HELP ME - Lift equation for Helicopter Fan

[iwannafly]

NOOB ALERT - I'm not trying to design a helicopter or a spaceship or something ridiculous, I just want to design a little hovercraft with a computer fan, so don't get all indignant and righteous at me.

Anyhoo, I found this Lift equation and tried experimenting with some numbers, just to get a hang of it. I used specs from a 21,000 RPM RC heli engine and a .5 ft blade.
Here's the engy:
http://www.rcplanet.com/ProductDetails.asp?ProductCode=TTR9606&click=109537&gclid=CLWdw925-LMCFYN_QgodngcAUQ

L = .5 * ρ * V^2 * CL * Sref
p = .002377 slugs/ft^3
CL = 2 * pi * angle of attack (I assumed a 1° (pi/180) angle of attack)

My problem, though is with the velocity. I assumed it was rad/sec and converted 21,000 RPM to 2199 rad/sec, and plugged it in. (Some website said it was right.)
However, I got 316.8255 lbs of lift with that velocity, which means that little RC heli engine could lift the combined weights of me, my mom and my dog (a really messed up answer.)

Some site suggested the velocity was the airspeed over airfoil, another said it was the change of velocity over time. After hours of searching I became flummoxed, so I decided to ask the experts.

The question, stated bluntly: What is the velocity measured in (ft/sec, rad/sec, etc.) for fans in this lift equation? Did I do anything else wrong? And if anyone has experience in hovercraft build-age, how did you go about calculating lift and motor/engine selection?

Thanks in advance for your gratuitous and gracious answers :3

Note: My unrealistic dream is to make a human-sized hovercraft large enough to fit my fat arse on it, so if you can help me with that too, please do :) I have taken electronics classes and 1 basic physics class, so hopefully my basic understanding of stuff is enough (likely not)

 

[mfb]

To get matching units, your velocity should be calculated in ft/s. 2200 rad/s should correspond to 1100ft/s at .5 ft radius (assuming that value is the radius). Depending on your definition of Sref, you might have to use a smaller value, as not the whole rotor has this velocity.

SI-units would make that easier.

1° angle of attack looks a bit small.

 

[iwannafly]

I was also unsure about the angle of attack. I though it was the angle between where the wind hits the airfoil and the chord line of the airfoil, but I didn't know what to plug in for the lift formula. Is that something I randomly approximate the range (like from 0° to 15°)?

It's weird because at 0° the lift equation becomes 0. That's just weird to me. Doesn't the heli hover at a 0° angle of attack...? It can't do that with 0 lift, soo... -__-" Magical force of God lifts at hover? I am so confused :(

 

[mfb]

It depends on the blades and their angle relative to their direction of motion.

 

[Aero51]

You may want to take a look at a tool called Javaprop. It uses simple blade element theory (Basically you divide your fan blades into sections and compute the local aerodynamic forces) to compute the lift (thrust), power requirements, RPMs for a blade geometry you create. Here is a link:
http://www.mh-aerotools.de/airfoils/javaprop.htm

Regarding your velocity question: Velocity, regardless of application, always has units of length/[unit time]. Angular velocity, on the other hand, is a measure of rotation rate and has units of angle/[unit time]. The latter has the same units of frequency.

 

[iwannafly]

I looked at Javaprop - though I've done Java a long time ago, I don't feel like re-learning everything, for a propeller :-l

I made this spreadsheet for the Lift equation: can something PLEASE download it and check if it's alright? I'm getting a few outrageous answers (such as 1297.661361 lbs for a 12in radius prop, at 17,000RPM, pitch=1°) that don't feel right.

 

[Aero51]

You obviously didnt look at it hard enough because it doesn't require any programming. Give it a shot I assure you it will save you time in the long run.