# Does a train really jerk backwards at the moment that it comes to a complete stop?

When a train is decelerating to a stop, standing passengers have to brace themselves or hold onto something to prevent themselves from falling forward towards the front of the train. They find themselves leaning forward and any loose objects will tend to slide or roll towards the front of the carriage.

At the moment that the train stops decelerating and comes to a stop, the standing passengers experience the subjective impression that they are suddenly and briefly jerked towards the rear of the train, and that they are at risk of falling over backwards.

(I believe this phenomenon is noticeable in cars and buses also but I decided to limit the question to trains to remove the complication of the vehicle changing pitch as the front suspension is compressed and decompressed.)

Is this an illusion or real? Is it purely because they are bracing themselves against deceleration and so when the apparent force in the forward direction is removed they are at risk of falling backwards? Or is there an actual measurable jerk in the direction opposing the initial deceleration?

If a marble were rolling forward along the carriage floor as a result of the train decelerating and had reached the mid-point of the carriage at the moment of complete stop, what would happen to the motion of the marble at that moment?

If a mass (on wheels) were attached by a spring to the rear wall of the carriage and the deceleration caused the spring to extend, what would happen at the moment of complete stop?

There would be a very small amount of rearward movement due to various bits of the train compressing under breaking load and then returning to normal. I don’t think that would be perceptible though and what you feel as a passenger is your own body pushing you backwards as a result of bracing against the breaking force (as you surmise).

The marble would keep rolling forward because it needs a force acting on it to stop it. The only force it has is from rolling resistance which is very small, so it will keep rolling until it hits an obstacle. A more interesting question would be what does the marble do if it is against an obstacle preventing forward movement but it is free to move backwards. If the train did have a small “rebound” when it stopped, the marble would start rolling backwards.

I think the mass on wheels, held by a spring, would rebound backwards when the train stopped. This is basically amplifying the very small compression / rebound the whole train would experience.

This is generally vection, or illusion of self-motion. As well as the occasional train experience, I’ve had a few freaky moments with this when braking (normally) to a full stop in a car - MY FOOT’S PUSHING HARD ON THE BRAKE BUT I’M ROLLING BACKWARDS! I’m glad to say it doesn’t happen very often, but I swear it takes a year off my life whenever it does.

A couple of notes, a train has brakes on all the cars. I don’t know much beyond that, if the brakes are set more strongly in the end cars to pull the front when braking, or set equally to slow the train without straining the couplings or what. Also the train starting up may reverse a bit first to compress all the couplings so the cars, when the engine starts to pull forward, will be started into motion one at a time. I assume the rolling stock still have compression in the same way an auto does when braking, so I would expect the same “settling back” sensation that you get in a car when it stops completely. I have to go ride a train now and pay attention.

If the train jerked backward at the moment it stops, the passengers would feel an extra forward force. If they feel a momentary backward force, it would imply the train had a sudden forward jerk.

I think it’s just an illusion. It’s more your body readjusting it’s center of gravity from being towards the front of you during deceleration to shifting back towards your center.
Think of a ball on a string hanging freely in the cabin. At a constant speed the ball stays in place. From the beginning of deceleration to the point of a complete stop the ball will swing forward. The moment you stop the ball not only returns to it’s original position it also swings backwards.

[quote=“pmwgreen, post:4, topic:944705”]
I don’t know much beyond that, if the brakes are set more strongly in the end cars to pull the front when braking, or set equally to slow the train without straining the couplings or what. Also the train starting up may reverse a bit first to compress all the couplings [/quote]

Might not have needed to post on the subject, then.

Train brakes aren’t that sophisticated; they are set or released. All wheels get the same impulse, whether an air brake piston or the electric current used for dynamic braking (on trams and some rapid transit trains). Leaks in hoses and other vagaries mean all the wheels in a freight train don’t get the same resistive force—but they all get the brakes applied and released at essentially the same time.

Freight trains have slack coupling so they can get one car rolling at a time, and you can hear the couplers clunking from one end to the other as a train gets rolling, or as it slows down. However, for passenger comfort, passenger trains are “close-coupled,” meaning they start and stop as single units.

I only rode a train once in the States decades and decades ago but rode the trains many times a day in Japan.

Sometimes they overshoot the stop line and clamp on the brakes, sending you forwards if you aren’t holding on or sitting down.

I saw a program in Japan for the training drivers and they had a line of tall blocks that would fall over at different rates of deceleration. The trick is to decelerate at the right rate, not too fast since that throws passengers forward and not too slow since that wastes time, and Japanese worry about that.

The other element here is that brakes tend to slow a vehicle smoothly but then “grab” immediately prior to the vehicle stopping.

We’ve all experienced this with car braking where if you want to brake to a halt very smoothly, you need to decrease brake pressure subtly just as the vehicle comes to a complete stop.

I think this adds to the feeling that the train jerks backwards as it stops completely.

Jerk is the derivative of acceleration/deceleration. When a train stops, it decelerates until its velocity is zero, and then the deceleration stops abruptly. By definition, yes, this is a jerk.

OTOH, I doubt that there is much of a backward movement due e.g. to compression. If it was the case, then observers standing outside the train would see it, so that movement would be familiar to e.g. metro commuters. Assuming that a backward movement exists but is too small to be seen (e.g. in the millimeter range), then it would not cause passenger inside the train to fall.

Let’s crunch some numbers. The basic principle of postural control, when you are standing, is that you try to place your body’s center of mass (COM, basically located in the belly) above the center (more or less) of your base of support (your feet).
When the train decelerates (typical deceleration are in the order of 0.5-1 m/s2, i.e.0.05-0.1g), the gravity vector appears to swing forward by ~3-6deg. Considering that the COM is ~1m above the feet, this results in an apparent motion of the COM of 5 to 10 cm relative to the feet (an uncompensated motion of ~3-4 cm would make you fall, IIRC).

In contrast, if compression caused a small backward movement which is too small to see, i.e. a few mm, then the feet would move by a few mm while the COM remains roughly in place. This is relatively harmless. Also, the sensation would be that the feet are slipping, not that the body is being jerked.

Note that postural control and motion sensations are two different things. Postural control is mainly the spinal/cerebellar/vestibular circuits doing what they can to maintain balance in face of a strange physical situation. The passenger’s sensation is another matter (and yes, I guess they probably feel they move backward).

Here is a paper I quickly googled that gives you some figures:

Other than this:
A marble rolling on the carriage floor would continue rolling forward: basically it would follow its inertia and continue rolling at the train’s initial velocity (before decelerating).
Your spring-attached mass would indeed cause the spring to extend. After the stop, the spring would go back to its resting length. However, since spring/mass systems are oscillators, it would oscillate a few times while doing so. The same would happen to a pendulum fixed to the ceiling.

It definitely is jerk in the mathematical sense, i.e. acceleration (in this case, deceleration) suddenly changes from a nonzero value to zero.

Jerk is also observed in airplanes when the plane is lined up for takeoff, but the pilot stands on the brakes while they spool up the engines; when the brakes are suddenly released, acceleration suddenly increases from zero to some high value, suddenly shoving passengers back in their seats.

Jerk is also caused by crappy limousine drivers. Want to give your passengers a smooth, comfortable ride? Ease on the brakes gradually as you start to decel, and ease off of them gradually in the final moments before your speed approaches zero. Likewise with the accelerator pedal; gradual changes to acceleration/deceleration are least jarring for passengers, and that applies whether they’re in a plane, train, or automobile.

Isn’t the jerk backwards caused by the train’s suspension settling back into a neutral state?

As Senegoid pointed out above:

As I often do, I was bicycling next to the big Chicago Amtrak yard this afternoon, and stopped to watch a long train being slowly brought into the yard for servicing. I happened to be watching the locomotive wheels as it came to a stop and . . . saw a noticeable movement backwards as it came to a complete stop. This would be on the order of 15º (out of 360º) retrograde motion. I’ve probably watched hundreds of commuter and intercity trains stop at platforms over the years and never before have I noticed anything like this. It could be something related to the train having been run a few hundred feet south and then back north to position it to enter the wash shed (meaning a hostler at the south end had a hose with a valve to dump the air if an emergency stop were needed during the backup move, but AFAIK an engineer was at the throttle and brake stand in the lead locomotive, like normal operation.

I shall make further observations.

For a 28" wheel, that’s 3.6 inches of backward motion. I’ve never noticed a passenger train doing that when I was standing on a platform watching.

A car certainly appears to its passengers to back up at the moment of stopping. I assume we have all noticed this. When you put on the brakes, the inside appears to move forward a bit on the springs and the instant of stopping allows those springs to relax. It seems plausible for the same to happen in a train.

There may be a little bit of fore-and-aft compression of the rubber bushings in the suspension linkage and the tread of the pneumatic tire, but I think most of the suspension movement that’s felt (in a car) is the vertical movement of the suspension due to weight transfer. When you’re hard on the brakes, the front end of the car dives and the rear end rises, and both ends of the car suddenly settle back to their normal height when the deceleration suddenly ends. This is more noticeable in a big luxury car with a super-soft suspension, and less noticeable in a sportscar with stiffer suspension.

A rail car has a very long wheel base and a fairly low center of mass, and modest levels of decel, so not much weight transfer. Moreover, the suspension is stiffer than on a road-going car because rail cars don’t have to deal with things like potholes and speed bumps. Bottom line, there isn’t a lot of weight-transfer-related suspension travel to undo when the rail car hits 0 MPH. Next time you’re waiting for a train, watch while it comes to a stop at your platform; make a note of whether there’s any backward motion or suspension movement after it comes to a stop.

A little game I sometimes play with myself is, when slowing for a red light and no one is around, trying to decelerate so slowly that I don’t feel the little jerk when the car finally comes to a complete stop. I don’t think I’ve ever done it.

In Japan, the conductors of regular trains often neglect to ease up on the brakes as they come to a stop, and yes, the passengers all experience high jerk when the speed hits zero. The Shinkansen conductors are much better at easing up on the brakes at the end (maybe a job requirement, to line up the train doors with the platform gates?); if you’re on board and close your eyes, it can be hard to tell when you’ve come to a complete stop.

Sure, but that’s not why standing passengers jerk backwards, it’s because they have been bracing against the deceleration and then can’t react in time or accurately enough to stop bracing as the train stops, it’s the passengers who launch themselves backwards. And as noted, if the train was jerking backwards significantly, the passengers would be jerking forwards, not backwards.