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Old Jul 28th 2018, 04:04 AM   #1
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Question Rotor and power of engine

The question and answer that I have problem understanding is as follows:

A helicopter of mass 800 kg rises to a height of 170 metres in 20 seconds, before setting off in horizontal flight. Calculate the potential energy gain of the helicopter, and hence estimate the mean power of its engine. State a form of kinetic energy that has been ignored in this model.


The first and second questions are easy to me.

Provided that g=10,

1) W2h2 - W1h1 = 8000 X 170 - 8000 X 0 = 1,360,000J

2) 1,360,000/20 = 68kW

But what I am struggling with is the third question - State a form of kinetic energy that has been ignored in this model.


The answer provided is "The kinetic energy of the rotor", and I just don't quite understand why it can be the answer for this question.


In this model, you need 68kW of power to lift up the helicopter 170 m in 20 seconds, right?


And the engine provides that amount of power "through" its rotor, correct?


So the rotor requires the same amount of power (i.e. 68kW) to lift up the helicopter 170 m in 20 seconds, correct?


Then why do we have to calculate the kinetic engergy of the rotor, which is the energy to rotate the rotor, and add it to the potential energy to figure out the total power required to lift up the helicopter???

Maybe there is something wrong with my understading of potential energy and kinetic energy and how they relate to power..

Anyway, I would much appreciate it if somone out there can help me to undersand this answer to this question in a way that it is easy to follow even for a beginner of physics like me.

Thank you.
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Old Jul 28th 2018, 10:20 AM   #2
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No there is nothing wrong with your understanding of energy and power.

Your issue lies in the mechanics of helicopter flight.



All the vertical lifting of the helicopter is achieved by the upthrust on the spinning main rotor, which spins in a horizontal plane.

The upthrust is due to the speed of the main rotor blades through the air as they spin.
Without that spin there would be no upthrust.

Thus the upthrust is axial to the blades.

That's all fine and dandy, but the main rotor is spinning - say clockwise.

There is therefore an anticlockwise reaction moment on the helicopter body.

This must be opposed by something providing a clockwise moment on the helicopter body.

This clockwise moment is provided by the much smaller tail rotor which spins in a vertical plane.

So the axial thrust it develops is horizontal.
Multiplied by the long tail length as lever arm this provides the resisting moment keeping the helicopter body from spinning.

Obviously the helicopter motor needs to also power this second rotor, which is your missing power.

Does this help without a diagram.
You should be able to draw one of your own from my description.

Edit I have managed to make a quick sketch of this.
Attached Thumbnails
Rotor and power of engine-hcopter1.jpg  

Last edited by studiot; Jul 28th 2018 at 11:52 AM.
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Old Jul 28th 2018, 10:38 PM   #3
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Originally Posted by Masaru View Post
. Calculate the potential energy gain of the helicopter,....... State a form of kinetic energy that has been ignored in this model. [/I]

The question seems to want you to indicate where there is a change in kinetic energy from when the helicopter is on the ground to when it is 170 m up...

Well ... where is there kinetic energy ??? there is some in the rotor ...

But it's not at all guaranteed that the speed of the rotor has changed .

The rotor can be spinning very fast on the ground , but may generate no lift until the pitch of the blades is changed, when this is done we have lift , the blades will tend to slow , but the engine may deliver more power to keep them fast....

So we do not know if the rotor is spinning faster of slower at 170m. or if it's changed at all.
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Old Jul 28th 2018, 11:58 PM   #4
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Smile Thank you so much.

Thank you for your explanation with illustration, which really helped me to understand what was missing in my attempt to make sense of the answer provided in the textbook.

I did not even know that there is such a thing as "tail rotor" on helicopter!

Yes, you are right. The engine requires the power to keep the helicopter's tail rotor moving on top of the power to lift up its body so that it will not keep going around and around rotating up in the air!


Thank you very much.
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