Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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**Helicopter Aerodynamics and Power Calculation**

**Problem Statement:**

A helicopter with a mass of 10,000 kg hovers at sea level while carrying an additional load of 14,000 kg. The helicopter's blades cause an air mass with an 18-meter diameter to move downward at an average velocity that is proportional to the rotational velocity of the blades. The velocity is given by the equation \( V = k\omega \), where \( k = 0.036 \, \text{m/s/rpm} \).

Tasks:
1. Determine the angular velocity (\(\omega\)) of the helicopter blades in revolutions per minute (rpm).
2. Calculate the required power output for this operation.

Assumptions and Conditions:
- The day has an atmospheric pressure of 102 kPa and a temperature of 25°C.
- Air approaches the blades from the top with negligible initial velocity and moves downward with uniform velocity through an imaginary cylinder whose base matches the span area of the blades.

**Diagram Explanation:**

The diagram features:
- A helicopter shown in side view hovering with its rotor blades extending horizontally.
- A load of 14,000 kg hanging from the helicopter.
- The rotor blade span is indicated to be 18 meters.
- The helicopter and load form a simplified model to illustrate the forces and motion involved, with arrows representing the downward air movement caused by the rotor blades.
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Transcribed Image Text:**Helicopter Aerodynamics and Power Calculation** **Problem Statement:** A helicopter with a mass of 10,000 kg hovers at sea level while carrying an additional load of 14,000 kg. The helicopter's blades cause an air mass with an 18-meter diameter to move downward at an average velocity that is proportional to the rotational velocity of the blades. The velocity is given by the equation \( V = k\omega \), where \( k = 0.036 \, \text{m/s/rpm} \). Tasks: 1. Determine the angular velocity (\(\omega\)) of the helicopter blades in revolutions per minute (rpm). 2. Calculate the required power output for this operation. Assumptions and Conditions: - The day has an atmospheric pressure of 102 kPa and a temperature of 25°C. - Air approaches the blades from the top with negligible initial velocity and moves downward with uniform velocity through an imaginary cylinder whose base matches the span area of the blades. **Diagram Explanation:** The diagram features: - A helicopter shown in side view hovering with its rotor blades extending horizontally. - A load of 14,000 kg hanging from the helicopter. - The rotor blade span is indicated to be 18 meters. - The helicopter and load form a simplified model to illustrate the forces and motion involved, with arrows representing the downward air movement caused by the rotor blades.
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