Airship Body Reference Frame (Controls 1)

Let’s go ahead and talk about the airship
body reference frame. This reference frame is fixed to the body
and so when the body pitches up or when the body yaws or rolls, it’s going to pitch
up as well or yaw as well or it’s going to roll as well. It’s a little bit different for an airship
then for an aircraft and that’s mostly on where the origin of this reference frame is. For an airship, the origin lies at the center
of volume (CV). Now, something to note about this center of
volume is that it is the center of volume of the envelope and not of the entire airship. Basically, we do that because the gondola
is such a small volume compared to the envelope and it just makes it easier to put it at the
center of volume of the envelope because then this x-axis will actually lie on the plane
of symmetry, both between the top and the bottom as well as the left and the right with
the x-axis going out the nose. The y-axis would be going out the right side. And then the z-axis is going straight down,
following the right-hand rule convention. Let’s go ahead and look at the translational,
or in other words, linear velocities, accelerations, and forces. Along this x body axis, we can break the motion
of the airship into the different components along the x body or the y body or the z body
axes. And when we do that, we can get a velocity
and acceleration terms, along the x-axis. We’ll call these U and U dot. We can also take the total aerodynamic force
and break it into a component that runs also parallel to the x body. We’ll call that “F of a in the x direction”. Then we can do the same thing with the total
thrust force. We can break that up into components and we
have a thrust force in the x direction. Alright, looking at the y-axis. Again, we can break up the motion of the aircraft
into its components and look at the velocity and acceleration along this y-axis. And we’re going to go ahead and give those
components the symbol of V and V dot. We can also break the aero force up, and the
thrust force up, into components along the y-axis. That would be F_a_y and F_T_y. And then, last but not least, we have the
z-axis. Again, we can break up the motion, the aero
force, and the thrust force along the z-axis. And the symbols we will give those is W, W
dot, F_a_z, and F_t_z. Let’s go ahead and take a look at our angular
values, starting with rotation about the x body axis. We call this roll. We can have an angular velocity of P, an angular
acceleration of P dot. We can have moments due to aero and thrust
loads which we call L_a and L_t. If the airship rotates about the y-axis, we
call this pitch and we can have an angular velocity of Q, an angular acceleration of
Q dot, a moment due to aero loads of M_a, and a moment due to thrust of M_t. Now, let’s look at the z-axis. If the airship rotates about the z-axis, we
call this yaw and we can have an angular velocity term of R, and angular acceleration of R dot,
a moment due to aero loads of N_a, and a moment due to thrust of N_t. Keep in mind that if we’re wanting to convert
these from the body reference frame to another frame like the earth frame, or the wind frame
we’re going to need to use a transformation matrix. But we’ll talk about those in a future video. Something I want to bring up right now while
we’re talking about the body reference frame, is gravity. One of the common mistakes that’s made is
to think that the gravity acts along the z-axis of the body reference frame. However, since the gravity force is always
pulling from the center of mass of the airship to the center of mass of the earth it actually
acts along the z-axis of the earth reference frame. Now the z-axis of the body frame lines up
with a z-axis of the earth frame if you’re airship is at a zero pitch angle. Right, it hasn’t pitched up or hasn’t pitched
down. It’s level. However, the second you pitch the aircraft
up or down and it’s no longer level the z-axis of the body is no longer along that z-axis
of the earth and the gravity stays with the z-axis of the earth not the z-axis of the
body. This means that you can break this gravity
vector up into components along the x, and along the y, and along the z. Alright, that’s
all for this video. If you like what you saw, and you want to
see more videos from the channel, go ahead and subscribe to the channel and find a video
you like and share it with some of your classmates or coworkers. I’ll see you in the next video.

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