AeroBalance

Mean Aerodynamic Chord & CG Calculator

Precision Airframe Balancing & MAC Solver

Designed for RC scratch-builders, aeromodellers, and UAV drone designers. Determine the exact Center of Gravity (CG) balance point and Mean Aerodynamic Chord (MAC) without uploading classified CAD or custom airfoil designs to external servers.

1. Select Wing Geometry Preset

Choose a baseline planform to auto-fill inputs

2. Configuration & Units

3. Wing Planform Geometry

Wing width at the fuselage centerline / root
Wing width at the extreme wingtip
Total tip-to-tip wingspan (b)
in
Distance Tip LE extends back from Root LE
Distance from nose tip to Root LE (set 0 to measure CG from Root LE)

4. Stability & Static Margin Tuning

10.0%
0% (Neutral) 10% (Trainer) 25% (Ultra-Stable)
ℹ️

Static Margin: The distance between the Neutral Point (NP) and the Center of Gravity (CG), expressed as a percentage of MAC. Higher values increase pitch stability; lower values increase agility. AeroBalance models the wing alone, so the NP it uses is the wing’s own aerodynamic center at 25% of MAC.

Scaled Vector Blueprint

Hover blueprint to inspect coordinates
Wing Outline
MAC Chord Line
Recommended CG Target (🎯)
Neutral Point (⚓)
Recommended CG Position
3.15 in
Measured from Root LE (15.0% MAC)
CG from Nose Datum
3.15 in
Measured from Fuselage Nose Tip
Mean Aerodynamic Chord (MAC)
10.13 in
Effective aerodynamic chord length
MAC Y-Span Location (YMAC)
11.20 in
Spanwise distance from centerline
MAC LE Setback (XMAC)
1.63 in
Leading edge offset at MAC span
Wing Neutral Point (NPX)
4.17 in
Wing aerodynamic center (25% MAC)
Total Wing Area
480.0 sq in
3.33 sq ft
Aspect Ratio (AR) & Taper (λ)
4.80 AR
Taper Ratio λ: 0.67

Understanding Mean Aerodynamic Chord & Center of Gravity

What is Mean Aerodynamic Chord (MAC)?

In aerodynamics, a swept or tapered wing produces lift differently along its span compared to a uniform rectangular wing. The Mean Aerodynamic Chord (MAC) is the chord length of an equivalent rectangular wing that has the exact same aerodynamic force, pitching moment, and center-of-pressure characteristics as your actual planform.

Finding the MAC is essential because all stability and control calculations — including Center of Gravity (CG) placement and static margin — are referenced to the MAC rather than the physical root chord.

Aerodynamic Formulas & Equations

AeroBalance computes MAC, spanwise position (YMAC), and setback distance (XMAC) using exact planform integration formulas:

Taper Ratio (λ):

λ = Ct / Cr

Mean Aerodynamic Chord (MAC):

MAC = (2 / 3) · Cr · ((1 + λ + λ2) / (1 + λ))

MAC Y-Span Location (YMAC):

YMAC = (b / 6) · ((1 + 2λ) / (1 + λ))

MAC Leading Edge Setback (XMAC):

XMAC = Xsweep · ((1 + 2λ) / (3 · (1 + λ)))

Recommended CG Location (CGX from Root LE):

CGX = XMAC + MAC · (0.25 - (Static Margin % / 100))

What is Static Margin & Why Does It Matter?

The Static Margin measures pitch stability. It is defined as the distance between the Neutral Point (NP) and the Center of Gravity (CG), expressed as a percentage of the MAC. These are the four bands the calculator reports, and its banner switches between them at exactly these figures:

  • Optimal (8% - 14%): Standard recommendation for maiden flights, trainers, and scale models. Provides positive pitch stability — if a gust pitches the nose up, the plane naturally returns to level flight.
  • Acrobatic / Pitch Sensitive (3% - 8%): Used by 3D aerobatic RC pilots. Requires less elevator input for rapid maneuvers, but demands constant pilot attention.
  • Ultra-Stable / Glider (above 14%): Strong pitch restoration for thermal gliders and trainers. Safe, but the model needs more up-trim at low speed and gives away elevator authority.
  • Neutral / Tail-Heavy (below 3%): 🚨 DANGER ZONE. At a zero or negative static margin the CG is at or behind the Neutral Point. The aircraft becomes divergent — any slight pitch-up will rapidly amplify, causing an unrecoverable stall and flip.

Practical Field Guide: Maiden Flight CG Balancing

  1. Mark the Calculated CG: Use masking tape on the underside of both wing halves at the calculated CGX distance from the root leading edge.
  2. Use Fingertip or Balancer Rig: Place your fingertips (or a dedicated balance stand) directly under the CG tape marks.
  3. Check Pitch Angle: The fuselage should rest level or slightly nose-down (1°–2°). A slightly nose-heavy model flies safely; a tail-heavy model crashes.
  4. Shift Equipment: Move the LiPo battery or receiver pack forward/aft before adding dead lead weight.

What This Calculator Models, and What It Does Not

AeroBalance models the wing alone. The neutral point it reports is the wing’s own aerodynamic center, fixed at 25% of MAC, and the recommended CG is that point moved forward by your static margin. For a tailless design — a flying wing, a delta, a plank — the wing neutral point is the aircraft neutral point, and the number is the whole answer.

A conventional model with a horizontal stabilizer is a different problem. Its stick-fixed neutral point sits further aft than the wing alone, by the horizontal-tail volume term:

Tailed aircraft, stick-fixed (not computed here):

NP = XAC + VH · (at / aw) · (1 - dε/dα)

That term is strictly positive whenever a tail exists, and this page asks for no stabilizer area, tail arm or tail chord, so it cannot evaluate it. The consequence runs one way only: on a tailed model the CG this calculator recommends is forward of the true limit, which is the nose-heavy and therefore survivable error. A nose-heavy aircraft flies sluggishly and needs up-trim; a tail-heavy one departs in pitch and does not come back. Treat the result as a conservative starting point, and use the manufacturer’s published CG whenever you have one. (Neutral-point relation: J. D. Anderson, Introduction to Flight, longitudinal static stability; also Perkins and Hage, Airplane Performance Stability and Control, Wiley, 1949.)

Frequently Asked Questions

Centre of gravity on a tapered or swept wing is specified as a percentage of the mean aerodynamic chord (MAC), not the root chord. This tool derives MAC and its spanwise location from your root chord, tip chord, and sweep, then converts a target CG percentage into a measurable distance back from the leading edge.

What is mean aerodynamic chord and why not just use root chord?

MAC is the chord of an equivalent rectangular wing producing the same pitching moment. On a tapered wing the root chord overstates the average, so a CG set as a percentage of root chord sits too far aft — often dangerously so. MAC gives a consistent reference across any planform.

What CG percentage should I start with?

This tool models the wing alone, so it recommends 25% of MAC minus your static margin: 15% of MAC at the default 10% margin, and never further aft than 25%. That is a conservative, nose-forward figure for any planform and the exact answer for a flying wing. The familiar 25-30% of MAC quoted for a conventional trainer assumes a tailed aircraft, whose neutral point sits further aft than the wing alone by the contribution of the horizontal stabilizer, which this page does not model. Whichever figure you work from, start at the forward end and move the CG aft in small steps across several flights: a nose-heavy aircraft flies sluggishly but predictably, a tail-heavy one is unstable in pitch and can be unrecoverable.

How do I verify CG once I have the number?

Balance the model physically at the calculated station with the battery installed and the aircraft in flying condition. Use a balancer or two fingers under the wing at the marked point. Then test-glide before powered flight — a level glide confirms the balance, a dive or stall says move it.