Notes on some themes explored in the aerodynamic theory and experimental results sections of the Aeroexperiments website:
July 14, 2007 edition
Sections 11 through 18 of the site map for the Aeroexperiments website deal with aerodynamic theory and experimental results. Many of these areas are still under construction. Here are some of the themes that are dealt with in sections 11 through 18 of the Aeroexperiments website:
* A pilot does not feel gravity or "centrifugal force" -- instead, a pilot only feels the real, tangible aerodynamic forces produced by the action of the airflow against the aircraft.
* If an aircraft is not generating any net sideways aerodynamic force in the aircraft's own reference frame, the slip-skid ball will be centered and the pilot will not feel any side loads. This is true regardless of whether or not the wing is generating "enough" lift to counteract the downward pull of gravity. The slip-skid ball can be centered even if the aircraft is accelerating downward as it turns. The wing's lift vector acts "straight up" in the aircraft's reference frame and thus cannot pull the slip-skid ball to either side. And gravity is an "intangible" force that acts simultaneously on every molecule of the aircraft and contents, and so cannot pull the slip-skid ball to either side. The slip-skid ball is not directly affected by the balance or imbalance between gravity and lift, so long as the imbalance does not lead to a sideways airflow over the aircraft. In actual practice, during turning flight in a "conventional" airplane or sailplane, abruptly hauling back on the control stick to abruptly increase the G-loading does not make the slip-skid ball move off-center. Likewise, abruptly pushing forward on the control stick to abruptly decrease the G-loading in the middle of a turn does not make the slip-skid ball move off-center as the flight path curves into a descending trajectory. In actual practice, during turning flight in a hang glider, abruptly pushing forward on the control bar to abruptly increase the G-load does not make the glider slip or skid sideways through the air. Likewise, abruptly pulling in the control bar to abruptly decrease the G-load in the middle of a turn does not make the glider slip sideways through the air as the flight path curves toward a steeper glide path.
* To a first approximation (and in the case of a rudderless fixed-wing aircraft, it's completely true), the only thing that can make a sideways force in the aircraft's own reference frame is a sideways component in the relative wind that impacts against the side of the fuselage and other surfaces of the aircraft. In other words, if the pilot feels an unbalanced sideforce, the aircraft's nose is not quite pointing directly into the relative wind, i.e. the aircraft's nose is not quite aligned with the actual direction that the aircraft is travelling through the airmass at that moment. That's why a yaw string (which measures the direction of the relative wind) and a slip-skid ball (which responds to sideways loads) are essentially redundant. The rudder's main purpose is to allow the pilot to "help" the vertical fin to carry it out its assigned task of keeping the nose of the aircraft pointing directly into the airflow or relative wind at all times, so that the yaw string and slip-skid ball remain centered.
* Most flight training handbooks for pilots of "conventional" aircraft correctly identify the rudder as the main control that acts to prevent slips and skids, but fail to give a truly coherent explanation of why this is so. Most flight training handbooks for pilots of "conventional" aircraft fail to explain that "uncoordinated" (slipping or skidding) flight occurs when the nose of the aircraft does not point directly into the relative wind, due to adverse yaw, asymmetrical engine torque, intentional rudder inputs, or other factors that keep the nose yawed away from the actual direction of the flight path through the airmass at any given moment. In their explanation of slips and skids, most flight training handbooks for pilots of "conventional" aircraft fail to mention the real, tangible aerodynamic force created by the impact of the relative wind against the side of the fuselage and other aircraft surfaces, which is the real cause of the "uncoordinated" force that a pilot feels during a slip or a skid. Attempts to explain the forces present during slips and skids without mentioning this real aerodynamic sideforce are incomplete and misleading at best, and often lead to comically erroneous assertions, descriptions, and diagrams. For example it is misleading to say that the rudder is applied as needed to ensure that the turn rate is not "too high" or "too low" in relation to the bank angle. It is much more enlightening to say that the rudder is applied as needed to help the vertical fin do its job of keeping the aircraft's nose pointing directly into the relative wind, which is all that is required to ensure that there are no "uncoordinated" side loads acting on the aircraft and contents, regardless of the bank angle and turn rate.
* (Technically speaking this is not quite true in any case where the rudder is strongly deflected, e.g. when one engine has failed in a twin-engine airplane. If the rudder is strongly deflected and the nose of the aircraft is pointing directly into the relative wind so that yaw string is centered and drag is minimized, the slip-skid ball will still be slightly off-center and the pilot will still feel a slight "uncoordinated" side load. This is another situation that is rarely fully explained in flight training handbooks for pilots -- here the "uncoordinated" side load that is "felt" by the ball and by the pilot is the real aerodynamic sideforce created by the rudder itself, as an accidental byproduct of the rudder's yaw torque. The more efficient way to deal with this situation is leave the rudder in the position that centers the yaw string, and bank the aircraft as needed to produce a straight-line flight path. A slight bank in the direction of the deflected rudder will be required. The slip-skid ball will remain off-center. The less efficient way to deal with this situation is to further increase the rudder pressure until the ball is centered. Now the aircraft will fly in a straight line with the wings level. By increasing the rudder pressure beyond what is required to center the yaw string, the pilot has yawed the nose out of alignment with the relative wind so that the airflow strikes the side of the fuselage and vertical fin. This creates an aerodynamic sideforce that counteracts the sideforce from the rudder and brings the net sideforce to zero. This also increases drag.
* In practice in an engine-out situation, pilots sometimes think of the rudder as the control that determines the direction of the flight path, and think of the bank angle as the factor that determines whether the slip-skid ball is centered or not. This works well in practice, but obscures the true aerodynamic relationships at play.
* In theory, the above analysis applies to any situation where the rudder is deflected: if the rudder is deflected, the yaw string and the slip-skid ball can not both be centered. Whenever the yaw string and the ball disagree to a noticeable extent, the yaw string is the better flight instrument. The ball is really a "net aerodynamic sideforce meter", while the yaw string shows us what we really care about -- the direction of the relative wind, i.e. whether or not the aircraft is "streamlined" in relation to the airflow. However it is only when the rudder is strongly deflected that there is any significant difference between the position of the yaw string and the position of the slip-skid ball. If the amount of rudder deflection required to center the yaw string or the ball is small, then for all practical purposes there will be no difference between centering the yaw string and centering the ball.
* An analogous situation exists with helicopter tail rotors-- again it is most efficient to leave the ball slightly off-center, in which case the main rotor disk must be banked to yield a straight-line flight path.)
* Yaw strings aren't for sailplanes only! Any pilot with a good understanding of slips and skids will know what a yaw string is for. A yaw string on or near the windscreen is simplest form of heads-up display. Any aircraft that does not have a bothersome propwash over the nose should have a yaw string--especially if there is more than one engine!
* Many hang glider pilots have mistaken ideas about sideslips and believe that an aircraft tends to slip if it is allowed to accelerate and dive to a steeper flight path, while banked. In actual practice, sideslip is mainly a result of adverse yaw, and occurs mainly while an aircraft is rolling to a steeper bank angle, regardless of whether or not the airspeed is rising and the glide path is getting steeper. The pitch "coordination" inputs that a pilot makes while hang gliding actually have little influence on sideslip, and many of the sensations that hang glider pilots associate with sideslip are actually the sensations of an accelerating dive. Most of the maneuvers that many hang glider pilots call "slipping turns" are better called "accelerating, diving turns".
* It is not difficult to observe these relationships in flight in a hang glider -- all that is required is a yaw string (telltale), preferably mounted on the aircraft centerline in the pilot's normal field of view. A yaw string on the end of a dowel rod projecting forward from the centerline of the base bar works well for this purpose. When the yaw string blows toward the outside or high side of the turn, the glider is slipping. When the yaw string is centered, the glider is not slipping.
* It is true that on gliders with a lot of anhedral, abruptly pulling in the bar while making an abrupt roll input can produce an unusual amount of sideslip because the low angle-of-attack increases the wing's anhedral effect (see below) which allows a higher roll rate (see below) which increases adverse yaw. Even in these cases it seems likely that the sideslip itself is not increasing the rate of energy loss from the glider to anything like the degree that it would in a more "conventional" aircraft with a fuselage and tail, which would produce a large increase in drag in the presence of a sideways airflow component.
* In relation to diving turns: a sudden "zoom" climb does not mean that a glider's total energy state has increased. Instead, kinetic energy (airspeed) has been traded for potential energy (altitude). Likewise, a sudden, abrupt, temporary downward curvature in the flight path does not indicate that a glider's total energy state has decreased. Instead, potential energy (altitude) has been traded for kinetic energy (airspeed). However, a glider does experience more drag, and loses energy faster, when flying at a high airspeed than when flying at a low airspeed. In other words the average glide path is steeper when the glider is flying fast than when the glider is flying slow. This is why diving turns-- or fast downwind, base, and final legs-- do help bleed off energy for landing. The key factor is not the abruptness of the dive, but rather how much time the glider spends flying at a high airspeed with the bar well pulled in.
* To produce the highest possible average sink rate over a prolonged time period, the best strategy in a hang glider seems to be to pull the bar in as far as possible and leave it there, while also holding the glider in as steep a turn as seems prudent without imposing too many "G's". I'm skeptical of recommendations that involve repeated changes in bar position and/or bank angle that are intended to maximize the amount of time that the glider is sideslipping and/or boost the peak airspeed seen at some point in the maneuver. The amount that the sideslip from adverse yaw during rolling maneuvers increases the sink rate may be minimal, and any series of maneuvers that creates peaks in the airspeed and sink rate will also create minima in the airspeed and sink rate. In my experience a steady-state approach seems to be better. Going upright and spreading legs to expose the harness pod to the airflow may help, but will also limit the amount by which the bar can be pulled in. Staying prone and getting the knees over the bar to maximize the airspeed may be better, especially on a lower-performance glider with a "sinky" high-speed polar. Planning ahead and entering a straight-line course in time to fly out of the lift before reaching the cloud (which presumably is our goal here) is better yet. In fact it seems that in nearly all situations except for lift that extends for many miles in all directions, a maximum-speed straight-line flight path aimed away from the strongest lift would be the best plan.
* In any aircraft, the stabilizing effect of dihedral, and the destabilizing effect of anhedral, is entirely a result of the way that a sideways component in the relative wind interacts with the dihedral or anhedral geometry to create a difference in angle-of-attack between the left and right wings. If the airflow meets the aircraft head-on with no sideways component, a dihedral or anhedral geometry will not create a roll torque regardless of the aircraft's bank angle. These relationships also explain why a rudder can be used as a roll control in an aircraft with dihedral, and why a rudder can be used as a "backwards" roll control in an aircraft with anhedral.
* Almost all aircraft tend to show some amount of sideslip while banked and turning, in the absence of corrective rudder inputs from the pilot. This sideslip interacts with any anhedral that is present to create a destabilizing influence that tends to roll the aircraft into a steeper bank. Likewise, this sideslip interacts with any dihedral that is present to create a stabilizing influence that tends to roll the aircraft toward wings-level. (Other stronger destabilizing influences are also usually present, unless the aircraft has an extreme amount of dihedral.) On an aircraft with dihedral, if a pilot applies rudder inputs as needed to keep the yaw string and slip-skid ball centered at all times -- which will involve applying rudder toward the low wing whenever the aircraft is banked -- then the dihedral will not exert any stabilizing roll torque at all.
* A flex-wing hang glider has a complex wing shape and it is not adequate to quantify anhedral by measuring the droop in the leading edge in relation to the line of the keel tube or the wing root chord line. The billowed shape of the trailing edge creates a dihedral geometry in the inboard parts of the wing and an anhedral geometry in the outboard parts of the wing. The geometry of the outboard part of the wing is most important to the overall balance of roll torques, because the outboard part of the wing lies furthest from the CG. Therefore, from an aerodynamic point of view, loosening the VG to increase the sail billow increases the wing's overall anhedral geometry, and tightening the VG to decrease the sail billow decreases the wing's overall anhedral geometry. This can be seen simply by looking at the wing from the side. This can also be explored by flying with a keel-mounted rudder or wingtip-mounted drogue chute to create a yaw input.
* The flight characteristics of a flex-wing hang glider are influenced by the competing effects of sweep and anhedral. Sweep creates a dihedral-like effect that is most pronounced at high angles-of-attack. Therefore a flex-wing hang glider with both sweep and anhedral will seem to behave as if it has more anhedral at low angles-of-attack (high airspeeds) than at high angles-of-attack (low airspeeds).
* For most flex-wing hang gliders the competing effects of sweep and anhedral yield a net anhedral effect over most of the flight envelope. With VG fully loose or absent, this effect can be observed to be mild at high angles-of-attack (low airspeed), and much stronger at low angles-of-attack (high airspeed). With the VG fully tight, the net anhedral effect at any given angle-of-attack (or airspeed) is much milder than with the VG loose. With the VG fully tight, the net anhedral effect is relatively mild even at low angles-of-attack (high airspeed), and with some gliders a mild net dihedral effect can be observed at high angles-of-attack (low airspeed).
* In any part of the flight envelope where the wing experiences a net dihedral-like effect, when the pilot begins to roll the glider into a turn, the sideslip from adverse yaw will create a helpful roll torque, the sideslip from adverse yaw will create an unfavorable roll torque, slowing the roll rate. In any part of the flight envelope where the wing experiences a net anhedral-like effect, when the pilot begins to roll the glider into a turn, the sideslip from adverse yaw will create a helpful roll torque, boosting the roll rate. This favorable interaction between adverse yaw and anhedral is one of the reasons why hang gliders are more responsive with VG off than with VG on, and why hang gliders are more responsive at high airspeed than at low airspeed. This favorable interaction between adverse yaw and anhedral is consistent with the observation that adding a fixed vertical tail to a hang glider does not generally produce in increase in roll rate, as would be the case in an aircraft like a Zagi with sweep, no anhedral, and an observable tendency to adverse-yaw while rolling.
* We've observed that for most flex-wing hang gliders the competing effects of sweep and anhedral yield a net anhedral effect over most of the flight envelope. Detailed experimental observations in support of these ideas are given elsewhere on the Aeroexperiments website. However with many gliders (a good example is the Wills Wing Falcon), yaw inputs in the "normal" direction work well as a means of roll control during ground handling, launch runs, landing run-outs, etc., especially when the wing is allowed to fly at a relatively high angle-of-attack. In other words while running with the glider, the pilot would make left yaw input on the down tubes in order to create a left roll torque. I don't know how to fully explain this apparent contradiction between these dihedral-like handling characteristics, and the anhedral-like responses (even at high angles-of-attack) described elsewhere on the Aeroexperiments website. Some ideas: a glider may behave as if it has less anhedral when the glider is not bearing the pilot's full weight, possibly because the glider has less sail billow. On launch, sloped ground tends to create a dihedral-like effect because as one wing is yawed forward, it becomes exposed to stronger ridge lift.
* Many flex-wing hang gliders will enter into a series of Dutch-roll-like yaw-roll oscillations if the pilot holds the bar in a well-pulled-in position and carefully refrains from making any roll inputs. Unlike "classical" Dutch roll oscillations, these yaw-roll oscillations are more pronounced at high airspeed (low angles-of-attack) than at low airspeed (high angles-of-attack). These yaw-roll oscillations are more pronounced with the VG loose than with the VG tight. This is one of the reasons why it is helpful to apply some VG before aerotowing. It is a myth that the yaw-roll oscillations often seen during high-speed flight in hang gliders are always caused by improper control inputs by the pilot, though it is certainly true that these yaw-roll oscillations can be exacerbated by mis-timed control inputs or damped out by correct control inputs. I don't think anyone really understands what drives these yaw-roll oscillations -- for example, are they more pronounced with VG loose because the glider has more aerodynamic anhedral in that configuration, or because the glider is more flexible in that configuration, or both? What provides the restoring force in these oscillations? Why are some gliders (e.g. Aeros Stealth KPL topless, Wills Wing Falcon, Pacific Airwave Pulse) much less prone to these yaw-roll oscillations than other gliders (e.g. Wills Wing Spectrum, Airborne Blade, Icaro Laminar R12)?
* In turning flight, the relative wind is curved. This creates differences in the velocity (both speed and direction) of the airflow on various parts of any turning aircraft, especially during low-airspeed flight. This has important consequences for the stability and control of turning aircraft. One manifestation of this curvature in the relative wind: when an aircraft is turning, the outside wingtip is moving faster than the inside wingtip .
* Above, we observed that "with the VG fully tight, the net anhedral effect at any given angle-of-attack (or airspeed) is much milder than with the VG loose." This seems to contradict the fact that most flex-wing hang gliders are more spirally unstable (requiring more high-siding or less low-siding to hold a constant bank angle) with the VG on than with the VG off, at least with a pulley VG system. It's important to remember that there are many factors other than anhedral that contribute to spiral instability. In fact it usually requires a great deal of dihedral to counteract these other factors and make an aircraft that truly tends to return to wings-level after a disturbance. The vast majority of "conventional" airplanes and sailplanes show some amount of spiral instability in spite of the fact that they have some dihedral. One of the reasons for this is that as noted above, when an aircraft is turning, the outside wingtip is moving faster than the inside wingtip. Therefore the outside wingtip tends to creates more lift than the inside wingtip, and this tends to roll the aircraft into a steeper spiral. Note that at a high angle-of-attack (i.e. at a low airspeed for a given bank angle) the circle diameter will be smaller than at a low angle-of-attack, and the difference in lift between the wingtips will be more pronounced, which is one reason that aircraft tend to be more spirally unstable at high angles-of-attack. In a flex-wing hang glider, when we loosen the VG we increase the washout which unloads the wingtips and decreases the glider's "effective span", making the difference in wingtip airspeeds less important. The wing's flexibility no doubt comes into play in many other ways as well -- a more flexible wing would seem more able to equalize differences in lift between the inside and outside wingtips than a less flexible wing.
* With a cam VG system, there is no increase in airframe anhedral as the VG is tightened, so it will be true to an even greater extent that "with the VG fully tight, the net anhedral effect at any given angle-of-attack (or airspeed) is much milder than with the VG loose." With a cam VG this effect seems strong enough to approximately counterbalance the increase in effective span as the VG is tightened, yielding approximately no change in spiral instability (i.e. no change in the need for high-siding or low-siding) for a given angle-of-attack and bank angle as the VG setting is changed. Some pilots prefer the pulley VG system, so that they can use the VG as sort of a roll trim to adjust the amount of high-siding that is required for a given bank angle and airspeed!
*For further exploration, these articles might serve as the best place to start reading about the esoteric topics of turn physics, turn "coordination", slips and skids, aerodynamic sideforces, and aerodynamic coupling between slip (yaw) and roll. Many other similar articles also appear elsewhere in the Aeroexperiments website.
The Aerophysics Exploration Pages (12) (under construction!)
What makes an aircraft turn? (17b1)
Notes for new hang glider and trike pilots--on sideslips (10n and 16d)
Questions of interest part 1: Relationship between pitch inputs and sideslips in hang gliders and other aircraft (16a)
Questions of interest part 2: Aerodynamic sideforce created by the sideways airflow as a hang glider sideslips (16b)
Questions of interest part 3: Roll torque created by the sideways airflow component as a hang glider sideslips (16c)
Experimental results: adding a controllable rudder and wingtip-mounted drogue chutes to flex-wing hang gliders (11a)
Experimental results and interpretation: adding a controllable rudder and wingtip-mounted drogue chutes to flex-wing hang gliders (11b) -- same as above, but with more interpretation of results