# Magnetic Levitation Formula

• I

## Main Question or Discussion Point

Hi all,
Newbie here.. I am interested in making a magnetic leviation display like in this video:
My question is what are the necessary setups?
I know that I would need a strong magnet like neodymium magnet. But, i have no idea about the formula. Lets say i want to levitate a 1kg object, how strong should the magnet be? (In Tesla maybe?). Thanks :D

Related Other Physics Topics News on Phys.org
Hi navivanuva,

How coincidental, I just subscribed to this forum to get answers, while I try to build this kind of device !

My goal would be to levitate a 2kg object using two of these devices. As you just started a topic here, do you mind if we share the topic to compile our findings ? If you prefer that I start my own topic it is ok, just tell me.

For now, here is what I found (and understood) on the subject :

The device is composed of :
- One big (100mm diameter) ring magnet in the base, which if I understood correctly can be a "weak" (and cheap!) ferrite magnet, as it does not provide the strength to levitate but only a "base" receiving the floating magnet strength. (sorry for this description which probably contains absolutely no exact scientific terminology, I am a beginner ;-))
- Inside the ring magnet's hole, 4 electromagnets (copper coils with an iron core), responsible for correcting the floating magnet's position. 2 coils act as a x-axis actuator (moving floating magnet to the left/right), while the 2 others act as a y-axis actuator.
- In the middle of the for electromagnets, 2 or 3 Hall effect sensors, disposed the right way to sense the X and Y positions (also the Z position -- height -- if using 3 sensors)
- A temperature sensor, to avoid burning the house, and moreover to avoid damaging the device, because electromagnets get hot very fast when powered.

Here is how I understand the device should work. When the floating magnet is at the "sweet spot", it is repelled vertically and levitates. But this does not last long, because the magnet slides on its side. When this happens, the X and Y axis Hall-effect sensor must detect it very soon, and power the right electromagnets to push the floating magnet back to the sweet spot. The algorithm responsible for this is called a PID controller (proportional-integral-derivative), basically it tries to reach a setpoint (here the sweet spot) by continuously measuring the "error value" and turning on actuators (here the electromagnets / coils).

I am now trying to calculate the kind of magnets and electromagnets that should be used. As I said, I don't think the base ring magnet has to be very powerful, because it is the floating magnets that provides the repelling force to levitate. I think it just needs a big magnet on which to apply its strength. So basically I'd go for a 100mm ferrite magnet like this one : http://www.first4magnets.com/circular-disc-rod-magnets-c34/100mm-o-d-x-50mm-i-d-x-12mm-thick-y30bh-ferrite-ring-magnet-9kg-pull-p3679

As for the floating magnet, this one need to be really powerful, because it need to support its own weight + 1 or 2 kg at a given distance from the base. The strength of a magnet lowers exponentially as the distance increases, so a magnet that has a 10kg pull (or push) force at 0mm will only have 1.5kg at 10mm and 400g at 2cm. (I used this calculator : https://www.kjmagnetics.com/calculator.repel.asp?calcType=disc)

Using that same calculator, I think I can use a neodymium N52 disc magnet of 50mm diameter by 10mm thickness to support 2kg at 35mm high. That's because this kind of magnets has a 45kg pull (or push) force at 0mm !!!
I could stack 2 of these to get that kind of force : http://www.ebay.com/itm/1x-N52-Super-Strong-Round-Magnets-50mm-x-5mm-Hole-6mm-Disc-Rare-Earth-Neodymium-/311433370848
By the way, I also learned that stacking two identical magnets is almost the same as using a single magnet of twice the thickness.

Now I am trying to figure out what kind of electromagnet (core, number of turns, type or wire, ...) could be well-sized to act on the floating magnet. My intuition tells me the electromagnets should be scaled based on the floating magnet's weight and position (how high it will float) and also on the "payload" weight. And I could use some help here because I am a bit lost...

Of course there will be plenty of other stuff to figure out before starting to build this -- awesome -- device !

To finish that post, here are some interesting references that I was able to collect:

* Magnet repel force calculator: https://www.kjmagnetics.com/calculator.repel.asp?calcType=disc
* A good magnets Q&A: http://www.first4magnets.com/tech-centre-i61/frequently-asked-questions-i69
* Instructions for scaling and winding a coil: http://www.coolmagnetman.com/magelect.htm and http://info.ee.surrey.ac.uk/Workshop/advice/coils/index.html
* A blog from a student's personal project of an attempt to build this kind of device. This includes tearing apart a Levitron Revolution device ith some precious photos and measurements: http://blogs.swa-jkt.com/swa/11131/2011/12/15/personal-project-journal-planning-creating-stage/
* A video of a homemade levitating device by a student: * And the arduino code for the pid algorithm he used: http://blog.sina.com.cn/s/blog_71afdbfd0100ssuk.html
* Blog from a guy that made a floating hoverboard...: http://modthis.com/2012/02/23/my-real-hovering-hoverboard/
* ... Using these expensive Crealev devices: http://www.crealev.com/product/clm-1/
* Another company that makes educational repulsive maglev devices (but no kits and instructions to sell... I asked): http://www.zeltom.com/product/repulsivemls
* And of course the Levitron Revolution which can hold up to 13 oz (almost a pound) (I found some of these for only 45 usd, but it is still too weak for me and I want to build it myself): http://www.fascinations.com/unique-toys-gifts/levitron-revolution-ez-float [Broken]

That'is it ! Thanks for reading ;-)

Last edited by a moderator:
Wow, nice to have someone with the same interest..

Thanks a lot for the infos you are willing to share..

So far i found this:

There are some methods to do magnet levitation as described here:

Also there is a guy in youtube that makes this kind of device.. his channel name is Nicanor Apostol.

I'll postit here when i found new Stuffs.

Last edited:
Thanks for sharing.

So according to this list I think we're dealing with case 10: "Repulsion between and electromagnet and a magnet, with sensors and active control of the current to the electromagnet used to maintain some distance between them."

I'm pretty sure I came across this youtube channel but I didn't notice there were so much videos! Thanks for pointing this. I will have a better look at it and I think I will reach out to this guy and see if he is willing to share more on his circuit.

For now, it seems to me that he is using something similar to Levitron Revolution-like devices :
- 1 levitating magnet
- 1 large ring magnet (which is actually made of 9 block magnets as we can see in video "Levitated magnet at center of segmented ring magnets")
- What looks like 6 (!) electromagnets controlled by an arduino microcontroller, to achieve stable levitation
- Position sensor is apparently optical (see video "reflective optical sensor center position sensing") instead of using hall sensors. According to him, "Reflective optical sensors for center position sensing surpasses the height limitation of hall sensors with respect to center position sensing of levitated large area platform and heavy payload systems". Altough there seems to be a drawback that I don't quite understand : "but background lighting needs to be physically addressed to be effective."

This makes me think I am on the right track, but there are still plenty to figure out! (which hall sensors / optical sensors to use ? how strong permanent magnets must be ? how strong electromagnets need to be ? ...) I hope this guy can give us some answers...

If someone knows a bit about magnets or magnetic levitation, you are very welcome to enlighten me on the workings of such devices :-)

Update:

I tried wrapping 10 meters of 0.8mm copper coil around an iron core(Around 5cm in diameter). No power at all. i only manage to attact 1-2 paperclips.
Then i found this article: http://uzzors2k.4hv.org/index.php?page=magneticlevitation. He used around 70 meters of 0.45mm copper coil. So if i am using 0.8mm coil, does the length needed becomes around 35 meters? Thanks

Hi,
I am going to build a magnetic levitator very soon.
Thank you marianmr for sharing so much information, they has helped me to progress.
Having researched electromagnetics and PID controllers, I have made up a different approach, it goes like this:
In popular levitation schemes, hall effect sensors are embedded in base.
I have been considering that sensors could also be embedded to levitating object. I will give a try to put a gyro or hall effect sensor and PID controller on top of the levitating object and regulate its horizontal axe with angular momentum. when the object is compelled to stay parallel to the base it will always locate in theorical equilibrium distance ( where MagneticForce-GravitationalForce = 0). So, only a ring magnet stays in the base.
Somehow I predict that there will be larger gap between the object and the base because controlling the object should be much easier than controlling it with magnetic differences
I might be wrong, when I try it i will give further details. And I am hoping to hear your critics about this method.

Hi onkkil,

Glad I could help. Although, I am nowhere near your knowledge of electromagnetics and physics (my usual field of work is software), so I won't be able to comment on your project. If I understand correctly, you will build some sort of "invert pendulum" onto the levitated magnet, which goal will be to correct and stabilize the levitated magnet's position ?

As an update to my own project, and to share my experience, I will soon write a longer post describing what I was able to build back in february. To sum up, with some help I managed to build two devices which, side-by-side, levitated a cardboard "hoverboard" wheighing about a hundred grams or so.
I made a few videos that I still need to make public, and I am willing to share every detail on how I built it (dimensions, characteristics of the coils, the magnets, the power supply, ...).
Also, I cannot thank enough Mr Apostol, with whom I discussed my project and who is really willing to share his knowledge on subject. I can only recommend that you reach to him.

Hello marianmr,

I found this thread by happy accident. I am very excited for repulsive levitation for a long time, but I am still at the beginning.
My biggest obstacle is the diagram (electronic scheme). I found some video on youtube made by Nicolae Ilie , and he is describing the main parts, but very general. So i need more information about the electrical layout.

I would like to build such simple device, but i cannot find the scheme (diagram) anywhere. Could you please help me with this? Do you have any similar diagram I could use?

Thank you very much,
Martin.

Nidum
Gold Member
A search on ' magnetic levitation projects ' will generate lots of information about hobby and science fair type projects .

nb :Searching on images could be easiest route to finding what you want .

Hi Martin,

I went quickly through the video, and my guess is that he is building an "analog" levitator -- by opposition to a digital approach using an arduino, as I did. I won't be able to help regarding the analog approach, my electronics standard not being high enough. But if you are comfortable with analog electronics, I understand that hall-effect sensors are compared together by pairs using differential op-amps. The resulting signal (the error from the setpoint) is then amplified and sent to the coil controller. This must do for the "P" part (proportional feedback) of the PID algorithm. However I can't start to imagine how you handle the Derivative and Integral feedback...

As I said, I recommend that you try and reach Nicanor Apostol, who works on both analog and digital levitators and is willing to share his schematics, which even include PCB layouts. But I don't feel like sharing it on his behalf -- this is not my work.

If you are going for a digital levitator, schematics is very basic : everything is wired to the arduino -- hall-effect sensors, coil controller (I used simple L298D dual h-bridge). If you are interested, I could probably make a small diagram of my setup.

Hello marianmr,

I found this thread by happy accident. I am very excited for repulsive levitation for a long time, but I am still at the beginning.
My biggest obstacle is the diagram (electronic scheme). I found some video on youtube made by Nicolae Ilie , and he is describing the main parts, but very general. So i need more information about the electrical layout.

I would like to build such simple device, but i cannot find the scheme (diagram) anywhere. Could you please help me with this? Do you have any similar diagram I could use?

Thank you very much,
Martin.

I wanted to point you to a thesis which was a great help to me, going into great details (and force calculus) about designing and building a repulsive levitator. Unfortunately it looks like the thesis is not online anymore. Yet the guy made a video of his final device :

You could reach out to him and see if he is still willing to share his thesis work. If I remember correctly, his thesis contains plenty of calculus, coils and magnets dimensions, and even some arduino code.

hi all.
have anybody information about circuit of the levitation globe or other information?

Hi everybody, I want know what happend with your research about this project of levitation repulsive. I want know how to do it?

I know it's been a while since anybody posted something here but I wanna build a repulsive magnetic levitation device myself and this threads has been a great resource! At the moment I'm asking myself how strong the electromagnets should be (seems to be a general problem with these projects). While thinking about this aspect I asked myself: wouldn't it be better to buy electromagnets online? All in all they seem cheaper than the used materials to build them and my intuition would tell me that they are stronger to (I haven't played with self-build vs. bought electromagnets yet). But the biggest advantage of them might be that you know exactly how strong they are. So if the is a formular which would give you the strength your e-magnets need (in dependence of your levitation height, the power of your other magnets etc.) you could buy the perfect one without the problem that they aren't all the same strength which could happen if you build them yourself.
So is there
1) Any formular like this (or could anybody tell me whisch forces I need to think of to get it)?
2) Any reason you prefer a self-build magnet over a bought one?

Well, this is also a formula I was looking for at the time. My initial goal was to determine the devices dimensions and characteristics (including coils / electromagnets) stringer than the "usual" devices we see online. Unfortunately I was in a hurry (I had to build two devices to levitate a "hoverboard" prop in 6 weeks...) and I ended up using dimensions I found online (look at Nicanor Apostol's work).

From the top of my head, here was what I wanted to understand / calculate :
* As I understand it, the weight of the levitated object is not "cancelled" by the coils but by the permanent magnet ring. This magnet arrangement is what keeps the object from falling "downwards".
* I can't remember if there is a name for it, but the fact that the ring magnet has to "push" the levitated object with its "lower pole" (I know this is not the right saying, just look at the ring magnet's flux lines and see how that flux is "pushing upwards" at the center) also made me wonder how to calibrate the ring magnet in relation the the object's size and weight (because the weight would affect the levitation height, and therefore the size / strength of the "sweet spot" pushing upwards.
* Thus, the coils are only responsible for moving the levitated object sideways. How much force is needed for the coils depending on the object's characteristics, I don't know how to calculate. I guess it mainly depends on the friction characteristics between the object and the air, gravity force being already taken ware of by the permanent magnets...