Surface areas of a scalene ellipsoid and sphere

[flintknapper81]

Hi all,

I was hoping someone could help me out with Excel formulas for calculating the surface areas of a scalene ellipsoid and sphere:

The equation are as follows, just not sure how to enter them into Excel.

The scalene ellipsoid formula I wish to use

4PI[(a^pb^p+a^pc^p+b^pc^p/3]¹/p

p is 1.6075 and a, b, and c are thesemi-axes of length, width, and thickness

Some hypothetical values would be 5 cm for length (a), 10 cm for width (b) and 12 cm for thickness (c)


The sphere equation I wish to use is:

S = 4PI(3V/4PI)⅔

A hypothetical value for V (volume) here could be: 15

Thanks in advance all

Cheers

Andy

 

[DSCfromCFA]

G'day Andy

There is a parenthesis missing from your formula which Google tells me is this
S » 4p [ ( a^pb^p + a^pc^p + b^pc^p ) / 3 ] ^1/p

The trick is to build this formula up from its individual components which will be assigned their own cell

For example assign A1, A2 & A3 to your variables Length, Width and Thickness into which you simply type the number to be used

Assign cells B1 & B2 to your fixed values for Pi and p (B1 you would actually enter =Pi() and for B2 simply enter the number 1.6075)

You could name each of these cells to its corresponding value if you wish but it is not necessary.

You now have two choices - put in the final formula that replaces all the terms with the corresponding cell address

I.e in cell C1 =4*B1*(A1^B2*A2^B2 etc, but that is quite tedious and will require a close eye kept of the brackets you will need to use to ensure the operations are done in the correct order

I would suggest some intermediate steps:
Cell D1 =A1^B2
Cell D2 =A2^B2
Cell D3 =A3^B2
Cell D4 =1/B2

You could then go to another level and do the 3 internal multiplications
that would be E1 =D1*D2, E2 =D1*D3 & E3 =D2*D3 in individual cells and then sum the result into E4 =SUM(E1:E3)

You would then in your final cell F1 have
=4*B1*((E4/3)^D4) (if I have all my terms correct)

Do the same for your sphere formula which won't need as many steps

Good luck

shane

 

[flintknapper81]

That's awesome Shane, many thanks!!!

Just did a trial run and it worked like a dream

 

[flintknapper81]

Hey Shane,

Hit a bit of a snag with the second equation, i.e., S = 4PI(3V/4PI)⅔ and could use a sanity check:

If:

Cell A1 = PI
Cell A2 = V
Cell A3 = 1/2 (i.e., 0.5)

would the single line formula run as follows:

=4*A1*(3*A2/4*A1)^A3

Using 15 for V I get: 74.7

Just not sure what the absence of "[" symbol in this equation means re formula

Thanks in advance

 

[flintknapper81]

Apologies Shane, just noticed a mistake there...

Cell A3 should be 2/3 not 1/2 (i.e., value of 0.6666)

Using 15 for V I get: 135.33

 

[DSCfromCFA]

G'day Andy,

Thanks for the feedback and I'm glad it all worked out. Excel is an amazingly flexible tool that even allows a mathematics minnow like me to look a lot smarter than I actually may be.

cheers


shane