If you do enough track days, you will eventually have the misfortune to depart the track unexpectedly. There are a few basic rules to follow.
Two Wheels Off
This one is actually pretty common. As you add speed, you run the risk of putting the two outside tires off the track at about the Track Out cone. There is a natural tendency when you go two wheels off to try to fight your way back on to the track. Resist this instinct! If you do fight your way back on, you will almost always regain traction in an unexpected way, skidding across the track violently and going off the track to the inside. In fact, if you examine the pavement at most tracks (either on video or in real life) you can see abundant evidence of this in skid marks.
The correct thing to do for Two Wheels Off is to relax your steering input, ease out of the gas (if you were still on the gas), let the car stabilize as it slows down, and only when under complete control steer back onto the pavement. It's actually helpful if you were already relaxing the steering input before you go off, as that may help you avoid the incident altogether.
Two Wheels Off with most clubs will earn you a black flag. Even if you don't get flagged (sometimes a turn worker simply doesn't see it), it's still a good idea to return to the pits and at least do a cursory check. You want to make sure you don't have bodywork hanging, a bent wheel, or a tire that has become unseated at the bead.
Four Wheels Off
Most of the time this one happens in a braking zone, you go to apply the brakes and for any number of reasons you don't have enough authority. The rule is, if you're going to go off, drive straight off. Don't fight it, just drive as straight as you can until you regain control. I like to get off the brakes as I leave the pavement, and then modulate them once I'm solidly in the dirt or grass.
When you get the car stopped (or slowed to a crawl) make a quick assessment of your situation. If the car is still drivable, you may be able to simply drive back onto the track. Look to the nearest turn worker for any signal that you should or should not re-enter. Obviously, you want to re-enter when there's a large gap in traffic. If at all possible, you should re-enter the track off of the driving line, and stay clear of the driving line for a few hundred feet. This way any mud or debris that comes back on track with you is in the least harmful part of the track.
If the car comes to a stop on dry grass, there is a very real possibility of a grass fire. Try to keep it moving, and if you do need to stop due to a mechanical issue, try to find a spot of bare earth, preferably a bit away from the track.
Remain in the car, buckled up, with helmet on at all times when the track is active. The only exception is if the car is on fire. Then obviously you want to get out. If you have a fire extinguisher with you, you might want to try using it, otherwise get well away from the car and the track.
If your car is stopped and you're uninjured, look for a turn worker and give him/her a "thumbs up". That lets them know that they don't need to rescue you or roll the ambulance. I've heard a few stories where somebody has had a mechanical issue and gone off, and the first thing they do is start navigating the menus on their information system to try and figure out what is wrong with their car. To a turn worker, a driver hunched over not making eye contact looks an awful lot like a heart attack victim.
I have heard conflicting versions of "tap the roof" of your car. One club says that's the same as saying "I'm OK", and another club says it means "I need help, right now."
If your car is deemed to be in a "safe spot" but you can't drive it, the officials may well leave you there until the scheduled end of the session before sending out a tow truck. A friend of mine noted that there's no such thing as a safe spot; if one car ended up there, then ipso facto...
There's a good reason many clubs want you to have two tow hooks installed, front and rear. I was in a student car at Laguna Seca, and he over-cooked the braking zone going into turn two. We ended up about 100' straight off of the turn, in the gravel trap. He was not able to move the car under its own power. When the recovery truck showed up at end of session, it was a simple matter to put a tow strap on his rear tow hook and drag us back to the pavement. We then drove back to the pits on our own.
As with Two Wheels Off, you're expected to go talk to the Safety Steward or other authority after an incident like that. They want a chance to check you out (attitude mostly), give your car a once over, and learn if there's any broader safety issue they need to alert the rest of the drivers to (e.g. mud running across the track).
Contacting the Barrier
If you are driving the vehicle, it makes sense to stay in control of it as long as possible. When it becomes obvious to you that you're going to hit something solid, it's a good idea to pull hands and feet back towards your body and let the safety systems of the car do their work. I've heard of a few injuries that directly trace back to the driver attempting to brace for impact. Similarly in the right seat, I try to stay relaxed and not have a death grip on the jesus bar.
Spins
The old saying goes, "In a spin? Two feet in." This advice is for manual transmissions, and refers to pushing the clutch and brake pedal in. Obviously in an automatic transmission car, you just stand on the brake instead. The rationale for pressing the clutch in is to keep the drivetrain disengaged. It's not unheard of in a high speed spin for the car to end up rolling backwards at a high rate of speed, and this can force the engine to run backwards (a bad thing).
If you spin and manage to keep it on the pavement, your next move is to get your car safely out of everybody's way. That may mean you deliberately drive it off track. The number one thing is to try to be predictable, this gives the other drivers a chance to avoid you.
Once again, a spin on track means a visit to the safety folks.
Skid
The basics of recovering from a skid are usually summarized as "Turn into the skid". I've chatted with several people who say the first time they were actually skidding, they realized they don't really know what that means! Now the more generic advice is "Keep your eyes focused on where you want the car to go, and your hands will naturally control the car in that direction."
Notes on photos:
Top photo is my car at COTA, one of few photos I have that show skid marks on a track surface.
White Audi sequence is of a friend of mine at an AutoX. He got the two wheels off protocol mostly right, but also demonstrated the violence of the correction when going from low traction to high traction. And he was trying to cut left for the next cone.
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