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Is this expression for the efficiency of a fan blade correct?
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Is this expression for the efficiency of a fan blade correct?

I'm making a ducted fan and seeing as these things take a long time to draw and a lot of money to manufacture I want to have some idea of the efficiency even if it's basic. I'm worried because it's a 12 blade fan which means the blade angles have to be quite steep in order for it to all fit together. Other EDF manufacturers seem to have done the same thing and theirs works fine but I want to check anyway because mine is much bigger.

If pic related is right then I can compute the coefficents of lift and drag on the chosen NACA 4412 airfoil using XFOIL and hence the efficiency. Vortex losses are being ignored because it's in a duct.
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the page with the final answer
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If /sci/ helps me out I'll post a video of it in operation. It's gonna sound amazing. Might rice it out as well with supersonic swept back blades and afterburners
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Oh come on seriously fuck this board, Loads of people eager to spew bullshit about quantum mechanics or inter universal teichmuller theory but these same people somehow don't know enough physics to verify a simple efficiency expression? I'd use physicsforums if I was good at LateX.
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Your result seems pretty correct, but I only ever did a minor in aircraft engineering so what the fuck to I know.

Keep in mind that this approach assumes that the air that hits the fan was in free stream before, but in reality it's not since there is a fan in front of it. Also, these formulas only hold when incompressibility is assumed, which is until about Mach 0.3 if I recall correctly.

All in all the accuracy of this calculation is dubious at best, you might get more realistic results if you put your model through a flow simulation. Solidworks does a pretty good job at this.
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>>8047599
>tfw Mach 2 at the tips
This is haram right?

I can neither afford nor know how to use Solidworks.
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>>8047711
Learn LaTeX and go to physicsforums. /sci/'s only good for making engineers feel inferior to physicists anyway, lel
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>>8047740
Where's a good LateX guide?
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>>8047711
>mach 2 at the tips
this pleases me
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>>8047711
Speeds like that put enormous forces on your blades, and I'm not even considering the heat and noise it will produce. To make your fan stable at those speeds requires some precision engineering.
Also, the efficiency of your blade drops very quickly after you pass the sound barrier, so having half of your fanblade at supersonic speeds is probably not such a good idea.
How do you even plan to make it go that fast in the first place?
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>>8047753
Ok well thanks for nothing /sci/

I'm gonna build it. Pic related works so why won't mine when it's the same shape?
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>>8047812
>How do you even plan to make it go that fast in the first place?
A big ass motor. No but seriously a 8000 W brushless inrunner.

It really sucks balls when an entire project has to be abandoned because just one number fucks your shit up. I was really excited for this. Only hope is to find a motor with a lower RPM but I don't think I can.
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>>8047832
Link to your motor? You need a very low KV motor.

What diameter were you planning to make your fan?
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>>8047812
You know what the real problem is? The voltage. The motor can handle 90 A max but at 8000 W that requires 89 V minimum. Since the RPM of a electric motor depends on the voltage that means the thing will spin too fast.
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>>8047847
http://alienpowersystem.com/shop/brushless-motors/5860-inrunner-brushless-motor-300kv-15000w/

400 mm diameter
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>>8047865
What kind of ESC do you want to use with it?

Since the motor takes AC power, you can always put it through a transformer to increase the voltage. This does decrease the current though.
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>>8047582

>all kinds of theory around on this board
>basically the low-hanging fruit of science
>OR rainman levels of math that will never be used other than in a computer program

Came to the wrong place for applied science and math.
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>>8047878
I haven't chosen an ESC yet

No no that would make it worse as I said before it's because there is so much voltage why the thing will spin so fast To stay under the speed of sound I would need no more than 50 V however to supply 8000 W (actually 9000 W to be safe) I would need 180 A which is double the maximum the page says that the motor can handle.
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>>8047912
Well the motor will never take 180A if you run it at 50V. It will only take what it needs.

The page says that its max rated amperage is 90A, and its max voltage is 166V. The power at this voltage is 166*90=15000W, which is conveniently also its max rated power.

So putting this all together the motor will take about 27A at 50V, and will only put out 50*27=1350W of power.
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>>8047912
>>8047931
So what I'm saying is, if you want to run your motor at 8000W, you need to find a motor with a lower KV, or you need to make some kind of transmission in between the motor and the fan to make it spin slower.
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>>8047938
>make some kind of transmission in between the motor and the fan to make it spin slower.
Yes! Fuck Yes! Why was I so dumb? Why did I not think of this? It will hurt efficiency though.
>>8047931
It's running at 8000 to 9000 W
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>>8047938
Let me email the guy, I think he can supply gearing. I can't be fucked to make it myself. I'm shit at it anyway, they never mesh good.
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>>8047582
You are not entitled to an answer retard. Also, googling drag equation and doing some algebra is really nothing to do a fucking thread on.
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Keep in mind that the KV value on the website is for when the motor is not under load. When you put a bigass fan on it the kv value drops about 30%, probably even more with such a high tip speed
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>>8047964
>You are not entitled to an answer retard
It's not about getting no replies, I make plenty threads all over 4chan that get no replies and I don't care. It's making a legit science thread and seeing it getting ignored in favour of some racebait or "can schrodinger's equation send me back in time" that niggles me
>googling drag equation and doing some algebra is really nothing to do a fucking thread on.
Exactly what I am talking about. Someone posts a classical mechanics problem some arrogant undergrad student comes along and calls it "babby tier" despite him only managing 70% on his last mechanics exam. To cap it all off this same guy then jumps right into a General Relativity thread to act like an expert on things that he knows absolutely nothing about.

And FYI my problem is actually quite advanced I am just trying to simplify it as much as I can. As one of the few people to be helpful pointed out I incorrectly assumed a free stream and didn't take into account the Mach number.

Classical mechanics isn't just "here's the equation, plug n chug?" you have to think "is this equation valid?" "What other things must I account for?" "How many things can I account for until the model becomes uncomputable in reasonable time?" But of course for an intellect as great as yours airfoil analysis is beneath you, Only String Theory is worthy of your genius.

>>8048017
Anyway fuck that guy, thanks for your help
I know, but it's the best estimate I can get without experiment.
Thread replies: 25
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