[EZ] I could really use some help understanding the following symbols....

[Wetter42]

TL;DR Summary

Forgive me for my noobishness as I'm not a physics major of any kind, but I'd love some help splashing into the world of Aerodynamics / flight mechanics to understand a bit more of how it works! Any assistance is greatly, greatly appreciated!

Hey guys! I'm looking at a few resources and I came across an interesting one on the Aviation Stack Exchange Page. Interestingly enough, another individual is working on implementing flight mechanics / aerodynamics using code and had similar questions to me, but to be honest, I'm not quite sure I understand the symbols fully; Now I've referenced resources like this to try to track down the symbols, but I've noticed that sometimes, symbols are shared / interpreted slightly differently. Not to mention the subscripts on any symbols can change the context completely. For example CL - The coefficient of lift can be changed to the max coefficient of lift by adding another (base)max to the symbol.

But I'm rambling. Anyways, here's what the symbols (kinda) look like

=========
α=arctan(w/u)
From research, I was already able to determine that that 'a' looking thingy is the angle of attack and the w is the speed along the z axis, and the u component is the speed along the x axis. This was taken from this NASA memorandum. (Top of Page 4)

========
Lz=−2π⋅α⋅q
WTH is q? I'm assuming from the context from the original source that this is Lift? But what is the context of the z component?

==================
gz=9.81⋅cos(bank)⋅cos(pitch)
What is the G component? What is subscript z? What do they represent?

=======
wz⋅=Lz+gz
Not sure what w is. Also, what does the subscript z denote here as well? Lastly, some follow up questions so I don't end up back here (and for others who want to learn, too ;D ). As you can see I was unsuccessful searching which brought me back here!

1. What's the name of the symbol for angle of attack? (Nevermind, it's "Alpha" - of course it is...)
2. I've noticed the symbols for w and u also look strange. Are those symbols as well? do they have a name?
3. What about q?
4. The base / subscript "z" - Am I using the terminology correct? I tried searching "L base z" or "L subscript z" but google knew as much as I did it seems
5. Are there any other resources (books, publications, etc) that will help me sort of understand this context in the future? The people on Avi-Stack-Exchange seemed to ask and answer the question without needing any sort of context, so I'm assuming there's at least a few resources out there that'll do the job...Thanks a million times over to anyone who spends time to help me understand. Please know that the knowledge I acquire will go to helping others understand as well! Cheers! :D

 

[Baluncore]

The symbols come from the Greek alphabet.
https://en.wikipedia.org/wiki/Greek_alphabet

 

[Wetter42]

Well that helps with Alpha, but not as much with the post question 1, but not as much with the symbols as they relate to the study of aerodynamics. For example:
q
g(base)z
L(base)z
w(base)z

have any references for those?

 

[Baluncore]

z is almost certainly a subscript, not a base. It refers to the vertical component of a 3D vector.

u, v and w are the wind tunnel axes. They may be in italics.

q I cannot find the equation using q in the reference.

 

[Wetter42]

Thanks for that! It helps tremendously so far! <3

 

[Lnewqban]

That q should be all the factors on which Lift/radians of AOA depends.
Please, see:
https://www.grc.nasa.gov/WWW/K-12/FoilSim/Manual/fsim0007.htm

The responses that the other person received at that other site are very good.
Could you describe your specific difficulty?

 

[FactChecker]

Any reference should define the symbols that it uses, but there are no "symbology police" to enforce that. Usually, a published article or book will have been thoroughly checked for undefined symbols, but nobody is perfect.
That being said, q in the context of your equation usually represents the dynamic pressure from the air, but there should be a coefficient of lift in the equation. If that equation is directly from your reference and is used differently without a definition, then it seems sloppy to me.

PS. Please make all your subscripts appear as subscripts. ( $L_z$, not Lz)

 

[FactChecker]

I wouldn't worry about the reference that you first looked at. That post and its equations are amateurish with respect to aerodynamics and flight simulation. I don't think that the replies in that post link will be very helpful to you because they would have to address all of the problems on the initial question.
The list of symbols in your second reference is a reliable source, but they need much more definition than that list gives. In general, a list of symbols will not give enough detail unless you also look at the accompanying text where each symbol is defined. Doing that might require an entire book like Aircraft Control and Simulation A free, initial reference is NASA SP-367.pdf, which does not address simulation.

 

[berkeman]

Thanks for that! It helps tremendously so far! <3

One other thing that will help a lot going forward -- please see the "LaTeX Guide" link in the lower left of the Edit window. That will get you started using LaTeX to post math equations, which makes it much easier to read and more unambiguous. Thanks.

 

[Wetter42]

That q should be all the factors on which Lift/radians of AOA depends.
Please, see:
https://www.grc.nasa.gov/WWW/K-12/FoilSim/Manual/fsim0007.htm

The responses that the other person received at that other site are very good.
Could you describe your specific difficulty?

Any reference should define the symbols that it uses, but there are no "symbology police" to enforce that. Usually, a published article or book will have been thoroughly checked for undefined symbols, but nobody is perfect.
That being said, q in the context of your equation usually represents the dynamic pressure from the air, but there should be a coefficient of lift in the equation. If that equation is directly from your reference and is used differently without a definition, then it seems sloppy to me.

PS. Please make all your subscripts appear as subscripts. ( $L_z$, not Lz)

Oh, man! I absolutely wish this were a thing: Like each aviation resource should specify something like: "If you're going to post an eq, please post the referencing link a well as a breakdown of the equation name and the representation of the symbols. This would close a lot of confusion for people just looking to understand what the OP is referring to!

What about the other symbols such as $w_z$ (which I'm unsure of) and $g_z$ (which I'm assuming is the acceleration of gravity, but not sure).
Lastly, will do! Thanks!

I wouldn't worry about the reference that you first looked at. That post and its equations are amateurish with respect to aerodynamics and flight simulation. I don't think that the replies in that post link will be very helpful to you because they would have to address all of the problems on the initial question.
The list of symbols in your second reference is a reliable source, but they need much more definition than that list gives. In general, a list of symbols will not give enough detail unless you also look at the accompanying text where each symbol is defined. Doing that might require an entire book like Aircraft Control and Simulation A free, initial reference is NASA SP-367.pdf, which does not address simulation.

Agreed! I feel like the question wasn't fully addressed. Wish there were more experienced users on aviation stack! Anyways, those are great resources, and I actually have never come across this specific NASA publication from my research...and I've come across a LOOOT of publications (NASA and otherwise!)!

One other thing that will help a lot going forward -- please see the "LaTeX Guide" link in the lower left of the Edit window. That will get you started using LaTeX to post math equations, which makes it much easier to read and more unambiguous. Thanks.

You $L$earn something new every day! Thanks for the help! Thanks everyone! Contributions like this really make the space a lot more beginner friendly! <3

 

[FactChecker]

What about the other symbols such as $w_z$ (which I'm unsure of) and $g_z$ (which I'm assuming is the acceleration of gravity, but not sure).

He has not defined his coordinate system, so it would require guesswork. $g_z$ doesn't make sense in the Earth axis because gravity always points down, in the Earth Z-direction -- no need for a subscript. So I guess that he is referring to the component in the airplane body Z-axis. But that is just a guess.
On the other hand, I don't know if $w_z$ is a z-component of weight or a component of the velocity vector, $w$ in the body axis. But the w velocity vector is traditionally always pointing in direction of the z-body axis, so what is the subscript for? Is he working in the Earth axis system? It's all a confusing guessing game.

Agreed! I feel like the question wasn't fully addressed. Wish there were more experienced users on aviation stack!

I would assume that the people replying are reasonably expert and are struggling with helping a person who has not defined his question very well (or just doesn't know what he is doing).

 

[Wetter42]

Absolutely! Thanks for your assistance today buddy! :D
A much needed sanity check in an insanity inducing world! Cheers!