Longitudinal Stability (fixed stick)
DWT automatically runs multiple Cmarc analyses in order to calculate the stability derivatives necessary for longitudinal analysis. Parameters are automatically varied over a prescribed increment in order to use first order differencing to calculate the derivatives. The calculation of the necessary parameters requires two parameter variations, elevator deflection and the angle of attack (alpha). In order for the longitudinal calculation to be most accurate, it is best to perform the differencing at the trimmed condition. Once this point is established (elevator deflection and aircraft angle of attack) at some given flight condition, alpha may be varied in order to calculate the stability derivatives that are a function of alpha and the elevator may be deflected in order to calculate derivatives that are a function of delta. Although DWT does calculate derivatives that are a function of elevator deflection, at this time DWT is limited to calculating the short and long term (fugoid) frequencies and damping in the stick fixed condition. Future versions of DWT will include stick free dynamic analyses.
Elevator deflection is handled by what AeroLogic is calling the "tilt vector" approach. Tilt Vector is a numerical enhancement to Cmarc, which allows for the modification of the panel normal vector about a hinge line. It has been shown that this technique is accurate for movable surfaces such as elevators, rudders, ailerons, etc. up to approximately 15 degrees of deflection. This technique allows for deflecting control surfaces without having to modify the paneled model, which can be a time consuming task. Colored in red in the following figure are the panels
The first step in a longitudinal stability analysis once the model has been created in Loftsman/P is to go to the stability form. The delta symbol signifies differencing or the calculation of rates of change with respect to some variable. The following form is brought up. Each section of this form will be described more fully.
The first section is where the physical properties of the aircraft are defined as well as the flight condition for the analysis.
The next section is where some values are set for the calculation of the trimmed condition as well as the longitudinal derivatives.
If the "Calculate Trimmed condition" and "Use Calculated Trim" boxes are checked, DWT will calculate the elevator position and alpha that correspond to the flight condition of interest. The results of this series of Cmarc runs are "Base Alpha" and "Elev Def" which are the starting values of alpha and elevator deflection (baseline) to be used in the differencing process. Alpha Start, Alpha Stop, Alpha Inc and Ele Start, Ele Stop, Ele Inc must bracket the unique alpha and elevator deflection, i.e. extrapolation is not done. Multiple alpha and elevator deflections are permitted in this calculation to account for any nonlinear effects in order to arrive at a more accurate solution.
In the Cmarc bulk data deck, there are NNROT (see the Cmarc reference manual) specifications of tilt vectors. Ele Tilt indicates which corresponds to the elevator. DWT will be automatically varying the value of elevator deflection and thus needs to be able to distinguish the elevators from the rudders and ailerons. The form also needs the size of the increment of alpha and elevator deflection to be used in the differencing runs. Typically 1 degree is adequate.
The right side of the above form is where the results of the Cmarc runs are displayed.