# Calculating magnetic strength required to hold an objects weight + wind speed?

Note: I'm a bit new to this subject, so I'm looking for some general answers, ballparks, and direction to continue my research.

Scenario: I have three electromagnets capable of X amount of holding force attached to a surface. There's a small metal object that weighs 10lbs that will be attached to the magnets. The object is rectangular 36"x5"x5". Wind will be blowing and/or the surface will be moving at a particular speed.

Question: How do I go about solving the strength my magnets need to be in order to safely/securely hold an object of a certain weight with windy conditions?

I started researching about MPH to PSF conversions where it reads that 100mph translates to 25.60psf.

• Is that accurate, and if so, is that additional force applied to my object?
• Since the object is 36" (3 feet), would that be 25.60psf mean: 10lbs over all / 3 feet = 3.334lbs per foot + 25.60 ... So 28.934lbs of force on each magnet? Is that in the ballpark or am I making this up?

I'm assuming that lift may play a part in this as well, or is that in some ways being accommodated by this MPH->PSF conversion?

I imagine the shape of the object would play a role with regards to lift, so would a rectangular simple object as stated have a minimal, near insignificant, amount of lift for this discussion? Again, I'm not exactly sure what I'm talking about here, so please correct me.

Assuming I can figure out the holding force required per magnet per object per conditions here... is there a safe amount/rule of thumb to add to account for unexpected shocks or gusts? Would a steady wind of 70mph be different than 20mph with a 70mph gust?

Sorry for all the questions. It's something I'm trying to read more about and understand better. Again, it's a bit of an open ended question because I'm trying to learn about it/understand it and don't actually have these materials yet.

There are two questions being asked:

1.) How do I calculate how much force my electromagnets can exert

and

2.) How do I calculate the aerodynamic forces acting on an object that will be blowing in the wind, so that I can know how strong my electromagnet needs to be.

I'll answer question 1 first:

Just for future reference, the force exerted by an electromagnet is: $$F = \frac{\mu^2 N^2 I^2 A}{2\mu_0 L^2}$$ where $$N$$ is the number of times your wire wraps around your electromagnet, $$I$$ is the electric current going through it, $$A$$ is the cross sectional area of your electromagnet, $$L$$ is the length of the electromagnet. $$\mu$$ is the magnetic permeability of whatever your electromagnet core is made of, and $$\mu_0$$ is the magnetic permeability of free space. This equation appears about half way down the wikipedia article titled "Electromagnet".

A couple of problems with this are that most electromagnets sold commercially do not state the exact number of turns $$N$$. Any number that they place on the packaging (if one is stated at all) is likely a rough estimate. Furthermore, most electromagnets sold commercially may state something like "iron core" on the packaging, but that doesn't mean it's made of pure iron. Hence, it is difficult to know for a fact exactly what the core is made of. This makes is more-or-less impossible to know $$\mu$$, the magnetic permeability of the material from which the core is made.

The answer to question 2 goes like this. In principle, the aerodynamic forces acting on your "object" might could be calculated. But I guarantee you that this is beyond the scope of your project. Such a feat would require years of work by a team of engineers working full time. This isn't the direction you want to go.

In all seriousness, the best approach I see is to just trial and error your way through whatever it is you are designing.

Lastly, while doing so, bear in mind that many electromagnets sold in science kits are not very powerful at all. They are wimpy little things that barely exert any force on anything - it require a delicate touch to determine that they are exerting any force on anything at all. Be sure that you get something stronger than this. The strongest electromagnet I've ever encountered outside of a laboratory was the electromagnet that held the back door security gate closed at a restaurant I worked at many years ago. These electromagnets must be professionally installed and cost many thousands of dollars. Not to mention the fact that they can be quite dangerous in a wide variety of bizarre ways.

Best of luck with your project.

• Thanks for the comment. Can't agree with the "most electromagnets are not very powerful at all" statement though. There are videos on YouTube showing an electromagnet made from a microwave transformer very easily lifting +200lbs. I consider that to be powerful, and it costs about \$30 on eBay to make. – Matt Kenefick Apr 1 at 14:55
• Thanks Matt - I edited my post just a bit. I really should say that if you need a really strong one, you need to make your own or buy an industrial use one. – the_photon Apr 4 at 0:40