# Is there a terminal velocity upwards?

• Storm Savage
In summary: I've always found the more subtle case is the automobile with constant rolling resistance and fixed horsepower that reaches terminal speed.
Storm Savage
We are all familiar with the concept of terminal velocity due to air friction in the direction towards the earth, but what about the other direction? Given enough applied force, is it possible to experience a terminal velocity upwards?

Let's say you take a toy balloon, fill it with helium, and let it go. It will accelerate for a while due to the buoyant force, but soon enough it will reach a constant rate of ascent. That's its terminal velocity equivalent. I.e. there is an approximately constant force acting upwards, that is counteracted by drag until they add up to zero.

In the horizontal direction, the maximum speed of an aeroplane is a similar concept.

Klystron, RPinPA, Delta2 and 2 others
Storm Savage said:
Given enough applied force, is it possible to experience a terminal velocity upwards?
Do you mean a rocket with continuously applied thrust? It is possible for weight and drag balance the thrust, but that's not what you usually want in space flight. Also if you escape towards infinity, then you also approach a constant final velocity.

Storm Savage
A.T. said:
Do you mean a rocket with continuously applied thrust? It is possible for weight and drag balance the thrust, but that's not what you usually want in space flight. Also if you escape towards infinity, then you also approach a constant final velocity.
That's what I was imagining, that a rocket with enough thrust would be inefficient, although given the distance to space I assume this wouldn't be a concern.

Storm Savage said:
That's what I was imagining, that a rocket with enough thrust would be inefficient, although given the distance to space I assume this wouldn't be a concern.
If you you want to go into orbit you need to gain speed, so raising at const speed would be very inefficient. See also:
https://en.wikipedia.org/wiki/Gravity_drag

Storm Savage said:
We are all familiar with the concept of terminal velocity due to air friction in the direction towards the earth, but what about the other direction? Given enough applied force, is it possible to experience a terminal velocity upwards?
A falling object experiences acceleration downwards due to gravity. Resistance will impose a terminal velocity. If the vertical acceleration upwards is positive (i.e. the net acceleration of engine minus gravity) then exactly the same effect of terminal velocity effect can will apply if the journey is long enough and the air resistance doesn't get less due to practicalities such as a thinning atmosphere.

F=ma

Anything not accelerating has a net force of zero acting on it. Terminal velocity of a falling object is just an example situation where the drag force equals weight.

There are many other examples and some have already been mentioned.

Here is a rotary example...

Consider a typical DC permanent magnet motor, as found in many toys. When connected to a battery it will accelerate until it reaches some maximum rpm. At that rpm the net force on the armature is zero. If it wasn't it would accelerate.

CWatters said:
Consider a typical DC permanent magnet motor, as found in many toys. When connected to a battery it will accelerate until it reaches some maximum rpm
Unfortunately, the situation is not as straightforward for an electric motor. The rotating armature induces a 'back emf' which means the current and hence the torque drops with increasing rotational speed. That's in addition to the limit that would be imposed by resistive forces.

Storm Savage said:
That's what I was imagining, that a rocket with enough thrust would be inefficient, although given the distance to space I assume this wouldn't be a concern.
As I understand it some rockets deliberately limit there initial velocity to keep aerodynamic drag forces within limits. They then accelerate once high enough that the air density has reduced. I might be wrong but I thinks that what they are doing when you hear/heard "go with throttle up" during a space shuttle launch.

sophiecentaur said:
Unfortunately, the situation is not as straightforward for an electric motor. The rotating armature induces a 'back emf' which means the current and hence the torque drops with increasing rotational speed. That's in addition to the limit that would be imposed by resistive forces.
+1

That's why I said net force on the armature.

CWatters said:
+1

That's why I said net force on the armature.
That's very true but would the questioner get the message from such a condensed / sophisticated explanation? I know you know and you know I know you know .

Klystron and CWatters
sophiecentaur said:
That's very true but would the questioner get the message from such a condensed / sophisticated explanation? I know you know and you know I know you know .
I've always found the more subtle case is the automobile with constant rolling resistance and fixed horsepower that reaches terminal speed. Not complicated but sometimes befuddling

CWatters said:
As I understand it some rockets deliberately limit there initial velocity to keep aerodynamic drag forces within limits.
Is this done to increase efficiency, or rather to avoid structural problems?

A.T. said:
Is this done to increase efficiency, or rather to avoid structural problems?

https://aerospace.honeywell.com/en/blogs/2016/april/flight--we-are-go-for-throttle-up

"During every launch of NASA’s Space Shuttle, an important radio call transmitted from Mission Control Houston - “go for throttle up”, noting that it was safe for the Space Shuttle Main Engines to be throttled back up to full power. The throttling of these engines was a critical feature that kept the maximum dynamic pressure on the vehicle within acceptable limits."

More detailed explanation here..

https://www.whitewingcrow.com/2012/06/20/go-at-throttle-up/

CWatters said:

https://aerospace.honeywell.com/en/blogs/2016/april/flight--we-are-go-for-throttle-up

"During every launch of NASA’s Space Shuttle, an important radio call transmitted from Mission Control Houston - “go for throttle up”, noting that it was safe for the Space Shuttle Main Engines to be throttled back up to full power. The throttling of these engines was a critical feature that kept the maximum dynamic pressure on the vehicle within acceptable limits."

More detailed explanation here..

https://www.whitewingcrow.com/2012/06/20/go-at-throttle-up/
Thanks, for looking it up. I assumed it would be structural, because efficiency-wise the reduction in drag shouldn't offset the longer acting gravity drag for a slower ascent.

CWatters said:
Aka "max q":
During a normal Space Shuttle launch, for example, max q occurred at an altitude of approximately 11 km (35,000 ft).[1] The three Space Shuttle Main Engines were throttled back to about 60-70% of their rated thrust (depending on payload) as the dynamic pressure approached max q;[2] combined with the propellant perforation design of the solid rocket boosters, which reduced the thrust at max q by one third after 50 seconds of burn, the total stresses on the vehicle were kept to a safe level.
https://en.m.wikipedia.org/wiki/Max_q

Storm Savage said:
We are all familiar with the concept of terminal velocity due to air friction in the direction towards the earth, but what about the other direction? Given enough applied force, is it possible to experience a terminal velocity upwards?
Strictly speaking, the term "terminal velocity" refers only to falling through an atmosphere in gravity. However, this is only a special case of basically every constant speed motion against variable/speed dependent opposing forces. So there are lots of similar examples.

What's called terminal velocity is is a special case in which it's assumed that there's no other downward force than gravity to overcome air resistance. Please imagine a person falling at terminal velocity shooting an arrow from a bow toward the ground below. The downward velocity of the arrow will exceed the terminal velocity of the archer -- there's a force other than gravity in the mix -- just as there is when an object travels upward. In order to determine terminal velocity, downward, upward or in whichever direction, you have to take into account each force in each direction.

Storm Savage said:
We are all familiar with the concept of terminal velocity due to air friction in the direction towards the earth, but what about the other direction? Given enough applied force, is it possible to experience a terminal velocity upwards?

Air bubbles in a glass of fizzy drink.

Zz.

CWatters
Storm Savage said:
We are all familiar with the concept of terminal velocity due to air friction in the direction towards the earth, but what about the other direction? Given enough applied force, is it possible to experience a terminal velocity upwards?

yes. terminal velocity is when a driving force is in equilibrium with the drag force. the faster an abject goes in the atmosphere, the more air resistance it experiences. if the rocket engine can only reach a certain thrust, the air resistance may push back at the same thrust preventing acceleration. no acceleration means constant velocity.

## 1. What is terminal velocity upwards?

Terminal velocity upwards refers to the maximum speed that an object can reach when moving upwards against air resistance. It is the point at which the force of gravity pulling the object down is equal to the force of air resistance pushing the object up.

## 2. Is there a limit to how fast something can go upwards?

Yes, there is a limit to how fast something can go upwards. This limit is known as terminal velocity upwards and is determined by the object's mass, surface area, and the density and viscosity of the surrounding air.

## 3. How is terminal velocity upwards calculated?

Terminal velocity upwards can be calculated using the equation Vt = √(2mg/ρAC), where Vt is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the air, A is the cross-sectional area of the object, and C is the drag coefficient.

## 4. Can an object exceed terminal velocity upwards?

No, an object cannot exceed terminal velocity upwards. Once an object reaches its terminal velocity, the forces acting on it are balanced and it will continue to move at a constant speed without accelerating further.

## 5. How does altitude affect terminal velocity upwards?

Altitude can affect terminal velocity upwards because the density of the air decreases with increasing altitude. This means that at higher altitudes, the air resistance is lower, allowing an object to reach a higher terminal velocity upwards.

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