Air plane and Helicopter

self-leveling? what do you mean?

check out tbe book Physics for Game Developers

I was wondering about how helicopters seem to self-level. But for now I read up on plane physics.

Airplane

Seems simple enough.
Main formula (lift and drag nearly identical)

L = 1/2 * d * V^2 * S * Cl
D = 1/2 * d * V^2 * A * Dc

d=air density
V=veloctiy
S,A = area of wing, or area of rigib body
Cl, Dc = coefficient of lift, coefficient of drag

I think drag is right I might have to double check... but basically you take your velocity, square it, and mutiply it by a couple arbitrary numbers to get your lift. Same with drag.

So basically once you thrust reaches you to a velocity in which your lift force is greater than your weight force, you should become airborne. You also have to worry about drag which will determine your terminal velocity just as much as thrust.

So if you plane is banking hard, you appearantly are actually falling since nothing is counter-acting against your weight force.

Also to get quick elevation you translate some of you thurst force in an upward direction (pulling up) which adds more to counter-act your weight force thereby getting a quick incline...

now to helicopters which I am sure will not be easy...

[edited by - JimmyNelson on February 3, 2004 12:00:04 PM]

quote:

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Original post by jimmynelson
L = 1/2 * d * V^2 * S * Cl
D = 1/2 * d * V^2 * A * Dc

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You should be consistent in your notation. Use CL for lift coefficient (capital ''L'' implies a 3-dimensional lift. A lower-case ''l'' implies a 2-dimensional lift.) And use CD for drag coefficient. Also, for airplanes, the reference area is the same reference area used for lift, so you should have (and this is only a notation edit):

L = 1/2 * rho * V^2 * S * CL
D = 1/2 * rho * V^2 * S * CD
 

rho, the greek letter rho, is the traditional symbol for air/fluid density. And, S is the reference area for both drag and lift. S typically is taken to be the total wing area projected into the horizontal plane.

Now, having those two equations is almost no help at all for a simulation!! You need values for CL and CD to calculate the lift and drag force. But, what values are you going to choose for CL and CD? Lift is a function of angle attack, along with the geometry of the wing (aspect ratio, wing sweep, etc.) and ultimately the speed of flight. Lift can be approximated as a linear function for small angles of attack (less than, say, 10 degrees). Drag can be written as a parabolic function of lift, again only for small angles of attack.

If you search the forum archives ("CL", "drag", "lift", etc.) you should find some old threads that give some useful formulas for approximating CL and CD.

The other thing you need, which enables you to understand the self-leveling, is a pitching moment. The equation is:

Pitching_Moment = 1/2 * rho * V^2 * S * chord * CM

where CM is the pitching moment coefficient, and chord is the average chord width of the wing.

For small angles of attack, pitching moment can be represented as a linear function of lift. For an airplane to be self-leveling, the slope of the CM-CL graph must be negative (pitching moment decreases as lift increases), and the CM curve must cross through CM = 0 for some achievable value of CL (on the order of -1.0 to 1.0 or more for very efficient wings). If CM is zero at a CL that corresponds to a lift force equal to the weight of the airplane, then the airplane will self-level at exactly the right lift for flying straight and level.

quote:

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Original post by jimmynelson
So if you plane is banking hard, you appearantly are actually falling since nothing is counter-acting against your weight force.

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If you are banking with the wings straight up and down, you won''t be generating much lift against gravity, but you may be generating some. The fuselage can generate lift when the airplane has banked 90 degrees. But, just as easily the fuselage can generate a downward lift force that will cause you to accelerate faster than free fall. Further, the wings almost never lie in a plane, e.g., there is a dihedral angle between the wings. Because of this, when the plane is actually turning in a bank (vs. flying in a straight knife-edge line), there can be a component of lift generated by the wings that also either counteracts gravity or acts in the same direction as gravity....The real physics of banking is tricky. Your equations above don''t begin to address this.

quote:

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Original post by jimmynelson
Also to get quick elevation you translate some of you thurst force in an upward direction (pulling up) which adds more to counter-act your weight force thereby getting a quick incline...

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I worked in the full scale wind tunnel at NASA Langley for a year back around 1991. At the time they were just starting to free fly the X31 thrust-vectored concept fighter jet. I wasn''t allowed to see any of the tests of this thing, but later it was publically revealed that the X31 can fly horizontally while pointing almost straight up in the air. The thrust fully balances the weight and also provides a component of force to move the airplane forward. Of course, some of these fighter jets can act like rockets, requiring no lift at all---just engine.

http://www.dfrc.nasa.gov/Gallery/Photo/X-31/Small/EC94-42478-4.jpg

Note that in this photo the airplane is not climbing. It is moving horizontally to the right.

quote:

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Original post by jimmynelson
now to helicopters which I am sure will not be easy...

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There are some fairly simple flight models for helicopters. But, that''s not my forte.

There is a book called "Helicopter Theory" by Wayne Johnson, published by Dover. Honestly, it isn''t a great book. You will find it difficult to impossible to use. But, you may be able to find a copy cheap somewhere, since Dover basically provides cheap paper back technical books----reprints of classic texts.


Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

Thanks grhodes_at_work,

I always enjoy your posts. I was just wondering if you think for pratical game usage that I could get away with ignoring the reference area for drag and lift. I was just gonna set them someplace that works and go with it. My plane would fly and the drag and lift wouldn't be realistic per say... but I would be creating a terminal velocity, elevation change, etc...

And I don't really understand jet physics so much. You would have to have some lift though, to counter-act the inevitable force of gravity (even bullets can't ingnore this.) I also never understand pictures like that, where the jet can almost be perpendiculat to the ground and climb without engine failure (man it sure would be fun to be in it though).

I also have read before that although jump jets can take off in very little space, they burn up such a large amount of fuel on take-off and landing that is wasn't the most practical jet.

[edited by - JimmyNelson on February 3, 2004 9:08:01 PM]

quote:

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Original post by jimmynelson
I also have read before that although jump jets can take off in very little space, they burn up such a large amount of fuel on take-off and landing that is wasn''t the most practical jet.

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In any manouvre where gravity is completely countered only through engine thrust, the total energy for this manouvre must be derived from chemical potential energy... which means that while certain aircraft (Harrier/AV8,X31, etc) can counter gravity with thrust alone, they cannot do it for extended periods and maintain effective flight endurance.

The Harrier was originally designed to be effective on bomb damaged runways and to be deployable from short roads, making it harder for an enemy strike to neutralise the British air defences as often happened during the early days of WW2.

For the original poster... you need to make another decision with your aircraft sim: are you going to utilise a point-mass approximation for your aircraft, or are you going to simulated the lift and drag components of airframe parts (wings, tailplane, fuselage, undercarriage, etc.)? While the former is far easier to implement, it is also far less realistic.

Good luck with your project,

Timkin

Doesn''t lift depend on the angle of attack? As does drag. I don''t see it in the formulas? ;/

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shurcooL`

Timkin:

I am actually using Tokamak''s Rigib Body simulator. I am creating just a simple point mass (rigib body) and it will be used in a large mutiplayer type game (FPS not flightsim). I am wanting to add as little math as possible, seeing as there might be 6-7 of these planes in the world as well as many other objects.

shurcool:

It is in there...

L = 1/2 * rho * V^2 * S * CL
D = 1/2 * rho * V^2 * S * CD

S = is the reference area for both drag and lift

Why parachutes work so well, S jumps up from nearly nothing too creating a terminal velocity around 5 m/s and reaching that in approx 3 meters... so says my physics book...

I didn''t see this posted, so-

Helicopters and many airplanes keep themselves in a stable level attitude because the wing or rotor is on top of the plane. The fulcrum of the aerodynamic lever is just under the rotor and well above the center of gravity.

quote:

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Original post by Timkin

you need to make another decision with your aircraft sim: are you going to utilise a point-mass approximation for your aircraft, or are you going to simulated the lift and drag components of airframe parts (wings, tailplane, fuselage, undercarriage, etc.)? While the former is far easier to implement, it is also far less realistic.

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My (open-source) gliding sim

http://www.rowlhouse.co.uk/sss

implements both methods - the single-point method being lifted from another open-source sim called crrcsim. You can get good flight physics out of either method, but to get the single-point method working right you''ll need to use a lot of non-intuitive parameters, and I think this maybe makes it harder! You have the problem of where to get those parameters from. With the component-based approach you can pretty much guess the parameters for all the components, and sensible behaviour (including stalls, spins etc) will just happen naturally. However, one benefit of the single-point method is that it''s almost certainly faster. However, flight physics is not a big issue for current (or even moderately old) machines - my sim will run at least 50 or so gliders on an machine at least a couple of years old... (and it''s not a very efficient implementation).

Incidently, helicopters behave pretty much as expected except:

1. the rotor acts like a massive gyroscope - this effect dominates the rigid-body motion. To pitch about a left/right axis the rotor blades are actually angled to generate torque around a forward/backward axis.

2. to get realistic behaviour you have to bear in mind that the helicopter''s environment is significantly influenced by the presence of the helipcoter itself. For example, when hovering the helicopter gets its lift by accelerating air downwards through its blades. However, the air is already moving downwards because of the circulation set up, so the lift is actually a bit less than you''d neively expect... Once the helicopter starts moving forward it effectively gets "fresh" air which is not already moving downwards, so the amount of lift increases. This is called translational lift, and results in the helipcoter gaining hight as you go from a hover to forward (etc) flight....

3. R/C helicopters at least are always(?) controlled indirectly via gyroscopes. The control input simply biases the output of the gyros, which are themselves designed to automatically adjust the tail rotor to maintain a particular heading...

Don''t know how relevant all of this would be for a game (rather than a sim), but there''s some stuff to think about!

quote:

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Original post by shurcool
Doesn''t lift depend on the angle of attack? As does drag. I don''t see it in the formulas? ;/

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shurcooL`

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Yes, that part was missing. See my post. Actually, for very simple simulation it is more common to represent drag as a function of lift rather than angle of attack, since you can create a simple parabolic shaped "drag polar" (which is a CD vs. CL graph or table).

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:

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Original post by Timkin
For the original poster... you need to make another decision with your aircraft sim: are you going to utilise a point-mass approximation for your aircraft, or are you going to simulated the lift and drag components of airframe parts (wings, tailplane, fuselage, undercarriage, etc.)? While the former is far easier to implement, it is also far less realistic.

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VERY good point. The most immediately important part of simulating lift and drag on, say, the tail surface in addition to the main wing, is the pitching moment contribution, which actually flips that CM-vs-CL curve from a positive (unstable) slope into a negative (stable) one (depending on the location of the center of gravity). Also, they''d have to simulate lift at least on the vertical stabilizer if you include lateral/directional motions.

Of course, if realism is the goal, you''d have to deal with the effect of wing downwash on the tail surface angle of attack, etc.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

quote:

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Original post by Phlegmy
I didn''t see this posted, so-

Helicopters and many airplanes keep themselves in a stable level attitude because the wing or rotor is on top of the plane. The fulcrum of the aerodynamic lever is just under the rotor and well above the center of gravity.

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As far as airplanes are concerned, this fulcrum effect only contributes to the stability----it is not required for stability. (You might notice that quite a few airplanes such as Piper Cherokees, Beechcraft Bonanzas, Grumman Cheetahs, lots of big things made by Boeing et. al., and a number of fighter aircraft, all have low wings---yet most are inherently stable due to the clever balance of aerodynamic forces vs. all other mechanical and gravitational effects.) See my post for a brief discussion of the pitching moment curve (CM vs. CL), which describes the real reason for stability. It just happens that for a high wing airplane vs. a low wing airplane that are otherwise the same----the CM vs. CL curve for the high wing airplane will have a larger negative slope than the low wing airplane.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

K i got no idea about the actual physics but i fly RC helis and planes.
The self leveleing you speak of is -- -- the pilot. Helicopters are inherintly unstable (larger is more stable so i'm working from an extreme of the scale with very small responsive craft) If a heli was left without computer or pilot control in a hover it would be in the ground in seconds or less.

As for planes High wing aircraft are more self leveling due to dihedral -- the angle that the wings are off of horizontal -- kind of their V shape, and the low CG. There should be a formula somewher for this tendancy.

Heres a site that goes into basic helicopter aerodynamics link doesn't have formulas but gives an overveiw and lots of big words for google with although alot of it really isn't that relevent
EDIT: fixed link
EDIT2: Typo's
[edited by - Spitfire_mk5 on February 4, 2004 9:21:18 PM]

[edited by - Spitfire_mk5 on February 4, 2004 9:55:29 PM]

On the issue of high vs low wings... I learned to fly in a low wing aircraft (Piper Tomohawk) and later moved to a high wing aircraft (Cessna 172). I can tell you that while both were stable, the agility of each aircraft was completely different. The Tomohawk was particularly affected by turbulence but could also react quickly for a required change in attitude (landings in crosswind were always fun!). The C172 however was a lumbering oaf in comparison. It was slow to be affected and slow to react. In the Tomohawk you had the feeling of sitting on the air, while in the C172 you had the feeling of handing on the air. This agility is why all single engine, prop driven fighter aircraft were low wing. It wasn''t until the advent of jets that one could get away with a high wing fighter because of the speeds involved.

MrRowl, thanks for the link to your OS Gliding Sim. It looks great. I had been thinking some time ago that I should write one of these (I''m a long time RC Glider Guider and Powered Jockey and I''ve always wanted to write a good RC Glider Sim). Now I don''t have to! If I come up with any useful additions to your system, I''ll be sure to pass them back to you! Now, where''s that download button?

Cheers,

Timkin

I wish I was a pilot or... at least race car driver. Nah, nm being a college student is just as much fun and they can''t fire me for being a drunk. Although my low GPA might yeild me the same results.

Could any body send me any formula to calculate the maximum and minimum helicopter weigth and also send me how to calculate the gravity center of helicopters?????

Formula for weight? You mean how to calculate momentum?

L=mv;

Also for the center of mass just place in somewhere in the middle of the cab. Probably yeild about the same results.