Neutral Point Calculator

Every aircraft has a point on its wings where longitudinal stability is surreptitiously lost. If the center of gravity is ahead of that point, flight behavior is stable and easy to control. If it's behind, one gust can cause the plane to immediately pitch nose down or roll over.

This point is the neutral point. This calculator allows you to determine this point directly from the external shape of your aircraft. Simply measure with a ruler the wing area and tail volume coefficient, the wingspan, the angle of attack, and the distance between both to calculate the average aerodynamic chord, the tail volume coefficient, and the neutral point. The tool will then show you exactly where the center of gravity should be placed.

What is a neutral point?

The neutral point is the position of the center of gravity where the longitudinal stability of an aircraft is zero. If the center of gravity is exactly here, the airplane will maintain its attitude caused by external influences and not return to a trimmed state on its own.

If the center of gravity is ahead of the neutral point, the aircraft is stable; if it's behind, it is unstable. In a winged airplane without a tailplane, the neutral point is at the aerodynamic center of the wing itself, about one-quarter of the way back from the leading edge. By adding a tailplane, the neutral point moves aft and normally lies between 35% and 55% of the way back from the leading edge, which allows for a larger and safer range for the center of gravity.

This is how this calculator works.

This tool does not require the input of any aerodynamic coefficients. It starts with the actually measurable geometric dimensions. Based on the root and tip chord lengths, as well as the back sweep angle, it calculates the average aerodynamic chord length and its position.

The area of the main and tail surfaces, aspect ratio and distance between the two main surfaces are used to calculate the volume coefficient of the tail system. This value indicates what pitch stability the tail provides. The neutral point is then determined, and the desired trim position is specified taking into account a certain static stability margin. This position is measured as an actual distance from the leading edge of the wing spar and is a value that should be marked on the model.

Formula:

The average aerodynamic chord of a straight tapered wing can be calculated from the root chord length A and the tip chord length B with this formula:

The volume coefficient of the elevator system is a combination of area and moment arm. Assuming that the area of the wing S, the area of the elevator system S_t, the moment arm of the elevator system l_t (from the aerodynamic center to the aerodynamic center) as well as the MAC (mean aerodynamic chord) of the wing are known.

The neutral point is expressed as a ratio to the average chord and starts at the aerodynamic center which is located one quarter of the way back from the leading edge and moves aft through the tail.

Here a and a_t are the lift curve slopes of the wing and tail respectively determined by aspect ratio. 0.7 represents the efficiency of the tail in the wake of the wing, and the last term accounts for downwash from the wing on to the tail. Based on "Model Aircraft Aerodynamics" by Martin Simons this calculator uses a downwash model that reduces the effectiveness of the tail by about 40 percentage points and uses modified lift curve slopes adapted to finite wingspan. So you only need to enter geometric dimensions.

Calculation example:

Let's take a sport model made of kirrenwood as an example. The root chord length of the wing is 250mm, the tip chord length is 200mm, the leading edge sweep is 10mm and half the wing area is 900mm. The root chord length of the horizontal stabilizer is 150mm, the tip chord length is 100mm and half the wing area is 300mm with it being in a position 600mm behind the wing.

The MAC (mean aerodynamic chord) of the wing is about 226 mm. The tail volume coefficient is approximately 0.47 and the neutral point is at about 41 percent of the chord, or about 97 mm behind the leading edge of the root of the wing. If one chooses a relatively generous static stability margin of 10 percentage points, the calculator recommends trimming the model to 31 percent of the chord, or about 74 mm behind the leading edge.

Static stability margin: degree and size of stability

The static stability margin is the distance by which the center of gravity is ahead of the neutral point, expressed as a percentage of mean aerodynamic chord. The larger the margin, the more stable and easier to handle the aircraft will be, but the response will be sluggish. A smaller margin makes for a more maneuverable airplane, but requires more stable control inputs.

Most model and light aircraft can fly stably within a range of 5 to 15 percent points. A setting of five percent gives sporty handling with quick response, which is popular among aerobatic pilots. At fifteen percent the aircraft is very stable and easy to control, making it ideal for training purposes and maiden flights. If the value falls below zero, the center of gravity is already outside the neutral point, and the aircraft is unstable. It can only be controlled with continuous corrections or a stabilization system. This is a configuration used in fighter jets and winged drones where stability has been intentionally reduced.

Wing load and stall speed

The same wing area that determines the neutral point also affects how the model flies. When you enter the total weight in the "Wing Loading" section, the tool calculates the wing loading by dividing the weight by the wing area. This is an important value for determining the landing speed and smoothness of the model's landing.

If you enter the maximum lift coefficient, it will also estimate the stall speed. This is the lowest speed at which an airfoil can fly before losing its lift. A light model airplane with a low wing loading may be able to land gently while walking along, whereas a heavier model airplane with the same wing area would need sufficient speed to take off from a runway.

Typical values

The actual values are used to determine whether the results make sense. These are only rough guidelines for typical model aircraft and light aircraft, and do not represent design goals.

Estimated scope of application:

This is a simple preliminary estimate based on a standard trapezoidal wing planform and the lift curve slopes of Simons and a downwash model. It assumes a single-surface wing with the tail behind the main wing.

Multiplane wings, canard configurations, flying wings, biplanes and non-standard tail arrangements are all subject to the same physical laws but require an individual consideration of their respective geometry. The center of gravity may also shift slightly due to actual wing profiles, interference between wing and fuselage and propeller effects. Before fully trusting the results make a slow and careful maiden flight ideally with the assistance of an experienced observer to check trim position.