I've been writing a flight sim for some time now and it's slowly coming together.

This morning I was testing an F4 and had problems doing a simple loop. After some head scratching and debugging I discovered the pitch moment due to the elevator was too small and increasing it solved the problem, but in doing so I began to wonder about inverted flying.

When the F4 finally pulled it's nose through the vertical plane I stabilized it at a 45 degree nose up angle, but inverted.

It lost altitude like a streamlined stone.

That's fine. It's a big heavy aircraft with comparatively small wings, it's going to lose altitude when inverted.

However it is normal for most modern jets to be able to fly inverted, so how the hell do they get lift?

The wing section is designed to give lift when in a normal attitude, so when it's inverted, lift will now be pointing towards the ground aiding gravity rather than opposing it.

Might just be tired, but it's worrying me.

Even inverted you should be able to find an angle of attack for the wings to get lift in the right direction. The required pitch may be different than when flying upwards, depending on the shape of the wings, but it's still possible.

But the idea of an aerofoil is that the air passing over the top of the wing has to move faster than the air under the wing, which produces a pressure differential and hence a force.

When the wing is inverted it is still going through the air and the faster moving air is now below the wing producing a force down.

Stunt planes, designed to fly both ways, have almost symmetrical airfoil, and the lift is produced by the angle of attack.

Planes with asymmetric airfoils designed to mostly fly right-side-up (designed to reduce the angle of attack, but still produce lift) would need a steeper angle of attack to fly upside-down.

These guys have more detail: http://physics.stackexchange.com/questions/15981/how-can-airplanes-fly-upside-down

You don't need airfoils to fly, you can fly with any flat surface, it's just less efficient.

But the idea of an aerofoil is that the air passing over the top of the wing has to move faster than the air under the wing, which produces a pressure differential and hence a force.

When the wing is inverted it is still going through the air and the faster moving air is now below the wing producing a force down.

This kind of asymmetric wing will produce lift at a zero attack angle, true, and if the plane is upside down, still with a zero attack angle, then as you say it will produce a force down instead of up. Then you need to change your pitch to have the correct attack angle to generate lift again.

Any (reasonable!) shape can produce lift when given the correct attack angle. Of course the whole point when designing a wing is to generate more lift than drag.

The lift force produced by a wing is given by:

liftMagnitude = CL * dynamicPressure * wingArea

dynamicPressure = 0.5 * airDensity * square(airSpeed)

CL = lift coefficient, which depends on the aerofoil and the angle of attack.

The lift acts in a direction perpendicular to the local airflow (this is not the same as the wing "up" direction).

If the wing isn't stalled, then a fair approximation for CL is CL = CL0 + alpha * 0.1 where alpha = angle of attack in degrees. However, for general flight you need to have lift/drag etc calculations over the whole range of angles.

CL0 is the coefficient of lift when the angle of attack is zero. For symmetric aerofoils this is zero. For asymmetric aerofoils this may go up to to 0.3 or so.

You'll also need to calculate the drag (which acts in the direction of the local airflow), and the pitching moment - the torque around the direction perpendicular to the drag and lift directions. When you look info about this it typically indicates the pitching moment assuming the lift force is applied at the "quarter chord" point - i.e. 25% of the way back from the leading edge of the wing.

Also - if you're representing the plane with a single lift/drag/pitching force/torque you'll also need additional terms to represent things like the rolling moment due to sideways movement etc.

Alternatively you can represent the plane with multiple lifting surfaces. If you do this make sure that the airflow is calculated taking into account the rotational velocity of the plane itself (otherwise if you roll the plane, then centralise the stick, the plane will carry on rolling etc).

I'm afraid if you're writing a simulator you can't neglect any of these things, and it's worth getting a handle on them before getting too far with the coding. There's an old simulator I wrote with source code: http://rowlhouse.co.uk/sss/ A new version, using the same system of representing planes using multiple (partly interacting) lifting surfaces is available at http://rowlhouse.co.uk/PicaSim/ - no source code for this, but you can use it to display graphically the CL/CD/CM curves and lift/drag for each component in the plane, and see how they're affected by changing the controls (you're welcome to reverse engineer this!).

I have a complex FDM in place which mostly works, I still have some issues to resolve when the nose is vertical (maybe a bug in my quaternion code), but I have most things in and working.

This was just a brain fart when thinking about inverted wings. A pure aerofoil shape, at least in my head, would have to be pretty far off horizontal to move the lift vector above the horizontal.

Luckily I designed for aircraft with complex wing topology and can easily incorporate symmetric aerofoils into the system, I just hadn't thought about it before I started this thread.

Cheers guys