Hi again!
Sorry but....I still have problems with trying to reproduce the behaviour of an XY plane aerofoil by using the current Vertical and Horizontal aerofoil lift/drag functions. The problem is one of geometry this time.
Maybe someone can see where I'm going wrong(?).
I'm just going to consider profile drag for this purpose.
Lets assume that my "XY plane" aerofoil (I'll call it XYP) is symmetrical around the Z-axis, and instead of using angle-of-attack (aoa) or slipangle (beta) to set the Cd, we use the angle between the airflow vector and the normal to the aerofoil surface (vessel -Z axis). We'll call that angle "angle of incidence" (aoi).
So for a capsule flying with blunt end (-Z) directly into the airflow:
aoa = 180
beta = 180
aoi = 180
if we pitched the capsule blunt end down 10deg we get
aoa = 170
beta = 180
aoi = 170
or if we yaw it 10deg we get
aoa = 180
beta = 170
aoi = 170
The drag for XYP is calculated in the same way as for Vertical and Horizontal aerofoils by Orbiter:
Drag = Freestream-dynamic-pressure * wing-area * Cd
For this discussion lets set Freestream-dynamic-pressure = 1, so:
Drag = wing-area * Cd
For XYP lets say wing area is 10m^2 and we set the Cd so that:
at 180 aoi, Cd = 1
at 170 aoi, Cd = 0.9
Lets say we use two identical (for symmetry around Z axis) Vertical and Horizontal aerofoils to mimic the behaviour of the single XYP. They each have area 5m^2, and we can set the Cd according to aoa or beta thus
Horizontal Airfoil:
at 180 aoa, Cd =1
at 170 aoa, Cd = 0.8
Vertical Airfoil:
at 180 beta, Cd =1
at 170 beta, Cd = 0.8
Let's see how this works out for some different orientations......
For aoa = 180, beta = 180, aoi = 180:
For XYP, Drag = 10 x 1 = 10
For Vertical + Horizontal aerofoils, Drag = (5 x 1) + (5 x 1) = 10
That works ok!
For aoa = 170, beta = 180, aoi = 170:
For XYP, Drag = 10 x 0.9 = 9
For Vertical + Horizontal aerofoils, Drag = (5 x 1) + (5 x 0.8) = 9
That works ok! And similarly ok for aoa = 180, beta = 170, aoi = 170.
BUT.... what happens if we have both aoa and beta angles??
If we assume aoa and beta are equal, and aoi is 170, a little work with vectors(which I can show if required ;-)
shows that aoa and beta must equal 172.89
So, assuming linear interpolation between Cd points:
Cd for the Vertical and Horizontal aerofoils is:
Cd = 1 - { (180 - 172.89)/(180 - 170) } * (1 - 0.8) = 1 - (0.711) * (0.2) = 1 - 0.1422 = 0.8578
So for aoa = 172.89, beta = 172.89, aoi = 170:
For XYP, Drag = 10 * 0.9 = 9
For Vertical and Horizontal aerofoils, Drag = (5 * 0.8578) + (5 * 0.8578) = 8.578
Drag is not equivalent!!!
Or you could take a simpler case where say the Cd for XYP is 0.4 at aoi = 120
and you have the situation where: aoa = 120, beta = 180, aoi = 120
For XYP, Drag = 10 * 0.4 = 4
In this case, Horizontal aerofoil would require negative Cd!
i.e. For Vertical and Horzontal aerofoils, Drag = (5 x 1) + (5 x -0.2) = 4
I conclude that in situations where neither aoa or beta are 0, there is no exact equivalence of behaviour between XYP and
Vertical+Horizontal aerofoils. Its down to the geometry of using two angles vs. just one.
Maybe one can use a transformation of aoa and beta in the lift/drag functions to compensate.
Or use some kind of non-linear interpolation, but...ugh!
And to have negative Cd seems weird.
I still think AIRFOIL_CAPSULE concept has value
Phew! Had to get that out....it was making my brain itch!
If you bothered to read all the above...thanks for your interest!!
Cheers,
BrianJ