How does hovering and constant climbing differ?

[day_nite]

Hi, quick basic question.

Alright let's say I have a little drone with rotors that only allow the drone to move up and down (in the y-direction). I need help differentiating between these two situations:
1.) I want the drone to start on the ground, accelerate upwards (to a certain velocity), then hover.
2.) I want the drone to start on the ground, accelerate upwards (to a certain velocity), then continue moving upwards at that constant velocity.

Now, simple Newtonian Physics would tell me that in either of these situations, the lift force will have to be greater than the force of gravity to accelerate the drone upwards. Also in both situations, a balance of forces is needed to hover and move with constant velocity. The problem I'm having is that I don't know how to make the drone hover vs continue upwards with constant velocity. I get that I accelerate up, then (once reaching my certain velocity) match F,lift and F,gravity but I don't now if that's supposed to make me hover or continue moving up with constant velocity.

How would I differentiate/achieve both situations?

 

[PeterDonis]

1.) I want the drone to start on the ground, accelerate upwards (to a certain velocity), then hover.
2.) I want the drone to start on the ground, accelerate upwards (to a certain velocity), then continue moving upwards at that constant velocity.

There is a difference between these two scenarios: they are identical up to a point, and then scenario #1 does something different (whereas scenario #2 keeps doing the same thing). Can you see what that is?

(Note: it helps if you imagine that you have to move upwards at the constant velocity for a short time after reaching it, in both scenarios.)

 

[day_nite]

Well both involve reaching a net force of 0, that is for certain. I am not 100% certain if I can see the difference, but if I had to guess; Id say in scenario 1 the drone would decelerate (from the "certain velocity" to 0), so that the velocity (momentarily) reaches 0, then apply the F,lift to equal F,gravity which results in it hovering. On the other hand, scenario 2 would involve just instantaneously applying a net force of 0 (f,lift=f,gravity) to continue moving the drone upwards at constant velocity.

Right?

 

[PeterDonis]

in scenario 1 the drone would decelerate (from the "certain velocity" to 0), so that the velocity (momentarily) reaches 0, then apply the F,lift to equal F,gravity which results in it hovering

How would you make the drone decelerate? Or, taking a step back: what are the forces on the drone while it is moving upward at a constant velocity? (Note that "constant velocity" means its acceleration is zero.

scenario 2 would involve just instantaneously applying a net force of 0 (f,lift=f,gravity) to continue moving the drone upwards at constant velocity.

"Instantaneously applying"? If you're just continuing to move the drone upwards at constant velocity, then what had to change?

 

[day_nite]

To achieve this drone deceleration, I would decrease F,lift such that it what less than F,gravity. Thus there would be a net downwards force and a decreasing change in the velocity . Then once velocity decreases to 0, I would increase f,lift such that it is equal to f,gravity so that net forces = 0.

F,lift>mg (Drone up - a>0)
F,lift<mg (drone slows down - a<0)
F,lift=mg (Drone hover - a=0)

in scenario 2, F,lift is initially greater then F,gravity which results in the drone accelerating upwards. Then once I want the drone to continues upwards at constant velocity, I would decrease F,lift such that it equals F,gravity. which means no acceleration or change in velocity.

When i said "instantaneously apply net force of 0, i meant that F,lift would decrease to equal F,gravity

F,lift>mg (Drone up - a>0)
F,lift=mg (Drone up at const vel - a=0)

I hope this is right.

 

[PeterDonis]

I hope this is right.

Yes, you've got it.

 

[sophiecentaur]

match F,lift and F,gravity

If you are concerned with battery life, wouldn't you need to consider the drag factor too? This is not an abstract problem of an ideal ride in an ideal elevator. Moving through the air (upwards) involves work so the vertical force would need to be greater than the weight force alone. Whether or not this is relevant in practice would depend on the actual climb rate.

 

[jbriggs444]

If you are concerned with battery life, wouldn't you need to consider the drag factor too? This is not an abstract problem of an ideal ride in an ideal elevator. Moving through the air (upwards) involves work so the vertical force would need to be greater than the weight force alone.

Induced drag is a problem even for hovering. The wing span is not infinite, so there will be an induced down-draft.

 

[sophiecentaur]

Induced drag is a problem even for hovering. The wing span is not infinite, so there will be an induced down-draft.

Now you mention it, it's hardly surprising is it? So are we real or ideal in this thread? (Question for the OP, I think)