Airplane propeller and plane's velocity relative to the ground.

In summary, the speed of a point on the tip of an airplane's propeller, at radius 1.5 m, is 345.57 m/s as seen by the pilot and as seen by an observer on the ground. This is found by using the equation v = w * r * sin delta, where w is the rotational velocity of the propeller and delta is the angle between the plane's velocity and the propeller's axis of rotation. To find the speed as seen by the pilot, the rotational velocity must first be converted from 2200 rev/min to m/s. To find the speed as seen by an observer on the ground, the magnitude of the resultant velocity must be found using Pythagorean's theorem.
  • #1
rosstheboss23
37
0
[SOLVED] Airplane propeller and plane's velocity relative to the ground.

Homework Statement


An airplane propeller rotates at 2200 rev/min while the airplane flies at a speed of 550 km/h relative to the ground. The plane's velocity is parallel to the propeller's axis of rotation.
Part a) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by the pilot?

Part b) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by an observer on the ground?

Homework Equations


v=w times r
v=w times r times sin delta



The Attempt at a Solution


I got part a asking speed relative to pilot by converting 2200rev/min to m/s, but part b has me stuck...I don't know if I am missing an equation that I could possibly use but I tried to convert the speed relative to ground to m/s and add it to the 345.57m/s I got as the answer for part a.
 
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  • #2
rosstheboss23 said:

Homework Statement


An airplane propeller rotates at 2200 rev/min while the airplane flies at a speed of 550 km/h relative to the ground. The plane's velocity is parallel to the propeller's axis of rotation.
Part a) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by the pilot?

Part b) What is the speed of a point on the tip of the propeller, at radius 1.5 m, as seen by an observer on the ground?

Homework Equations


v=w times r
v=w times r times sin delta

The Attempt at a Solution


I got part a asking speed relative to pilot by converting 2200rev/min to m/s, but part b has me stuck...I don't know if I am missing an equation that I could possibly use but I tried to convert the speed relative to ground to m/s and add it to the 345.57m/s I got as the answer for part a.
Notice that the linear velocity of the propeller tip is perpendicular to the velocity of the plane.
 
  • #3
Remembering that how would I relate 550km/hr to the speed seen by the pilot that is what has me confused. It should form a 90 degree angle and be the same as I calculated in a, but that doesn't work...I tried v= w times r times sin delta and it didn't work.
 
  • #4
rosstheboss23 said:
Remembering that how would I relate 550km/hr to the speed seen by the pilot that is what has me confused. It should form a 90 degree angle and be the same as I calculated in a, but that doesn't work...I tried v= w times r times sin delta and it didn't work.
The speed is the magnitude of the resultant velocity. How do you normally find the magnitude of two perpendicular vectors?
 
  • #5
Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.
 
  • #6
rosstheboss23 said:
Oh...now I understand this. I would use pythagorean's theorem to get the resultant velocity. Thanks I appreciate your help.
Correct! No problem :smile:
 

1. How does an airplane propeller work?

An airplane propeller works by converting the engine's power into thrust, which propels the plane forward. The propeller blades are angled in a way that creates a pressure difference, pulling the plane forward as the blades rotate.

2. How does the speed of an airplane affect the propeller's performance?

The speed of an airplane directly affects the propeller's performance. As the plane's speed increases, the propeller needs to rotate faster to maintain the necessary pressure difference and generate enough thrust. However, if the propeller rotates too quickly, it can create drag and decrease the plane's overall efficiency.

3. What factors determine a plane's velocity relative to the ground?

The velocity of an airplane relative to the ground is determined by several factors, including the speed and direction of the wind, the angle of the plane's flight path, and the speed and direction of the plane's engines. These factors all work together to affect the plane's overall velocity relative to the ground.

4. Why does a plane's velocity relative to the ground differ from its airspeed?

A plane's airspeed is the speed at which it is moving through the air. However, due to the wind and other factors, the plane's velocity relative to the ground may be different. For example, if a plane is flying against a headwind, its airspeed may be lower, but its velocity relative to the ground will still be high.

5. How does the angle of the propeller blades affect the plane's velocity?

The angle of the propeller blades, also known as the pitch, can significantly impact the plane's velocity. A steeper pitch will generate more thrust but can also create more drag, while a shallower pitch will result in less thrust but also less drag. The angle of the blades is carefully designed to balance these factors and optimize the plane's overall performance.

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