A question about SkyHogg model in Aerospace Blockset

in the example model:

asbSkyHogg

in this block (asbSkyHogg/Vehicle System Model/Vehicle/3DOF to 6DOF/3DOF to 6DOF/calc alpha_dot) which is used to calcualate the rate of change of of angle of attack ()

The rate of change of of angle of attack is calculated based on the equation:

So, the acceleration (input #3) in body axes should be transformed to wind axes using the DCM Body-to-Wind as shown in the picture... but why the transpose block is added here???!! In this case, it's actually transformed to body axes again!!

Answer 1

[Paul]

Hi Islam

I agree with your equation for alphadot, but not the notation. By standard convention (at least what I'm familiary with), u is the component of the velocity vector along the x-axis of the body frame, not the wind frame. By definition, the component of the velocity vector alone the x-axis of the wind frame is the velocity vector. So I would write the equation as

Here, V(t) is the magnitude of the velocity vector and A_zw(t) is the component of the inertial accelaration along the z-axis of the wind axes.

If I followed the model correctly, the signal called Vw should just be [V(t) 0 0].

I agree with you that the the transpose block is an error.

There is also another error. The signal called Ab is NOT the inertial acceleration vector resolved in the body axes. According to the documentation Ab = [udot 0 wdot], which is not what we want. So even if you delete the transpose block, the alpha_dot signal will still be incorrect. Probably not by much, but incorrect. To correct this error you'd have to get the optional output from the 3DOF block, which is the inertial acceleration in inertial (earth) coordinates, and then resolve that into body coordinates and use the result as the input to the "calc alpha_dot" block, instead of Ab.

[Islam Elnady]

Hi @Paul

Thank you for the response.

I agree with your remarks. I'm now quite suspicious about the implemnetations of a lot of things in the Aerospace blockset examples.

I have used another formula of Alpha_dot to avoid the confsuion.

[Paul]

The expression alphadot = (wdot*u - w*udot)/(u^2 + w^2) has the correct form, but I disagree with their definitions. w and u should be the components of V = Vi - Vw, where Vi is the inertial velocity vector of the vehicle and Vw is the inertial velocity of the wind, resolved in the body-fixed frame, not the wind-reference frame. After all, in the wind-reference frame V only has an x-component, by definition (at least based on my understanding of the nomenclature).

" I'm now quite suspicious about the implemnetations of a lot of things in the Aerospace blockset examples."

As well you should be.

[Islam Elnady]

@Paul Since alpha dot is basically a parameter in the wind-axes.. why are the inertial frame components used here? Also as I know, the velocity in wind-axes has only x-component (Uw) if only the sideslip angle (beta) is zero.

[Paul]

I should have been clearer. When I said Vi is the inertial velocity vector I was assuming that the absSkyHogg model uses a flat earth model, so the velocity relative to an inertial frame would be the same as the velocity relative to coordinate frame "fixed" to the atmosphere.

In this equation: dalpha/dt = q + Z/(mU), the uppercase U in the denominator is the vehicle speed (relative to the atmosphere). That's not same as lowercase u in the other equation for dalpha/dt.

My understanding is that the x-axis of the wind frame is defined by the velocity vector. Therefore, by definition the y- and z-components have to be zero in the wind frame.

Here's one reference: flight dynamics