# Dimensional analysis with wingspan length?

I need some help in understanding the fundamentals of dimensional analysis. The following is is from "Fundamentals of aerodynamics" by John D Anderson, fifth edition:

Why is the wingspan length not added to the variables that the aerodynamics force R depend on?

• you should avoid posting an image full of text. you should really copy that text here, at least
– Federico
Jun 13 '17 at 7:27
• the text has lots of special texts and formulars, by the way I want to keep it original
– Dat
Jun 13 '17 at 9:08
• yes, right. the book is quite popular and it's fifth editon
– Dat
Jun 13 '17 at 9:31
• @DatXaLin You can use MathJax to typeset the formulas. The image is inaccessible to search engines and the partially sighted and neither of those things is good for the site. Jun 13 '17 at 9:43

In page 38 of the book you're quoting, the derivation goes on replacing $c^2$ with $S$, the planform area of the wing, implicitly introducing the wingspan...

• I have read to that page but it still does not help
– Dat
Jun 13 '17 at 9:12

The body is of a give shape and of a give angle of attack. The only variable left is then the scale of the body.

The author decided to use the chord length as reference length; if the shape is known and the chord length is known, all dimensions of the aircraft are follow from that. Alternatively he could have chosen the wingspan, tail height or any other length as reference length.

• I don't think so. Given shape only provides us the sectional airfoil and the chord length only give us the scale of this sectional, not how long the wingspan is.
– Dat
Jun 13 '17 at 9:11
• If the body is of a given shape, then the wingspan will X times the chord length. X will be dimensionless. Jun 13 '17 at 9:16
• thanks, if so, why X is not added to the variables. i am sure the aerodynamics force depend on X as well as c, V..
– Dat
Jun 13 '17 at 9:18
• It my also depend on 2, 0.5, $\pi$ and other dimensionless numbers that are not included either. It is dimensional analysis after all. Jun 13 '17 at 9:21
• Also X is not a variable, it is a constant for the given shape. Jun 13 '17 at 9:26