Glossary term

Elevator Control Effectiveness

Longitudinal control derivative that relates elevator deflection to pitching moment coefficient and available pitch-control authority.

Branch: Aerospace Engineering
Glossary type: quantity
Content: Glossary term
Updated: Jun 24, 2026
Revision: v1.0.0 · reviewed

Definition

quantity

Elevator control effectiveness is the change in aircraft pitching moment coefficient produced by elevator deflection, usually expressed as the derivative C_m_delta_e.

Elevator control effectiveness connects elevator motion to pitch-control authority, trim capability and longitudinal response. It depends on tail geometry, tail dynamic pressure, elevator size, hinge geometry, downwash, Mach number, angle of attack, center of gravity, configuration, structural flexibility and actuator limits. The derivative must be interpreted with the chosen sign convention and deflection units.

Elevator control effectiveness measures how strongly elevator deflection changes pitching moment coefficient. In a linearized longitudinal model it appears as:

\displaystyle C_m=C_{m0}+C_{m_\alpha}\alpha+C_{m_{\delta_e}}\delta_e+C_{m_q}\frac{q_b\bar{c}}{2V}

where $C_{m_{\delta_e}}$ is the elevator pitching-moment derivative and $\delta_e$ is elevator deflection. The derivative is usually reported per radian, but some test and handling-quality documents report it per degree. The unit convention must be explicit.

Engineering Role

Elevator effectiveness determines whether the aircraft can trim, rotate, flare, reject disturbances and retain control reserve across the approved envelope. A stable aircraft can still be unacceptable if the elevator cannot generate enough moment after accounting for center-of-gravity limits, flap setting, icing, Mach effects, tail stall, actuator saturation or structural flexibility.

The sign of $C_{m_{\delta_e}}$ is convention-dependent. Under one common convention, positive elevator deflection may produce a nose-down or nose-up moment depending on how elevator angle is defined. A derivative value without the deflection sign convention is incomplete.

Worked Example: Trim Deflection and Moment Reserve

At a flight condition, an aircraft model uses:

Parameter	Value
Dynamic pressure, $\bar{q}$	$4200\ \text{N/m}^2$
Reference area, $S$	$17.5\ \text{m}^2$
Mean aerodynamic chord, $\bar{c}$	$1.60\ \text{m}$
Untrimmed pitching moment coefficient, $C_m$	$+0.045$
Elevator derivative, $C_{m_{\delta_e}}$	$-1.15\ \text{rad}^{-1}$
Positive elevator limit	$+15^\circ$

For steady trim, neglecting pitch-rate effects:

C_m+C_{m_{\delta_e}}\delta_e=0

so:

\displaystyle \delta_e=-\frac{C_m}{C_{m_{\delta_e}}}

Substitute the data:

\displaystyle \delta_e=-\frac{0.045}{-1.15}=0.0391\ \text{rad}

Convert to degrees:

\displaystyle 0.0391\frac{180}{\pi}=2.24^\circ

The elevator can trim the condition. The remaining positive deflection reserve is:

15.0-2.24=12.76^\circ

The dimensional pitching moment generated by this elevator increment is:

M_{\delta_e}=\bar{q}S\bar{c}C_{m_{\delta_e}}\delta_e

M_{\delta_e}=4200(17.5)(1.60)(-1.15)(0.0391)

M_{\delta_e}\approx -5290\ \text{N m}

This cancels the untrimmed positive moment:

\bar{q}S\bar{c}C_m=4200(17.5)(1.60)(0.045)\approx5290\ \text{N m}

Engineering comment: the trim check passes because the required deflection is small compared with the limit. A release decision would still need margin for turbulence, speed error, CG uncertainty, actuator tolerance, sensor bias, aeroelastic deformation and failure cases.

What Changes the Derivative

Elevator control effectiveness changes with:

tail area, tail arm and elevator chord ratio;
tail dynamic pressure and downwash from the wing;
Mach number, Reynolds number and compressibility;
angle of attack, sideslip and separated flow;
flap, slat, landing-gear and store configuration;
center-of-gravity position and reference point used for moments;
structural flexibility, control-surface free play and hinge moments;
actuator rate, travel limits, gearing and control-law scheduling.

Because of these dependencies, a single derivative should not be reused across the envelope unless the aerodynamic database, flight-control law or certification evidence explicitly supports that interpolation.

Relation to Static Margin

Static margin describes the aircraft restoring tendency produced by the relative positions of center of gravity and neutral point. Elevator effectiveness describes how much pitching moment the elevator can command. They are related in practice but not interchangeable.

An aft center of gravity may reduce static stability and increase the required elevator authority for trim or recovery. A forward center of gravity may improve static margin but require more elevator authority for rotation and flare. Both cases must be checked against elevator effectiveness, actuator limits and handling-quality requirements.

Validation and Common Mistakes

Elevator effectiveness can be estimated from analytical tail-volume models, CFD, wind-tunnel testing, system identification, flight-test maneuvers or control-law tuning data. A defensible value states configuration, Mach number, dynamic pressure, CG, angle-of-attack range, deflection range, sign convention, units, actuator limits and uncertainty.

Common mistakes include:

mixing per-radian and per-degree derivatives;
using an elevator derivative with the wrong sign convention;
checking trim without checking remaining control reserve;
applying a clean-configuration derivative to flaps, icing, tail stall or damaged-state conditions;
ignoring actuator saturation, rate limits or hinge-moment limits;
treating static stability as proof of control authority;
using wind-tunnel derivatives without accounting for Reynolds number, support interference or aeroelastic effects.

REF

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