Discussion of How to Understand Brick Wall Stop Measurements and Issues
by Jeff Davis
The discussion regarding Brick Wall Stop concepts and measurements and resulting headway issues has been an ongoing for some time and hopefully the following non-technical discussion will help some.
First a couple of definitions
Headway is the time it takes for the same location on two successive vehicles (or trains) to pass the same point on a track.
Vehicle (or Train) Spacing is the time between the rear bumper of a lead vehicle (or train) and the front bumper of a following vehicle (or train) to pass the same point on a track.
Normal Deceleration is the deceleration rate used during normal station stops
Emergency Deceleration is the deceleration rate used when an unsafe event or situation has been detected by the control system
Safety Distance is a predetermined distance behind a lead vehicle to create a safety margin such that if a following vehicle’s actual braking performance is less than assumed it may not collide with a lead vehicle
This discussion is limited to a vehicle control system whereby vehicles continuously transmit their current location, and each vehicle is given a stopping point ahead of it by a wayside controller. The control system onboard the vehicle uses this stopping point to determine if the vehicle can accelerate, maintain current speed, or must begin decelerating in order to not violate, or potentially stop beyond the current stopping point.
The discussion is also limited to autonomous, self-propelled vehicles.
Part 1, Vehicle to Vehicle Interaction
The vehicle spacing, or separation is determined by answers to the following questions:
1. Is the stopping point the current position of the rear bumper of the vehicle ahead of it, or the results of some calculation of where the rear bumper will be if the lead vehicle begins to decelerate? In the first case, the assumed or theorectical rate of deceleration of the lead vehicle is not important, but the rate of deceleration of the following vehicle is important. In the second case the calculation uses an assumed rate of deceleration for both vehicles.
2. If a lead vehicle decelerates, should following vehicles decelerate at the same rate or some lesser rate?
3. Are vehicle to vehicle collisions allowable?
4. What is the worst case communications delay time measured as follows; 1) Wayside to vehicle, vehicle back to wayside, wayside to following vehicles, plus the 'dead' time between data transmissions, or 2) Some means for onboard vehicles to directly measure the rear position of lead vehicles.
So, for comparison, the longest time between vehicles is when the control system uses current location of the rear bumper of the lead vehicle as the stopping point, following vehicles will decelerate at the normal rate used for station stops, and collisions are not allowed. The shortest time between vehicles uses the projected location of the rear bumper of the lead vehicle for the stopping point, following vehicles decelerate at the emergency rate, and collisions at some predetermined speed are allowable.
The majority of suppliers of vehicle control systems design using the first set of criteria (stopping point is the current location of the rear bumper of the lead vehicle and following vehicles should decelerate at the normal rate if a lead vehicle applies brakes, normal or emergency) because it is believed to be the safest, albeit conservative. However, there are other options and opinions.
Some variations on a theme;
The stopping point is to be the projected location of the rear bumper of the lead vehicle:
If following vehicles use the projected location, then some other assumptions come into play. Will following vehicles decelerate at the normal or emergency rate?
If following vehicles are to decelerate at the same emergency rate as the lead vehicle, then the following must be considered:
1. If the lead vehicle's emergency brake rate is higher than assumed and the following vehicle's brake rate is lower than assumed, the potential for a collision exists if there is no safety distance assumed behind the lead vehicle, or the safety distance proves insufficient.
2. In the event of a lead vehicle applying emergency brakes all vehicles following at the minimum vehicle spacing will apply emergency brakes and any mis-matches between braking efforts may result in collisions depending on spacing (length of safety distance, if any).
If following vehicles are to decelerate at the normal rate and the lead vehicle decelerates at the emergency rate, then we have the following to consider:
1. The vehicles will be spaced further apart, as compared to the above, creating longer headways.
2. Small mis-matches in deceleration rates will not result in collisions assuming an appropriate safety distance is chosen.
In regards to the communications delay almost all vehicle control systems rely on a vehicle constantly transmitting its’ current location and braking status, and at least one system uses a method whereby vehicles directly measure the distance to the lead vehicle.
In regards to how vehicles determine their current position note the following:
1. The position determination must be implemented vitally meaning; 1) Multiple sensors are used and 2) Each sensor output is compared to the outputs of the others and if there is a mis-match the vehicle protection responds by stopping the vehicle.
2. The tolerance or position error of the sensors is known and included in the position determination calculation.
Wheel slip/slide could provide incorrect position data but since the sensors are vitally compared the slip/slide will result in a mis-match, which will cause the vehicle protection to stop the vehicle.
As noted above it is possible to increase safety, reduce the chance of a collision, by adding some distance to the rear bumper of the lead vehicle, meaning if the rear bumper is at X, then the stopping position is based on X minus safety distance.
In summary, be careful when reading equations about safe separation between vehicles. Some authors have simplified a complex equation using some assumptions that might not be obvious to the reader, such as lack of safety distance, and/or one that might not be correct, such as equal braking performance for autonomous self-propelled vehicles.
Be wary of unsubstantiated and untested claims. One example is the minimum safe headway entry in Wikipedia for PRT that uses 0.01 seconds as the reaction time without any supporting proof.
Part 2, Vehicle Interaction With Fixed Locations
The following discusses fixed stopping points such as switches/crossovers, crossings, or objects (such as people) intruding into the track or guideway envelope.
This discussion is limited to an alignment that is suited to a PRT System, i.e. no mixed mode or at-grade crossings, and normally no intrusions or interference by people or objects. In other words, an exclusive Right-Of-Way (ROW). Such alignments include elevated, at-grade with security fencing, or tunnel.
For exclusive ROW alignments, the typical fixed stopping points are station berths or platforms,
merges, and diverges.
For this discussion station berths are assumed to be off-line meaning that once a vehicle enters a berthing position following vehicles may continue to operate normally on the main line. Therefore, the fixed stopping points are the merge and diverge areas.
Merges need special (vital) safety logic to handle three different scenarios:
1. For track mounted switches, the switch must be positioned in the desired position.
2. A vehicle approaching a merge must not be allowed to travel into the merge area due to conflicting
traffic.
3. A vehicle approaching a merge is allowed to proceed through the merge area and its’ stopping point becomes the rear bumper of any lead vehicle in the direction of travel.
For CASE 1, if the track mounted switch is not in the correct position then the entrance to the merge area becomes the stopping point. This is only applicable for systems with track mounted switching. For systems using vehicle mounted steering or switching there is no need to consider whether or not a track mounted switch is aligned in the desired direction of travel. However, the logic onboard the vehicle must confirm proper steering or switching either before or as the vehicle enters the merge area. Since this logic is performed onboard the vehicle the time delay is very short.
For CASES 2 and 3 the merge logic must contain appropriate control logic to prevent collisions with other vehicles. This means as vehicle A enters a merge area, vehicle B from the other track cannot be allowed to enter the merge if there is a vehicle following vehicle A at minimum headway. In other words there must be a gap or space behind vehicle A to allow vehicle B into the merge area. If the merge control logic is designed to assume that vehicles will proceed normally through the merge area without stopping, the merging vehicles can be spaced closely together. However, in this case same as for the discussion regarding vehicle-to-vehicle interaction in Part 1, if a merging vehicle stops unexpectedly there will be the potential for a collision if the vehicle approaching the merge are is not appropriately spaced.
Diverges need special (vital) safety logic to handle three different scenarios:
1. For track mounted switches, the switch must be positioned in the desired position.
2. A vehicle approaching a diverge must not be allowed to travel into the diverge area due to conflicting traffic.
3. A vehicle approaching a diverge is allowed to proceed through the diverge area and its’ stopping point becomes the rear bumper of any lead vehicle in the direction of travel.
For CASE 1, if the track mounted switch is not in the correct position then the diverge area becomes the stopping point. This is only applicable for systems with track mounted switching. For systems using vehicle mounted steering or switching there is no need to consider whether or not a track mounted switch is aligned in the desired direction of travel. However, the logic onboard the vehicle must confirm proper steering or switching either before or as the vehicle enters the merge area. Since this logic is performed onboard the vehicle the time delay is very short.
For CASES 2 and 3 the diverge logic must contain appropriate control logic to prevent collisions with other vehicles. This means as a vehicle approaches a diverge area, its’ stopping point becomes any vehicle located in the path of the desired direction of travel.
An intrusion into the exclusive ROW is typically alarmed such that all vehicle traffic in and around the intrusion detection is stopped.
Last modified: August 19, 2012
