Can you explain why the prop must be tilted up? (part 2)

From Don Stackhouse:

(And now for part 2)

Now we're FINALLY ready to discuss thrust lines! (See, I told you I'd get back to that!)

A number of years ago, in a "previous lifetime", I was involved in some discussions regarding fitting a turboprop engine to a single-engine (full scale) amphibian. This particular aircraft used a pylon mounted engine, a pusher prop and a taller pylon, but was otherwise similar to the Herr Aero Star in general configuration. This aircraft was limited in the amount of additional horsepower it could tolerate, because of the severe nose-down trim effects of the increased thrust. Even relatively small increases in power would try to shove the nose under the water during the beginning of the takeoff run. The increased propeller diameter required to efficiently absorb the increased power, and the resulting higher pylon required for prop clearance with the wing, only made the problem even worse. Any aircraft with very high-mounted engines would probably have similar problems.

The line of action of the thrust vector of your model (which of course we call the "thrust line") is well above the C/G, and therefore has a moment arm. The thrust, times this moment arm, yields a nose-down "torque". On a conventional model with the engine in the nose, if you tilted the engine up or down, you could make the thrust line go above, below or through the C/G, changing the size and direction of the moment arm between the thrust line and the C/G, resulting in a nose-down, nose-up or zero torque respectively about the pitch axis. In this particular model that doesn't work very well. If you angle the thrust line up or down, but the engines are mounted almost directly above the C/G, then the moment arm does not change significantly, and the nose-down torque stays about the same. Don't despair yet though, there are some other factors involved that I'll discuss in a moment.

The tilt of the propeller discs relative to their inflow creates side forces in the propellers themselves that could influence pitch trim. There will be a force in the plane of each disc, away from the inflow angle, so that a prop with down thrust will have a downward lateral force, and one with up thrust will have an upward lateral force. If an upward-angled prop is ahead of the C/G it will tend to pull the nose up, and behind the C/G it will tend to pull the tail up (and the nose down). Since this force is in the plane of the propeller disc, and the moment arm it acts on depends on how far that propeller disc is located ahead or behind the C/G, I would estimate that in this particular case the forces due to this effect are low, as well as their moment arms, so they are not likely to be significant players in this particular situation. In something like a Dornier Do335, with props at both extreme ends of the fuselage, this effect could be more important. In the case of the V-22 Osprey this effect is very important, since it provides a good portion of the aircraft's total lift during transition between helicopter and airplane mode.

There will also be moments (a "couple" in this case) due to different amounts of thrust generated by the blades on one side of the disc compared to the other, but that will create influences on yaw, not up or down effects, so they will not influence pitch trim. BTW, these are among the effects that tend to swing the nose to the left during climbout with a right-handed prop on most aircraft.

The drag of the water on the hull is below the C/G, and also creates a nose-down torque, one which can be quite significant.

The aerodynamic drag of the wing is probably above the C/G, so it tends to pull the nose up. The drag of the tail may be above or below depending on the configuration, so that could go either way.

More importantly, the downward "lift" vector of the tail, acting on the tail moment arm, is trying to push the tail down, pull the nose up and prevent the model from deciding it's a submarine. This is probably the most important factor that is trying to keep our model at an altitude higher than the local water level.

So what can we do to help the tail keep the nose up, despite the high thrust line? This is where thrust line changes can help, but you may need to alter the tail to make it work.

The air behind the prop is moving faster than the free stream air, as a natural result of the creation of thrust. In fact, one of the most fundamental measures of propeller efficiency is the ratio of the speed of the free stream to the speed of the slipstream (i.e.: the faster the slipstream relative to the free stream, the worse the propeller efficiency). BTW, this is why propeller efficiency is generally lower at low airspeeds than at higher airspeeds; at low speeds, the slipstream is going quite fast as a result of the thrust-making process, but the freestream is quite slow (zero in fact at the beginning of takeoff run). So how can we use this faster-moving air in the slipstream, that also isn't necessarily going in the same direction as that of the freestream (such as when the thrust line is not parallel to the direction of flight)?

If we mount the motors with "up thrust" (i.e.: the front end of the motor is mounted higher than the back end, regardless of whether it's a pusher or tractor), then the slipstream will be directed downward relative to the rest of the aircraft. If we then mount the stabilizer in the propeller slipstream, the angle of attack of the stabilizer will be more negative (the downward component of the tilted slipstream has changed the local relative wind at the tail), causing its lift force to be more negative, which will tend to push the tail down and the nose up. The additional airspeed of the propeller slipstream will enhance this effect, particularly at very low aircraft speeds when we need this help the most (such as the beginning of takeoff run). At higher speeds, as the thrust of the propeller decreases, this effect will naturally decrease as well, helping to keep the whole system in balance. If you look closely at the full-scale aircraft I used as an example (I won't say the name, but it has four letters and starts with an "L"), you can see this same technique in practice; the engine is mounted with obvious up-thrust, and the tail is cruciform-style, with the vertical position of the stabilizer approximately on the thrust line. On that aircraft they also have a large adjustable "trim tab" taking up a big portion of the center of the elevator area, right in the core of the slipstream, and this trim tab is normally deflected up quite a bit for takeoff.

A stabilizer airfoil with the cambered side down would increase the effect of slipstream speed on downward lift. The trim tab I mentioned above has this same effect, by changing the effective camber (as well as incidence) of the stabilizer when it's deflected. Unfortunately, it might not reduce its effects as desired at higher airspeeds.

Now if you were paying attention earlier, you might have figured out that if the vertical location of the C/G were higher, approximately on the thrust line, there would be a zero moment arm for the propeller thrust vector to push on, and therefore no nose-down effect due to thrust. Why can't we just put a post on top of the motor pylon with a large counterweight the top of it (maybe the battery?), and move the C/G upward enough to get it on the thrust line? Great idea, except that in the process the moment arm for the drag vector of the water on the hull, and the moment arms for aerodynamic drag on the wing, fuselage, and just about everything else on the model is now further below relative to the C/G than before. The nose-down effect of the thrust will be eliminated, but the other nose-down effects will be increased enough to completely cancel out the benefit. Some days you just can't win!

Aircraft with high thrust lines tend to have power-related pitch trim problems. It's the nature of the beast. Aerodynamic "tricks", such as the stabilizer position and thrust line fix described above can help, but it's tough to come up with one combination of factors that works for all airspeeds and power settings. If you really want to have a high thrust line, be prepared to put up with some quirks. You may need to apply power slowly on takeoff until you have enough airspeed to hold the nose up with elevator, and expect to use lots of elevator at low speeds. Chances are you will also have to adjust pitch trim for different power settings. You might get lucky, but don't count on it. Still, with some number crunching, and experiments in thrust line, tail incidence and tail airfoil, you might come close. In any case, it's worth a try!

Don Stackhouse @ DJ Aerotech
djarotec@bright.net
http://www.bright.net/~djwerks/