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Generally, you want your col behind and above your com, beware however as you burn fuel it can shift your com around. A flat spin probably means you had a jet engine burnout, as they usually burn out unequally the misaligned thrust will put your plane into a spin.

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It depends where you have your fuel on your plane. If the fuel is in front of the wings, you'll want to have the CoL behind the CoM because as the tanks deplete, the CoM will move back. This is the usual configuration of fuel.

However, if you have a radical design with fuel behind the wings, then you'll want to place the CoL in front of the CoM because as the tanks deplete the CoM will move up.

As for a flat spin, I'll let someone else answer since I'm not particularly knowledgeable about that.

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From my experience being obsessed with SSTO space planes, I have found this:

Keep your CoM as far back as possible. This way you can put rear landing gear farther back and still pitch up on the runway, giving you a reduced chance of tail strike.

Keep your center of lift behind the center of mass. On larger craft, get the lift vector to point through the very rear portion of the center of mass ball indicator. Lighter craft should have centers of lift farther behind than this. This way as your fuel burns your craft will stay fairly well balanced. Corollary to this: part of your lift balancing plan should include some lift near the very front of the craft (but don't overdo it by shaping on too many control surfaces!).

A winglet tail fin is a good idea. Stick it right on your plane's butt.

For small craft, put one jet engine in line with the fuselage so burnouts don't affect your yaw. For smallish craft, use a bi-coupler or a tri-, to keep your engines as close as possible to the long axis of your craft. This helps control the problems associated with flameouts, if they happen.

Slap some RCS thrusters on. A couple fore and aft, and a pair at the tips of your wings. Save your monopropellant by keeping RCS off until some arbitrarily high altitude where your plane stops feeling like a plane and starts feeling like a Subaru drifting through the snow.

On a similar note, control surfaces are important. Too many and you can't control your craft. Too few and same problem. Put some on your wings, behind your centers of lift and mass. If your craft pitches too quickly, remove a set of control surfaces. If your craft always tries to pitch up or down, it is imbalanced. Fix the design, or alternatively, angle your control surfaces down or up by 5°, respectively.

Use more wings than you think you need. Two symmetric sets of delta wings with control surfaces is about right for a cockpit, one mk2 fuselage segment, two mk2 adapters (which contain fuel), couple small bipropellant tanks and four engines. If your prograde vector is at 15° to the horizon when your heading is at 45°, add more wings. There is a spot at mid-altitude, maybe 15-20 km, where you haven't accelerated enough but havereached thinner atmosphere, and your heading and prograde directions will drift apart from each other. You can be at a 30° pitch and your prograde vector is 2°, so you are predominantly accelerating horizontally. That is ok, and once you get to high (> 1 km/s) velocity your vector and heading will align better. In fact, I have had flyavle but less than stellar designs that reach a ceiling around 17 km, but with a little rocket boost can keep going on just jets until 25 km.

On that note, you also need enough air to get the velocity you need with jets. Otherwise your SSTO is not doing its job. You need tons of intakes, at least 5 per jet engine. At extreme altitude, intakes = thrust. Want to get up over 2 km/s on jets? Try >10 intakes per engine. After 15 km, keep your vertical speed around 20 m/s and crank it horizontally.

The perfect mix is tricky to find. I know this is more than what you asked about, but I hope these tips give you some inspiration. Nothing more rewarding than hooting orbital velocity at 35 km and drifting up peacefully.

Cheers,

Llama

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http://forum.kerbalspaceprogram.com/threads/52080-Basic-Aircraft-Design-Explained-Simply-With-Pictures

This thread is a great start for any aircraft in KSP.

http://forum.kerbalspaceprogram.com/threads/54903-KSP-Quick-Guides-Everything-from-airplanes-to-interplanetary-SSTO-s!

And this just further reinforces it.

My only suggestion is get the FAR mod, it will help with aircraft design and control, they will behave like planes.

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In general aircraft terms, its usual to have the CoL behind the CoM, but not greatly so. But your design and goals will tend to dictate the actual position spacing.

Another thing is to make sure that they are centered on each other laterally when you are viewing them from the front or rear; this means they are laterally balanced. That's not an issue when symmetry is adhered to during construction.

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