Neutral point (fluid dynamics)

The neutral point (NP), also profile neutral point , or the aerodynamic center , is the fixed point on a profile for which the torque remains approximately constant when the angle of attack is increased. The distance between the pressure point and the neutral point is shortened to the same extent as the lift force increases.

The neutral point lies roughly on the profile chord in 25% of the profile depth .

The torque or its torque coefficient refers to this neutral point of the wing profile. The moment coefficient relates exactly to the t / 4 point of the profile chord. ${\ displaystyle M}$ ${\ displaystyle C_ {m}}$ ${\ displaystyle C_ {m25}}$

For stability calculations , the concept with the constant torque and the fixed NP position on the wing is easier to use than the pressure point (DP) with the angle-dependent position on the profile chord. The moment coefficient is roughly proportional to the curvature of the profile and its reserve (Cm = f * xf * -6).

definition

Neutral point (N) and pressure point (D), x _N ≈ t / 4 and Δ x _D = C _m · t / C _a

Neutral point

{\ displaystyle {\ partial c_ {m} \ over \ partial c_ {a}} = 0}

${\ displaystyle c_ {a}}$ is the lift coefficient and is the moment coefficient ${\ displaystyle c_ {m}}$

Moment coefficient

Sometimes the moment coefficient C _{m25 of} a profile is shown in a diagram as a "curve" over the angle of attack or over the lift coefficient. However, since the change in this curve is small in the normal angle of attack range, only the mean value of the torque at the neutral point C _m is often used in profile descriptions .

{\ displaystyle c_ {m} = {\ frac {\ Delta x_ {D}} {t}} \ cdot c_ {a} = {\ text {constant}}}

${\ displaystyle \ Delta x_ {D} = x_ {D} -x_ {N}}$ The distance DP - NP is related to the profile depth (t = 1). The moment coefficient often has a sign . Minus means that the profile nose is pressed down.

The distance between the pressure point and the neutral point depending on the angle of attack is approximately: ${\ displaystyle x_ {D}}$ ${\ displaystyle \ alpha}$

{\ displaystyle \ Delta x_ {D} (\ alpha) \, = \, t {\ frac {c_ {m}} {c_ {a} (\ alpha)}}}

The moment coefficient is negative for curved profiles without an S-runout. This means that the neutral point of these profiles is always before the pressure point. This has an impact on pitch stability: In dynamic equilibrium, the center of gravity of an aircraft coincides with the pressure point. If the angle of attack increases a little due to a small disturbance in the inflowing air, then the lift coefficient of the wing also increases. Since this quantity is in the denominator of the fraction, the distance between the pressure point and the neutral point is reduced. The pressure point moves forward. Since the position of the center of gravity does not change, the force of gravity no longer acts on the pressure point, but a little behind the pressure point. This causes a righting torque that further increases the angle of attack. The increased angle of attack leads to a correspondingly stronger migration of the pressure point. ${\ displaystyle C_ {a}}$

Thanks to this positive feedback , the aircraft quickly reaches such a high angle of attack that the flow stops . A slightly reduced angle of attack compared to equilibrium leads in a similar way to an accelerated angle of attack into a negative pulling angle. This behavior can be summarized in the statement that a curved profile on its own is unstable with regard to the angle of attack.

Position of the neutral point

For a profile with incompressible, frictionless flow, skeletal theory results in a constant neutral point at 25% of the profile depth (t / 4), which is independent of the profile shape and curvature. When flowing around real profiles, this shifts only slightly due to the effects of Reynolds number and Mach number . It remains almost constant when the angle of attack is changed . In the case of the laminar profiles generated by Richard Eppler , it is around 26%, and in the case of profiles for slow aircraft a little further ahead (around 24%). In the supersonic range it is 50% profile depth for the flat plate. ${\ displaystyle \ alpha}$

In addition to the neutral point of profiles, a distinction is made:

The neutral point of the wing (mean aerodynamic center, MAC).
The neutral point of the entire aircraft (wing, fuselage, tail unit). It can be roughly calculated from the neutral points of the individual components and their geometric position.

In conventional configurations, the neutral point of the aircraft lies behind the neutral point of the wing. The following describes the aircraft's neutral point.

Longitudinal stability

Longitudinal stability is the stability of the aircraft around its transverse axis . The corresponding movement is called "nodding". For stable behavior, a restoring torque must occur on the aircraft in the event of a small disturbance in the angle of attack , which tries to reduce the disturbance. On the one hand, a low center of gravity and, on the other hand, the lever arm to the horizontal stabilizer contribute to this restoring moment . The distance between the aircraft center of gravity (SWP) and the aircraft neutral point (NP) is also important. ${\ displaystyle \ Delta \ alpha}$

SWP before NP. The additional buoyancy generates a top-heavy (backward turning) moment in relation to the SWP ⇒ stable behavior
SWP in the NP. The additional buoyancy does not generate any moment, the disturbance remains ⇒ indifferent behavior (= neutral stability)
SWP behind NP. The additional buoyancy generates a tail-heavy moment in relation to the SWP ⇒ unstable behavior

In practice, the position of the neutral point depends exclusively on the wing and tail plan and the arrangement of these two surfaces with respect to one another. If the angle of attack is increased by, the lift increases by . Since the pitching moment around the neutral point must remain constant, the additional lift can only act in the neutral point itself. The center of gravity should therefore be in the neutral point. ${\ displaystyle \ Delta \ alpha}$ ${\ displaystyle \ Delta c_ {a}}$

The requirement for stable flight means that the leading wing must generate a greater lift coefficient than the following. The use of positive cambered wings with negative profile moment further increases this difference. This consideration applies to conventional aircraft as well as to duck configurations and to swept and non-swept flying wings . The front wing (or part of the wing) always has the higher angle of attack than the rear.

A measure of the longitudinal stability is the restoring torque per pitch angle. Another dimensionless measure of stability is the distance of the center of gravity in front of the neutral point in relation to the mean aerodynamic wing chord. ${\ displaystyle {\ frac {{\ Delta} M} {{\ Delta} {\ alpha}}}}$

Trim speed

The trim speed of an aircraft is usually set so that the best glide angle is achieved. This is done by horizontally positioning the center of gravity (SP) or adjusting the horizontal stabilizer (see setting angle difference ).

Controlling the speed of a planing aircraft means changing that trim or setting. This is achieved by mechanically shifting the center of gravity or by aerodynamically shifting the pressure point. The pressure point can be moved with the horizontal stabilizer or - slightly - the rear flaps on the wing. In motor-powered aircraft, the position and power of the drive play an essential role for stability and control. However, since all aircraft have to fly stably without propulsion with appropriately adjusted trim, the above generally applies to aviation.

literature

Götsch, Ernst: Luftfahrzeugtechnik , Motorbuchverlag, Stuttgart 2003, ISBN 3-613-02006-8 .

swell

Flight stability

NASA Aerodynamic Center

Wolfgang Kouker: Flight Physics - Neutral Point . IMK, Research Center Karlsruhe, 2003, archived from the original on November 15, 2014 .; Retrieved January 1, 1970

Basics of gliding. FSV Tölz, 2003, archived from the original on October 1, 2007 .

Individual evidence

↑ Prof. Dr.-Ing. Peter R. Hakenesch: Profile Theory. (pdf) Munich University of Applied Sciences - Faculty 03, accessed on January 20, 2020 .

[1] Prof. Dr.-Ing. Peter R. Hakenesch: Profile Theory. (pdf) Munich University of Applied Sciences - Faculty 03, accessed on January 20, 2020 .