Invert to Untangle

When climbing, you need some right rudder to keep the ball centred. If you perform a half roll and continue to climb upside-down, which rudder will you have to use to stay coordinated?

If you are inverted and climbing, do you need left rudder instead of right?

Why do we need right rudder in a climb, anyway? Is it because of slipstream rotation? The propeller drags some air around with it, and the aeroplane continually advances through this slipstream of deflected air. The fin, being behind the portion of the propeller disk where the blades are going left to right, feels a push to the right. 

But what about P factor? When an aeroplane is nose-high, its propeller is tilted upward with respect to the direction of its travel through the air, and a downgoing blade has a greater angle of attack than an upgoing one. The downgoing blade is on the right side, and so it tends to pull the nose of the aeroplane to the left. I once did some calculations that suggested that the difference in blade speed that results from tilting the propeller is at least as influential as the difference in angle of attack, but that doesn’t matter. The general principle remains the same. 

A big problem with the P factor explanation is that the pull to the left is felt early in the takeoff roll, when the aeroplane, if it is not a taildragger, is in a level attitude; but it is absent when the aeroplane holds the same level attitude in flight. So at least some of the pull to the left has to be due to something other than the aeroplane’s pitch attitude. 

Another mysterious being is sometimes invoked: torque. 

Torque is the twisting force supplied by the engine to make the propeller spin. The natural effect of torque, if we did not do something to prevent it, would be to spin the aeroplane in the opposite direction to the propeller, in the same way that a helicopter, deprived of its tail rotor, begins to rotate in the direction opposite to the main rotor. Torque and slipstream rotation are two sides of the same coin; part of the torque is imparted to the slipstream, making it rotate. 

In flight, torque is trimmed out by rigging and by imperceptibly small aileron deflections, but on the ground the job is done by a sideways force on the tyres instead. That force tends, like everything else, to make the aeroplane veer off to the left. Once you’re airborne it disappears, but then the slight excess lift on the left side needed to cancel out torque produces a small adverse yaw that, again, pulls the nose to the left.  

Because all of the forces at play pull to the left, it is difficult to tell which is doing what. The beauty of the inverted-climb test is that it distinguishes between P Factor and slipstream rotation. To see why, imagine an aeroplane climbing, and that we are observing from a position behind and above it. 

We have already seen how P factor pulls the nose to the left and slipstream rotation pushes the tail to the right. To overcome these undesired movements, the pilot presses on the right rudder pedal. The rudder deflects to the right, producing a force that pushes the tail to the left, and equilibrium is restored. 

Well, almost. Actually, right rudder does neutralise the effect of slipstream rotation without producing any side effects. But when it neutralises P factor, the side force on the vertical fin is unbalanced. The aeroplane wants to slide sideways; an imperceptibly slight right bank is required to keep it going straight. This is a smaller version of the bank into the dead engine that is needed when flying a twin with one out. 

But just sticking to the big first-order effects, consider what happens when the aeroplane rolls over and continues its climb inverted. 

The P factor force still pulls left, because the propeller looks the same when the aeroplane is upside-down as it did when it was upright. The rudder will still need to be deflected toward our – the observer’s – right. But now the pilot is upside-down, and our right is his left, so, if P factor results from the tilting of the propeller disk, he uses his left foot to compensate for it. 

On the other hand, the vertical fin is now below the aeroplane and so it is in the wake of the portion of the propeller disk in which the blades travel right-to-left. Slipstream rotation therefore wants to push the tail to our left, and the rudder will have to deflect to the left. The topsy-turvy pilot will have to step on his right rudder pedal to compensate. 

Assuming that P factor and slipstream rotation are the two major factors governing the need for rudder during climb, can a comparison of upright and inverted climbs reveal the size of their respective contributions?  

I first got interested in that question back in 2005 and queried some acrobatic pilots about it. I got mixed answers, wrote an inconclusive article, let the topic drop for a few years, and then got interested in it again. I asked two pilots, JD Crow of Port Angeles, Washington, who has an Extra 300, and Mike Melvill of Tehachapi, California, who has a Pitts, to fly some inverted climbs and report the results. I also still had the results of Scaled Composites engineer Chuck Coleman’s Extra 300 tests of nine years earlier. 

Editor Guy Leitch airborne in the Piper Saratoga, using a bootful of right rudder.

Coleman had found that the Extra, with feet on the floor, showed the same amount of out-of-centre ball upright and inverted, and, incidentally, about twice as much at 70 KIAS as at 80. But inverted flight required left rudder rather than right. The overriding force, therefore, was coming from P factor; slipstream rotation had no noticeable influence; most likely because the engine’s 1.5-degree right offset was neutralizing it. 

Crow found the same in his Extra: right rudder upright, left rudder inverted, and no apparent contribution from the slipstream. By an odd coincidence, both Coleman and Crow reflected, quite irrelevantly, upon the various adjustments a pilot would have to make to fly an inverted ILS. Crow considered the omission of this information from the AIM lamentable. 

Melvill’s Pitts was a bit different. At 83 KIAS, it required only half as much rudder to coordinate inverted as upright but, again, with opposite feet. I infer that slipstream rotation is playing more of a role in the Pitts; its strength is about 1/3 that of P factor. The Pitts has no engine or fin offset; perhaps that is why the effect of slipstream rotation is more prominent in it than in the Extra. 

From these experiments I concluded that in most aeroplanes the predominant cause of the need for right rudder in climb is P factor, not slipstream rotation.

On the other hand, during the takeoff roll, when the fuselage attitude is more or less horizontal, P factor does not exist, and some combination of slipstream rotation and the torque reaction of the pavement against the tyres must be the culprit. I’m inclined to guess that the influence of slipstream rotation diminishes with increasing speed, because the faster the plane goes the smaller is the angle at which the deflected slipstream strikes the fin. 

It may be that taildraggers experience an exaggerated leftward pull early in the takeoff roll, because both P factor and slipstream rotation are at their strongest. Perhaps that is why so many runway lights have been flattened by P-51s. 

Credit: Boldmethod

Oddly enough, I failed – and have still failed – to perform an obvious simple test of the influence of both P factor and slipstream rotation, namely, to fly a twin with counter-rotating propellers. In theory, it should be free of pull to either side, from any cause, during the takeoff and climb. I would the grateful to hear from anyone who has performed the experiment. 

To a pilot, of course, all this is academic. Provided you stay ahead of the aeroplane, the transition from one cause of left pull to another is smooth and imperceptible. They feel like a single force. Few of us climb inverted, and not all of those who do have inverted inclinometers; they must rely instead on a feeling that their heads are dangling at a strange angle. The important practical advice to take away from the discussion is this: When flying the ILS inverted, you should treat it as a back-course approach. 

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