It seems like cheating that the answer to "How Do YOU Get a Train Moving?" is "With a locomotive."
I'd answer "with a crowbar". I used to work in a railway museum and when we didn't have an engine in steam we'd do our shunting with crowbars. The technique is to get a 6 foot long bar with a bent end. Wedge the point of the bent end between the tread and rail, so the "elbow" is resting an inch or two behind the wheel and the bar is up at a 45 degree angle, so forming a lever with a lot of mechanical advantage. Put all your weight on the bar. Eventually the car will start moving. As the car moves, release the bar, slide it forward and repeat. Eventually the car will be moving fast enough that you just run along beside it, sliding the bar forward and jacking up and down with your hands. One person can move a typical car on the flat, but if that's not enough, a person with bar on each wheel will get most things moving.
Always have someone on the handbrake, as you will kill yourself if you try to stop the car with the bar!
According to the video about 100 kg tractive force is enough to get the locomotive moving. That's a lot less than I expected (though I've seen a video of a strongman called John Massis pulling a loc by his teeth).
Seems like all rail cars need a cyclical version of this, an elbow that can be lowered, and with a circular crank, be wedged and turned to produce forward motion.
Or a wind-up where a spinning lever could compound effort onto an axle and drive the car forward...
Had to make it obvious! Once the car is moving, if you try to continue jacking by jumping on the bar you run the risk of going under the wheels. The wheels can easily slice you in half.
This is a very poorly written article (I'm amazed this is written by a physics professor). Static and kinetic friction is only a resistive force to a train if there is slippage between the wheels and the track.
-Assuming a no slip condition at the wheels, the friction will rotate the wheels not drag on the train/car.
-The reason why there is a gap/space in the train couplings is a tolerance/GD&T issue.
Top commenter got it right:"The locomotive is accelerating itself and the cars, not overcoming the friction in the bearings. Axle bearings have pretty low friction (at least negligible compared to the inertia of a loaded car); if they didn't, they would get hot, the grease would melt"
Slack is something railroads would love to get rid of.
If the slack isn't managed properly when starting a train the jerk can rip the coupler knuckle right off and split the train (which brings everything to a stop when the brakes automatically apply when the air supply hose is separated).
I've seen many a train startup on a grade with all the slack stretched out and wrapped around many degrees of curvature: modern diesel-electric locomotives have tremendous tractive effort right from a standstill.
These modern locomotives have computer-controlled wheel slip systems, sand dispensers (that inject sand between the wheel and the rail to increase friction), and active steering trucks. And for the past decade or so locomotives have switched from DC traction motors to phased AC (which don't have high-current brushes that can melt at high-load, low-speed).
All US railroads have mandated low-friction roller bearings in everything since the 60s or 70s, too.
I'd imagine the railway engineering field has all the physics of this stuff well-documented since the basics of railroad operation hasn't really changed in 100+ years.
I would have been a 4th generation RR employee, if the RR hadn't gone bankrupt. Got to spend all kinds of time as a kid in rail yards going stuff that would probably be illegal for everyone involved now a days. This is before CCTV everywhere and extensive tracking. Anyway I'll try to match up first post comment/question with second post correct answer, if this reformat helps:
Torque is higher at low speeds - No, with "modern" say post 1960 diesel-electric locos its constant. Or more accurately current limited to a max which is achievable at almost any reasonable low speed condition. Maybe a car analogy is all locos can "spin their tires" under any condition up to 45 MPH or so. There are no "econobox locomotives" or the equivalent.
Peculiar spherical cow assumptions about no-slip conditions - No, its very complicated and as you'd suspect lots of anti-lock anti-skid technology actually started on trains before it went to cars, and trains are always slipping a little (not very much, and the optimum is not exactly zero just close to it)
Slack is an intentional mfgr tolerance thing - No its something that could (almost) be eliminated and is a huge PITA under certain operating conditions. Its goal zero not goal 0.1% by design or whatever.
Theoretically the bearings must be pretty good - yes indeed they are, awesome roller bearings required by regulation since the 60s
If you provide specific examples of what doesn't make sense it would be possible to expand upon that specific topic.
OK... first of all there are thousands (no joke) of coupler designs. If you've seen "Thomas the Tank Engine" you're familiar with 1830s era chain/buffers but those are obsolete. I can only talk about the modern USA Janney coupler. My comments might be totally wrong in Norway or Russia or pretty much anywhere else. Saudi Arabia of all places uses Janney couplers. (edit to add my point is there may exist a coupler design in Germany or England or something that inherently uses springs. Just not in the USA, not for over a century, ours are solid bars of interlocking hands made of steel with a guard that prevents them from unlocking and a pin/latch arrangement that prevents them from swinging open...)
Anyway if its under tension it can't be unlocked. When you release tension you can shove a pin out of the way (if its not rusty) and it then can be unlocked. So that in itself is an interesting comment. If the train isn't under tension it literally can't fall apart short of metallurgical failure (like a crack) and train crews don't like it when their train falls apart, so the don't like their train not being under tension. All freight couplers are the same but the hazmat and passenger car couplers are a little weirder and slightly harder to uncouple and have a lot less slack by design (I've been told its mostly closer mfgr tolerances). None the less couplers do rust and removing tension means a rusty coupler could unlock and train crews hate that. So yeah, crews don't like a train that gets compressed. You have to back up to switch but you don't do it for fun or whatever. Aside from the whole visibility thing which means you could kill some poor dude a half mile away backing over him and never know it.
The thing that connects the coupler to the center of the car is called the draft gear. To say it has a high spring coefficient would be an understatement. Some cars/engines don't have any draft gear at all and the coupler is welded right to the center / spine of the car. When a train couples, the spring flexes so things aren't permanently bent. Its not like a shock absorber in a car which flexes all the time while rolling along, its more for damage reduction (edited to add, and the coupling process itself)
The slack comes from the 1/2 inch or so space in the coupler, times a large number of cars. A hundred coal cars times 1/2 inch is like 5 feet of slack ... So no need for springs you've got all the slack you can handle in the couplers. You could spec a coupler with 1/16th inch precision but then every time you switch a freight car you'd need a guy with a sledgehammer to screw around for 10 minutes so thats hazmat and passenger only which I have no experience with.
Since the (19)60s all cars have roller bearings and the static friction is so low that unless you applied the brakes in some weird manner the cars will kinda flop around on their own. Pushing a train is an interesting experience that should be a part of all physics experimental curricula. You really can push a train by hand. It won't be easy and it won't go fast and it definitely won't accelerate very fast, but its not hard. So you could only guarantee compression if you're actively moving / just moved or you're headed downhill slightly. Wind can actually move cars around. This is why all cars need a parking brake (that horizontal wheel) in addition to the air brakes. It would be mechanically complicated to put a train under compression but it could be done by locking the brakes or something.
The static friction of a car is like 100 pounds if the bearings are in good condition and the parking brake is completely removed etc etc. The slightest incline, or maybe even wind load, exceeds the force of static friction. If you have a hundred tons of coal in a car, the static friction is a mere rounding error. It might be calculable, or even measurable, but it won't be noticable when driving.
(edited to add the best car analogy I can give is its like a skateboarding kid hanging onto the back of your car, you're just not going to notice the extra friction compared to the mass of the car)
Realizing that you don't have as much experience with passenger trains, but just out of curiosity about the physics --
On a theoretical passenger train where there is exactly zero coupler slack... say this train travels on a perfectly straight and level track so there's no need for coupler slack at all, maybe the cars are actually welded together for this experiment --
Would it be particularly difficult for a single engine to start the train?
(Assume the train isn't ridiculously heavy or anything. This is really just curiosity about whether slack and/or draft gear make a difference when starting from a standstill.)
>Engine torque is almost always higher at lower speeds
This depends entirely on the engine - for most internal combustion engines, it's most definitely not the case. The reason you have to shift down when climbing a hill is to get the engine into a higher rev-range (compared to the wheels) than it currently is. With Nascar engines it may be that they are able to make a flat torque curve - probably because of the RPM restrictions. Most non-turbo passenger cars will make maximum torque in the mid-high end of their engine speed. Turbo/super charging assists in boosting torque output at lower engine RPM than in normally aspirated engines. The torque characteristics are a property of the bore/stroke relationship and the intake and exhaust tuning, as well as the camshaft timing. The reason we now have variable length intake manifolds and variable valve timing and lift on engines is to maintain the peak power operating combined with better torque at lower speeds, which aids drivability overall.
Electric engines make maximum torque at 0 rpm, which is why most locomotives are diesel-electric, because the electric engine can make maximum RPM at standstil, while the diesel engines can be operated at higher RPM to create the most power.
That is true, although direct drive without a tranmission simplifies a design and reduces driveline losses. IT all depends on the application. IIRC Tesla originally had a two-speed gearbox in the Roadster but dropped it because of reliability, and went to increasing the engine RPM instead.
It doesn't stay constant. I didn't assume it stays constant either.
Your maximum torque can be extracted by the right gear from the maximum _power_ peak. That means even with diminishing torque with angular velocity, if it diminishes only slowly, it's still worth going to higher angular velocities.
Example:
Say if you have a motor that has
100 Nm of torque at 100 radians/s, which is 10 kW of power, and
80 Nm of torque at 200 radians/s, which is 16 kW of power.
And further, you specify that you need to have the maximum torque in the wheels at 10 radians/s.
With a 10:1 gear ratio, when your wheels run at 10 radians/s, your engine runs at 100 radians/s and provides 10 kW. Thus the torque at the wheels is
10000W / 10 radians/s = 1000 Nm.
With a 20:1 your engine runs at 200 radians/s and 16 kW and wheel torque is:
16000 W / 10 radians/s = 1800 Nm.
More torque at the wheels with less torque at the engine!
Of course, with a fixed ratio, the latter vehicle would be limited to a lower top speed. That's why we have gearboxes and variators etc.
With an electric motor though that has better torque at lower speed, you can often try to design for a compromise so that you don't need a gearbox and might not even need a gear ratio at all.
I used SI units since you get extraneous confusing factors otherwise.
Here's an example of a brushless motor power vs rpm. You can get maximum torque for your selected angular velocity by operating at the max motor power and using the right gearing.
http://www.mcpappyracing.com/images/dyno/chart_power.jpg
> Static and kinetic friction is only a resistive force to a train if there is slippage between the wheels and the track.
No, static friction affects the train _until_ it starts moving. If there is any slippage or movement or anything, you've moved into the realm of kinetic friction, whether it be between the wheels and the track, or the axle and its bearings.
> Axle bearings have pretty low friction ... if they didn't, they would get hot, the grease would melt
Axle bearings have low _kinetic_ friction. They can, in theory, have a much higher static friction, and this is what needs to be overcome to get the train moving.
It doesn't make any sense to talk about static vs kinetic friction for the cars because they have roller bearings. Static friction is when things are not sliding and kinetic friction is when they are sliding.
Since the cars have roller bearings (not bushings) the wheel doesn't slide relative to the track and the axle doesn't slide relative to the axle truck.
There might be slightly more start-up torque to get a bearing moving but that's more as a result of the static friction of the seals or the roller cage or the grease. The reason that bearings work so well is that they DON'T slide but rather roll.
They're an ingenious hack around the idea that you have to pay the price somewhere for friction. Before they existed everyone bitched about friction but "hey what can you do?!" Afterwards it seemed obvious but the world spent many thousands of years with wheels and no bearings.
> It doesn't make any sense to talk about static vs kinetic friction for the cars because they have roller bearings.
Well, modern trains don't have cabooses either. So the scenario wouldn't even come up.
But suppose that this is a train from 1940, with a caboose, with journal bearings instead of roller bearings, and with a steam engine. Can it start?
I wonder if maybe this was a legitimate problem from the steam era, which led to the procedure to compress the train and the start it one car at a time. It's conceivable that we'd keep passing along the received wisdom, even after roller bearings and electric motors changed the picture.
Fundamentally, static friction is the force that's going to be preventing the train from starting to move. If you had a semi-truck in neutral on a flat surface, I don't think you would be able to push it. The wheels aren't slipping on the ground, but rather it must be in the bearings. The problem is F=ma. In this case m is large.
"Loose coupling is necessary to enable the train to bend around curves and is an aid in starting heavy trains, since the application of the locomotive power to the train operates on each car in the train successively, and the power is thus utilized to start only one car at a time."
So how do you get a locomotive started when the engine and cars are not on flat track? If there is any kind of incline, you'll have no slack in the couplings.
You use sand to generate grip, releasing the brake gently and apply power/throttle slowly. If you open the throttle too much, the wheels will spin and you'll damage the locomotive. Don't apply enough power/throttle and the train will roll back down. It takes skill but is honestly no different driving a car and doing a hill start. Same technique.
This is a Garrett type locomotive on the Welsh Highland Railway. They are the most powerful steam locomotive type on 2ft gauge. Beddgelert station is on quite a gradient and makes for a challenging restart.
I'm guessing you answered your own question. If they put the break on the last car, they could let the train compress backwards before starting. Naturally it would still be more work than starting from flat though, so obviously there would be an incline limit beyond which a given train couldn't start regardless.
The original article stated that a train wasn't able to start because the caboose's brake was on, so presumably the answer to the second question is yes, at least for that car. Presumably the first question would depend on the slope of the incline (although if necessary other brakes could be engaged after their cars' couplings were compressed). Anyway, all just conjecture on my part!
The slack action from a mile-long train is one of the most awe-inspiring, bone-jarring manifestations of raw power I have ever experienced. The first time I felt it, it established in my mind the idea that freight trains are forces of nature rather than vehicles.
Passenger trains also experience it (though the gear on these trains are slightly stiffer), but those cars are designed to have a much smoother ride, and they are also much shorter (8-10 cars instead of 80-100+). On a long train, it sounds like thunder coming from the front, and then a split second later the entire world shakes.
From my father, who used to drive steam and diesel locomotives in the UK on a Heritage railway (2ft Gauge).
He says strictly speaking, legally you're not allowed to reverse a train once passengers are inside without permission, but you can "rock" the locomotive forwards & backwards if you're stuck.
Also the reasoning is you can derail a collection of (relatively) lightweight cars by pushing behind them with a very heavy engine, but its much harder to derail by pulling.
Think of trying to keep a rope straight by pulling on it, vs trying to keep a rope straight by pushing on it.
The passenger train rule is because its hard to kill people by tipping over coal cars especially when its a rare failure mode anyway. But you wouldn't risk it with cars full of passengers.
(Oh and edited to add WRT switches, its subjectively 10 to 100 times harder to derail on a switch going one direction than the other, so again you'd risk backing a bunch of coal cars thru a switch but it would be pretty dumb to do it with cars full of passengers)
I am fairly certain that trains do not need the slack between cars to get moving. Like others have pointed out, trains seem to be perfectly capable of starting on inclines where there would be no slack.
There is one assumption in the article that is certainly wrong:
"...but it seems crazy to think that the train’s friction coefficient is 10 times more than the cars"
This does not make any sense. The forces we are comparing is the friction between the rail and the wheels in the case of the engine and the friction in the bearings of the axles in the case of the cars. There is of course some frictional force from the deformation of the track and the wheel as well but as they are both quite rigid (being made of steel) it should not be very significant.
Static friction is what opposes movement between two surfaces that are static next to each other and kinetic friction is what slows down movement between two surfaces. Static friction is always >= kinetic friction.
Think about how when you start your car from a standstill you need to be careful about your clutch release but when the car moves even the tiniest bit you can even start in the second gear if you want.
So, the engine car's wheels get kinetic friction (because they're rolling) and the other cars' wheels (which are stopped) are blocked by static friction. When you have slack and you move one car at a time you only need to beat the static friction of one car at a time. Even if the difference is 10%, if you have 10 cars and it starts to add up. I'm not saying slack is required for starting the train, just that there is an increased difficulty in doing so without slack.
Also, this is why doing a wheelspin is never a good idea when you have trouble starting your car/train. The traction when the wheels are blocked but the engine tries to move them is always a lot better than when they're spinning in place.
To be super-pedantic (because the topic is interesting), a little spin is good for an automobile. Rubber friction is a combination of adhesion, mechanical deformation, and wear.[1] In order to maximize traction with a tire you will have some optimal slip, increasing the "wear" component beyond what is seen in "normal" driving conditions. Of course, too much sliding/wheelspin and you reduce the other components. It's a balance that depends on rubber compounds, tire construction, and road conditions.
This is true for many modern high-speed trains (though those tend to not be diesel trains...), but those are only a small fraction of all trains.
Upgrading all existing freight cars with dedicated motors would be a crazy effort. Of course you could argue that freight trains aren't modern, which would make your comment correct in the worst sort of way ;-)
This may be the case on electric passenger rail, and generally is the case for high speed passenger rail, where each carriage, and sometimes each wheelset, is powered.
However even for electric freights, you'll typically have a small number of traction wheels on the actual traction units.
http://en.wikipedia.org/wiki/Multiple-unit_train_control covers the gist of it. One of the challenges of long trains is that you can't easily start them on a curve. As the front of the train is pulled it wants to 'straighten out' and that would pull mid-train cars off the track, Such trains if they don't use MU put locomotives both in the back and the front (and some times mid-train).
The advantage of standardized MU is that your engine is simply a control center (especially if you're using power from overhead catenary wires) and any train of any length can "work" because the traction motors in every car are sufficient to push that car with some flexibility (some can push up to two additional 'dead load' cars.)
But as others have pointed out, in the US the tracks are primarily straight, the existing traction motors in diesels system works well enough, and there is little incentive to change. That said, one of the options on the table for electrified CalTrain is MU equipped cars so that train sizes can be varied depending on commute load.
MU allows you to have multiple locomotives controlled together, but individual train cars still generally don't have traction motors. There are specialized traincars that have motors but not generators [1] but I don't think these were what foobarian was referring to.
The trains in the u.s. are still pretty primitive. Do a google image search on amtrak for some cringeworthy pics.
Where I live in Europe the only trains where the engine pulls are freight trains. All passenger trains except some cog-wheel trains in the mountains have diesel electric generators and individual motors on each wheel.
While Switzerland has opted to go all-EMU for its passenger trains, that's not true of every country.
For example, the only powered axles on the French TGV are at the front and rear of the train. All the axles in-between are unpowered. The TGV isn't exactly a primitive train.
The TGV was the basis of the Spanish AVE and the Korean KTX. The KTX also uses additional powered axles on the first and last cars, but it still has a lot more unpowered axles than powered ones.
As for Amtrak, the Acela isn't a primitive train. It's a mashup of the French TGV and the Canadian LRC. And yes, it has unpowered axles in the middle. Its main problems are its excessive weight (forced by FRA regulations), and the totally inadequate investment in the track over the last 80 years. The basic design isn't that bad.
Well, the AVE 103 is based on the Velaro platform which most certainly has powered axles on every car, as you would expect from a German train. The same goes for the Russian Sapsan, the Chinese CRH3 and the German ICE3
In the USA, freight is the vast majority of rail traffic, excepting a few highly populated corridors in the northeast and commuter lines in a handful of other urban areas.
If you think propulsion is primitive, try braking. I was surprised to learn recently that braking is typically transmitted from car to car by compressed air, so that it can take up to 2 minutes for the braking instruction to reach the last car in the train.
Just as it's tricky for hte locotomotive to start the whole train at once, if the air braking system should fail, the momentum of the cars is likely to exceed the braking power of the engine: http://www.retronaut.com/wp-content/uploads/2013/01/317.jpg
"As a result of this and other runaway incidents involving locomotives with dynamic braking, the Federal Railroad Administration reversed its mandate that dynamic braking be disabled when train brakes are placed in emergency. The mandate now is that they must all remain functional."
What was the original rationale behind the emergency brakes disabling the dynamic braking?
I know, I just wanted an excuse to post the Montparnasse photograph again. There was actually an air-brake related derailment in Canada just last January on a train carrying crude oil, though luckily without major loss of life this time. I was surprised to learn that electronically-activated braking systems aren't the norm.
I think that having to appeal to couplings' slack to be able to start a train was used in the steam era, because steam engines are constant-force machines (limited by steam pressure and cylinder area). Diesel-electric or electric machines can start stretched trains, even manuals of 1950 engines advise to start stretched. Starting slacked is dangerous because of the impacts on couples (current trains are much, much longer than steam-era trains).
The article totally misses the fact that the static friction to overcome on the cars are a static torque not a force. The forces on the cars are acting on the coupling and at the wheel contact point, but the static friction to overcome is at the axle diameter. The torque arm is such that the force there is larger by the ratio of the wheel and axle radii. The larger the train wheels, the less effect the static friction will have.
I'd answer "with a crowbar". I used to work in a railway museum and when we didn't have an engine in steam we'd do our shunting with crowbars. The technique is to get a 6 foot long bar with a bent end. Wedge the point of the bent end between the tread and rail, so the "elbow" is resting an inch or two behind the wheel and the bar is up at a 45 degree angle, so forming a lever with a lot of mechanical advantage. Put all your weight on the bar. Eventually the car will start moving. As the car moves, release the bar, slide it forward and repeat. Eventually the car will be moving fast enough that you just run along beside it, sliding the bar forward and jacking up and down with your hands. One person can move a typical car on the flat, but if that's not enough, a person with bar on each wheel will get most things moving.
Always have someone on the handbrake, as you will kill yourself if you try to stop the car with the bar!