# Math Problem ### Help Support HomeBuiltAirplanes.com: #### Flying Boat

##### Active Member
To all the engineers and mathmaticians out there,

I ran into an equation while checking FAR part 23 to see if my design would pass. The equation appears to want the tangent of the hull deadrise angle taken to the power of 2/3 and the seaplane weight taken to the power of 1/3. I have never seen numbers taken to the power of fractions before and wondered if I was reading the equation correctly. We've all seen squares, cubes etc but fractions? Any one wanting to see the equation I am refering to it is FAR 23 sub 23.527 (2) "Hull and main float load factors" (a) (1)&(2).

I have no idea how to write the equation out for you or I would.

Thanx

#### orion

##### Well-Known Member
Looks like my copy of the FARs is a bit out of date as I don't have that particular section. I did find it though in my short copy of the NAS 807 document. This National Aircraft Standards Committee document defines the loading requirements for a twin seaplane float design and I think that this is what got incorporated directly into the FARs.

Although you may not recognize it, you've probably seen a fraction in the exponent before, but in a different form. The square root of a number is the same as writing that number to the power of one half. A number to the power of 1/3 is really the cube root of the number. By the same token, any other fraction can be represented.

As such, you read the equation correctly. Probably the best way that I can direct you to proceed is to get yourself a calcualtor that has the power function capability ("y" to the "x" power). To calcualte the power, convert the fraction to its decimal equivalent (1/3 = .3333 and so on) and plug those numbers into the calcualtor.

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#### wassbiplane

##### Well-Known Member
You can do this with a simple calculator or even a pencil & paper---If you have a table of logarithms----the only tricky part is assigning
a prefix to the logarithm--Basically it works like this:

take the number you want to raise to an odd power:

Look it up in the table of logs(logarithms)

multiply the log by the power desired--

then , working backwards, look up this number in the tables , and write down the number that the
log represents. -----Try it with a few simple numbers & powers until you get the hang of it.

ps. my old college physics textbook had a simple
table of logs.(4 significant figures ). Before computers they had log tables to 20 or more sig-
nificant figures.

hope this helps.--Jerry

#### Flying Boat

##### Active Member
Bill and Jerry,

Its funny how now that you mention it, I do recall these areas of math. Thank you very much for reassuring me.