Air Resistance: Exploring Hooke's Law

[Gustavo Reis]

TL;DR Summary

Today during my class I had this idea and I would like to know your opinion.

Basically the air works like a spring, it always tries to get back to its resting state. And it's like Hooke's law, the more it deforms the more elastic potential energy it has. That's why the faster you are, the air resistance is greater. Thinking in this way, I imagine that in fluid mechanics the particles on the top of an airplane wing will travel faster than those on the bottom because they have suffered a greater deformation. I asked some people and no one could explain it to me, so I would like to know your opinion. And I'm Brazilian, so forgive me for my English, and I'm here to try to explain if anything sounded weird.

 

[Baluncore]

Welcome to PF.

Probably not a useful analogy. Your statement is too general to be useful. Keep the concepts separate.

Potential energy is stored when compressing a gas or a spring, but;
When you compress a spring, the force is linear with length, Hook's Law.
When you compress air with a piston in a cylinder, the pressure rises slowly at first, then approaches infinity as the volume approaches zero and the air gets hot.

Many low-speed fluid dynamics problems can assume that air is an incompressible fluid, like a liquid. Air resistance is the force needed to move a mass of air, out of the way of a moving object, no compression need be considered.

 

[snorkack]

Potential energy is stored when compressing a gas or a spring, but;
When you compress a spring, the force is linear with length, Hook's Law.
When you compress air with a piston in a cylinder, the pressure rises slowly at first, then approaches infinity as the volume approaches zero and the air gets hot.

When you try compressing a spring to zero length, Hooke´s law will also break down... you cannot compress a spring to zero volume, you will face infinite force. And to the contrary. When your cylinder´s deformation is a small fraction of total volume, the force will also be linear.
Note that when you sit on the airbag, initially the air is compressed and warms up. Once you sit on it with constant force, the airbag will slowly cool down and contract... but not to zero volume. (Unless your body is heating the airbag above the ambient temperature). And when you get up, the airbag will cool down to below ambient, and will not resume its initial volume.
But solid springs also usually change their temperature on compression... in either direction. Especially rubber springs.

Many low-speed fluid dynamics problems can assume that air is an incompressible fluid, like a liquid. Air resistance is the force needed to move a mass of air, out of the way of a moving object, no compression need be considered.

And that´s the key evidence. Air in a confined airbag indeed behaves like a spring, but when air is free to flow out and around, its compressibility is a minor contributor to resistance and lift. That will change when you approach speed of sound.

 

[Baluncore]

Probably not a useful analogy. Your statement is too general to be useful. Keep the concepts separate.

@snorkack Do you disagree with this also ?

 

[snorkack]

@snorkack Do you disagree with this also ?

I think that concepts should be kept distinct but analyzed for precisely where the similarities and differences lie.
The difference between air and a spring is not Hooke´s law (air also obeys it at low pressures, spring also gets nonlinear at large deformation, to infinite force at zero volume), nor heating (spring also changes temperature, air still resists compression when allowed to cool). The real difference is that air, like liquids, escapes sidewards unless held in place, but the spring holds itself in place.
So when air is not confined and also not moving at near-sonic speed, it behaves like a liquid, not like a spring.

 

[Baluncore]

... (spring also changes temperature, air still resists compression when allowed to cool) ...

All air is heated by compression, only cheap inefficient springs are heated.

An elastic band heats when stretched, then cools when released. Air is the opposite.
https://en.wikipedia.org/wiki/Rubber_band#Thermodynamics

The real difference is that air, like liquids, escapes sidewards unless held in place, but the spring holds itself in place.

Your argument is desperately hilarious.

 

[PeroK]

TL;DR Summary: Today during my class I had this idea and I would like to know your opinion.

Basically the air works like a spring,

I'm struggling to see that air is anything like a spring.

 

[russ_watters]

I'm struggling to see that air is anything like a spring.

All air is heated by compression, only cheap inefficient springs are heated.

+2; yeah, in my opinion that's a pretty big/important difference.

 

[Drakkith]

Basically the air works like a spring, it always tries to get back to its resting state. And it's like Hooke's law, the more it deforms the more elastic potential energy it has. That's why the faster you are, the air resistance is greater.

A 'spring' is usually regarded as a specific mechanical 'thing' or device whose purpose is to store energy and/or exert a force proportional to the displacement of some part of it. In this sense air can be used as a spring, as in the case of shock absorbers and gas springs. However, while free air can be compressed by an airfoil moving through it, saying that air is 'like a spring' is a description that, at best, poorly describes how airfoils work.

Yes, free-flowing air is 'like a spring' in the sense that it can be compressed, and this compression results in a pressure differential that can exert a force on something, but to say that the air flowing around an airfoil does so in its specific way because the air is 'like a spring' is a gross simplification that obscures much of the fundamental reasons why lift is generated.

Thinking in this way, I imagine that in fluid mechanics the particles on the top of an airplane wing will travel faster than those on the bottom because they have suffered a greater deformation.

No, that's not correct. Let's replace 'deformation' with 'compression' since deformation applies more to rigid bodies and not fluids. The air on the underside of the wing is actually more compressed than the top since it is slamming into the wing's lower surface, while the air going over the top is less compressed, flows at a faster rate, and generates a pocket of low pressure that helps generate lift when combined with the high pressure underside.

The underlying reason why the topside air flows faster is a bit beyond my understanding. My best guess is that it's because the topside air is moving from an area of higher pressure in front of the wing (where it may have been compressed) into a region of lower pressure above and behind the wing's upper surface, where the airfoil is leaving behind a slight 'void' by moving the air out of the way as it passes. Then throw in some other things like the difference in velocity between the streamline next to the skin of the topside airfoil and the streamlines just above that one...Bernoulli's principle or something... and in the end you wind up with a low pressure pocket above the wing. I think. That's mostly me piecing different things together from various things I've read.

Here's a couple of links that I've looked at.
http://warp.povusers.org/grrr/airfoilmyth.html
https://en.wikipedia.org/wiki/Lift_(force)
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/foilw1/ (interactive airfoil simulator on this page)

 

[Lnewqban]

 

[Lnewqban]

That's why the faster you are, the air resistance is greater.

Welcome, Gustavo !

I would say that it is the inertia of the molecules of air what offers resistance to any perturbation, rather than the capability of a group of molecules to be compressed or expanded.

Yes, you could use air to work as a metal spring.
The two problems are:
1) Increase in temperature as air is compressed (air compressors need some cooling device). As temperature increases, so those the specific volume and pressure.
2) Condensation of humidity contained in the pre-compressed air (tanks of air compressors need a drain at the bottom, and delivered compressed air needs a water separator).
Where possible, dry inert gasses are used in closed pneumatic systems as the one shown in the previously posted video.

Regarding a wing, according to your reasoning, the top airstream should be resisting and pushing down the wing harder than the less deformed bottom airstream pushes it up.

Actually, the top airstream is sucking the wing up, as any pressure distribution diagram shows.

The shape of the leading edge of the wing is very important to achieve that, reason for which lift enhancers (slots, turbuletors, etc.) and de-icing devices are mainly located there.

 

[Mister T]

Springs and air each have an elasticity. If you deform them correctly, they will try to return to their original shape. They share that qualitative property, but the quantitative properties are different.

Look up, for example, Young's modulus versus bulk modulus.

 

[PeroK]

Springs and air each have an elasticity.

Both a climbing rope and air have elasticity. But, few rock climbers would claim that "air is like a climbing rope"!

 

[JT Smith]

It's more like: "Because of air I like a climbing rope."