Misconceptions: the "sideways gravity" and "missing lift" explanations of dihedral

Misconceptions: the "sideways gravity" and "missing lift" explanations of how dihedral contributes to roll stability

Steve Seibel
www.aeroexperiments.org

This page is still under construction!
This page was last modified on September 14, 2006

 

The "sideways gravity" explanation of how dihedral contributes to roll stability goes something like this: an aircraft's weight or gravity vector remains vertical with respect to the external world. When an aircraft with dihedral tips into a bank, the weight or gravity vector can be broken into a component that acts in the "upright" direction in the aircraft's own reference frame, and a component that acts in the sideways direction in the aircraft's own reference frame. The component of weight or gravity that acts in the sideways direction in the aircraft's own reference frame will make the aircraft slip sideways through the air, toward the low wing. This will create a sideways component in the relative wind over the aircraft. The sideways component in the relative wind will create a difference in angle-of-attack between the two wings, which will create a roll torque, as described in "Oblique views and side views of aircraft with dihedral".

The "sideways gravity" explanation of how dihedral contributes to roll stability appears on the surface to be much better than the "simple view" of how dihedral contributes to roll stability. For example, the "sideways gravity" explanation of how dihedral contributes to roll stability is compatible with the idea that the rudder can be used as a roll control on an aircraft with dihedral.

But the "sideways gravity" explanation of how dihedral contributes to roll stability does contain a fatal flaw. The fact that the weight or gravity vector contains a sideways component in the aircraft's reference frame does not actually mean that the aircraft will slip sideways through the air. After all, in a normal, "coordinated", non-slipping turn, gravity still contains a sideways component in the aircraft's reference frame, and the wings' combined lift vector continues to act "straight up" in the aircraft's own reference frame and does not contribute any counterbalancing sideways force in the aircraft's own reference frame, and yet the aircraft does not slip sideways through the air. When an aircraft is banked, the fact that the gravity vector contains a sideways component in the aircraft's own reference frame is really just an expression of the fact that the aircraft is banked.

It's important to keep in mind that in turning flight the forces are not balanced. From the viewpoint of the external world, the fact that the wing is banked leads to a net sideways (horizontal) force, which makes the flight path curve. We could make the case that in the aircraft's own reference frame, the sideways component of gravity is what makes the flight path curve. We'll generally avoid this approach because we really don't want to go through all the effort of analyzing the acceleration (curvature) in the flight path from the viewpoint of an accelerated reference frame (i.e. the aircraft's reference frame)! But there are no grounds for assuming that the aircraft will slip sideways through the air just because gravity has a sideways component in the aircraft's reference frame, any more than there are grounds for assuming that an aircraft will slip sideways through the air whenever the wing is banked and the lift vector has a sideways component in relation to the external world. As long as the aircraft's nose is remaining pointing directly into the airflow, the aircraft will not be slipping sideways. To analyze when the aircraft will tend to sideslip, we need to look at the interaction between yaw rotational inertia and changes in turn rate, and we also need to look at asymmetrical drag effects and other adverse yaw effects, etc.

Independent of our examination of sideslip, we should point out that in the aircraft's own reference frame, the reason that the sideways component of the weight or gravity vector is not "felt" as a tangible unbalanced sideways force is simply that gravity is a "non-tangible" force that simultaneously acts on every molecule of the aircraft and contents--for more on this see the related article on the Aeroexperiments website entitled "You can't feel gravity".

Here are some sources that advocate the "sideways gravity" explanation of how dihedral contributes to roll stability:

"Model Aircraft Aerodynamics" by Martin Simons. 2d edition 1987. Argus Books. See pp. 166-167, especially figure 12-17.

A somewhat similar explanation of how dihedral contributes to roll stability is the "missing lift" explanation, which holds that when an aircraft tips into a bank, the aircraft sideslips because the aircraft's lift vector has not yet increased above the normal 1-G value (i.e. above the aircraft's weight.) However, since the wings' combined lift vector acts "straight up" in the aircraft's own reference frame, it is not at all obvious why a deficiency in the wings' combined lift vector should tend to create a sideslip. As is discussed extensively elsewhere on the Aeroexperiments website, through practical experiments in airplanes and sailplanes and hang gliders I've observed that when an aircraft is steeply banked, "unloading" the wing to an angle-of-attack that yields 1 "G" or less than 1 "G" of lift generally does not create a sideslip--the root cause of a sideslip is not a "lack of lift". Likewise, I've found that rolling an aircraft rapidly into a turn without making an accompanying pitch "coordination" input creates no more sideslip than does the same rolling motion matched with an accompanying pitch "coordination" input to prevent the flight path from arcing downward and the airspeed from rising. To really understand these results, we have to think about the fact that as long as the aircraft is banked, "inadequacies" or changes in the magnitude of the lift vector will affect the turn rate, which will affect the yaw rotation rate, which will create non-obvious consequences as to whether or not we will likely see any slipping or skidding. Again, as noted above, to analyze when the aircraft will tend to sideslip, we need to look at the interaction between yaw rotational inertia and changes in turn rate, and we also need to look at asymmetrical drag effects and other adverse yaw effects, etc. To take an extreme example, we certainly can't model the situation by imagining that we start the clock at time zero with the aircraft suspended in a banked attitude with zero airspeed, and then let the aircraft drop toward earth (due to the "missing lift") and note the resulting direction of the airflow! The 3-dimensional dynamics at play are much more complex than that. For example we could point out that if the pilot increases the wing's angle-of-attack at the same moment that a gust tips the aircraft into a bank, this will limit the aircraft's tendency to gain airspeed, which will decrease the radius of any resulting curvature in the flight path, which will cause a greater difference in airspeed between the high (outside) wing and the low (inside) wing, which will create a difference in drag between the wingtips that would tend to yaw the nose to point toward the outside or high side of the turn. In other words, when we consider the relationship between lift, airspeed, turn radius, and the difference in airspeed and drag between the two wingtips, we might actually expect to see more sideslip if the pilot does make pitch control inputs to prevent a "lack of lift" as the aircraft is tipped into a bank, than if the pilot makes no pitch input and allows the wing's lift vector to initially remain constant as the aircraft is tipped into a bank! Whether or not this efect is actually observable, it should be clear that the "missing lift" explanation of how sideslip arises when an aircraft is tipped into a bank is not adequate. For some other related notes on some of the physics at play in this situation, see the related article on the Aeroexperiments website entitled "Accurate diagram of forces in a “fully coordinated” turn with no sideslip and adequate lift (G-loading), a turn with inadequate lift (G-loading) and no sideslip, and a slipping turn with adequate lift (G-loading)."

Here are some sources that advocate the "missing lift" explanation of how dihedral contributes to roll stability:

"Swept Wings and Effective Dihedral" by Bill and Bunny Kuhlman. From RC Soaring Digest, January-March 2000.

"Roll Stability and Control" by Don Stackhouse, from the on-line feature "Ask J and D"-- see the paragraph that begins "So how does spiral stability work?"

 

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