Calculating Power for Hovering Thrust of a Fan

[reebrah]

Basically I am doing work that requires me to calculate power for given thrust of a fan which is hovering.

Variables known:
diameter of fan: 0.8m, thrust output of fan: 250kg, rho=1.1455 kg/m^3 which is the density of air at 35Celcius , and eta which is the fan efficiency = 0.8



I tried this equation I found on wikipedia:

P^2 = (T^3) / ( (eta^2)(rho)A)

using this equation I got 7322w of power to attain a thrust of 250kg...This seems a little off. What is wrong here? does anyone know if this is even the correct value or even correct equation? thank you and appreciate it!

 

[Aero51]

You can always use this equation which is valid for cases when the initial velocity of the air is 0.
Here is the link:
http://en.wikipedia.org/wiki/Thrust#Thrust_to_power

and in case you are feeling lazy:

$P^2 = T^3 / {4 \rho A}$

 

[reebrah]

True but in this equation the eta^2 is replaced with a 4. This would then further decrease the power estimated from this relation. Anybody else know anything for hovering thrust?

 

[Aero51]

Visit this link, specifically check pages 281. I think it has the equations you are looking for. The book also has a nomenclature section at the front of the text. Hopefully this helps:
http://books.google.com/books?id=Sg...gSBv4CQBA&ved=0CEUQ6AEwAg#v=onepage&q&f=false

 

[AlephZero]

Did you forget that thrust is in Newtons, not "kilograms"?

 

[reebrah]

I think that might just solve my problem lolz

 

[AlephZero]

At least it will give you a bigger number. 7kW is obviously way too small for a quarter-tonne chopper with a teeny little 0.8m dia rotor