What Do Symbols 'R', 'S', and 'b' Mean in Aerodynamics Equations?

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Discussion Overview

The discussion focuses on the meanings of the symbols 'R', 'S', and 'b' in aerodynamics equations related to golf balls, specifically in the context of lift coefficient (CL) and drag coefficient (CD) equations. Participants seek clarification on these symbols as they appear in various articles and equations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks for clarification on the meaning of 'R' in the equation for CL, suggesting it might refer to the radius of the ball.
  • Another participant cites a Google Books reference indicating that 'R' is indeed the radius of the ball.
  • There is a query about the meaning of 'S' in the equation for CD, with one participant proposing it might be a non-dimensional constant.
  • A participant suggests that 'S' could represent the spin rate parameter, defined as the ratio of the equatorial velocity at the edge of the ball to its translational velocity, with a specified range for golf balls.
  • One participant expresses uncertainty about the placement of closing brackets in the CD equation, indicating a need for experimentation to resolve this issue.
  • A later reply indicates a belief that 'S' can be calculated using the formula (BallSpin * BallRadius) / BallVelocity, while reaffirming that 'R' represents the BallRadius.
  • Participants share that they are obtaining drag coefficient results that align with field measurements, although this is presented with some uncertainty.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the meanings of 'S' and 'R', as there are multiple interpretations and some uncertainty remains regarding the equations and symbols discussed.

Contextual Notes

There are unresolved questions regarding the definitions of 'S' and 'S' in the context of the equations, as well as the correct placement of brackets in the CD equation. The discussion reflects varying interpretations of the symbols based on different sources.

icandothemath
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Hi,

In this article there are some symbols that I do not know what they are can you help me identify them?
http://www.ijimt.org/papers/419-D0260.pdf
Page 347 at the top the equation for CL what does the 'R' stand for? And while we are looking at the same equation. |w| is the magnitude of ball spin and |v| is the ball speed right?
Next on the same page at the bottom of the same column, the equation for CD what does 'S' stand for?
And can someone tell me where the closing brackets are to be on the CD equation? The opening and closing brackets do not equal.

Thanks, to you smart people out there. :)
Also found a simular equation for CL here on page 4 but do not know what 'b' is. Which i believe is the same as 'S' above. http://www.researchgate.net/publication/267680093_Interactive_3D_Golf_Simulator
 
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icandothemath said:
Hi,

In this article there are some symbols that I do not know what they are can you help me identify them?
http://www.ijimt.org/papers/419-D0260.pdf
Page 347 at the top the equation for CL what does the 'R' stand for? And while we are looking at the same equation. |w| is the magnitude of ball spin and |v| is the ball speed right?
Next on the same page at the bottom of the same column, the equation for CD what does 'S' stand for?
And can someone tell me where the closing brackets are to be on the CD equation? The opening and closing brackets do not equal.

Thanks, to you smart people out there. :)
Also found a simular equation for CL here on page 4 but do not know what 'b' is. Which i believe is the same as 'S' above. http://www.researchgate.net/publication/267680093_Interactive_3D_Golf_Simulator

In the equation for CL, it appears that 'R' in Kim and Baek is the same as 'b' in Ahn, Kang, et al.; namely R = b = radius of the golf ball = 0.2135 m or 21.35 mm. Apparently, regulation golf balls must have a minimum diameter of 42.67 mm, so this figure seems about right.

In Kim and Baek, it's not clear what 'S' is, but I don't believe it is the radius of the golf ball. It's not clear what S is, but from its use in the formula for CD, it appears to be a non-dimensional constant of some sort.

From this paper:

http://conferences.ucdavis.edu/ces_pages/Download/Past Conferences/ISEA04/ISEA_example.pdf

it appears that 'S' is the 'spin rate parameter' for the spinning ball. S is defined as the ratio of the equatorial velocity at the edge of the ball to its translational velocity.
For golf balls, the range of S appears to be 0.04 < S < 1.4.

As far as balancing the parentheses in the CD equation, you may have to experiment to find out where the missing ) goes.
 
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Thanks, CWatters and SteamKing, you 2 were a big help!
I *think* I have it under control now.
I *believe*:
S = (BallSpin * BallRadius) / BallVelocity
R = BallRadius.
And I think the equation was missing all the closing brackets on the end.
I have been at this for days. :)

I seem to be getting Drag Coefficient Results similar to field measurements.
At least according to this image from http://physicsworld.com/cws/article/print/1998/jun/01/the-physics-of-football
world-11-6-8-3.jpg

Feel free to correct me if I miss understand.
Thank you again. :)
 
Last edited:

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