Propeller Problem

  • Thread starter Kenchin
  • Start date
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1590Nm to the propeller, which starts from rest.

Question I:
What is the average power output of the engine during the first 5.00 rev?

Question II:
What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 rev?


I've already solved for the angular accelleration (after 5 revolutions) which is alpha, angular speed omega (after 5 revolutions), and work after 5 revolutions W, moment of inertia 42.18kg*m^2.

For the last two parts I've tried to solve using P=torque+angular velocity .... that turned out to be wrong. Then I tried using P=Change in work/change in time but that failed. So now I'm a little at a loss. Is there any suggestions where to try next?:cool:

I figured it out, my methods were correct...... my ending units were wrong! @_@
 
Last edited:

Andrew Mason

Science Advisor
Homework Helper
7,472
274
Kenchin said:
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1590Nm to the propeller, which starts from rest.

Question I:
What is the average power output of the engine during the first 5.00 rev?

Question II:
What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 rev?


I've already solved for the angular accelleration (after 5 revolutions) which is alpha, angular speed omega (after 5 revolutions), and work after 5 revolutions W, moment of inertia 42.18kg*m^2.

For the last two parts I've tried to solve using P=torque+angular velocity .... that turned out to be wrong. Then I tried using P=Change in work/change in time but that failed. So now I'm a little at a loss. Is there any suggestions where to try next?:cool:

I figured it out, my methods were correct...... my ending units were wrong! @_@
Energy is torque x angle (force x distance).

[tex]\tau\Delta\theta = \text{Work}[/tex]

So [tex]P_{avg} = \Delta E/\Delta t = \tau\Delta\theta/\Delta t[/tex]

All you have to do is figure out how long it takes to move the propeller 5 revolutions with that torque: Use [itex]\theta = \frac{1}{2}\alpha t^2[/itex] and [itex]\alpha = \tau/I[/itex] to find the time in terms of angle and torque (and I).

To find instantaneous power, use:

[tex]P = \tau\omega = \tau\alpha\Delta t[/tex]

You have to assume that in the first 5 revolutions, the resistance to motion is only the moment of inertia of the propeller, not the propulsion of air by the propeller.

AM
 

Want to reply to this thread?

"Propeller Problem" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top