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I experienced negative G with the control stick FULL AFT near the top of a loop.
My questions:
Aerodynamically, what happened? Was the wing meeting the air at a negative-lift angle-of-attack (creating a skyward lift force) at this instant?
How can I change my technique to prevent this?
You were too slow.
Start the loop with more speed and pull more (if the g limit of your aircraft allows) at the beginning, so you have more speed at the top.
Aerodynamically, what happened?
Without aerodynamics, you feel -1 g at the top of the loop, simply by having inverted the plane. Since the plane feels the same acceleration, both of you move together - until vertical speed picks up and drag will keep the airplane back. This is when you have the sensation of negative gs. In order to stay with positive gs, you need a centrifugal force to compensate for earth's gravity. This is the product of pitch rotation speed squared and the radius of the loop. If your flight speed drops, the radius will drop as well and leave little centrifugal force, even at a high rate of pitch. Dan Pichelman correctly describes how this kind of loop looks to an outside observer.
So there is little aerodynamics involved here besides drag - low speed will reduce all aerodynamic forces. The angle of attack on the wing is insignificant - what counts is the inertial force of the moving aircraft (besides gravity, of course).
If your airplane places you behind the center of gravity, pulling hard will give you the sensation of negative gs even when the aircraft as a whole is still at positive gs. Any maneuvering will add inertial effects which grow with the pilot's distance from the center of gravity.
How can I change my technique to prevent this?
Fly faster, and be fast enough at the top to push in order to round out the loop, so it will look more like a circle. But make sure to stay within the limits of your plane. Again, Dan is right: It really sucks when the wings fold up.
Negative gs are completely normal at the top of the loop. When I did my first loop in an open-cockpit aircraft (a Boeing Stearman, no less), I did exactly that: Push near the top. However, this did not last long because my instructor immediately whined "pull, pull!". He had not closed the pockets of his flight jacket and started to lose their contents. So make sure that all equipment is secured before doing aerobatics.
A typical "for fun" loop flown by someone with little experience is typically shaped like a cursive lower case "L" or "E" rather than a circle. There's a fairly gentle pull from horizontal to vertical, then a sharper pull at the top.
If that was the case, you could have easily pulled to vertical, let up on the stick pressure to go nearly straight up for a while, then pulled a bit harder to bring the nose over the top.
You'd then be left hanging from your seat belts for a few seconds (more if you didn't keep pulling back on the stick) until the nose pulled through back to level flight.
- Aerodynamically, what happened? Was the wing meeting the air at a negative-lift angle-of-attack (creating a skyward lift force) at this instant?
Yes, from the point of view of the wing, you briefly had a negative lift angle of attack.
- How can I change my technique to prevent this?
Learn where to look:
Keep the "rate of pitch change" constant.
Gravity and/or "centrifugal force" don't contribute to force "felt" by the pilot (and by the aircraft structure.) Only aerodynamic forces do. Actually the apparent centrifugal force created by the rotation ABOUT THE AIRCRAFT's CG is "felt" by the pilot, but that would appear to contribute a positive G-load component to a pilot sitting in front of the aircraft's CG during a loop. This would surely only be significant in an aircraft with the cockpit far in front of the CG, rotating very rapidly about the CG.
For negative G to occur near the top of the loop, the wing indeed must have been at a negative angle-of-attack at that point, even with the stick full aft. Here's how that could happen:
At the top of the loop, the airspeed was quite low, meaning that the flight path had a very tight (small) radius of curvature of the flight path due to the low airspeed. Note that gravity and aerodynamic force both combine to determine the aircraft's total curvilinear acceleration through space, and gravity is forcing the flight path to curve earthward at the top of the loop, even if the aerodynamic lift force is very small or even negative (skyward). Since various molecules of the aircraft are moving in different directions at any given instant (think of a flat spin for an extreme example), the relative wind (meaning the undisturbed airflow-- the apparent wind created by the motion of the aircraft-- the direction the airflow would be coming from if not altered by the disturbance created by the physical presence of the aircraft) "felt" by any given point on the aircraft's surface curves to follow the path of the turn. This means that the actual airflow will also have a curvature to it. If the loop has a very tight radius at the top, this effect will be extremely significant.
Unless the fuselage is able to bend like a banana (with the "canopy" side being the concave side and the "belly" side being the convex side) to conform to the curving flow, we can visualize (loosely speaking) that the curving flow will tend to "push up" against the bottom ("belly" side) of the horizontal tail and pitch the nose toward the aircraft's belly-- toward the sky in this case. It's as if we're giving the aircraft some negative decalage. Due to this pitch torque, full aft elevator may be insufficient to command a positive AOA at the wing. A faster entry speed (or stronger initial pull) increases the airspeed over the top of the loop, increasing the radius of the loop and avoiding the issue with negative G.
Another way to think of the "curvature in the relative wind" is to note that a pitch rotation always leads to some amount of "pitch damping" effect. Pitch damping and curving relative wind are two sides of the same coin. Either way we look at it, we see that the "free-stream" or undisturbed relative wind tends to be directed "up from below" (i.e. has a vertical component aimed from belly toward canopy) at the rear end of the fuselage during a loop, which tends to pitch the nose "down" (toward the belly), decreasing the angle-of-attack of the wing. The actual airflow over the rear end of the aircraft will be affected by the wing's downwash, but a given nose-up elevator input will still end up creating less nose-"up" pitch torque when the flight path is curving in the nose-"up" direction (toward the canopy), than it would if the flight path were completely linear and the pitch rotation rate were zero. The curvature of the relative wind--the pitch damping effect-- effectively reduces the elevator's "purchase" or "leverage" on the air and reduces the amount of nose-"up" (towards the canopy) pitch torque created by the raised elevator, compared to what we'd see at the same airspeed if the flight path were linear. A normal constant-airspeed turn also involves some pitch rotation, so the same effect is present to some degree-- more on this later.
These dynamics are a reason why an all-moving horizontal tail can be a good thing-- especially in radio-controlled model aircraft where stick force is provided by springs in the transmitter and thus the stick-force-per-G characteristics aren't a concern. Fully all-moving stabs may be poor in terms of giving a nice increase in stick force with G-loading but look at the tail of this Fox aerobatic glider -- the elevator comprises more than half of the total horizontal tail area. (This is NOT the glider in which I experienced negative G over the top of the loop!)
In my personal experience, if the loop is in the clockwise direction and 12 o'clock is the top of the loop, and the airspeed gets too low over the top of the loop, the negative G (with stick full aft) will occur from about the 12:30 through the 1:30 or 2:00 positions, not at the very top of the loop. It appears that the point of lowest airspeed does not occur at the point of strongest negative G, and the G-load may in fact have be positive at the point of lowest airspeed, which probably occurs somewhere between the 12:00 and 12:30 positions. I don't know the reason for this. Perhaps I was mis-perceiving the aircraft's position in the loop due to the unusual attitude and un-accustomed sight picture, but I don't think so. Since pitch torque commands a change in rotation rate, rather than directly governing rotation rate, perhaps there was simply a time lag between the time the tail started "feeling" a strong change in the direction of airflow due to the decreased radius at the top of the loop, and the time that the aircraft's pitch rotation rate had been altered enough by this pitch torque, relative to the (not necessarily constant) pitch rotation rate that would have been required at any given instant to hold the angle-of-attack constant, to drive the wing to a negative angle-of-attack. This is only a hypothesis.
The negative G was very mild, but enough to make objects rise up against the canopy.
My recollection is that the problem was avoided if I did not let the airspeed drop below 40 mph at its lowest point.
The curvature in the relative wind is also present in a normal turn and requires the stick to be further aft to command a given angle-of-attack while turning than in wings-level flight. Due to the low airspeed involved, this effect is extremely noticeable during a thermalling turn in a sailplane. I know of at least one sailplane in which the total "up" elevator throw is somewhat limited to help prevent stalls and spins, and heavy pilots (who move the aircraft's CG to near the forward edge of the allowable envelope) find it is not only nearly impossible to stall in a turn (absent a sudden sharp gust from below), but difficult to maintain a slow enough airspeed for optimum thermalling, even with the stick full aft. They simply don't have enough elevator power to put the wing at the optimum (high) angle-of-attack during a steep thermal turn. During wings-level linear flight, those same pilots have no problem commanding a stall, or putting the wing at the optimum (high) angle-of-attack required to achieve flight at the lowest possible sink rate.
On a more fundamental level, the reason we don't "feel" gravity is that gravity exerts an equal force per unit mass on every molecule of the aircraft and pilot's body, all at the same time, thus creating no stresses or strains with the body or structure, and creating no tendency for the pilot to move toward or away from the seat of the aircraft. In flight, we only feel aerodynamic forces. Examples: 0G flight-- total acceleration-- 1G downward-- felt acceleration -- 0G. Flying straight and level-- total acceleration--0G-- felt acceleration-- 1G upward lift force (per unit mass) generated by wings. Standing still on solid ground-- total acceleration--0G-- felt acceleration-- 1G upward push force (per unit mass) of floor against soles of feet. In all cases "felt" force + gravitational force = "total" force.
IF we adopt the aircraft as our reference frame, THEN we have an accelerated reference frame and we do have to consider centrifugal (inertial) force. Also, if we consider the aircraft to be a fixed reference point, then it is valid to say that the pilot will tend to "feel" gravity pulling him against his seat in normal upright flight, and against the seat belts in sustained inverted flight. At any given instant, the total force that we compute that the pilot will end up "feeling" will come out the same whether we choose the aircraft as a reference frame, which requires us to consider centrifugal (inertial) force and gravity, or we choose a true inertial reference frame, in which case centrifugal (inertial) force vanishes and gravity is a force that creates an acceleration but cannot be "felt". However in an accelerated reference frame it is no longer true that F=ma, so this is not a good choice of reference frame if we want to discover the fundamental cause of the total force acting on the aircraft, the total acceleration acting on the aircraft, and the G-load "felt" by the aircraft and pilot.
To put it another way-- the apparent centrifugal force created by the rotation about the center of the loop (as opposed to the rotation about the aircraft's CG) is a pseudoforce that is simply equal and opposite to the real, aerodynamic centripetal force generated by the aircraft. That's all it is. Whether or not we count it in our calculations depends on whether we are using an accelerated reference frame that is tied to the aircraft, or an inertial reference frame such as the earth or airmass (in the latter case, assuming that any wind present is linear and not a rotating such as a dust devil or rotating thermal column etc.)
To help understand the advantage of choosing a true inertial reference frame such as the earth over an accelerated reference frame such as one moving with the aircraft, consider this question-- at an instant in time where the G-load is negative (with the stick full aft) near the top of the loop as described in the original question, if we suddenly took away the atmosphere so that the plane was in a vacuum, while preserving the same initial velocity and the same gravitational force, would the "felt" G-load-- the G-load on the G-meter-- instantly go to zero? Why or why not?
Outside links pertaining to the curvature in the relative wind in turning flight (not loops specifically)
"Circling the Holighaus Way" by Richard H. Johnson--A key point is that as a glider circles, if the fuselage is tangent to the curving flow near the CG, then it will not be tangent to the curving flow near the nose--and the yaw string will be slightly deflected to the outside of the turn. There's a bit more to it than that though.
"Spiral Stability and the Bowl Effect" series-- by Blaine Beron-Rawdon-- pertains to stability and control of rudder-controlled rc sailplanes--
