Infinite Acceleration (Arguing about Larry's Exponential Handle)

[Tim Wescott]

   "Lovely" and "accurate enough to compete with David and Paul" are two different things. Recall that at the entry and exit of every corner, and the intersection of the round loops, and even the round loop entry and exit ALL require infinite acceleration to perform.

and In the real world with gravity and atmosphere, there is no such thing as "infinite acceleration"

Brett's key word is "require".

If you do the calculus on the pattern, you find that the transitions from straight to corner and from corner to corner (in the eights) do not require infinite acceleration from the center of mass of the airframe -- they only require that the acceleration of the center of mass of the airframe change instantaneously, either from zero (straight-line flight) to canopy-up or canopy-down (corners), or they require that the acceleration change from canopy-up to canopy-down, or visa versa.

So the center of mass of the airframe isn't accelerating infinitely, but it does need to generate infinite jerk (for non-mechanical types, 'jerk' is name used by mechanical engineers and physicists the first derivative of acceleration.  I'll let you draw whatever linguistic parallels with the people involved in this discussion that you may wish).

If the aircraft needs to change pitch to change acceleration, however, then to follow the pattern exactly it would need to change its angle instantaneously at these transitions -- that would require infinite angular velocity, acceleration, jerk, and everything else.  This would, in turn, require infinite "everything" everywhere on the airframe except around the axis of rotation.  So there would, indeed, be infinite acceleration.

Even if you avoid the need for instantaneous angular displacement of the whole airframe by trimming your ship so that the fuselage angle of attack is zero in a corner (which you can achieve by fiddling with the flap-elevator ratio), you would still need to move the controls instantaneously to make the transitions.

Some people, Paul Walker among them, are very good at approximating this.  If you watch Paul or one of these others fly (in a non-gale, Eugene this year doesn't count) then you can almost perceive a "click" at the intersection to the eights.  I'm not sure if it's there when Paul does his square corners -- I'll have to pay attention the next time I see him fly.

So, yes, infinite acceleration is required.  And infinite acceleration is never going to be achieved.  But like the joke about the engineer, the mathematician, and the pretty girl, those of us with the right training know that you can get close enough.

[Howard Rush]

It takes a step change in lift.  Flaps let you come close.

[phil c]

Actually, why bother.  If I'm seeing things right my stunter only requires about 1/4 in, maybe 3/8in. of handle movement to do a loop.  That can be done in well under 1/10 of a sec.  When I manage to do it smoothly(like a ballerina, no jerks allowed) neither I nor the judges can see it.  The trick is after that, from something Ted F. pointed out, you have to constantly make small, imperceptible corrections to keep all three loops on the  same track with the wind fighting you all the way.

The intersections on round eights are twice as hard since you have to go twice as far while the plane only moves 6 feet or so.

Phil C