Paper 'helicopter' experiment - Adding Weight Decreases Flight Time?

[Mahid]

Homework Statement

How does adding more paper clips (adding more weight) to the base of a paper helicopter (whirlybird) increase the rate at which it falls?

Relevant Equations

Idk any formulas I'm new to physics

Is the speed at which the paper helicopter falls due to its increased weight because gravity is stronger, or is it because air resistance is unable to keep it in the air because the weight is stronger than air resistance?

 

[haruspex]

is it because air resistance is unable to keep it in the air because the weight is stronger than air resistance?

Air resistance doesn’t keep things in the air (i.e. make them float). What does it do?

 

[Mahid]

Idk, but from my understanding, air resistance is like an opposing force when an object collides with air particles

 

[jbriggs444]

Idk, but from my understanding, air resistance is like an opposing force when an object collides with air particles

The "collisions" explanation is over-simplified. For instance, it would not explain Bernoulli. But we need not belabor that point.

More important is that air resistance increases with air speed. Perhaps your class material has touched upon the concept of "terminal velocity".

 

[kuruman]

Idk, but from my understanding, air resistance is like an opposing force when an object collides with air particles

Your understanding is OK. Now see if you can take it farther by using reasoning. You have two forces acting on the helicopter in opposite directions. Gravity is down and air resistance is up.
Please consider answering the following questions.

1. Can the force of gravity be larger in magnitude than air resistance? What would happen in that case?
2. Can the force of gravity have equal magnitude to air resistance? What would happen in that case?
3. Can the force of gravity be smaller magnitude than air resistance? What would happen in that case?

 

[haruspex]

Idk, but from my understanding, air resistance is like an opposing force when an object collides with air particles

Objects exposed to the air have collisions with air particles, all over the surface, all the time. Can you be more specific about the circumstance in which air resistance arises and the direction in which the force acts?
My detailed questions might seem tedious , but I feel sure you know the answers, with a bit of thought, and that in putting your answers together you will find you could have answered the question.

 

[Mahid]

The "collisions" explanation is over-simplified. For instance, it would not explain Bernoulli. But we need not belabor that point.

More important is that air resistance increases with air speed. Perhaps your class material has touched upon the concept of "terminal velocity".

We haven't touched base on terminal velocity yet, but I know that terminal velocity is the maximum speed an object can fall.

 

[Mahid]

Your understanding is OK. Now see if you can take it farther by using reasoning. You have two forces acting on the helicopter in opposite directions. Gravity is down and air resistance is up.
Please consider answering the following questions.

1. Can the force of gravity be larger in magnitude than air resistance? What would happen in that case?
2. Can the force of gravity have equal magnitude to air resistance? What would happen in that case?
3. Can the force of gravity be smaller magnitude than air resistance? What would happen in that case?

1. If gravity is larger in magnitude than air resistance, I'm guessing that an object would fall at its terminal velocity because the force opposing gravity (air resistance) is less.
2. I'm stuck on this question. Does the object slowly accelerate? It can't stay stagnant in one place, or move upward, so it has to go down.
3. I'm assuming that air resistance would allow the object to fall slower.

 

[Mahid]

Objects exposed to the air have collisions with air particles, all over the surface, all the time. Can you be more specific about the circumstance in which air resistance arises and the direction in which the force acts?
My detailed questions might seem tedious , but I feel sure you know the answers, with a bit of thought, and that in putting your answers together you will find you could have answered the question.

My original question was how adding weight to my paper helicopter made it fall faster because the only thing that changed was the weight and the design was kept the same.

Air resistance is what makes the paper helicopter fall slowly in the first place because as gravity pulls the helicopter down, air resistance opposes it in an upward direction. When you add weight to the paper helicopter, air resistance does not decrease because it's the same paper helicopter (no design changes, no material changes) and I don't think gravity increases (or maybe it does because the more mass an object has the more gravitational pull it has)

 

[haruspex]

Air resistance is what makes the paper helicopter fall slowly in the first place because as gravity pulls the helicopter down, air resistance opposes it in an upward direction.

Right.

When you add weight to the paper helicopter, air resistance does not decrease

Air resistance when falling at the same speed doesn’t change, but it won’t be falling at the same speed.

I don't think gravity increases (or maybe it does because the more mass an object has the more gravitational pull it has)

Yes, the weight is increased, and that is key. But so has the inertial mass.
You have identified the two vertical forces. How, roughly, does each depend on mass, speed and shape?

 

[kuruman]

1. If gravity is larger in magnitude than air resistance, I'm guessing that an object would fall at its terminal velocity because the force opposing gravity (air resistance) is less.
2. I'm stuck on this question. Does the object slowly accelerate? It can't stay stagnant in one place, or move upward, so it has to go down.
3. I'm assuming that air resistance would allow the object to fall slower.

It looks like you have an incomplete understanding of Newton's laws and that you are confusing velocity with acceleration. This is not uncommon, but needs fixing.

Let's take your answer to 1 first. You brought in the idea of terminal velocity. Terminal velocity is the constant velocity that the helicopter achieves after falling through air for some time. You say that the helicopter is falling at its terminal velocity when gravity down is larger that air resistance up.
Question 1a: Does the helicopter accelerate? Please explain your answer in terms of Newton's second law that says Net force = mass × acceleration.

Note that it's really easy to write down and memorize the second law but understanding what it's really saying and how to use it is another matter. Eventually you will answer your own original question. Question 1a is a step that will get you there. Here are some that you might find useful:

1. The net force is the sum of all the forces such that forces pointing up have a $+$ sign in front of them and forces pointing down have a $-$ sign in front of them. Here, one would write
Net force = (- Weight) + (Air resistance)
2. Acceleration is the rate of change of velocity and always points in the direction of the net force.

 

[Mahid]

It looks like you have an incomplete understanding of Newton's laws and that you are confusing velocity with acceleration. This is not uncommon, but needs fixing.

Let's take your answer to 1 first. You brought in the idea of terminal velocity. Terminal velocity is the constant velocity that the helicopter achieves after falling through air for some time. You say that the helicopter is falling at its terminal velocity when gravity down is larger that air resistance up.
Question 1a: Does the helicopter accelerate? Please explain your answer in terms of Newton's second law that says Net force = mass × acceleration.

Note that it's really easy to write down and memorize the second law but understanding what it's really saying and how to use it is another matter. Eventually you will answer your own original question. Question 1a is a step that will get you there. Here are some that you might find useful:

1. The net force is the sum of all the forces such that forces pointing up have a $+$ sign in front of them and forces pointing down have a $-$ sign in front of them. Here, one would write
Net force = (- Weight) + (Air resistance)
2. Acceleration is the rate of change of velocity and always points in the direction of the net force.

1a. I understand now, that if gravity is larger in magnitude than air resistance, the object will keep accelerating. Newton's second law says Net force = mass × acceleration, so if acceleration increases, the net force will also increase.

Also, terminal velocity is a constant which means it doesn't change (doesn't accelerate or decelerate) so that means Net Force = Mass x 0 (because acceleration is zero and acceleration is the change of velocity as you said, and since it is not changing, it should be 0) So when an object is at it's terminal velocity, Net Force = 0.

 

[haruspex]

Just to note that in practice things are a bit more complicated. Adding weight in the right way can increase the flight time of a paper plane.
First, it means that when you throw it you give it more momentum, helping it maintain its forward speed against drag. More forward speed means more lift.
Secondly, it can improve the balance, avoiding rising too steeply and stalling.

 

[Mahid]

Right.

Air resistance when falling at the same speed doesn’t change, but it won’t be falling at the same speed.

Yes, the weight is increased, and that is key. But so has the inertial mass.
You have identified the two vertical forces. How, roughly, does each depend on mass, speed and shape?

So as the speed of an object increases, air resistance increases? This would explain why my paper helicopter would fall for a bit, but as its fall speed increases, it would slow down and spin.

 

[Mahid]

Okay, so in my experiment, when I dropped my paper helicopter, I only measured its flight time (How long it stayed in the air from the moment I dropped it and the moment it landed) When I added more paper clips, the paper helicopter's air time would decrease, and I thought because it was falling faster. The paper helicopter has two "phases" while it's falling. The first phase is the moment where I dropped it, it would accelerate, and phase two where the paper helicopter would be at a constant falling speed as it was spinning. As I added more paper clips (weight to the paper helicopter) it would stay in phase one for a bit longer

 

[Mahid]

Just to note that in practice things are a bit more complicated. Adding weight in the right way can increase the flight time of a paper plane.
First, it means that when you throw it you give it more momentum, helping it maintain its forward speed against drag. More forward speed means more lift.
Secondly, it can improve the balance, avoiding rising too steeply and stalling.

yeah I attached my paper clips to the bottommost part of the base

 

[jbriggs444]

So as the speed of an object increases, air resistance increases?

Yes.

 

[Lnewqban]

So as the speed of an object increases, air resistance increases? This would explain why my paper helicopter would fall for a bit, but as its fall speed increases, it would slow down and spin.

As the speed of a falling object increases, the vertical air resistance or friction drag increases to the square.

In the case of our toy, the rate of rotation simultaneously increases, which is an additional horizontal-rotating drag work in which gravity has to expend extra time and energy.

Without a rotation being induced by the shape and twist of the “propeller”, our toy would fall faster.

When conditions change (greater weight in this case), there is a transition time before a state of equilibrium of forces is naturally reached.

Please, see:
https://en.m.wikipedia.org/wiki/Autorotation

 

[haruspex]

which is an additional horizontal-rotating drag work in which gravity has to expend extra time and energy.

It is far from clear that that would result in extra drag. Why would it not simply be that the energy consumed by the drag takes a different path, spending part of the time as KE?
E.g. we could make a parachute then add angled vents through the canopy to make it spin. I don’t think that would make it fall more slowly.
As I understand it, a helicopter pilot executing autorotation sets the blades to have negative pitch so that the passage of air up between the blades keeps them rotating forwards. Since they have aerofoil cross section, this continues to generate lift.

 

[Lnewqban]

It is far from clear that that would result in extra drag.

I don't fully understand the reason, but it is known in the world of airplanes that a wind-milling propeller induces higher rearward drag than the same propeller in a dead stick condition or emergency landing.

Please, see:
https://www.peter2000.co.uk/aviation/misc/prop.pdf

 

[haruspex]

I don't fully understand the reason, but it is known in the world of airplanes that a wind-milling propeller induces higher rearward drag than the same propeller in a dead stick condition or emergency landing.

Please, see:
https://www.peter2000.co.uk/aviation/misc/prop.pdf

I don’t dispute that it does increase vertical drag. I can even suggest why: rotating blades interact with more air; if not rotating, most of the air beneath the aircraft would miss the blades, little affected by them.
My objection was to the hand-waving "an additional horizontal-rotating drag work in which gravity has to expend extra time and energy" explanation.

Note that the link you posted is for an airplane, not a helicopter, so the extra drag from the rotation of the blades is vertical in this thread, not horizontal.