How these are worked out — the equations behind this sheet, their sources, and what each one assumes.
Where people go wrong
The errors this method actually invites, and what it does about each. Every one of them is already a warning somewhere — in a note that appears when your own figures trip it, in the scope statement, or in the equations behind the page. Collected here so you can read them before you need them.
Sizing the fin and forgetting the fuselage. A fuselage in a sideslip is a badly shaped wing with its lift pointing sideways, and most of it sits ahead of the centre of gravity where that lift is destabilising. On the default trainer it gives back about a fifth of what the fin produces.
Assuming a swept wing behaves the same slow and fast. The sweep contribution to dihedral effect is proportional to lift coefficient, so it doubles when the speed halves. A swept model is a different aeroplane slow than fast, and the slow one is the one that wallows.
Reading the balance band as a boundary. Two aircraft with identical derivatives and different inertias behave differently, and the modes themselves need the moments of inertia this sheet does not have. The chart draws a region rather than a line for that reason.
Taking a positive dihedral effect as slightly too little dihedral. It is the wrong sign. A sideslip then rolls the aircraft further into the sideslip instead of picking the wing up, and no amount of fin fixes that.
| Contribution | Derivative | Value, per radian | Share | What moves it |
|---|
Fin efficiency, the fuselage volume relation and the wing-position allowance are compiled from published preliminary-design practice, not measured.