Calculating Power for Hovering Thrust: What is the Correct Equation?

In summary, the conversation discusses the process of calculating power for a given thrust of a hovering fan with a diameter of 0.8m. The equation P^2 = (T^3) / ((eta^2)(rho)A) is used, but there is some confusion about the correct value and equation. The conversation also mentions another equation found on Wikipedia that replaces the eta^2 with a constant of four. The conversation concludes with a clarification that the fan efficiency definition may vary and the equation provided is accurate.
  • #1
reebrah
10
0

Homework Statement


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



Homework Equations


We are given the diameter: 0.8m, thrust output of fan: 250kg, rho=1.1455 kg/m^3, and eta which is the fan efficiency = 0.8


The Attempt at a Solution



I found this equation in 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!
 
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  • #2
Your equation looks fine (although, It depends on how the fan efficiency is defined).

One thing which is not right is that you've put thrust in units of kg, but thrust is a measure of force, not mass.
 
  • #3
BruceW said:
Your equation looks fine (although, It depends on how the fan efficiency is defined).

One thing which is not right is that you've put thrust in units of kg, but thrust is a measure of force, not mass.

Theres also another eq. I've found on wikipedia which replaces the eta^2 with a constant of four. How can i confirm this is correct? Also you are right about the thrust units.
 
  • #4
The constant of 4 is assuming that no energy is lost as heat when the air is accelerated. You can derive the equation by considering the volume of air which passes through the fan in some time interval. It is the very simplest model you could imagine, since it neglects the effects of viscosity, turbulence, etc

For your homework, are you meant to be explaining why a particular equation is the correct one? Or were you just asking about the equation because you were curious?
 
  • #5
No i am just trying to find an accurate way to model power consumed given an amount of thrust and radius of fan. Are their any other factors i should be worried about?
 
  • #6
Your equation is fine. As I said, you just need to be careful what you use as your fan efficiency, since different people might define it differently. For example, you could keep the constant of 4 in the equation, as well as the fan efficiency, in which case, the fan efficiency would be defined differently.
 

1. How is hovering thrust calculated?

Hovering thrust is calculated by considering the weight of the object that needs to be lifted, the air density, and the acceleration due to gravity. Using this information, the force required to counteract the weight and maintain a steady hover can be determined.

2. What factors affect hovering thrust?

The main factors that affect hovering thrust include the weight of the object, air density, and the design and efficiency of the propulsion system. Other factors such as altitude, temperature, and air pressure can also have an impact on hovering thrust.

3. How do you measure hovering thrust?

Hovering thrust can be measured using a variety of methods, including using load cells or force sensors, thrust stands, or by calculating it using mathematical equations and data from the propulsion system.

4. What is the importance of calculating hovering thrust?

Calculating hovering thrust is crucial for designing and testing aircraft, drones, and other objects that require vertical takeoff and landing. It allows engineers to determine the necessary power and performance of the propulsion system to achieve a stable hover.

5. Are there any challenges in calculating hovering thrust?

There can be challenges in accurately calculating hovering thrust, as it requires precise measurements and data. Factors such as wind, turbulence, and air temperature can also affect the accuracy of the calculations. Additionally, the design and efficiency of the propulsion system can also impact the accuracy of the calculations.

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