Maths question

[solarengineer]

Hey List I have a question regarding tail weight and mount angle and just want to do a sanity check on my math.

Ed @ windstuff now has a great site as you all know, but im stumped at one formula as follows

Snip from Ed's site:

The Rotor thrust can be calculated by using the following formula.

     Rotor Thrust = Diameter^2 * Velocity^2 / 24

     Rotor thrust is in kg - to convert to lbs multiply kg by 2.2

To Calculate the tail weight or to find the tail mount angle... we need to know...

     Rotor Offset ( meters )

     Diameter of Rotor ( meters )

     Wind Speed ( meters/second )

     Tail tip weight ( kg )

     Length of tail ( meters )

Then we need to calculate....

     Rotor Thrust = Dia of Rotor^2 * Windspeed^2 / 24

     Tail moment = Tail tip weight * Length of tail

     Rotor moment = Rotor Thrust * Rotor offset

     Tail mount Angle = sin-1(Rotor moment / Tail moment)

If you need to find the Tail tip weight at a given tailmount angle then...

     Tail moment = Rotor moment / ( sin(Angle in degrees))

     Tail Weight = Tail moment / Length of tail

For a 7ft machine with a rotor offset of 3" I get

rotor thrust = 7ft^2 * 5m/s / 24 = 10.2

tail moment = 10lb tail * 4ft long tail = 40

rotor moment = 10.2 * 3" = 30.6

NOW HERE IS THE PROBLEM I RUN INTO

When calculating the tail mount angle with the sin-1 i get an error on the calculator

tail mount angle = sin-1(30.6 / 40) = 50 degrees

DAMMIT now it works!!!!! I'm doing the math as I type it and all last evening my numerator was always larger than the denominator which the sin-1 doesn't like. but somehow i may have got it right and instead of deleting this post I'll keep going in case I'm wrong or perhaps someone else can get some insight.

So then my final tail wight at 50 degrees is

tail weight = 40 / 4ft = 10lbs.

Ya somethings not right! I think i commited a major math sin by mixing units. all units except the tail lenght are metric.. I should have converted 4ft to meters.

Well Have a good day anyhow list I just wasted about 1k of banwidth you can never get back lol

[Flux]

Don't want to spoil the fun, but I don't see how any formula is going to account for a prop seeking force that depends on a lot of factors.

Flux

[imsmooth]

You have units mixed up in the forumla (feet and meters) and this might be how you are typing them into your calculator.

convert feet to metric: 7 feet = 7 f * 1/3.3 m/f  = 2.12 m

thrust = 2.12^2 * 5^2 / 24 = 4.69 kg

thrust = 4.69 kg * 2.2 lbs/kg

thrust = 10.3 kg

which is what you wrote.

As far as the Sin function goes, Sin can only be between -1 and 1, so if the numerator is bigger this is impossible.  The opposite side of a triangle can never be bigger than the hypotenuse.