Velocity Calculation for helicopter rotor question

[helinewbie]

Hello, I'm creating an excel file to calculate the velocity of one rotor of a helicopter, and I'm getting really weird answer, in comparison to the one a friend of my who does aerospace engineering give me.

I don't do an aerospace engineering course but this is a project I've been researching at my own time so I'm really eager to learn how to work out equations by myself. And I've lost contact to that friend who gives me his excel file so I don't have anyone to help me really.

I have attached 2 XLS files.
- Basic Aero Dynamics of Helicopter.XLS is from my friend
- VelocityCalculation.xls is what I'm trying to achieve

The formula I was using is Force of Lift = p * Cl * U^2 * S/2 = Kl * w^2
where
p is air density
Cl is lift coefficient
U is flow velocity
S is the reference area
Kl is some K variable I don't understand.

Also, Force of Drag = p * Cd * U^2 * S/2 = Kd * w^2
where Cd is the drag coefficient

If you can help explaining what U really represent, it would be really helpful. I looked it up for aerodynamics of helicopter lift equation (http://helicopterflight.net/lift_equation.htm ) and find U is the same as w. Is this correct?

Another thing I don't quite get how my friend work out the velocity by sqrt(2*Force/(Density*Span*CoefficientLift)) What is the reference area of a helicopter? From http://www.aerospaceweb.org/question/aerodynamics/q0015b.shtml, it's the 2*PI*span, but he uses the span as the reference area.

His answer however is a lot more sensible than mine: ~1200RPM compared to ~153RPM. It's a small RC helicopter I'm looking at, and most commercial ones are 1200RPM-2000RPM. So I'm really confused.

Please have a look at the Excel Files. Thanks.

 

[eng leopard]

thanks freinds

 

[NatSusan]

Hi there,

First of all, I commend you for taking on this project and trying to learn and understand the equations on your own. It's always great to see people taking initiative and expanding their knowledge.

As for your question, U in the lift equation represents the flow velocity of the air. In the case of a helicopter, this would be the velocity of the rotor blades as they rotate. So yes, U and w are essentially the same thing in this context.

As for the reference area, it is important to note that the reference area used in the lift equation is not the same as the reference area used in the drag equation. In the lift equation, the reference area is the area of the rotor blades that is contributing to the lift force. In the drag equation, the reference area is the frontal area of the helicopter. This is why your friend is using the span of the rotor blades as the reference area in the lift equation, but the frontal area of the helicopter in the drag equation.

Now, as for the K variable, it is a coefficient that takes into account other factors such as blade shape, airfoil design, etc. This is why it is different for lift and drag. It is not a constant and can vary depending on the specific design of the helicopter.

I took a look at your Excel files, and it seems like you have made some errors in your calculations. Your friend's answer of 1200RPM seems more reasonable given the information provided. I would suggest double checking your equations and variables to see where you might have gone wrong.

Hopefully this helps clear things up a bit. Keep up the good work and don't hesitate to ask for help if you need it. Good luck!