HELP Helicopter Center of Moments

[fred64]

Hi,
I am creating an helicopter simulation and have a question about calculating the correct helicopter origin of moments.

In its simplest terms, ignoring drag and tail rotor forces and torques I have the main rotor generating an upward thrust from the rotor hub, and gravity generating weight from the center of gravity.

In normal rigid body physics the center of moments is in the center of gravity, being the helicopter suspended at a rotor in my opinion it should be somewhere in between the two.

It can't be at the center of gravity as if the helicopter is inclined in any direction i.e. forward, the main rotor will generate a pitch torque which is not balanced back and the helo will fall nose down...

From my tests the ideal position is centered on the main rotor axis and in line with the perpendicular to the main rotor axis that intersects the tail rotor axis, which otherwise will cause a rolling torque.

I also looked at several helicopter aerodynamics books (especially Bramwell and Johnson) but found no answer.

thanks in advance

Fred

 

[Cyrus]

Are you using BEMT in your simulation?

 

[fred64]

No I wrote my own sim in NET, I don't know BEMT. Actually it's a flight simulation software.

 

[Phrak]

I take it you are at the first stage of analysis where you don't yet look at gyroscopic forces.

Find the center of mass of the helicopter. Gravity pulls this directly downward.

Lift acts from the center of the rotor plane. The force of lift due to the rotor is directed along it's axis of ratation.

Both of these forces pass through the center of mass; no torsional forces arise on the aircraft.

 

[fred64]

thank you Phrak,
yes gyroscopic forces are next. BTW where can I find a formula to simulate the gyroscopic stability generated by the turning rotor (I think it will depend on Moments of Inertia, angular velocity, force applied) maybe the formulas for a bycicle could work...

Regarding my question, i think your answer is fine as long as the rotor force is in line with the center of mass. when I incline my rotor forward the force is inclined forward, this should create a torque equal to square the distance from the rotor hub to the center of mass per sin the inclination angle.

If the center of moments is at the center of mass, there is no corresponding countertorque from the gravity force and the helicopter will be unstable (fall forward), so my guess is that the center of moments is in between the two and that weight creates an opposite torque (very much like a pendulum), but I found no way to calculate this...

thanks in advance
Fred

 

[Cyrus]

No I wrote my own sim in NET, I don't know BEMT. Actually it's a flight simulation software.

Errr...BEMT is the theory you use to calculate the rotor thrust, torque etc. Its not a language. As a flight dynamcist that does simulation, I've never heard of net before. Is this some sort of freeware?

 

[Brian_C]

I'm not an expert on helicopter simulation, but I think you need to first define an appropriate body frame with origin at the center of mass. The aerodynamic/propulsive forces and moments can then be calculated in the body frame, and the appropriate equations for translational and rotational dynamics in the body frame are used. If you don't have any background in flight dynamics, I strongly suggest reading chapter 4 of Pamadi's book. It clarifies a lot of these concepts.

 

[fred64]

thank you Brian,
in fact the simulation as you mentioned it is already almost finished and it works quite well (it's a module that integrates into Microsoft Flight Simulator), I studied all the formulas from different books and adapted them for the software, Bramwell gives some indication on the Center of Moments being the perpendicular from the center of gravity to the main rotor axis, but this gives an unstable model when the center of gravity is on the same axis as the main rotor axis, so possibly he meant the "vertical" from the rotor axis which would give a more stable configuration except for the following.

From how helicopter are designed if you consider also the tail rotor this will also bring a torsional moment in case it is not on the same axis as the center of moments, so possibly the center of moments is a cross line between the main and tail rotor axes (that's how I designed it for the moment)

Thanks
Fred

 

[fred64]

Errr...BEMT is the theory you use to calculate the rotor thrust, torque etc. Its not a language. As a flight dynamcist that does simulation, I've never heard of net before. Is this some sort of freeware?

Sorry I did not know the acronym, I guess it means blade element theory. To calculate rotor thrust and torque, induced velocity, H forceI mostly used formulas taken from Johnson's Helicopter theory, which uses blade element theory. I used a simplified iterative calculation between thrust and induced velocity as I need to perform all the aerodynamic calculations (including drag, stabilizers etc...) 20 times a second...

Fred

 

[Cyrus]

Sorry I did not know the acronym, I guess it means blade element theory. To calculate rotor thrust and torque, induced velocity, H forceI mostly used formulas taken from Johnson's Helicopter theory, which uses blade element theory. I used a simplified iterative calculation between thrust and induced velocity as I need to perform all the aerodynamic calculations (including drag, stabilizers etc...) 20 times a second...

Fred

Great! I'm glad (finally) someone's coding a sim around here correctly!