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Linear magnetmotor - the basics for a beginner Answered

Designing what is said to be impossible can be tricky, so I will try to give you some tips to reach your goal a bit quicker.

A lot of people these days try to start with a wheel.
Makes sense in one way as the final goal obviously is something that would rotate.
However, considering angles in a rotating system is far easier with a usable baseline!
We developed the liear motor well after any rotating electric motor.
But only because someone already invented it for us.
Making it flat was then more or less about finding a need for it first, like the modern highspeed trains on a maglev principle.

If you want to make something move then it makes no big difference if you do it in flat or round.
Flat however leaves you more options and much easier adjustments.
And you will need a lot of the later...
IMHO the best size and option for linear is the N0 model railway system.
Tracks are only 3CM wide and second hand carriages to salvage the wheels is cheap.

Either way, how would you start?
We have multiple choices, like single row of magnets or double, maybe even tripple.
Same for the actual magnet orientation.
Flat, angled, attracting or repulsing...
They all work if you understand how they actually work.
Not the principle, the magnets ;)
You see, a magnet always has two poles and without trickery both poles will be of even strenght, size, angle to each other and so on.
Playing on a small and flat track with little resistance allows to use tiny magnets, like 5mm disc ones.
If you follow the common concept of two magnet rows either side at a slight angle then you are half way there.
People spent a lot of time trying not only to let the cart being attracted by the first magnets but also to let them pass out at the other end.
In case you wonder why:
Being able to be "sucked" in means you will have some force pulling on your cart from the next stage.
Being able to fully pass through and preferably gain speed, means the cart would go from one set of magnets to the next - motion is accomplished.
Let me give you my personal favourites for 5mm disc magnets:

1. The rows are at an angle of 4-5° like a slim V-shape.
2. Same as above by with the orientation changed by 90°
The first basically means you have the magnets facing up while in the second you would have them mounted vertically.

Both have good and bad sides and I think it is easiest to start with the first option.
Here you would have a row of magnets at a slight angle either side of the track.
Lets say it is all pointing away from you, then the north row would be left, south row on the right of the track.
If you start narrow or wide depends if you want attraction or repulsion forces to work with.
Again, it makes no big difference really, just a different way of operation, most seem to prefer repulsion though thinking the forces are greater - this is not true though ;)
A very often copied way of mounting the working magnet (s) on the cart is by placing a magnet with south facing down on the left and one with north facing down on the right of the cart.
Here you have the big problem of manipulating fields.
The forces are quite strong and it seems the obvious choice but should be left for the advanced classes.
Let me try to explain:
No matter the site of your work magnet it has a very narrow acting field.
Means you have a lot of attraction forces going only downwards and not providing any energy to move your system ;)
If you orientate a magnet (stack) so north faces to the right and south to the left on either side of the cart you have more options.
If the stack or single magnet has the correct length to match the angle of the magnet rows then a funny thing happens.
Assume the outer most magnet is at about the same distance from center as the first magnet in the row.
Means the inner most and opposing one is further away and the attraction forces gain the upper hand.
While moving along though it moves away from the magnet row and whie still gaining force the last magnet in the row stops the cart dead center.
This is the common scenario you see on the web when people try and fail.
Now if you change the length of your working magnet and position in relation to the magnets in the row you can use the changes to your advantage.
You can add slim disc magnets either side of your stack and observe the change in behaviour and where the cart starts to be repelled or gets stuck.
In a bad case it starts fast but then stops with a big wobble back and forth.
The perfect balance and size means the cart is attracted once it comes close to the magnet rows.
There should only be a tiny sopt of very little repulsion right before the cart takes off.
Like a hair trigger on a good gun if you know what I mean.
It should then see some accelleration till about magnet 5-7 in a row of 14.
From there it should level out and roll trough and keep rolling.
I assume your first attempts now get you to the point where you cart start really nice, slows down a bit and seems just to miss a tiny extra push to make it out.
It it shoots to the last magnet in the rows and then settles back to one or two before the end you are close!
We have now two basic ways of manipulating the magnetic fields in our favour, or to "cheat" phsyics.

Closing the gap.
You will have realised by now that you need at least two stages for your system to be tested properly.
Preferably 3 to get a 120° angle in a rotary conversion, but 5 would make sure there is hickups.
This also means distance is now something to play with.
Remember the pull before get at the same level with the first magnet in the rows?
This is the first force we utilise by bringing the second stage at a distance CLOSE to take over the pull.
Close because we don't want it to pull the cart out just like that.
It would create a big "bump" and in a rotary system massive and unwanted vibrations.
Instead we weaken the last magnet in either row.
We still want to keep its pull but not so much the holding force that makes our cart go stuck here.
Placing a magnet orientated in the same direction as your rows at the end of the row will change how and where the field of the last magnet in the row goes ;)
Just to be precise: If the magnet in the row is north up and south down then the added magnet should have the poles 90° to that and in the same direction as the row.
Depending how high, how close and with wich pole you place it the fields will change.
You want to lower the locking force by at least 50% here - that will be suffient to overcome the holding force and gives the next stage a good chance to take over.
It can also help to provide a sacrificial pole below the last magnet in the row.
Again if north would be facing up then the lower magnet would also face north up but with a small distance to the upper manget.
Ok, what happens here exactly?
If I would want to be precise here you would need to read an awful lot, so make it simple...
The lower magnet provides a way for the upper magnets south pole to get somewhere else instead of back to its original north pole.
It also means there is another north pole "pushing" the north of the upper magnet more flat at the bottom half.
This weakens the field strenght.
Distance is key.
The added magnet at the end does a similar thing.
It provides attraction or repulsion forces that affect the field shape of the last magnet in the row.
Imagine you have north facing towards the last magnet:
You would push the last bit of the field up while also providing a very sharp end instead of a big round shape.
The south pole of the last magnet also gets attracted by this added magnet, even more with one magnet below it.
With those two added magnets you should be able to fully overcome the binding effect stopping your cart.
It won't start and keep going when you let go of it half way down the track though, you need to start with the first magnet or give it a push to overcome the first binding effect.
After that momentum takes over.

If it really is that simple then where are all the successful videos about it?
They are out there, you just need to look quite long for them.
Most people still literally think only linear.
A magnet has north and south and we can't change it - but we can...
With field manipulations as above and shielding we get so much more than what physics currently dictates.
Keep in mind that adding shielding under your rows of magnets will also affect how all works together ;)
Some people forget this when using ferromagnetic things way too close to their testing area.
Distance is also vital to keep in mind when experimenting.
The closer two magnets are greater their forces to each other.
You can utilise this for example by lowering magnets that seem to be far too strong in your configuration and cause a binding effect ;)
And as said, shielding is nice thing for triack too - imagine what would happen with sielding on the sides of your magnet rows... ;)

Make a negative into a positive!
Extremly strong binding forces at a certain point in your track design can mean you might be able to utilise it instead of trying to waste it.
Added magnets can divert the field to quite some extend.
Shielding however can also direct them somewhere else - like in the core of a transformer where it all goes in a great circle.
Even strips of shielding connecting magnets from one row to the one on the other side of the track can be utilised.
Like that you turn two small magnets into one long one with twisted poles at the end.
Provides more field strenght too and makes it good for areas with little to no attracting force to the cart.
Then there is bigger design...
Some people add a center magnet.
With one on the cart and one in the center of the track you can create a cancellation field.
The rows bind while the center magnet wants to push.
If place where there is still enough forward momentum or even acceleration but close enough to the binding magnets it is possible to greatly lower the binding effect.
But keep in mind you need to consider the added repulsion or compensated the field so it is most active towards the moving direction and less strong to where the cart is coming from.

Advanced manipulations.
You can machine magnets, sandpaper, file, grinder, CNC....
Imagine you cut a square dice magnet from one corner to the other.
Depending on how you have the field orientation you can end up several variations.
But if north faced up in your dice then it will still face up in the cut pieces!
Cut a pyramid and you end with a big flat south pole and a pointy north pole - and with extreme field strenth in this pointy bit.
Similar story with half moon shapes.
Imagine you machine a flat block magnet so you have a half moon with its pointy bits facing down and big round bit up.
If north was up in the block and you shape the moon correctly then you end with two strong south pole points and a north pole that is strongest right between those points.
Why is this so interesting you might wonder?

Imagine you already know a magnets pole does not care if gos back to its own opposite or that of a different magnet.
Then you also know you can machine and shape magnets to your will.
Now imagine that for a change:
Precisely machined pyramids that have the top chopped off.
All tops in this example facing being the north poles and big bottom south.
If you then machine a precise iron core block you make a nice cube.
With magnets we need really good glue and a good press to make it happen.
But if the center core is of proper size then we end with a block magnet that has a south pole on all sides.
Of course to be 100% perfect we would need a zero tolerance gap but good glue and high forces can come quite close.
Works as a sphere too but would even have clue where to start to machine the magnets LOL

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