# Calculating rotation based on multiple accelerations

1. Sep 16, 2014

### RuhigBrauner

Hi,

I would like to ask you If you could help me with a (I guess quite simple) problem I have to solve. To put it into context: I want to program a helicopter for a videogame with a physical model. So the player controlls throttle, pitch, ... and the game calculates the correct response.

A helicopter basicly generates lift by spinning the rotor. So you have a acceleration vector at the rotors pointing up and the accelecation vector from the graviting pointing down.
Now when the rotor tilts to generate lift forward or to the side, the vector changes direction and does not align with the gravity vector. That's why the helicopter tilts as well.

The question I have is how can I calculate exactly how much a helicopter rotates when the rotor tilts.

I guess what you need is where the two accelerations take place (center of mass for gravity, rotors for lift) and where theyare pointing.
The mass is needed as well but I think what is also needed is the distribution of the mass. A object where 90% of the mass is near the center would rotate faster than
an object where the mass is mostly located away from the center.

Do you have an idea, how to solve this problem or what kind of model would work well here?
Btw. here is a simple graphic showing the problem:
https://studi.f4.htw-berlin.de/~s0539750/LiftMass.png [Broken]

Last edited by a moderator: May 6, 2017
2. Sep 16, 2014

### RuhigBrauner

Mhh,
Why do you have two propellers? I understand the equation for F2 but I don't realy get what you mean with F1.

What I can tell is that we have an object with two accelerations. The one is gravity pulling the whole thing down on the center of mass. The other acceleration is the rotor pulling the thing to where ever the rotor is facing. (In most cases upwards.)

For the "level flight" these two accelerations cancel each other out assuming that the rotor is over the center of mass.

My Problem si figuring out what happens when the acceleration of the rotor isn't facing straight up anymore but also a bit forward / left. In this state, the helicopter should tilt in the direction the rotor is facing. The question is how this is calculated "exactly".

I had the idea that you can calculate the tangential acceleration and use this, but I am not sure.
So when the rotor acceleration points towards (0.1, 1) the tangential acceleration would use a vector of(0.1, 0).
The radius would be the distance from the center of mass to the rotor.

3. Sep 16, 2014

### CWatters

The helicopter tilts due to drag (edit: and inertia if accelerating) The center of drag (and mass) is below the centre of thrust and this causes a couple which causes the helicopter to tilt/rotate.

Last edited: Sep 16, 2014
4. Sep 16, 2014

### RuhigBrauner

@domenico, I can follow some of your terms but my math is a bit rusty.:(
Regarding the props: the tail rotor can be ignored since it is only used to corret the torque that the main rotor generates more or less as an side effect.

@CWatters,

this is true but I guess the affect is minor.
I've noticed that I had a mistake in my thoughts. Instead of only changing the lift vector, the rotor itself generates a rotation.
The reason is that the rotorblades move so they generate lift upwards when they are at the back and downwards when they are in the front. (For forward movement)
Thus, the rotor tilts and the helicopter tilts as well. Since the mass of the helicopter can't be ignored, the center of rotation shouldn't be the rotor like I marked it in the graphics: https://studi.f4.htw-berlin.de/~s0539750/LiftMass2.png [Broken]

Is it possible to calculate the center of the rotation when we know the mass and the rotation force/acceleraion?

Last edited by a moderator: May 6, 2017
5. Sep 16, 2014

### A.T.

No, this is not how you tilt a helicopter forward. There is a 90° offset between the aerodynamic torque on the rotor, and the resulting tilting of the helicopter. So to tilt it forward, you have to generate a lift difference between left and right, not between back and front.

http://en.wikipedia.org/wiki/Precession#Torque-induced

Last edited by a moderator: May 6, 2017
6. Sep 16, 2014

### CWatters

Just because the rotor tilts doesn't mean the helicopter must. You can tilt the rotor without tilting the helicopter. For example while it's on the ground.

7. Sep 16, 2014

### A.T.

Helicopters (most modern ones) don't need drag to tilt, and they don't tilt the rotor relative to the body. They use cyclic blade controls to generate differential lift, and thus a torque that tilts the rotor and the helicopter with it.

RuhigBrauner's description in post #6 is basically correct, except for the 90° offset I mentioned #8.

Last edited: Sep 16, 2014
8. Sep 16, 2014

### CWatters

9. Sep 16, 2014

### A.T.

There are many effects on a helicopter. But I think the OP is asking how controlling the tilt is realized. And that is explained on the very next page of your reference Figure 2-29 page 2-16.

10. Sep 16, 2014

### RuhigBrauner

I didn't include the 90° offset because I think my explenation skill in english is bad enough. ;) For people who don't know the 90° offset, this would make the question even less understandable. :D

The linked document is quite nice but it doesn't seem to realy go into the mathematical aspect.
I've also implemented a simple version of the model. For now, it just "magicly" rotates the helicopter and the rotor generates the thrust to move in every direction.

I think what I will try to do next is model the tilting of the blades. So user input will controll the tilt of the blade and these will create a thrust / rotation based on what was explained above.
The question I had which is still open is how to calculate, how the helicopter would tilt, when the rotor generates an angular force (tilted blades). So instead of just magicly rotating the helicopter, tilting the blades and by this rotating the rotor would bring the helicopter to tilt forward.

I hope you can still follow me, my english should be fine but explaining physical problems isn't realy a common thing for me to do in english. ;D

Btw.: Do you know a forum where people could help me with the specific problem (helicopters)? I've worked on it a bit and noticed that there are still many more question I have to think about at some point. (drag, affect of the air speed on the helicopter, some reasonable values like thrust, mass, and so on...)

11. Sep 17, 2014

### Domenico94

Re:

Have you tried the model we talked about yesterday?

12. Sep 17, 2014

### RuhigBrauner

Which one do you mean?

Many of the equations you mentioned are somewhere hiden in the model, at least when it comes to creating lift.

Currently, the helicopter constantly creates lift in the direction of the rotor, the specific amount is controller by the player.
To move the helicopter, radial forces are just magicly applied to the whole body what changes the direction of the rotor and creates horizontal thrust.
This is what is implemented right now.

I've gone through the document and noticed that simulating a helicopter could be realy complex.
For example, the difference in lift created by the two rotor halves (left/right) can make some problems. The relative airspeed of one half is adding up while the other one goes down. For example, when the blade move with 400 mph (or km/h?) at the tips and the helicopter moves with 400 mph as well, one side would theoreticaly generate no lift because the relative air speed would be 0.

13. Sep 17, 2014

### Domenico94

I understand :) what do you study in life sorry?

14. Sep 17, 2014

### RuhigBrauner

Computer science which is why I programme games in my free time. ;D
However, my math skills and my physics knowledge are both a bit rusty. Thats why I tend to need some help with things like this.

Last time I tried to write some sort of flight computer which controlls the height of some "hovering vehicle", took me forever.

15. Sep 17, 2014

### Domenico94

I'm studying telecommunications engineering :D Nice to meet you anyway :D
Anyway, we didn't study very well that part of physics...that's why I chose to approximate the helicopter to a body like that ...