Thursday, January 20, 2011

115> Swing Low, Sweet PRT...

Sometimes a technology pops up out of the blue that unexpectedly solves stumbling blocks that have been around for years. In this case I will refer the reader to the 3-axis accelerometer, a nifty little device that you probably own a few of. Own a car? There’s probably one in the airbag controller. Own a digital camera? Probably one there too, to help you take a clear shot with shaky hands. Got a smart phone? That’s how that nifty feature that keeps the screen upright works. Game controllers. The Segway. The list goes on.

What I am exited about is how the device can operate as a level, a feature that was exploited to create the iPhone app above. You see, because gravity and acceleration are essentially interchangeable, an accelerometer senses gravity as constant acceleration. Zero this force out with software, and your accelerometer senses “acceleration” every time you tip it in any direction… a thousand times a second.  Voila! A level! Or actually, to be more precise, an inclinometer!

Meanwhile, in the world of motion control, engineers are redesigning the electric motor. In the old days, it was realized that rather than putting bunches of electromagnets in a large circular array to make a motor, just a few would do, if the rotation were faster. That way, the same magnets could come around and around again, faster. More power, less materials. Magic! Only problem was that many people didn’t want fast rotation, and a century’s worth of bulky and inefficient reduction gearboxes ensued. Recently, a revolution has been taking place in the world of motors, the conversion from mechanically switching the electromagnets off and on (brushed motor) to using an external controller. Now, rather than simply rotating at a given speed, motors can be made to stop, change speed, reverse, hold a position, etc. The modern servomotor has been born.

Now a new generation of brushless, direct-drive motors is emerging which return to large diameter magnet arrays for torque, rather than gearboxes. These offer powerful and accurate rotational control without requiring that a machine be designed around standard gearboxes and motor mounts. I am referring, specifically, to frameless torque motors, which have reduced this architecture down to a simple pair of concentric rings. They are simply inserted between the machine and the shaft to be turned, like a bushing or ball bearing unit.

So here’s how it all comes together. Pictured above is the swing-arm for the PRT vehicle that I have detailed in previous posts. Two pair of frameless torque motors (shown in red) are controlled by an accelerometer. These keep the vehicle in line with the normal gravitational forces. The accelerometer-torque motor combination can, in theory, eliminate any errant, sideways G forces. The idea is to emulate a free hanging system, without really being one. Why not just let it hang? Unbalanced or shifting loads, sudden gusts of side winds, or continual rocking back and fourth are all effects that need to be canceled. Other than that, a free hanging design has the wonderful effect of self-canceling motion-related forces from acceleration, deceleration, or turning. It’s like a bucket on a rope. No matter how you swing it around, water in the bucket won’t spill, because all gravity gets shifted toward the bottom of the bucket. With a vehicle-mounted accelerometer, any forces that it senses other than “downward” (in a relative sense) would cause the motors to lock up to arrest that movement, with the exception of a slight dampening, to control of the tendency to swing repeatedly like a pendulum.

I have mentioned in previous posts how the swing-arm design is extraordinarily safe, because rather than throwing occupants through the windshield in a head-on collision, the cab would swing forward, absorbing shock and transferring the direction of momentum so that it would essentially push the occupant into the seat instead of out of it. In this system, extreme forces will initially simply break the magnetic bond, allowing this forward swing. As the swing continues toward its apogee, however, the relative strength of the torque motors increases geometrically, applying ever greater braking force. Meanwhile the cab has gone from traveling forward to traveling upward, so it is additionally fighting gravity. All of this absorbs the force of impact without any mechanical damage to the vehicle. Combine this with bogey-to-bogey bumpers, and you have an extremely effective crash protection system. There are theoretical and mathematical ways demonstrate that split-second headways are not dangerous for PRT vehicles, but it’s pretty hard to beat coming out of a crash test damage-free to drive the point home.

Bottom line:
 You could set down a full cup of coffee and be whisked away at high speeds without spilling a drop. There is no reason why PRT can’t put any luxury car to shame in ride quality. An added bonus is unprecedented safety.  


Lars Endre said...

I'm sorry this is off topic, but thinking about G's;

Has any solution considered to make the off-line station elevated (say 1-2m) compared to the driving lane, so that the pod decelerates mechanically by utilizing G-forces and accelerates down-slope when taking off again?

Maybe a "bumpy" ride, (but only one down and one up per trip!) and other advantages might appear from it?

Andrew F said...

That would work well for stations that are integrated into buildings or are otherwise elevated. It strikes me that most stations should be at ground level except in very dense areas. Elevators are to be avoided!

This would, however, help with making tight turns. If, in advance of a turn, the guideway rose a few meters to help bleed off some speed, allowing smaller turning radius without unacceptable Gs (and should also reduce stress on the guideway). Once the turn is complete, the potential energy could be released as the guideway slopes down. I can't recall the formula for how much of a change in elevation is necessary for a given change in speed--I'm not an engineer so all the kinematics stuff has gotten lost in my head.

Dan said...

Dan the Blogger Responds...

Lars, Thanks for bring this up. I am not aware of any literature on the subject, and there ought to be. I think the idea is worthy of a separate post, and I think this is a good time to go into it, because it is actually rather related to the swing-arm discussion. I think some pictures would help, though, so give me a few days to put it together and we can give the topic the attention it deserves.

Andrew, I have done my share of elevated station bashing in this blog, but I have to say there are some advantages. For one thing, it is far more energy efficient to lift a passenger than to lift the passenger and the pod both. It is really a matter of what the realities are on the ground. One thing that warms me up to elevated stations a bit is the idea that they could be modular – Factory built and simply trucked in and bolted down. Don’t get me wrong. I don’t think we should be tied to them. Most inexpensive ground stations, however, involve quite a bit of real estate, even if they are mechanically simpler and dirt cheap. If the vehicles are strong enough to do fast highway speeds, then they probably can lift themselves very steeply if the track and bogeys have anti-slip modifications. Weaker vehicles, however, might need longer ramps, which could block driveways. Remember, even though the track might be high enough, the pods hang down and could get hit. Luckily the hanging design lends itself to all kinds of stations, for all kinds of situations.

As for going uphill before a sharp turn, I could see that in some instances, particularly if the turn corresponded to needing height to clear a street anyway, and if it could be done gradually enough to not cause more passenger discomfort than simply taking the turn faster. This is, again, situation specific. If there are lots of tight turns there is little to gain by speeding up between them; If there is a long leading straightaway, there is probably plenty of room to simply coast to a slower speed. This, too, touches on a subject that is probably deserving of it’s own post, that being the question of preferred track height. Is there even such a thing?

Lars Endre said...

Ride height; my vote:

Anything but ground level. And the reasons for it; 1) never design a solution that is depending on "yet another thing" (in this case, ground) and 2) if You design without the necessity for on-ground development, the sky is Your limit.

PRT can, and should, take the "virgin third dimension" to good use based on its low weight and rail-like driveway (which has to be built whether on or off ground).

"How high?"; that's a question that doesn't need an optimized answer. I'm thinking the "value" of the station elevation will most often override the varying costs of different heights.

Andrew F said...

Lars, I think the idea is that many PRT designs require elevated stations as a consequence of their maximum slope, etc. What I'm suggesting is a system that does not require elevated stations. Elevated stations may be appropriate in many areas, but that added flexibility to provide inexpensive stations is quite valuable in serving lower-density areas.

Rick said...

The change in Potential Energy should equal the change in Kinetic Energy (delta_PE = delta_KE). This works out to 30ft(9.1m)of elevation change to stop from 30 mph (48.3kph).
The formula is m.g.h = (m.V^2)/2. Mass, m, cancels out so h, height = V^2/(2.g) where acceleration of gravity, g = 9.81 m/s^2.
A ramp 2m high would stop you from 6.3 m/s(14mph). This is not a significant amount of energy savings (22% of the KE at 30mph).

Lars Endre said...

Rick, You're right. Seeing that "brake-height" needed is proportional to the square of speed, normal-to-high speeds will start to require roller coasters!

You are also right that if one goes for a "standard elevation" on stations of, say, 2-3 m, that would not take out much energy compared to the total needed.

However, and purely from a "green" perspective, something is better than nothing, in the sense that (some) energy conversion from mechanical-to-electrical (and back) would be saved. And conversion is loss. I'm not letting the notion go altogether, so moving on to next article, where Dan highlights design issues and if it is - in fact - smart to do this for other reasons too.

Dan said...

Thanks for the math, Rick. It is appreciated. I can’t tell you how many times I’ve had to beg the time of guys like you. That being said, I think 22% is very significant. In the old days, if an appliance, vehicle or process was 22% less efficient, it was no big deal. Nowadays endeavors of all sorts live and die on efficiency margins far less than that. Let me offer a perspective that is a little bit more for the layman. As an American who started getting his hands into machinery back in the sixties, I still have a tendency to think in somewhat imprecise non-metric measures, so bear with me for a moment. This is for us old fossils in the US. (Here is a torque conversion calculator for you youngsters who like Nm better.)

The vehicle will weigh, perhaps, 1100 lbs., which happens to be a nice round number for those of us who have a feel for horsepower. One horsepower is the power required to lift 550 lbs. one foot in one second. In a scenario where the vehicle is raised 6 feet, if it took 6 seconds it would be an expenditure of 2 horsepower for those 6 seconds. That’s like, three seconds of your lawn mower (on a very good day) One horsepower is also 746 watts, so we can say that we will be burning off the power of around 20 75-watt light bulbs during the climb. This, minus friction, is what gets returned to help launch the vehicle. A lot? A little? It is what it is.

Let’s not lose track of the repeating nature of the thing. That (20 75w bulbs for 6 seconds power savings) is per vehicle, and there could be thousands per day per station.

Figures like this always end up on a balance scale, of sorts, mixed in with a lot of other factors that get weighed in the grand compromise of mechanical design. A century of building automobiles, for example, and we haven’t even settled on front or rear wheel drive. There is rarely a right or wrong way to design complex systems. There are just convergences of strategies and/or benefits that tip the scale one way or the other.

One such convergence may be architectural. If you take a look at the second illustration in the next post, you can see that if decking were installed on top of the track, people could exit the station on the ends to access gardens or whatever, and even the station roof becomes accessible by making stairs up the sloping track. I can imagine variations that could span a street with elevators on either side. You could build an elevated linear park where PRT comes up from beneath you. Hmmm. Virgin 3rd dimension indeed!

Dan said...

Oops! the link doesn't work! It's just the torque converter from

Anonymous said...

Hey, you Americans didn't invent a separate unit for second? How come...? :P

Rick said...

In your reference to Nm you have made a common mistake (even among engineers)of confusing torque and energy. They often have the same units, in the English system, but are not interchangeable.

You can calculate power, Hp, if you know the torque at a particular rotational speed, RPM, with the formula: Hp = T[]*N[RPM]/5252
The constant 5252 comes from (33,000 ft·lbf/min)/(2π rad/rev). This is copied from Wikipedia.

I was taught that, to avoid confusion, the units for torque should be [lb.ft] and for energy [] but I don't think that there is a standard that says that.

Bengt Gustafsson said...

Regarding the possibility to use the up-swing of the cabin to mitigate crash forces I'm quite sceptical. As was calculated in this same set of comments h = v2/2g, so at speeds higher than 5 m/s or so the rotational movement would have to be stopped to avoid crashing into the guideway from below, creating a mess.

Dan said...

I’ve got bad, bad habits, Rick. There’s an “Energy/Work” calculator on that AskNumbers page as well, but I just don’t use it much. Most of my experience is with stationary equipment, where the penalty for over-sizing something is a beefy machine that vibrates less and lasts forever. Motors draw in as much juice and put out as much power as is required, unless something is wildly undersized. To be honest, anything that I design for mass production is going to need to have a lot of “fat” trimmed by an engineer. (Hopefully by one who knows enough about machine and fabrication shop practices to not drive the cost through the roof!)

Bengt, I never said that gravity alone could do the job of absorbing the force of a collision. It would start with the wheels braking, while the emergency mechanical brakes clamp onto the track. Assuming that this did not stop our vehicle, the next thing would be the bogies hitting. I envision that both (the back of the leading bogie and the front of the following one) would each be capable of retracting, say, 50 cm each, for a meter of combined cushion. The swinging action would add, perhaps, another meter of deceleration space. Since the momentum would easily break the vehicle free of the magnetic constraints of the torque motors (and gravity, as you point out) some sort of additional (presumably hydraulic) shock absorption would be required. At the very end of the swing would be a bumper to stop the vehicle from hitting the track. Anyway, I look at it as two meters of cushion, (controlled deceleration) only some of which would include conversion of horizontal force to vertical lift.

Dan said...

One more point… In practice, the full rotational momentum would only happen if the vehicle hit something with no warning. That way it starts from a position of hanging straight down. Any braking prior to impact is going to preposition the vehicle in a forward leaning pose, changing the dynamics greatly.

I think you are right in having doubts about the amount of force that this scheme can absorb. Both forward and the resultant upward momentum need to be arrested in a carefully crafted logarithmic fashion, and even then, only slow crashes could be absorbed. Still greater “bogie-to-bogie” impact absorption measures could be employed, but I really think this is largely for show anyway, and going too far risks making it seem like collisions are actually a real possibility.

I am particularly interested in how this applies to platooning. On one hand, if the vehicles are in a platoon, they have no relative differences in speed, so no protective headway is required. If they are widely spaced, the relative velocities could change, but the headway allows time to brake. But what about the act of joining or leaving a platoon? Doesn’t this action totally disregard the whole concept of safe headway distances? In the US, as I understand it, we have some quaint rules about safe headway and “brick-wall” stops that were written for the railroads. These clearly should not apply to PRT, but nobody has actually done the amending. Politically, it’s hard to reduce any safety measure that’s already on the books, no matter how wrong-headed it is.

I start with the assumption that there will be a great deal of skepticism about any higher-speed system’s safety. Perhaps moving the bar from “collision damage at any speed” to “collision damage only above “x” speed,” even if that number is low, will pay dividends in this respect. Maybe it’s all about feeling safe.

Bengt Gustafsson said...

Yes, the main safety problem with platooning is the formation and dissolving of them while running. Some more conservative ideas are to form and dissolve platoons only when stationary, or even connect the vehicles mechanically while standing still, like for railway cars.

Ingmar Andreasson has suggested that a coupling which automatically engages when vehicles get close enough and then disengages sideways if they take different ways in a diverge. This is very elegant, but the problem is that if three vehicles select left-right-left then the two lefties will be at an unsafe distance after the diverge. This led him to the conclusions that vehicles should only use this coupling in pairs.

Bengt Gustafsson said...

I checked the ETEL home page for those torque motors. To me it seems that you get too little torque out of them for it to be useful. That of course depends on what you are planning to use them for, but I would say that you would typically want to be able to at least force the cabin to be vertical in a strong crosswind. Such a wind can cause a force of maybe 1kN sideways on the cabin's pressure point, which typically would be 2 m below the point of rotation. This means 2 kNm while one of the larger motors could peak at 600 Nm.

To me it seems that while the design is neat, torque motors like this don't have the necessary torque/weight ratio required. A regular motor with a gear box can however easily do it.

Anonymous said...

Sorry guys, but I think you're partly trying to solve things that are not problems.

The platooning issue for example. We nowadays have cheap machine vision. The whole track can be automatically monitored for hindrances s.a. fallen trees or crashes (with acceleration sensors to detect sudden bumps). So why not simply forget the platooning - why is it even needed (any more)?

It may have made sense in the 1960's and 70's.

Rick said...

I agree with Bengt, a simple hydraulic damper (shock absorber) would cost less than $20 for each of these axes and would be very reliable. A progressively stiffening spring could prevent hard contact with the track and slightly less than critical damping would control swinging motion.

Dan said...

You caught me Bengt! When I was designing that swingarm, I was just thinking of unbalanced or shifting loads. The motors are drawn to scale based on those model numbers. They are, I believe, quite adequate for that, but nowhere near strong enough for those occasional super strong side winds. (qt pointed out that possibility in the upcoming post about winter weather.) You are right. A gearbox handles the problem nicely. I don’t want to get the thing too unresponsive with a little motor and a big gear ratio, but we certainly could lighten it up a bit over those heavy torque motors I chose…My gut tells me something like an 8 to 1 (gear ratio) planetary gear, since it would distribute force over more teeth and angles. Perhaps something like this.

Rick, it’s very hard (perhaps impossible) to adjust for unbalanced loads with ordinary shock absorbers and springs. The problem is a steady lean to the system or a bias toward swinging in that direction. This would lead to potential problems docking the vehicle. Even a steady side wind could create the effect. With no wind and a balanced load, you are quite right, but you still need to establish a baseline from G forces alone and then compensate for deviations from it.

Rick said...

Dan, I was thinking of using springs only for the fore and aft motion to control the pod in sudden stops (or accelerations).

Side to side unbalance does not need correction. For example:
A single 200 lb occupant with their CG 1 foot off center.
A pod weighing 500 lb empty.
Occupant and pod CG's 3 feet below pivot vertically.
The pod would rest at about a 5.5 degree angle and the pod CG would be a little over 3 inches off center.

The station should be designed to correct this lean and besides you wouldn't want the pod swinging around when people are loading.

The sidewind problem is in reality not a problem because to correct it you would need to apply a large torque to the track and bogie which would make them heavier. The ability to swing and releave these loads is one of the advantages of the hanging configuration. Gondolas and chairlifts handle sidewinds and unbalance without active control.

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