Receive your free introductory guide on UAV/Small Aircraft Design.
DOWNLOADIssue 5, 22 August 2022
By: Anthony O. Ives
\[ \]
The stability of an aircraft is really determined by how comfortable and safe the aircraft is to fly. If you have to continuely correct the aircraft so it does not fly of course then it can very tiring and potentially unsafe and very frustrating for the pilot in an overall unpleasant way.
Generally stability means something maintains a steady course with nothing unexpected happening. So in terms of an aircraft if the wind causes it to pitch up it should start to pitch down again as soon as the wind stops. It will then generally pitch up and down several times with pitch movement getting smaller until the aircraft settles down returning to the way it was originally as shown in the diagram, the intial movements in the diagram are very exaggerated for an airplane:
In this case the aircraft is considered to be statically and dynamically stable. Statically stable means the aircraft attempts to return to its originally position hence pitching down after the wind has caused it to pitch up. However, if the pitch movements getting larger even though the aircraft is trying to return to its original state it would be considered dynamically unstable as in the diagram:
Marginal stability is another term you may come across which generally means something which is neither dynamically stable or unstable. In the case of an aircraft it would pitch up and down with movements neither reducing or increasing hence not really stable but the pilot may not notice and assume the aircraft is unstable. See diagram below for example of marginal stability:
An aircraft would be statically unstable when it has no tendency to return to its original state hence if the wind causes it to pitch up it will continue pitch up as in the diagram:
We will now discuss how to influence stability both statically and dynamically about the various axis of the aircraft. Generally the present of stabilising surfaces such as a tailplane or tailfin will make the aircraft statically stable in the respective axis. Generally the larger the stablizing surfaces the more dynamic stability the aircraft will have. The diagram below shows the main control surfaces on an aircraft as well the pitch and roll axis:
Longitudinal stability of an aircraft is maintained through the use of the horizontal stabiliser or tailplane around in the pitch axis. Generally speaking the higher the tail volume ratio the more stable the aircraft will be in pitch, the tailplane volume ratio is defined by the following equation:
\[V_T={S_T l_T \over S c} \]
Where ST is the area of the tailplane. IT is the distance between the wing and tailplane aerodynamic centres. The aerodynamic centre is typically at the quarter chord position of a wing. S, c or wing area and chord as defined previously. A typical tail volume ratio for most aircraft is 0.6.
Control about the pitch axis is achieve is achieved using a movable surface section towards the leading edge of the tail plane called an elevator.
The elevator to tailplane ratio area is defined as follows: ArE=SE/ST. A typical ratio is 0.2 for most aircraft however aerobatic aircraft may have ratios as high as 0.5. The larger this ratio the more pitch control for less control surface movement.
Laterial stability of the aircraft is maintained through the use of the vertical stabiliser or tailfin around in the yaw axis. Generally speaking the higher the tailfin volume ratio the more stable the aircraft will be in yaw, the tailfin volume ratio is defined by the following equation:
\[V_F={S_F L_F \over S b} \]
Where SF is the area of the tailplane. IF is the distance between the wing and tailfin aerodynamic centres. S, b or wing area and span as defined previously. A typical tailfin volume ratio for most aircraft is 0.6.
Control about the yaw axis is achieved using a movable surface section towards the trailing edge of the tailfin. See diagram below which shows yaw axis and rudder:
The rudder to tailfin ratio area is defined as follows: ArR=SR/SF. A typical ratio is 0.3 to 0.5. The larger this ratio the more yaw control for less control surface movement.
Stability about the roll axis is achieved by dihedral angle with wing looking like shallow v shape if you are looking head on. Anhedral is the opposite, an inverted shallow v and would make the aircraft more unstable in roll. High wing aircraft are more naturally stable hence require little or no dihedral. Low wing are naturally unstable and will require dihedral about 5 to 10 degrees typically. See diagram below for explanation of dihedral angle:
Control about the roll axis is achieved using a movable surface section towards the trailing edge of the main wing called an aileron. The aileron is usually positioned outboard on the wing if it does not extend across the entire wing.
The aileron to wing area ratio is defined as follows: ArA=SA/S. A typical ratio is 0.1 to 0.3. The larger this ratio the more roll control for less control surface movement.
The following table shows how to calculate the remaining aircraft geometry using previously defined values including the aircraft wing area calculated in the previous sections.
| Symbol | Property | Example Value | Units |
|---|---|---|---|
| S | Wing area | 0.736 | m2 |
| lT/c | Tailplane arm length to wing chord ratio | 4 | None |
| lF/b | Tailfin arm length to wing span ratio | 0.5 | None |
| ST | Tailplane area | (0.6*0.736)/4=0.110 | m2 |
| SE | Elevator area | 0.2*0.110=0.022 | m2 |
| SF | Tailfin area | (0.04*0.736)/0.5=0.059 | m2 |
| SR | Rudder area | 0.3*0.059=0.018 | m2 |
| SA | Aileron area | 0.1*0.736=0.074 | m2 |
Generally airplanes are both statically and dynamically stable. In roll some airplanes may be static unstable particularly if there is insufficient dihedral. Instability can sometimes considered beneficial mainly with military aircraft because an unstable aircraft is more maneuverable. Some military aircraft have specifically design to be unstable hence cannot flown without a computer control system, Ref [1] and [2]. It also should be noted an aircraft that is too stable may be difficult or impossible to maneuver. Hence why heavy military transport aircraft have anhedral otherwise their inertia and high wing design would make them too stable.
Helicopters are generally statically stable but generally dynamically unstable for complicated reasons which future articles will attempt to explain. If you fly manned or remote controlled helicopters you may have thought they are statically unstable. However, for very good reasons you have not waited long enough when it's either pitches or rolls in one direction to pitch or roll in the opposite direction. Particularly in hover helicopters behave similarly in both pitch and roll. See Ref [3] for detail on helicopter flight stability.
Aircraft stability and control is a complicated topic, what this article has discussed is only the tip of iceberg. Future articles will get into more details and also discuss the complicated reasons why helicopters are unstable. Ref [4] and [5] give more information on aircraft and helicopter control stability.
Please leave a comment on my facebook page or via email and let me know if you understand the basic principle of how to make an aircraft more stable and how to make it more responsive to flight controls.
References:
[1] The Great Book of Modern Warplanes, Mike Spick, 2003, Greenwich Editions
[2] The Air Forces Monthly Book of the F-16 Fighting Falcon, Tim Senior, 2002, Key Publishing
[3] Principles of Helicopter Flight, 2nd Edition, W. J. Wagtendonk, 2006, Aviation Supplies & Academics
[4] Flight Dynamics Principles, M. V. Cook, 1997, Arnold
[5] Helicopter Theory, Wayne Johnson, 1980, Dover Publications
Disclaimer: Eiteog makes every effort to provide information which is as accurate as possible. Eiteog will not be responsible for any liability, loss or risk incurred as a result of the use and application of information on its website or in its products. None of the information on Eiteog's website or in its products supersedes any information contained in documents or procedures issued by relevant aviation authorities, manufacturers, flight schools or the operators of aircraft, UAVs.
For any inquires contact: [email protected] copyright © Eiteog 2022