Derivatives 21 Part 1c
The final three velocity disturbance derivatives are intuitively easy to understand — not like Xw and Mu, that I find it more difficult to get my head around.
The side-slip derivatives, Yβ, Lβ and Nβ, are simply designed to tell how the airplane handles the situation where it is flying straight ahead but for some reason the nose is pointing a couple of degrees to the left.
A conventionally shaped airplane flying a few degrees crooked will eventually start moving in the direction the nose is pointed. In our scenario the nose is pointed a couple of degrees left of the direction of travel, and the plane's travel direction will start to bend left as well. That effect is indicated by a negative Yβ.
Your stranger contraptions may not have a negative Yβ, but I am not entirely convinced if it is even important. The flying machine in this picture has a very positive Yβ value. I will admit that the only reason anyone would design a contraption like that is either to prove a point, or perhaps pure madness. The point though, is that those awkward angled wing parts do not prevent the plane from flying. The 'Stability Deriv Simulation' tab will verify that a side-slip subsides by itself.
It is convenient if the airplane you are flying wants to roll to where its nose is pointing. Imagine that the pilot yaw the plane left (uses left rudder). A yaw to the left is a turn, in the sense that you see the compass heading decrease. A conventionally shaped airplane will then start to alter its course to the left too (due to negative Yβ; see section above). Yet this is not the kind of turn most people think of when they hear of an airplane in a turn; a 'proper' turn is one where the airplane is banked. Most airplanes (not just Kerbal ones) will roll to a left bank when using left rudder in otherwise uneventful cruise flight. It is simply a nice feature.
An airplane with wings swept 'the wrong way' will typically exhibit positive Lβ. The ride may feel less comfortable, especially to the pilot, that may get the sensation that the airplane is 'not flying straight'. It is not nescessarily a problem though; the airplane variation in this image flies perfectly fine.
Just like a weather vane or a windsock a 'well designed' airplane will turn its nose to the wind. So if the nose is pointed a few degrees to the left the plane wants to right itself. The stronger that tendency, i.e. the stronger the resulting yaw right force, the greater Nβ.
Most of us Kerbal players have at some point designed a rocket with significant negative Nβ, and most of mine ended in Rapid Unscheduled Disassembly. Luckily it is easy to fix, you just slap on more fins at the back of the craft.
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