. Its maximum speed in first gear is 8.8 f/s. It takes 26.3 feet to reach its maximum speed in first gear. The crossing itself is 5 feet. The truck starts from a full stop with the front bumper 15 feet from the crossing. Clearing the crossing means the rear of the truck is 3 feet beyond the far rail. Assume a level, dry pavement and a straight approach and crossing.

Basically, if the truck is 65 feet long, the crossing is 15 feet away, the crossing itself is 5 feet wide, and crossing clearance is an additional 3 feet, then the question is how long does it take for the truck to move 88 feet from a complete stop?

I understand, I think, it’s two questions: (1) how long does it take and how much distance does the truck cover accelerating to its top speed and (2) once it reaches top speed, how much time does it take to cover the remaining distance to reach 88 feet? To the second question, it really isn’t an acceleration issue because it has reached its speed.

Relevant Equations

I think my assumptions negate the need to apply most equations (to find acceleration).

For the first part, the calculation is the time needed to reach maximum speed at the given acceleration rate.

For the second part, the calculation is really just the time needed to cover the needed distance at the given speed.

If the truck accelerates at 1.47 fps until it reaches its top speed of 8.8 fps, then it takes approximately six seconds to reach the top speed (1.47 x 6 = 8.82). In its first six seconds, the truck covers 30.87 feet (the truck reaches 8.8 after traveling 23.2 feet).

To cover the remaining 57.13 feet, traveling at 8.8 fps, it would take the truck another 6.5 seconds to cover the remaining 57.13 feet (57.13 / 8.8).

The solution would be from full stop to completely clearing the crossing (defined as 3 feet beyond the crossing), it would take the truck 12-13 seconds once it initiates its acceleration.

 

[erobz]

If the truck accelerates at 1.47 fps until it reaches its top speed of 8.8 fps, then it takes approximately six seconds to reach the top speed (1.47 x 6 = 8.82).

units are wrong for acceleration. $a= 1.47 \rm{\frac{ft}{s^2}}$, but you have the time $t$ to max speed correct.

In its first six seconds, the truck covers 30.87 feet (the truck reaches 8.8 after traveling 23.2 feet).

For constant acceleration to get the distance covered $\Delta x$ you can apply:

$$ v^2 = v_0^2 + 2 a \Delta x $$

or

$$ \Delta x = \frac{1}{2}at^2 $$

 

[kuruman]

Your solution is almost correct. I agree that it takes about 6 s for the truck to reach the full speed of 8.8 ft/s. However, the distance covered in that time would be the average speed, here 4.4 ft/s multiplied by 6 s which gives 26.4 ft. This doesn't make any difference to the final answer because it will still be a crossing time of 12-13 s.

I don't understand, though, how STOP signs increase the danger at crossings. Yes, the crossing time can be made shorter if the truck driver barrels across the intersection in 1/3 of the time without stopping to look right and then left and then right again for trains. That is shorter, but is it safer?

 

[pope]

Thank you so much for your help!

On the safety issue, the idea that a stop sign decreases safety has been mentioned in literature as a concept, though not universally accepted - evidenced by the requirement that certain vehicles stop at all crossings.

Under the stop sign increases danger concept, approach sight crossing, allowing a driver to confirm the presence of conflicting traffic on approach to the crossing to make a stop/go decision better serves safety where that safe stop/go decision can be made at a distance. Other than that, where a yield sign is deemed inadequate, certain crossing conditions would warrant flashing lights based on available sight distance instead of a stop sign where increasing the amount of time traversing the crossing would be greatly lengthened.

An example — a crossing is equipped with a stop sign. The above referenced truck would come to a complete stop before proceeding over the crossing. Clearing sight distance is a function of train speed and design vehicles. Where passenger trains use the crossing, a truck would need 1,925 feet of sight distance to determine it could safely proceed through the crossing. If, unbeknownst to the truck, the tracks service a high speed passenger line, and a passenger train traveling at or near 80 mph is approaching the crossing, the truck would need the full amount of sight distance to clear the crossing to avoid being hit.

If the truck stopped and had an inadequate sight distance of 1,000 feet, thinking it was clear to proceed, the train and the truck would collide if the train is traveling at 80 mph and the truck is proceeding in first gear.

Had the truck need not come to a complete stop, the collision would be avoided. Obviously the answer is, stop signs increase the danger when inadequate sight distance is provided. It isn’t the result of protective device.

 

[jbriggs444]

Had the truck need not come to a complete stop, the collision would be avoided.

Would it? We've not worked the calculation for a truck coming up to an intersection with a 1000 feet sight distance at an unspecified truck speed and with an unspecified braking rate.

Three obvious evasion possibilities exist: 1) Brake to a stop before the train gets to the crossing. 2) accelerate to scoot across before the train arrives. 3) Close your eyes and pray.

You will want to calculate a range of train positions where a collision by the at-speed truck could not be avoided and compare it to the range [1000 to 1925 feet as you have calculated] where the starting-from-a-stop truck can not avoid a collision.

Note that with 1000 feet of visibility, the starting-from-a-stop driver will have about 8 or 9 seconds advance notice of the need to bail from the cab and will be at a low enough speed to do so with a reasonable chance of survival. The prospect of a passenger trail derailment at speed is still concerning, to be sure. With 8 or 9 second notice, the train may be slowed by only 5 or 10 mph.

Trains are required to sound their horn between 15 and 20 seconds prior to proceeding through an at grade crossing on a public highway. As a truck driver, coming to a stop and opening the windows would be the prudent course of action. As a bus driver, it's mandatory.

 

[kuruman]

I can see your point about sight distance. So let's look at the following situation taking the crossing time 12-13 seconds after stopping at a STOP sign as a given. Assume that the sight distance is inadequate and cannot be improved because of existing structures and terrain. Also assume that it is unreasonable to expect the oncoming train to slow down when approaching the intersection. The goal is to avoid a collision. Without being a transportation engineer, I think that this goal can be reached in several ways. In decreasing order of cost, one can build

• An over- or under-pass for vehicle traffic. The town where I live has both.
• A gate with flashing lights that drops when a train is coming. We have these too and they annoy me.
• An un-gated intersection (outside of town) with flashing lights and clanging bells. Yup, we got them.

I agree that a STOP sign where on must come to a complete stop can be problematic when the sight distance divided by the speed of the oncoming train is less than 12-13 seconds. One gets a false sense of security that if one goes by the book, comes to a complete stop and then crosses, one would clear the intersection unscathed with 100% certainty. However, the existence of the STOP sign is not the problem because removing it would make things worse!

What does a truck driver do if he knows that the sight distance is inadequate at that intersection? Play Russian roulette and run the STOP sign hoping for the best? I think drivers are entitled to ascertain, without guessing and with 100% certainty, that it is safe to proceed. As far as cost is concerned, what is the cost of a train derailment and possible loss of human life?

 

[Lnewqban]

Copied from:
https://www.fmcsa.dot.gov/sites/fmc..._License_Manual_Railroad_Crossing_Section.pdf

2.15.3 – Driving Procedures Never Race a Train to a Crossing.

-Never attempt to race a train to a crossing. It is extremely difficult to judge the speed of an approaching train.

-Reduce Speed. Speed must be reduced in accordance with your ability to see approaching trains in any direction, and speed must be held to a point which will permit you to stop short of the tracks in case a stop is necessary.

-Don't Expect to Hear a Train. Because of noise inside your vehicle, you cannot expect to hear the train horn until the train is dangerously close to the crossing.

-Don't Rely on Signals. You should not rely solely upon the presence of warning signals, gates, or flagmen to warn of the approach of trains. Be especially alert at crossings that do not have gates or flashing red light signals.

-Double Tracks Require a Double Check. Remember that a train on one track may hide a train on the other track. Look both ways before crossing. After one train has cleared a crossing, be sure no other trains are near before starting across the tracks.

-Yard Areas and Grade Crossings in Cities and Towns. Yard areas and grade crossings in cities and towns are just as dangerous as rural grade crossings. Approach them with as much caution.

2.15.4 – Stopping Safely at Railroad- highway Crossings

-A full stop is required at grade crossings whenever: The nature of the cargo makes a stop mandatory under state or federal regulations. Such a stop is otherwise required by law.
-When stopping be sure to: Check for traffic behind you while stopping gradually. Use a pullout lane, if available.
-Turn on your four-way emergency flashers.

2.15.5 – Crossing the Tracks

-Railroad crossings with steep approaches can cause your unit to hang up on the tracks.
-Never permit traffic conditions to trap you in a position where you have to stop on the tracks. Be sure you can get all the way across the tracks before you start across. It takes a typical tractor trailer unit at least 14 seconds to clear a single track and more than 15 seconds to clear a double track.
-Do not shift gears while crossing railroad tracks.