The Physics of a Hang Glider (an unfinished work)
So what about the science of the system, because that's always been my thing?
Let's start with the basics and translate aeronautical speak into good, old fashioned physics.

Lift
The object of a wing is to provide lift. Lift being the force that pushes up and counters the effects of gravity without which the whole flying business is rather pointless. The only way to get lift is to accelerate air downwards and the most obvious example of that is the helicopter and the least obvious example is the parachute although they work in exactly the same way. (Think about it. Air that was otherwise minding its own business is suddenly caught up in this canopy and is accelerated downwards. If you apply a force accelerating something down the ol' equal and opposite reaction kicks in and it pushes back up at you.)

So that's what a wing does. It pushes air downwards. So how does it do that? Well the simplest wing was a sloped flat kite and when the air flow hit it the slope forced the air down. More complex wings use a smooth curved surface so that the path for air going over the top is longer than the path for air going underneath. The longer path means the air gets stretched out on the top so the pressure falls. On a well designed wing the pressure under the wing greater than the pressure over the wing the net force is up and the low pressure above the wing actually contributes more to the sum total of lift than the increased pressure below so an aircraft is actually 'sucked up'. Mostly. (Try Wikipedia on Lift (force) for a fun ride through the detailed physics because most of the simplified explanations are wrong.)

Of course you never get something for nothing and all this accelerating air downwards lark consumes power. This manifests itself as a second force acting on the wing 'dragging' it backwards and so, effectively, trying to slow it down. You either have something to push forward, like an engine, or you slide down through the air using the energy from your height to propel you much as a roller-coaster ride accelerates on the down hill leg. Please note that this drag, which is referred to a induced drag, is nothing to do with poor streamlining or design. It is just a consequence of getting lift out of our wing.

Hang glider wings use a bit of both tricks as do most aircraft. We almost always want exactly the same amount of lift as we have weight so we either maintain height or ascend and descend at a constant rate. Wing shapes are designed for one shape and , to a measure, for one speed. Look at a baby bird. The parents have to keep stuffing food down it until it is virtually their own size because the wing design they are passing on only works for that size. Similarly watch a big airliner setting up to land and you will see the wings virtually redesign themselves so they can fly slower to land.
On a simple hang glider all we can change is the angle off attack, which is is the angle that the air hits the wing and is how far we tip it up. More angle of attack and you get more lift but more drag until you finally ask for more than the wing can deliver and the air stops flowing nicely over the upper surface and you loose the 'suck' part of the lift. This is the dreaded stall.

Washout
A stall at its worst is just a plain 'fall out of the sky' but it can get far more complex than that. Since hang gliders are always a bit slow we don't want to stall until we can just walk it to a halt when we don't call it a stall (nervious twitch) but a flare (smug).

Washout is a design trick where we plan in a bit of twist in the wing so we have more angle of attack at the centre of the glider than at the wing tips. Look at the picture. See how the wingtip is pointing down while the centre of the wing is level. If the chump seen holding the front end puts the nose up too far in flight then the glider isn't getting enough forward push from sliding down through the air and starts to slow down. Now the centre part of the wing will have more angle of attack so it will stall first. Since the wings are swept that means the lift is now only coming from the further out, hence further back, parts of the wing so chump is now suspended from a point well in front of the centre of lift so the glider will nose down and get some speed up. Chump is saved from digging a hole in the field below despite himself.

Interestingly the Washout on the Spitfire was one of the novel features that allowed it to be flown to its limits by relatively inexperienced pilots. The wing roots stalled first and the whole airframe vibrated warning the pilot to adjust things before it stalled a wing and spun.

Reflex
See how the thinner wires coming from the top post pull the back edge of the middle part of wing up. This is reflex or reverse camber. This is another trick to make things more self correcting. The turn up at the back creates a small down thrust so when it is close to stalled it helps to flip the nose down. If the pilot has lost it this should put the glider back in a recoverable position quickly but if the stall happens low there might not be enough height left for a full recovery.
Early hang gliders, Google for the Rogallo wing, had a problem that if the nose got down too far in a stall they just flapped and never reinflated to get their wing shape back and the ensuing Luffing stall was irrecoverable and tended to end in a obituary.

Trim and Control
Right so now we have a reasonably safe flying machine. Now we have to add a pilot and get him to fly it. Well my Rio 15, for example, is just 25Kgs fully rigged and ready to fly. With all my kit and helmet on I weigh about 80Kgs so my weight is the most significant force available. I am suspended from a point virtually on the centre of lift for the wing when it is flying properly such that if I 'hands off' the controls it is in balance to fly a rather slow but workable glide back to earth. Move the hang point further forward and it nose downs a bit and flies faster, move it back and it flies slower. That is all the trim adjustment there is.

If I now pull the bar attached to the wing back towards rather than me swinging forward the wing tips nose down and the glide accelerates, push it forward and we slow down. Twist my body so instead of hanging straight down I am slightly offset and the wing rolls to try to put me back underneath and if I leave it at that rolled position I am turning. There are no controls, everything depends on how I hang. The design may be sophisticated but the actual control is about as basic as it comes. This is riding a bike not driving a car. Where you go depends ultimately on where you put your bottom. It's that simple.

So what do you have to learn? The first thing that took me a while to realise is that, just like a push bike, going faster makes it so much easier. The modern wings are so designed that they will still try to fly right down to a very slow airspeed but just as your bike got wobblier and wobblier as you slowed right down so does your hang glider. All those things they tell you about pitch and steering work a bit but the wretched thing really doesn't seem to cooperate when you're going too slowly.
Then you pluck up the nerve to pull the bar back a bit more and the wing speeds up. Suddenly the efficiency rises and your sink rate drops so that slope that you kept touching your feet down on before becomes flyable as you do more horizontal distance for your vertical sink. More importantly the steering and pitch control becomes far more crisp. Finally, far beyond where you got to last time, you run out of height and flare for a landing and it all happens quickly. You pass through the slow wobbles almost before they happen and there you are, standing stopped, holding your glider and feeling cool. Remember this is a glider and it glides. There is no 'down' control on a glider.

Glide slope
I started by flying too slowly and that doesn't work. You may be apprehensive about letting it speed up but it feels so much better, more in control, when you do.

On the left is a Polar Diagram.
This is a plot of sink rate against air speed. I've no idea what model glider this represents but apparently it is a hang glider. From the curve I'd say it's pretty sporty rather than a 'floater' trainer style thing.
My data is MPH across the top and feet per minute vertically (1 meter/sec = 197fpm) which is pretty normal in aeronautical circles.

I'd say it's pretty much as you'd expect. Go really slowly and nothing is working well so it sinks quite quickly. Go a bit faster and it gets better, go a lot faster and you're starting to burn up lots of energy to push air out of the way and the efficiency drops again.

Since we have speeds we can recalculate it all into feet per minute, apply an arctan and get the glide slope angle in degrees which is the diagram on the right.
Again pretty much as you expect with a rotten glide angle when you're slow and inefficient and although it drops off a bit as you go faster you are getting more airspeed and covering more distance so the higher sink rate doesn't cost you so much angle. Do notice that the best (least) glide angle is faster than the minimum sink rate. Your increased speed is getting you there faster.

However this is not how you react.

Imagine you are starting on a nursery slope that runs down at about seven degrees. See how your takeoff run puts you on a really bad part of the curve? If you are gliding down at more than seven degrees your feet keep touching down and if you are gliding at less than seven degrees you gain a little altitude. So to stop loosing height you must pull the nose down so you will accelerate. Every bit of speed you gain gives you a better glide angle so the slope you were running down does not come back at you so fast. You don't want to fly up at this point but down.

I found that very counter-intuitive at first but flying 'down' actually gains you altitude and when you do it it delivers all the advantages that higher speed gives as the control becomes crisper.

Let's poke our noses further into the physics of landing. What are we doing in a flare? Well we are using the wing as a huge air brake. Now the worst thing that could happen would be that we push out too little, fly up, then stop, then fall back to earth from a dead stall. So do some numbers working in old imperial units:
The first point is that we are descending at about 1 meter per second to maintain airspeed so if we stop descending we are slowing down. We don't have to worry about rising air at nill feet because there isn't anywhere for it to rise from.
Flying at nill feet at 20mph, that's about trim speed, is 29.3fps so kinetic energy is ½m(29.3)²
If this becomes potential energy at mhg at 100% efficiency the mass nicely cancels out so we could rise 13.4 feet so about 4 meters.
Now, admittedly, flaring at nill feet and suddenly discovering you are four meters off the ground would suck but conversely fly horizontally for four seconds and you would have totally run out of energy and stopped. This is where our one second comes from.
One second eats a quarter of your kinetic energy so you are about down to 17mph and dropping off the polar diagram so flying is getting a bit iffy so bang out the flare. The trick is that a flare is big. You must wack it out so it isn't a wing any more it is a wall. Then there is no flow over the top surface, where you will remember that two thirds of your lift comes from, You are too slow to fly up so the wing is now the big air brake you wanted swinging you forward which tips it up more. Bingo.

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