# 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.