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Neutral Point Calculator

There's a spot on every aircraft where stability switches off. Move the center of gravity past it and the plane wants to flip onto its back. Keep the CG well in front of it and the airplane flies steady and forgiving. That spot is called the Neutral Point, and this calculator finds it. Feed in five aerodynamic numbers (the wing's aerodynamic center, the horizontal tail's volume coefficient and efficiency, the lift-slope ratio between tail and wing, and the downwash gradient) and you get the chord fraction where pitch stability hits zero. Add a CG location and you also get the Static Margin, which is the number aircraft designers actually care about.

What is the Neutral Point?

The Neutral Point (hnph_{np}) is the CG location where an aircraft has zero longitudinal static stability. Park the CG there and the airplane will hold whatever pitch attitude you nudge it into. No self-correction, no nose-up tuck. Forward of hnph_{np} the airplane is stable; behind hnph_{np} it isn't. A flying wing with no tail has its neutral point right at the wing's aerodynamic center, around 25% of the chord. Add a horizontal stabilizer and the neutral point shifts aft, often to somewhere between 45% and 60% of the chord, giving the designer a wider window for placing the CG. The bigger the gap between hnph_{np} and the CG, the more stable the airplane feels, and the more sluggish.

How to use this calculator

Choose the formula set that matches what you want to know. "Neutral Point" computes hnph_{np} from five inputs. "Neutral Point with Static Margin" adds a CG field and returns SM=hnp−hSM = h_{np} - h. Every value is a decimal fraction of the mean aerodynamic chord, so 0.25 means 25% chord, not 25. The fields load with sensible defaults: hac=0.25h_{ac} = 0.25, VH=0.6V_H = 0.6, ηt=0.9\eta_t = 0.9, at/a=0.8a_t/a = 0.8, dϵ/dα=0.3d\epsilon/d\alpha = 0.3, CG=0.30CG = 0.30. Change any field and the outputs update. The secondary board splits the neutral point into its baseline and tail contributions, shows how hard the downwash drags hnph_{np} forward, and compares your static margin against real aircraft.

Understanding the formula

The full equation looks intimidating, but it splits cleanly into two pieces: a baseline and a tail contribution.

hnp=hac+VH ηt ata(1−dϵdα)h_{np} = h_{ac} + V_H \, \eta_t \, \frac{a_t}{a} \left(1 - \frac{d\epsilon}{d\alpha}\right)

The first term, hach_{ac}, is where the neutral point would sit on a tailless aircraft. For pretty much any conventional subsonic airfoil, that's around 0.25 chord. Everything multiplied onto it represents how far the horizontal tail drags the neutral point further aft. A larger tail (higher VHV_H), cleaner airflow over it (higher ηt\eta_t), or a more efficient tail planform (higher at/aa_t/a) all push hnph_{np} backward. The last factor (1−dϵ/dα)(1 - d\epsilon/d\alpha) is the spoiler: as the wing pitches up, it bends the oncoming air downward, and that downwash partially cancels the tail's contribution. A typical downwash gradient of 0.3 wipes out 30% of the tail's effectiveness. A worked example: 0.25+0.6×0.9×0.8×(1−0.3)=0.25+0.3024=0.55240.25 + 0.6 \times 0.9 \times 0.8 \times (1 - 0.3) = 0.25 + 0.3024 = 0.5524, so the neutral point sits at 55.2% chord. If the CG is at 30% chord, the Static Margin is SM=hnp−h=0.5524−0.30=0.2524SM = h_{np} - h = 0.5524 - 0.30 = 0.2524, or about 25%. That's well into stable territory.

Applications

Aerospace engineers run this calculation in every conceptual design pass. A commercial airliner usually targets a Static Margin of 10 to 20%, where the airplane handles like something heavy and forgiving and shrugs off turbulence and pilot inputs. Aerobatic and fighter aircraft aim for 1 to 5% so they respond quickly. Modern stealth fighters like the F-117, B-2, and F-35 fly with negative static margins on purpose: a relaxed or outright unstable configuration cuts trim drag and improves agility, at the price of needing fly-by-wire computers to stabilize the airframe continuously. RC modelers, UAV designers, and university student teams all use hnph_{np} to set CG limits before first flight. Passenger jets even track the CG live during flight as fuel burns off and passengers move around, making sure it never crosses hnph_{np}.

Tips

Double-check that every input is a fraction and not a percentage. So 0.25, not 25. Keep hach_{ac} near 0.25 unless wind-tunnel data tells you otherwise. If your VHV_H comes out above 1.0, look again at your tail area and moment arm. T-tails and high-set stabilizers usually have lower dϵ/dαd\epsilon/d\alpha (around 0.2) because they sit out of the wing wake; low-set tails see more downwash (around 0.4). Never trust a single calculation. Verify with CFD or a flight test before committing to a design.

Frequently asked questions

Why is the Neutral Point given as a fraction instead of meters?

Aircraft are sized by their mean aerodynamic chord (MAC), so positions along the longitudinal axis are normalized to that chord. A neutral point at 0.55 means 55% of the MAC aft of the wing's leading edge. It's a scale-free way to talk about stability.

What's a safe Static Margin for my homebuilt?

Most homebuilt and general aviation designs aim for 10 to 15%. That keeps the handling forgiving without making the airplane feel like a freight train on the controls.

Can the Neutral Point change in flight?

Yes. Extending flaps, deploying spoilers, or shifting into supersonic flow all change hach_{ac} and the downwash field, which moves hnph_{np}. Designers verify stability across the full flight envelope, not just the cruise condition.

How is VHV_H calculated?

Tail volume coefficient is defined as

VH=St⋅ltS⋅cV_H = \frac{S_t \cdot l_t}{S \cdot c}

where StS_t is the tail area, ltl_t is the moment arm from the wing's aerodynamic center to the tail's, SS is the wing area, and cc is the wing's mean aerodynamic chord. Typical values fall between 0.4 and 0.9.

What if my Static Margin comes out negative?

The airplane is statically unstable. It won't return to trim on its own and will need either active stabilization (fly-by-wire) or an aft-shift of the CG to become flyable.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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