How Do You Calculate Static Thrust from Fan Specifications?

[reebrah]

Hello,

How is it possible to calculate the static thrust from a fan given power, radius, air density, and propellor efficiency? I've did some research and found various equations that all gave me varying results. Does anyone know what the real static thrust equation is? Thanks...

 

[Simon Bridge]

Define static thrust - then apply that definition to how a fan moves the air about.
Some simplified model will have to be used though - which is why you see different equations online.
Which model you use depends on what you want to know for.

This is something that is usually measured at some point in the design process rather than relying on models and calculations.

 

[AlephZero]

Does anyone know what the real static thrust equation is? Thanks...

There isn't a simple "real static thrust equation", because (assuming we are talking about aircraft propulsion) the static thrust condition is so far away from the design-point working conditions of the fan that the "exact" value isn't very important.

 

[reebrah]

Okay to make it more clear, let's say vertical lift fan held in place at sea level. Given the parameters listed is it possible to calculate on paper the force of thrust provided by the fan?

 

[reebrah]

The parameters I have in mind are a 80cm diameter fan, with a high efficiency of 0.9, given a power of 40kW. How can I accurately model thrust given this type of set up?

 

[strive]

Well theoreticly you can go with the bellow equations. But as others have said, it's not exact (physical tests will vary from this, as there are many more variables).

m – mass flow [kg/s]
V – volume flow [m˄3/s]
v – air velocity (from the fan) [m/s]
A – fan cross-section area [m˄2]
ro – air density [kg/m˄3]
R – fan radius [m]
F – thrust force [N]
P – power [W]
Coeff – propeller efficiency coefficient [/]
Po – output power [W]

m = V * ro
V = A * v
A = pi * R˄2
F = m * v
P = F * v
Po = P * coeff

So: m = pi * (R˄2) * v * ro
F = pi * (R˄2) * (v˄2) *ro
Coeff * P = pi * (R˄2) * (v˄3) *ro

Thus: v = ( Coeff * P / (pi * (R˄2) * ro) ) ˄(1/3)
Use it to get »V« and from it »m«
Finnaly thrust is m*v.

 

[rcgldr]

Shouldn't thrust be mass flow (Δm / Δt) times change in velocity (Δv)?

 

[strive]

Shouldn't thrust be mass flow (Δm / Δt) times change in velocity (Δv)?

It is. But he's asking for static thrust, thus ambient (surrounding flow) velocity equals 0.
Thus: Δv = v – 0 = v

However i did forget something... the correct equations are:
F = 2 * pi * (R˄2) * (v˄2) *ro
Coeff * P = 2 * pi * (R˄2) * (v˄3) *ro

Thus: v = ( Coeff * P / (2 * pi * (R˄2) * ro) ) ˄(1/3)

 

[rcgldr]

Shouldn't thrust be mass flow (Δm / Δt) times change in velocity (Δv)?

It is. But he's asking for static thrust, thus ambient (surrounding flow) Δv = v ...

My issue was with the mass component, it should be a mass flow component, so (Δm / Δt) v instead of (m) v for static thurst. Note that the units, which should be netwons or pounds, come out wrong if you use m v instead of (Δm / Δt) v. For netwons, the units shoud be kg m / s^2 which is the units for (Δm / Δt) v , but m v would be kg m / s.

 

[strive]

Well it's just that I'm in the habit of writing »m« instead of m with a dot or (Δm / Δt)... but i did specify this:

m – mass flow [kg/s]

 

[rcgldr]

Well it's just that I'm in the habit of writing »m« instead of m with a dot or (Δm / Δt)... but i did specify ...

I just saw the "m" and didn't pay enough attention to the fact that you specified that m would mean mass flow in your example.

 

[reebrah]

Well, given i need to find out mass flow or velocity, how can i convert the propellor power delivered, propellor efficiency, diameter/radius, or air efficiency to provide me with mass or velocity flow?

 

[strive]

m – mass flow [kg/s]
V – volume flow [m˄3/s]
v – air velocity (from the fan) [m/s]
A – fan cross-section area [m˄2]
ro – air density [kg/m˄3]
R – fan radius [m]
P – power [W]
Coeff – propeller efficiency coefficient [/]

Insert your given values in:
v = ( Coeff * P / (2 * pi * (R˄2) * ro) ) ˄(1/3)
m = A * v * ro

 

[rcgldr]

Complicating matters is viscosity increases the effective radius of the air affected by a propeller to be greater than the actual radius of the propeller, at least on the intake side. On the output side, ideally the effective radius decreases as velocity increases, but vicosity cause the surrounding air to be drawn into the output flow from the propeller. Nasa article showing ideal flow case:

http://www.grc.nasa.gov/WWW/K-12/airplane/propanl.html

 

[bkiag]

To strive:

Since kinetic energy is 1/2 mass * velocity^2, shouldn't power be 1/2 mass flow * velocity^2