Don talks about an accident of a scale model B-52

From : Don Stackhouse

Good posts by a number of folks on this thread. However, I think I detect the same problem in this discussion that is typical in discussions of aircraft accidents - it seems like most of the participants are looking for the "cause" of the accident.

Note my use of the singular: "cause". What we should be looking for are the "causes" of the accident. Occurrences like this one are almost always the result of a combination of factors.

Yes, it's possible that it could be radio failure, such as a stuck aileron servo, or even more likely a stuck rudder servo, although that's not the conclusion I reach looking at the video.

First, let's talk about banks and turns and their effect on stall speeds. The basics of this subject are covered in some detail in any good full-scale private pilot's license ground school course, and it's on the FAA written test, as well as being demonstrated in pilot training.

When you go around a tight curve in a car at a reasonably high speed, you feel what's commonly referred to as "centrifugal force" (actually the correct term would be "centripetal force", not "centrifugal", but even engineers tend to be pretty sloppy about using the two terms interchangeably) pulling you across the seat, away from the direction of the turn. Actually, your body's mass wants to go in a straight line in accordance with Newton's law of inertia, and it takes a sideways force to accelerate it to one side to make it follow a curved path.

The same is true of an airplane in a turn. There is this same sideways force opposing the turn, and so we need an equal and opposite force towards the inside of the turn to overcome it and pull the airplane around the turn. In a typical "coordinated" turn, this force comes from the sideways component of the wing's lift. The lift vector of a wing is perpendicular to the wing when viewed from in front or behind, so when we tilt ("bank") the wing, we also tilt the wing's lift. Since the wing's lift is now directed to one side, some of the lift effect is now pulling the airplane to that side, creating the turn.

Unfortunately, the plane still weighs the same as before, and if some of the lift is being used to pull the airplane around the turn, only part of the lift is still directed upward. Since that upwards portion of the lift must still equal the plane's weight, then we have to increase the total lift to make that happen. We can do this by increasing the airspeed, or we can add some "up" elevator to increase the angle of attack, and therefore increase the wing's lift coefficient.

The total lift we need is the "vector sum" of the upward component that's opposing the weight, plus the sideways force. Since we're talking about forces at right angles to each other, they form the legs of a right triangle, and what we want to know is the long side of the triangle, or the "hypotenuse". As Pythagoras figured out about two and a half millennia ago, the square of the hypotenuse is equal to the sum of the squares of the other two sides (I know a pretty good joke based on that if anyone wants to hear it). So, to find our total lift required in a level turn, all we have to do is square the weight, square the centrifugal force, add them together and then take the square root of the result.

If we study that a little further, we find that it gets even simpler. It turns out that the total lift required for a level (i.e.: constant altitude) coordinated turn is the plane's weight divided by the cosine of the bank angle. Instead, we can also talk about "G" forces, or how many times heavier than their own weight the plane and its occupants feel during the turn.

We can also figure out how much the plane's stall speed increases. Since lift is proportional to the square of the airspeed, the stall speed in a banked turn increases in proportion to the square root of the G force.

OK, so before everyone gets too glassy-eyed with all this math and physics, let's put that in practical terms:

A couple things become obvious:

Up till about 30 degrees bank, the G forces aren't particularly noticeable, and the stall speed is not significantly affected, unless we're already at the edge of a stall to begin with, or some other factors make things worse.

However, above about 30 degrees, things start to get worse increasingly quickly. In a 60 degree bank, the plane and its occupants feel twice as heavy as they did in level flight, and the stall speed is 41% faster than in level flight. If your model stalls at 20 mph in level flight (you're still using those heavy nicads instead of those much lighter Li-polys, I see!), then in a 60 degree bank it will stall at 28 mph.

Just 15 degrees beyond that, at a 75 degree bank angle, the G forces are approaching 4, and the stall speed is now nearly double the wings-level level stall speed. That's right, our model that stalled at 20 mph wings level will stall at 39 mph in a 75 degree bank!

Of course at 90 degrees bank angle, exactly all of the wing's lift is directed sideways, so exactly none of it is directed upwards to support the plane's weight. We would need a total lift from the wing of more than infinity (infinity is a pretty strange number; more than infinity is still equal to infinity) in order to get an upward component of it that is equal to the plane's weight. Obviously it's impossible to maintain altitude in a 90 degree banked turn using wing lift alone.

The other thing to bear in mind is the effect of all this on induced drag, the drag that is the natural by-product of the lift-making process. For a given airspeed, the induced drag will be proportional to the G force, and the induced drag increases as the airspeed decreases. At the best glide speed (best L/D speed) the induced drag is exactly half the airplane's total drag, and it is more than half the total at all speeds below best L/D speed. Also, best L/D speed increases as the G force increases, so more G force increases the importance of induced drag. If you try to pull a tight turn with marginal airspeed, the extra induced drag is likely to kill off whatever airspeed you had even faster than usual, unless you have the extra power to overcome it.

There is a lot of data we don't have, that we really need in order to properly analyze this crash. However, some of it we can deduce from the video and the photos of the model.

First of all, it appears that the plane uses approximately scale incidence between the wing and the fuselage. As a result, the wing is at a very high angle of attack when the fuselage is level. This is accentuated on takeoff by the wing flaps, which increase the effective incidence, but is still true with the flaps retracted in flight.

One of the more insidious hazards of this is that it leads to a false sense of security; the plane looks to a ground-based pilot like it's in a comfortable configuration, but is actually fairly close to stall.

It appears that the flaps were retracted during the fatal final turn, which reduces the effective incidence, but also increases the stall speed. The wing with those huge Fowler flaps retracted probably has less than half the max lift coefficient it had with the flaps extended, which would increase the stall speed by something more than 40%. More importantly, the flaps increase the effective washout of the outer panels, so the tendency to tip stall is greater with the flaps retracted.

The sweep of the wing greatly worsens this whole picture. Swept wings unload the center section and shift the lift distribution out towards the tips. These tips that now have to work harder than normal make swept wings far more prone to tip stall than a straight wing. To make matters even worse, since the tips are further aft than the root, when the tip stalls, the loss of lift back there also shifts the center of lift of the portion of the wing that is still "flying" further forwards, which then tries to pull the nose up even more, further worsening the stall. Quite a few swept wing airplanes (the Mig 15 being but one notable example) have notoriously vicious stall characteristics. It is possible to compensate for this somewhat in the aerodynamic design of the wing, but from what I could see in the pictures, I don't know how much of this compensation (if any) was incorporated in the design of the B-52 model's wing. My gut feel says they probably used the scale airfoils and washout, so I doubt that the stall characteristics of this model with the flaps retracted are something any of us would want to experience first-hand.

Watching the video, they retracted the gear during initial climbout, and it appears that they retracted the flaps sometime around then as well. The wing appears to be "clean" (i.e.: flaps retracted) by the time they get halfway around that first 180 degree right turn. Since the plane was able to complete that turn successfully, obviously it was above the flaps-retracted stall speed at that point, but exactly how much margin above stall existed at that point is anyone's guess.

During the straight downwind leg after the first turn, it looks like they transitioned from climb to level flight, and my guess is that they reduced power from a takeoff setting to a cruise setting at that same time. There is also a slight nose-up change in the plane's pitch attitude early in the downwind leg, without a significant increase in altitude. This suggests that the plane does not have a huge surplus of airspeed at that point. This happens only briefly, then the plane noses over again into a very shallow descent, just before entering the second turn. The nose-up plus any reduction of power would cause a decay in the airspeed, but that would be masked to the pilot on the ground by the illusion caused by the downwind flight path, lulling him into a false sense of security. In level flight the plane is OK, but there is little margin for additional lift from the wing. Also, if there was a reduction in power, the nose-over into the shallow descent might not be enough to arrest the resulting decay of airspeed.

Just as all these insidious things are conspiring against the further existence of the model, the pilot begins what appears to be a turn to the left.

Things look normal at first. The pilot initiates a roll to the left at what appears to be a smooth, scale-like roll rate, then, as the bank angle reaches about 20 degrees or so and the plane has just started to turn, all you-know-what breaks loose. It's very subtle, you have to watch the video very closely to see it, but most certainly it did indeed break loose.

The roll rate had just started to slow down just before then, just faintly, as if the pilot was starting to arrest the roll rate and hold the bank angle for the turn. At that moment, the roll rate suddenly increases. Note, it isn't a sudden change in the bank angle itself (no airplane with that much mass out on the wings is going to make a sudden change in bank angle), but rather a sudden increase in the RATE at which the angle is changing. It's as if the pilot suddenly added some more aileron. I think what we see here is the point at which the inboard wingtip actually stalled.

All that mass in those outboard engine pods is definitely a contributing factor here. The act of rolling an airplane to a given bank angle is actually a far more complex operation than many folks realize. It actually involves at least three sequential events. The significance of these is much greater if the plane has long, heavy wings. It's hard to think of a more appropriate example of this than the B-52.

Aero texts often talk about how deflecting the aileron down on one side and up on the other side causes a difference in lift between the two wings, causing the airplane to roll. This is actually only the first action in the sequence. Yes, we have to have to provide these forces to get the mass of the wings accelerated into a rolling motion. If there is a lot of mass well outboard on the wings, such as a total of 8 jet engines, then the required force could be very high.

However, as the roll rate gets established, the wings are no longer moving through a uniform flow field. The wings are moving through the air in a corkscrewing ("helical") motion, and to the wings, the air coming at them also appears to be moving in an equal and opposite helix. This changes the angle of attack along both wings, counteracting the differential lift caused by the initial deflection of the ailerons, until the difference in camber and incidence caused by the ailerons is exactly cancelled out by the changes in local alpha along the wing caused by the helical airflow. At this point the differences in lift and the resulting net rolling forces between the two wings are exactly zero. All the forces and moments are in balance. There is no longer a force trying to accelerate the mass of the wings into a roll, and so the roll rate becomes constant. It will continue rolling in that direction at that rate until something changes.

Of course at some point the plane reaches the desired final bank angle for the turn, and we now want to stop the roll rate and hold the bank angle constant. At this point we center the ailerons. This removes the differences in camber and effective incidence between the two wings, but we still have the helical flow field, and we still have the kinetic energy of the rolling motion that has been stored up in all that mass out on the wings, and which now has to be dissipated in order to stop the roll. The helical flow field, no longer cancelled out by the deflected ailerons, causes differential angles of attack ("alphas") on the two wings, resulting in differential lift that opposes the roll. This force accelerates the rolling masses in the other direction until the kinetic energy is all cancelled out and the plane stops rolling.

See? A lot more going on when you move that aileron control stick than you probably thought there was! Note, if you use spoilers for roll control instead of ailerons, some of the details change, but the net result is still pretty much the same.

In the case of this B-52 model, we also have the probability that the plane was flying too slowly for its "clean" (i.e.: no flaps or landing gear extended) flight configuration, the increase in stall speed due to the bank angle, the increase in aerodynamic loading on the tips due to the sweep, the lower Reynolds numbers at the tips due to the taper (lower Reynolds numbers generally mean lower max lift coefficients and lower stall angles, unless the designer has done an especially good job in the local airfoil designs along the wing), and the lower airspeed at the inboard tip because of the turn (which was also mentioned in another post to this discussion). Yes, if the plane is in a coordinated turn and the bank angle is less than 90 degrees, the inboard wingtip is (by definition!) closer to the center of the turn than the outboard wingtip, and therefore has a lower airspeed, all other things being equal.

To make matters even worse, all other things might very possibly not be "equal". If you were watching the video very carefully, you may have noticed that right after liftoff and all through the initial climb, the plane oscillated quite a bit in yaw, with some accompanying oscillation in roll. We call this combination of yaw and roll oscillations "dutch roll", and it's the result of a combination of too much mass in the extremities (which this model has on a grand scale, as I mentioned earlier), too much dihedral effect, and/or too little vertical tail.

OK, the mass and the vertical tail issues might be fairly obvious, but this airplane has very little dihedral, so how can it have too much? Once again, the sweep of the wing is the troublemaker. As we discussed in another thread on this list not too long ago, swept wings act like extra dihedral, but the amount of dihedral effect depends on the angle of attack and the resulting lift coefficient. This means that a swept wing at high speed and very low lift coefficient has very little added dihedral effect from the sweep. That same wing at a high angle of attack will have gobs of extra dihedral effect from the sweep. The plane that does not have a dutch roll problem in cruise could have a serious dutch roll problem in takeoff and climb.

BTW, if you watch that final "death spiral" closely, you can see that the plane is dutch rolling all the way down. This tells us two things - the plane was at a high angle of attack, and that the uncontrolled rolling in the final dive was probably the result of piloting and aerodynamic factors (i.e.: it was in a spin), which also implies that it probably was not something like a servo failure.

So, lets recap that final entry into the turn:

The pilot, perhaps fooled by the perceptual illusion of the downwind flight path, and the illusion of the low fuselage angle caused by the high incidence of the wing, pitches up slightly for a moment and gets the plane a little too slow.

The power was also probably reduced about that point in the flight. We can hear what sounds like a small power reduction at just about the point that the roll into the turn started to go sour, but because of the distance from the plane to the microphone, that change in power actually occurred a second or two earlier, back when the plane was still level in roll but going through some pitching maneuvers. This time lag should be about the same as the time lag between when we see the plane's impact and when the impact noise occurs in the video.

OK, so the airspeed appears to be slow and getting slower, and the wing appears to be at fairly high alpha, a fact which is masked by the low fuselage angle. At this point the pilot initiates a left roll from approximately level flight to what appears to be a 20-30 degree bank angle. As the rolling continues, the plane begins to change heading, which means that it is now feeling the G forces, further reducing the stall margin. The inside wingtip is feeling the effects of the curved flight path in the turn, further reducing its airspeed and stall margin.

As the plane approaches the target bank angle, the pilot centers the ailerons (and/or retracts the roll control spoilers). The mass in the wings wants to keep rolling, so the right wingtip has to make less lift and the left wingtip has to make more lift in order to stop the rolling motion. This also causes an increase in the induced drag of the left wingtip, causing a yaw to the left, the motion of which further reduces the airspeed of the left wingtip. At that point the airflow over the left wingtip has had enough of what it perceives are unreasonable demands on the part of the wing, and goes separating off to go play somewhere else. In other words, it stalls. The additional drag resulting from this separated flow further aggravates the yaw.

Meanwhile, the right wingtip is still flying, and in fact the yawing motion and the extra airspeed from being on the outside of the turn has made its job easier. The difference in lift between the right wingtip and the stalled left wingtip gets the roll going again to the left, and the yawing from the differential drag starts angling the nose towards the ground. As the roll rate increases, the helical airflow it causes keeps the angle of attack high on the left wingtip and low on the right wingtip, locking in the stalled condition. With the two wings busy chasing each other around the roll axis like a dog chasing its tail, nobody is holding the airplane up anymore, and the plane does an absolutely "textbook" spin into the ground.

Given the altitude, and the unusual amount of mass in the extremities of this model, once the rotation got started (and the fact it was rolling into a turn just before that means that the rotation was already partially started), the spin was probably unrecoverable. Once it began, it was already too late to stop it.

Probably the only things that the pilot could have done to prevent it would have been to maintain more airspeed (on a model this size and this unusual, some in-flight telemetry to tell the pilot on the ground what his actual airspeed and/or alpha was could have overcome the illusions caused by the downwind flight path), and the pilot should have also recognized that extreme care was needed in all control inputs, including when centering some already deflected controls. It was the attempt to stop the roll rate too suddenly by centering the controls too abruptly that finally triggered the fatal tip stall.

As far as the model goes, in addition to the telemetry I mentioned (and a co-pilot to watch it and call off airspeeds to the pilot, as is the practice in full-scale large aircraft), some extra work in the design phase could have helped. Some deviation from the scale airfoils in the tip, and possibly from the scale incidences, could have improved the stall characteristics. A simple rate gyro could be used to provide yaw damping and suppress the resulting dutch roll, just as is quite common on large full scale aircraft (including, I believe, the B-52). And of course, as with any airplane, all reasonable efforts should be made to keep the weight in the extremities as low as possible, although the B-52 does have some inherent limitations in that regard.

Is this what actually happened to this particular model? It's my best guess based on the data available to me. Yes, some or all of it could be off the mark, but until I see some more details, this is the explanation that (in my opinion) best fits the available data. More importantly, the factors cited here are all very real, although admittedly in some cases they are more of an issue than usual with this particular aircraft. However, negligible or not, it is wise to be aware of these matters. Whether or not they were the actual causes of this crash, they certainly could be the causes of a crash, if not this particular one, then maybe some other model. The bottom line is that although there is much we do not know (and possibly never will) about the details of why airplanes behave the way they do, it is certainly a good idea to learn everything available, and plan for the things that we do know.

Don Stackhouse
DJ Aerotech