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Design => Engineering board => Topic started by: Craig Beswick on December 28, 2016, 05:06:23 PM

Title: Scale of wing area
Post by: Craig Beswick on December 28, 2016, 05:06:23 PM
Hello all,
I am in no way an engineer so I hope someone can explain this wing area question.
The MK22 Spitfire had a wing span of 37.1 feet and the information I have is it had a wing area of 252 square feet. Is this then 34,848 square inches?
My question is, if I want to make a model of say 60 inches wing span that is a scale of 1 to 7.42, if I am correct, so if I divide 34848 by 7.42 I get a massive wing area that can't be right!
Can anyone explain where my logic is wrong please?
Much appreciated
Craig
Title: Re: Scale of wing area
Post by: Mark Scarborough on December 28, 2016, 05:30:04 PM
one square foot is = 12" * 12"  = 144 square inches per square foot.
144" square*252 'square=36,288 "square
 span is single dimension, so
37 ' * 12" = span of 444"
60" is 13.5% of 444 inches
square is x*x with x = 13.5%  (.135)
.135 * .135 = .018225
.018225*36,288 " square  = 661.34 square inches of wing area for a 60 inch span
I THINK I got this right,,
the key is remembering that when you change span you are only changing one dimension of the Square inch,, so you need to change both dimensions,, as in X by Y squares,, whereas span only changes the one dimension... essentially you were shortening the span to 60 inches but leaving the chord of the wing as per full scale,, so a very stubby wing planform,, longer front to back than tip to tip

Title: Re: Scale of wing area
Post by: pmackenzie on December 28, 2016, 07:16:09 PM
Or put another way, area goes by the square of the scale. (Both span and chord are reduced and area = span *chord)

252 sq ft = 252*144 = 36288 square inches  (you must have made a math error here :) )

Scaled down by 444/60 = 1:7.4

New area = 36288/(7.4 *7.4) = 662.67 square inches.   

Close to what Mark got, he had more rounding error when he calculated 1/7.4. I left the rounding to the end so preserved the accuracy.

Pat MacKenzie
Title: Re: Scale of wing area
Post by: Craig Beswick on December 28, 2016, 07:57:58 PM
Thank you gentleman.
It had really been bothering me.
My typing error, should have been 242 square feet
Thank you once again
Craig
Title: Re: Scale of wing area
Post by: Avaiojet on December 28, 2016, 08:37:02 PM
Craig,

I've never used squares to scale a model, just the span.

And I check a few sources for measurements, just to be sure.

The Spitfire is a great aircraft to model.

Charles
Title: Re: Scale of wing area
Post by: Paul Smith on February 01, 2017, 11:14:35 AM
Given 252 square feet and 37.1 foot wingspan.

The Aspect Ratio (AR) is 6.8.

Your model has a 60" wingspan.  So you multiply the span by the AR and get 408 square inches.  Not so tough.

Given the span and area, which are usually published, you can get the AR, which makes model-sizing easy.
Title: Re: Scale of wing area
Post by: Tim Wescott on February 01, 2017, 11:50:12 AM
Given 252 square feet and 37.1 foot wingspan.

The Aspect Ratio (AR) is 6.8.

Your model has a 60" wingspan.  So you multiply the span by the AR and get 408 square inches.  Not so tough.

Given the span and area, which are usually published, you can get the AR, which makes mode-sizing easy.

Uh...

Nope.  And, unfortunately, nope.

AR is the area divided by the span squared.  For the given numbers, the Spit has an AR of 5.46 (which sounds a lot better than 6.8 -- the Spit just has stubbier wings than that).

Area is span squared divided by AR, so for a 60" span it's 3600 / 5.46, or 659 squares.

Pat and Mark and I are all giving you slightly different numbers because of rounding errors, but they're all close enough to 660 squares to make no nevermind.

I'm going to bang a drum here that I usually only bang on for junior (and senior) engineers: dimensional analysis would have caught this.  Area is length * length, so if you carry your dimensions and get something other than you expect, you know that you've made a mistake.  Ratios are usually dimensionless -- the aspect ratio certainly is.  So if you divide 252 square feet by 37.1 feet you get 6.8 feet, and you know you absolutely positively can't have an aspect ratio.  It's a pain to carry the dimensions in calculations like this, but the pain of getting a calculation wrong when you could have caught it can be many times worse if you actually go into production with the error in your design (think dead people, or crashed Mars rovers, or, worse, union sheetmetal fabricators giving you the eyeball).
Title: Re: Scale of wing area
Post by: Avaiojet on February 01, 2017, 12:01:05 PM
I've got 565, I believe, with the 55" Phoenix Spitfire wing I'm using for the GBR3.

So at 60" I would think 600 + is more accurate.

Charles
Title: Re: Scale of wing area
Post by: Mark Scarborough on February 01, 2017, 04:53:41 PM
I've got 565, I believe, with the 55" Phoenix Spitfire wing I'm using for the GBR3.

So at 60" I would think 600 + is more accurate.

Charles
its math not guess work