A constant-banked climbing or descending turn involves a continual rolling motion

A constant-banked climbing or descending turn involves a continual rolling motion

Steve Seibel
www.aeroexperiments.org

This page was last modified on September 14, 2006

 

A constant-banked descending turn ("helix") actually involves a continual rotation about the aircraft's roll axis, with direction of the roll being the same as the direction of the turn. The extreme case of this would be a rolling vertical dive. If you are having trouble visualizing this, just "fly" your hand (or a hand-held model plane) through a constant-banked turn, allowing the descent rate to gradually increase. Keep the "nose" of the aircraft aligned with the actual direction of travel through the airmass (i.e. don't just slide the model downwards in a slipping maneuver!)

We should note that the key factor here is the descent rate with respect to the airmass, not with respect to the ground--these dynamics apply even when a glider is climbing with respect to the ground by a steadily circling within a thermal updraft.

A constant-banked climbing turn ("helix") involves a continual rotation about the aircraft's roll axis, with direction of the roll being the opposite the direction of the turn. The extreme case of this would be a rolling vertical climb. If you are having trouble visualizing this, just "fly" your hand (or a hand-held model plane) through a constant-banked turn, allowing the climb rate to gradually increase. Again, keep the "nose" of the aircraft aligned with the actual direction of travel through the airmass

Again we should note that the key factor here is the climb rate with respect to the airmass, not with respect to the ground. So we're basically talking about a powered climb here, or a very temporary "zoom" climb in a glider where airspeed is exchanged for altitude.

We noted in "The main cause of adverse yaw during rolling motions: the 'twist' in the relative wind" that a rolling motion creates adverse yaw, and also creates an aerodynamic damping effect in roll which creates a roll torque that opposes the rolling motion.

Therefore in a constant-banked descending turn, the inherent rolling motion will contribute an adverse yaw torque that tends to swing the nose toward the outside or high side of the turn, promoting a slip. If the aircraft has dihedral or sweep, a slip will tend to create a rolling-out torque, and if the aircraft has anhedral, a slip will tend to create a rolling-in torque. Of course, other yaw torques will also be present and will help to determine the degree to which the nose of the aircraft actually tends to point toward the outside or high side of the turn, which will determine the actual roll torque created by dihedral, sweep, and/or anhedral.

Meanwhile, another effect will be acting to create another roll torque that will likely be quite significant: the roll damping effect will contribute a roll torque that will tend to create a decrease in the roll rate. Since a constant-banked descending turn involves a continual rolling motion toward the inside of the turn, inhibiting this rolling motion will create a decrease in the bank angle. In other words the roll damping effect creates a rolling-out torque.

We don't mean to imply that the combination of these effects will generally overpower the rolling-in torque created by the difference in airspeed between the two wingtips, as described in "Roll and yaw torques due to the difference in the airspeed of the left and right wingtips". But as a diving spiral develops, at some extreme descent angle and some extreme bank angle the damping effect will become strong enough to prevent any further increase in the roll rate, i.e. to prevent any further increase in the bank angle, assuming that the aircraft has not yet overstressed and disintegrated!

In a constant-banked climbing turn, the inherent rolling motion toward the outside of the turn will contribute an adverse yaw torque that tends to swing the nose toward the inside or low side of the turn, promoting a skid or reducing sideslip. If the aircraft has dihedral or sweep, a skid or a reduction in slip will tend to create a rolling-in torque or a reduction in rolling-out torque respectively, and if the aircraft has anhedral, a skid or a reduction in slip will tend to create a rolling-out torque or a reduction in rolling-in torque respectively. (In practice I know of no aircraft that actually tends to skid during a powered climb, except due to p-factor or torque effects. Other competing yaw torques also present, including the yaw torque toward the outside or high side of the turn created by the fact that the outside wingtip experiences more airspeed than the inside wingtip, as described in "Roll and yaw torques due to the difference in the airspeed of the left and right wingtips".)

Meanwhile, another effect will be acting to create another roll torque that will likely be quite significant: the roll damping effect will contribute a roll torque that will tend to create a decrease in the roll rate. Since a constant-banked climbing turn involves a continual rolling motion toward the outside of the turn, inhibiting this rolling motion will create an increase in the bank angle. In other words the roll damping effect creates a rolling-in torque. This is one of the main reasons why an aircraft generally shows a greater tendency to increase its bank angle in a powered climbing turn than in a gliding descent.

It's worth noting that when a great deal of power is available, an aircraft can perform a very steeply climbing turn at a low airspeed. It appears that this is the optimum situation to allow the roll damping effect to create a powerful rolling-in roll torque, because the turn radius will be low, and in order to keep the bank angle constant, the aircraft must maintain a relatively high roll rate toward the outside of the turn in relation to the forward airspeed. In contrast, it's difficult for an aircraft to perform a steeply descending turn at a low airspeed, unless the aircraft is very draggy or has very effective air brakes. It appears that for a given bank angle and a given climb or descent angle, the stabilizing or destabilizing roll torque arising from the roll damping effect will be much smaller at high airspeeds than at low airspeeds.

Here are some outside sources that make note of the way that the rolling-in motion inherent in a constant-banked descending turn leads to a rolling-out torque due to the roll damping effect, and/or make note of the way that the rolling-out motion inherent in a constant-banked climbing turn leads to a destabilizing rolling-in torque due to the roll damping effect:

"Climbing and Descending Turns" from John S. Denker's superb "See How it Flies" website--a slightly different approach, but we can still see the difference in angle-of-attack that the roll damping effect creates between the inside and outside wingtips. Denker notes that at typical light-plane speeds this effect is less important than the difference in airspeed between the two wingtips.

"Thoughts on Handling Under Power" by Richard Cobb--see the section entitled "Roll Instability", with the diagrams "Gliding turn to left" and "climbing turn to left".

 

Advance to Misconceptions: the 'simple' view of how dihedral contributes to roll stability"

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