wfooshee
O, Woe is me!!
The steering effects you describe would more properly be attributed to trail, not gyroscopic effects. As for the jump trick, there's definitely not enough speed in the rear wheel of an idling dirt bike to be gyroscopic. And yes, while airborne, they close the throttle.First off, the gyroscopic effect. It has been stated that it plays a major part, and that it plays no part what so ever. I think the truth falls into the middle. The gyroscopic effect plays a primary roll in the stability of the bike; the faster you go the more stable it is. Try riding without any hands on the handle bars at 10 mph, and then try at 50. The bike can wander all over at 10 mph, but stays fairly true to line at 50 mph. Also look at stunts that super cross racers do; the one in particular where they kick the back of dirt bike out about 90 degrees and then bring it back straight before landing. They can do that by manipulating the gyroscopic effect (as mentioned before with the 90 degree reaction force bit). The gyroscopic effect does not cause a bike to turn (unless you're airborne), quite the opposite, it resists the change in direction (hence giving the bike straight line stability at speed and at a given lean angle when cornering). Another way to practically see this in the real world is to weave between the dotted lane marker lines. Try it at 30 mph and then at 60 mph. Try to keep the tire close to the lines so you're side to side distance traveled is about the same. You'll find it takes a lot more input from the rider to weave back and forth rapidly at 60 mph then it does at 30 mph. I've done this myself and it can be hard to do it quick enough (even on a light weight dirt bike) at speed do you don't overshoot a line.
Think about how fast gyroscopes spin before they actually become, well, gyroscopes. I'm not sure a couple hundred RPM (wheel speed at 60 mph) makes enough of a gyroscope to actually affect the bike's physics.