Talk:Drag (physics)/Archive 1

Merge Drag equation with Drag (physics)
Merge?

Oppose. Two things:

It is a different subject. Fundamental and useful though the drag equation is, it is inapplicable to complete aircraft, ship hulls with wave drag, and just a minute part of what would be general drag article.

I believe that our efforts here are best directed to trying to make articles that are accessible, useful, and accurate. From the history and talk on drag_equation it can be seen that, even with such a narrowly bounded subject, a good deal of work is required to keep it comprehensible. Merging into a vast treatise on drag will not serve other users. Meggar 04:50, 5 March 2006 (UTC)

The phrase "Drag Equation" is ambiguous. Are we talking about drag in a medium like the atmosphere, or a medium more like thick honey? Drag (physics) is hardly a "vast treatise" and would serve to give this equation context and help a reader quickly and easily find related topics - like terminal velocity and drag through a viscous medium.JabberWok 03:21, 7 March 2006 (UTC)
 * Merge
 * Merge --MarSch 15:06, 13 April 2006 (UTC)

Oppose. Does it matter what type of medium we are talking about here? Density can be changed for the type of medium making it applicable to all mediums. It is an extensive topic in its own right. I think it is more fit as a separate article where it can be modified and added to on its own, as merging it would only bring more confusion to it.--Jadian Prime 19:06, 5 May 2006 (UTC)


 * I'm not quite sure what you're talking about? The issue here is whether Drag equation should just be a redirect into Drag (physics). The physics article is more general and already contains all the information found in the drag equation article. JabberWok 21:35, 5 May 2006 (UTC)


 * Merge - however the topic would need some scaling down. I think merging would allow a better discussion of why the equation is inaccurate in many cases - as meggar noted. Fresheneesz 06:24, 30 May 2006 (UTC)


 * Also, a large portion of this page was a simple duplicate of the information on drag equation, and so I removed it - replacing it with a very short suppliment. The information really belongs on one page (here). Fresheneesz 17:16, 30 May 2006 (UTC)


 * Merge completed - I merged the pages, but moved the long derivation to its own page to make this page more concise. Fresheneesz 23:06, 31 May 2006 (UTC)

Unmerged. It works better here to talk and come to consensus. In a paragraph above Jabberwok expressed an opinion that is not correct. The term "drag equation" is not ambigious. A quick Google search shows a lot of articles about this exact equation. The top one on the list is a page from NASA titled "The Drag Equation", of course about just this equation and none other. This is not because the people who wrote it are lacking in knowledge or because it is oversimplified, but because that is unambigusly the long established usage of that phrase. As with wikipedia policy on neologisms, we don't use phrases for what we think they reasonably ought to mean, but as they are actually used. Therefore: The long discription and history about the drag equation belongs in an article titled "Drag equation". A suitably brief reference to it should be part of a general article on drag along with a lot of other approaches to the subject. Meggar 05:12, 15 June 2006 (UTC)

Merge The basic result of a merge would be to reorganize a chaotic mass. Technically, the term drag is only pertaining to fluid dynamics. Physics is the more broad subject, yet to include drag in physics might not be entirely correct. Sadly it is clear that the effort to merge drag with physics is a cover-up to hide the sorry state of our fluid dynamics entries. In time I suppose I will work to amend this. For the time being a merge with physics is most appropo I suppose. This will free up the base wiki for other things like a disambiguation page (slang, races, transvestites etc.) Eventually, once fluids is well developed, drag should join its fellows there.

b vs Cd
I would like to see some discussion about the relationship between b and Cd. Also, it would be very interesting and useful to have more discussion on when the approximations are accurate, and more importantly, when they are not accurate - and why - and what to do in those cases. Fresheneesz 06:51, 30 May 2006 (UTC)

v^4 term
there's a v^4 term and higher even powers of v involved. I would like to see something about this in the entry.

Clarity of v^2 term in drag equation
"Since v is a vector, it isn't entirely clear what v^2 means, since usual matrix multiplication doesn't work. Does the drag equation hold if you use component-wise multiplication to calculate v^2, or do you really mean speed, not velocity?  It would be great if this could be clarified in the article."

Seriously, it is clear that v^2 means speed squared, in the direction of the velocity. Mechanical Rose 06:12, 12 December 2006 (UTC)

Also, I edited the page to say v is "the speed of" the object. Now it is unambiguous and also technically correct. But I really want v to be velocity - maybe we should have |v| in the equation? Mechanical Rose 05:21, 28 March 2007 (UTC)

The problem here is with the standard notion. I checked my textbooks and found that when they are talking about vectors they use $$a \cdot b$$ indicate a dot product. Normally the vectors are indicated by small bold letters. If the context were matrix math they would use ABT. In a vector context the transpose is assumed as nothing else really makes sense. The shortcut v2 is often used for $$\mathbf{v} \cdot \mathbf{v}$$. Now the dot product results in a scalar equal to |v|2 which is exactly what we want in our case. We are however being a little loose with the signs and if we want to retain v as a vector it could causes problems.

Consider our opening equation:[[Media: $$\mathbf{F}_{N}=\mathbf{F}_{W}-\mathbf{F}_{D}$$]]We are talking about forces which are vector quanities. This formula assumes $$\mathbf{F}_N$$ and $$\mathbf{F}_W$$ as being positive in a down direction and $$\mathbf{F}_D$$ in an up directions. This is fine as none of these forces can ever be negative using these directional assumptions. The problem occurs at low Renynolds numbers where Stokes's Drag Equations applies. v appears unsquared so is still a vector. $$\mathbf{F}_D=-b\mathbf{v}$$ This works well as it rightly reports a force being applied in the opposite sense of the velocity. Now if we substitue this into our loose equation above we get: $$\mathbf{F}_N = \mathbf{F}_W + b\mathbf{v}$$ which is bound to cause problems. I think this is a problem we must solve before we can fully describe how to use Reynolds numbers to determine what estimating formula to use. RobertJDunn 15:50, 6 December 2007 (UTC)

Discussion of "Power equals force times velocity"
Someone added a paragraph about how the Power equation (proportional to v^3) is wrong. This person is incorrect, and I have removed his/her comment, and I will explain why here.

The person claims that work = force * (delta velocity). This has the right units, but is incorrect. Work is actually equal to force * velocity. If you push a block through a fluid at 1 m/s by applying 1 N of force, you are doing work. You are doing 1 watt of work, and the fluid is heating up at a rate of one watt. Saying that you are not doing work because velocity is not changing is absurd.

Put another way, d(work) = force * d(x). Differentiating both sides with respect to time, we find that d/dt(work) = power = force * d/dt(x) = force * velocity.

Mechanical Rose 06:12, 12 December 2006 (UTC)

I agree with User:Mechanical Rose and it looks like her comments have been incorporated into the article; however, I still believe that the text is is incorrect when it talks about the power quadrupling for a doubling of velocity. In fact the power goes up by a factor of 8 (as stated later on) not by 4. I am not sure what the protocol is for correcting this so I thought the discussion page was the best place to mention this. TRamsey 03:06, 14 January 2007 (UTC)


 * Since ground vehicles are discussed the power equation should be explicit with regards to ground speed, since as it appears here it is only correct when ground speed is equal to apparent wind speed. P= F Vg Or else make it clear what situation is being examined. — Preceding unsigned comment added by 2620:100:4000:142:0:0:0:4 (talk) 18:24, 24 May 2016 (UTC)

The text actually talks about the Force quadrupling for a doubling of velocity (which it indeed does, being proportional to v^2). Power gets multiplied by 8 (since it is 4 times the force in half the time). Also, I am a guy. Mechanical Rose 05:24, 28 March 2007 (UTC)

I think it might be good if the example hp/speeds for this section are adjusted. If you take the 80hp for 100mph figure, then 200mph would require 8 times the power, or 640hp, which sounds a little high, unless you are driving a brick. I've looked around, and haven't found any definitive sources, but I know I've heard that it takes around 400 hp to get to 200mph, and I found a comment on a car thread indicating 450hp. In any case, many of the people that read this article are reading to understand vehicle performance better, so a real-world example might be in order. --216.84.45.198 14:28, 24 July 2007 (UTC)
 * Adjust the numbers if you like, but it is the concept, the abstraction, that we are trying to state here. If you have data specific to cars it would go well in the automotive aerodynamics page. Meggar 06:01, 26 July 2007 (UTC)

1. The numbers in the example look wrong. Doubled speed should require eight times the power to overcome drag, not four times. 2. But then there is also rolling resistance which I believe is constant force, therefore power linear with speed. So total power used grows linear at low speeds, with the third power at high speeds. Gnasher729 (talk) 23:14, 13 July 2012 (UTC)

Limit of low/high velocity
Shouldn't one mention the concept of a Reynold's number here? --Benjamin.friedrich 15:28, 1 November 2006 (UTC)


 * Agreed, strongly. -- David W. Hogg 05:21, 9 January 2007 (UTC)

terminal velocity
The equation for the approach to terminal velocity is not particularly instructive, and only applies in the low-speed limit (viscous drag dominates). This should be noted or the equation (and section) should be dropped, leaving only a reference to the terminal velocity article. -- David W. Hogg 05:21, 9 January 2007 (UTC)

Would this formula derivation for the velocity over time be useful?
I am new at this so I am wondering if this work I did as I was studying this topic would be a useful addition and if so how to add it. You will need a mathml enabled browser to view it. Probably a links from where the formuls is cited on this page would be best.

Formula derivation page

RobertJDunn (talk) 02:13, 5 December 2007 (UTC)

Discussion for generalizing the page.
I have been thinking that the scope of this page is too narrow for the topic of drag. This is in part due to the example given of an object free falling through atmosphere. Though simple it does not stress the very important concept of drag force always being created in a direction directly opposite to the velocity.

I have been thinking of various examples that might be better that might be used in concert with the given example of an object falling.

1. A cart on perfect wheels (no friction) is taken up to the speed of 100 kilometers per hour and then let glide. Show how drag slows it down. This is a no external force example.

2. A plane on level flight at a constant velocity. Two external forces, one provide by engine and the other by gravity. Shows how lift generated by wing shape adds a drag component to the forward velocity of the plane. This is basically an equilibrium example with the two external forces, one vertical and the other horizontal balanced out by drag.

3. A glider flying at a constant velocity and falling at a constant rate (this is around 50 meters forward for every meter dropped). One external force but the shape of the wing causes the glider to be squeezed forward between the gravitation force and the vertical component of the drag force. The total drag force generated is of course opposite to the slightly downward velocity. Nice example of one external force generating motion in an oblique direction.

4. A sailing ship tacked slightly off from the wind being directly behind it. With a good hull design they can move faster than the wind. Considering good design the effect of the wind on superstructure should be minimum so we have the drag of the sail through the air and the drag of the hull through the water.

5. Water flowing downhill through a pipe. The drag force would tend to push the pipe the opposite direction to the flow of the water.

Just suggestions here. Feel free to correct or add or subtract. I feel that this general approach would add greatly to people being able to get a better grasp on the subject faster.

RobertJDunn (talk) 18:38, 7 December 2007 (UTC)


 * Example 1. Your "perfect wheels" would still have friction--static friction between wheel and ground, otherwise you might as well call the cart a sled. -- Another Stickler (talk) 17:57, 27 November 2008 (UTC)


 * Example 5. I think you have it backward. The drag force would tend to push the pipe in the same direction as the flow of the water. Drag tends to oppose the relative motion, not assist it. -- Another Stickler (talk) 18:25, 27 November 2008 (UTC)

Units for the Equation
Shouldn't the equation have units of measurement listed below it, where the legend is? Just to clarity things.

Also, for density in SI, is it measured in kg/m^3 or g/cm^3? 203.122.106.197 (talk) 18:02, 3 May 2008 (UTC)

I'm gonna say that it's *often* kg/m^3, at least in my courses. E.g. water is ~1000 kg/m^3, air is ~1.2 kg/m^3 Mechanical Rose (talk) 01:05, 9 July 2008 (UTC)

What does "E" stand for
In ?

it's e, as in, E_(mathematical_constant) Mechanical Rose (talk) 01:02, 9 July 2008 (UTC)

Categories and sections
I changed the categorisation and sections, since: -- Crowsnest (talk) 08:35, 31 August 2008 (UTC)
 * 1) parasitic drag is a term mainly used for lifting surfaces in aerodynamics,
 * 2) terminal velocity and power, as given, are for the quadratic drag law,
 * 3) Stokes flow is the linear drag limit for low Reynolds number,
 * 4) wave drag and lift-induced drag, as given, are as used in aerodynamics.

Deleted sentence
I deleted this sentence, at the end of section "Drag at high velocity":


 * "The reference for a wing would be the plane area rather than the frontal area."

What is the plane area? area of the plane? (what plane?) Area of the airplane? (what part of the surface of the airplane?). If you want to reinsert the sentence, please revise it to make it clear. Thank you. Paolo.dL (talk) 14:35, 1 September 2008 (UTC)


 * The plane area for a wing is the wing area, see e.g. here (see also drag in aerodynamics on the same website). Further a reference area is just what it says: it is a reference, which needs to be well defined in order to be able to use it in research and design. The cross-sectional area is not holy in this respect, since most often it is by no means clear this area is a better reference than several other area measures.
 * What is added now about non-hollow objects, cyclists and rolling tubes, in relation to drag, is rather cryptic to me. In that respect I think the previous formulation was clearer (apart from apparently not being very clear on what is meant with plane area of a wing).
 * What is missing in the description is the influence of the angle of attack, or flow direction with respect to the object orientation, which often is important. -- Crowsnest (talk) 16:28, 1 September 2008 (UTC)

this all has nothing to do with wat i looked up and thats air resistance!!! —Preceding unsigned comment added by 66.57.104.147 (talk) 23:03, 9 October 2008 (UTC)

Cleaning Introduction
I think second paragraph (cited below) is not vital (maybe even not appropriate) for introduction to the topic and while dealing with astronomy may be confusing. I would like to suggest, temporally (until someone could better integrate this idea into article) to move this paragraph to Trivia section.

Second Paragraph: "In astrodynamics, depending on the situation, atmospheric drag can be regarded as inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit."

--Fakedeeps 19:07, 13 October 2008 (UTC) —Preceding unsigned comment added by Fakedeeps (talk • contribs)

Typo?
Is the following sentence wrong? "For a solid object moving through a fluid, the drag is the component of the net aerodynamic or hydrodynamic force acting in the direction of the movement." Doesn't drag act against the direction of the movement of the object? -- Another Stickler (talk) 18:06, 27 November 2008 (UTC)

Yes, it would indeed be better to say 'opposite' - I made that change 76.247.112.48 (talk) 04:07, 1 January 2009 (UTC)

Reply to 76.247.112.48 (talk)
Hi! On 1 January you made some additions to Drag (force). You didn’t make any citation to indicate the source of any of your comments. When an addition is likely to be challenged it is very important to add a citation to indicate the source of the addition. Contentious statements that are not supported by a suitable citation are likely to be removed promptly. It is not sufficient for us to add statements based on nothing more than we believe them to be true. Also, the discipline of finding suitable citations significantly raises the quality of Wikipedia.

REPLY: Hi - thanks for all your comments. I've responded to them below.

I disagree with some of your additions. You might refine them or delete them. My comments are given below.

Finally, I encourage you to register as a User and thereby obtain your own identity and Talk page. That way others can communicate with you directly.

REPLY: Will do.



"Drag" (sometimes called fluid resistance) refers to a variety of forces that resist the movement of a solid object through a fluid.

COMMENT: Really? What is this variety of forces? Having stated that drag is a variety of forces your added text does nothing to explain the statement.



When an object experiences drag forces, then some of its kinetic energy will be converted ("dissipated") to heat.

COMMENT: Not true. An airplane in flight experiences drag, but when it is flying at constant airspeed its kinetic energy does not change and is not converted to heat.

REPLY: It is true. The system is in a non-equilibrium steady state. It stays at constant v because energy is constantly being dumped into the system (in this case, by the engines). The plane is continuously colliding with air molecules, and in every collision, some momentum is transferred from the plane to the air. This is why the air heats as the plane flies through the air. On average (!) the kinetic energy of the plane is constant, due to the action of the engines, but moment by moment it fluctuates about some mean value. The engines augment the kinetic energy, whereas momentum transfer due to collisions with air molecules bleeds off kinetic energy from the plane.



This is why certain airplanes and rockets must be designed to withstand significant thermal stresses.

COMMENT: Not true. The high temperatures experienced by supersonic airplanes, rockets and meteorites is the stagnation temperature that exists at and near the stagnation points (at the leading edges). The actual stagnation temperature is a function of Mach Number, not drag coefficient, so it is not reasonable to say stagnation temperature is a consequence of drag. (Two objects travelling at the same Mach Number will experience the same stagnation temperature even though the drag experienced by the two objects could be dramatically different.)

REPLY: It is true. I agree with what you say re. the stagnation T, but keep in mind that the molecular origin of the heat is the forced movement of the plane through the air.



Most moving objects will simultaneously experience several distinct forces that oppose relative motion.

COMMENT: Really? What are those several distinct forces? Having stated that moving objects will simultaneously experience several distinct forces your added text does nothing to explain the statement.

REPLY: For example, (1) momentum transfer via elastic collision and (2) chemical binding forces (this is what gives rise to "friction"). If you like we could change "Most" to "Some".



"Drag" is generally used to refer to forces that increase with relative velocity, whereas "friction" refers to forces that are largely independent of velocity.

COMMENT: The explanations of drag and friction to be found in Wikipedia are based on drag applying to a solid body moving relative to a fluid, and friction applying to a solid body moving relative to another solid body. The above sentence complicates Wikipedia unnecessarily by saying the difference between drag and friction is based on the way in which they vary with velocity, and therefore implying that both drag and friction are present when a body moves through a fluid, and also when a body moves in contact with another solid body.

REPLY: Consider a car. Both friction and drag are clearly present.



Some more specialized terms (such as "parasitic drag," which is used in aerodynamics) refer to particular combinations of drag and frictional forces.

COMMENT: What specialized terms do you have in mind, and what are the particular combinations of drag and frictional forces? Having stated that some specialized terms refer to a combination of forces your added text does nothing to explain the statement.

REPLY: For example, Parasitic drag = form drag + Skin friction + interference drag.



''The starting point of any mathematical treatment of drag is consideration of the Reynolds number of the system. If the Reynolds number is low, then the flow around the moving object will be laminar. This simplifies calculation of the drag. By contrast, if the Reynolds number is large, then the flow will be turbulent and dominated by inertial terms''.

COMMENT: Reynolds number is a guide to whether the boundary layer will be laminar or turbulent, but it won’t be a guide to the nature of the flow around the object. Consider a body moving with high Reynolds number through a stationary atmosphere. Most of the atmosphere is undisturbed by the passage of the body, so the general flow of the atmosphere relative to the body appears to be laminar. Even the relative flow in the vicinity of the body appears to be laminar. It is the flow of the boundary layer, greatly affected by viscous forces, that is turbulent.

REPLY - Agreed. Should I make the change or do you want to do it?

Dolphin51 (talk) 23:20, 1 January 2009 (UTC) 76.247.112.48 (talk) 02:39, 4 January 2009 (UTC)


 * Hi 76.247.112.48. Thanks for your prompt response.  I see that you are able to defend your position on the issues I raised.  The heart of the issue is the lack of appropriate citations for statements that are likely to be challenged, and now have been challenged.  I think you will find that when you dig into your books to locate chapter and verse for appropriate citations you will find the books don't actually say whay you have written.  For example, you have written above that The engines augment the kinetic energy, whereas momentum transfer due to collisions with air molecules bleeds off kinetic energy from the plane.  I dont' have any great objection to this sentence, but it's sentiment is not well encapsulated in the following sentence which you added to Drag (physics):  When an object experiences drag forces, then some of its kinetic energy will be converted to heat.


 * In a number of places you have made claims about certain things, but added nothing to explain the claim. For example, you have written Most moving objects will simultaneously experience several distinct forces that oppose relative motion.  What is the reader to make of the claim that there are several distinct forces?  Readers can't send you an email, or contact you on your cell phone to ask for more information to clarify the claim.  It is a bit like a Wikipedia article about President Jones saying he made five major improvements to society during his Presidency, but without attempting any explanation of what those five major improvements were.


 * If you check WP:Verifiability you will see it says The threshhold for inclusion in Wikipedia is verifiability, not truth. It is not sufficient that you believe what you have written is true - it is essential that other users are able to independently confirm that what you have written has been written before by someone else and publicly available in a reliable source.  I suggest you refine your recent additions because others will soon begin to scrutinise those additions very closely, and any that appear to be of doubtful authenticity and are not supported by appropriate citations will be deleted.  Best regards.  Dolphin51 (talk) 03:33, 4 January 2009 (UTC)


 * On 9 January I erased the changes made on 1 January by 76.247.112.48 (talk). See discussion above. I have no objection to the sentiment contained within these changes being restored to Drag (physics) in the future, providing they are an accurate reflection of what has been written in some reliable source on the subject, and providing suitable citation(s) are inserted to identify the source of the information.  Dolphin51 (talk) 02:21, 9 January 2009 (UTC)


 * Citation is good. Reverting uncited changes to an uncited original version under the argument that citation is necessary is a little strange. Adding a citation-needed tag would be preferable to reverting. 76.247.112.48 obviously knows this stuff and is still in the middle of a rewrite. Why not let 76.247.112.48 finish and then ask for citations rather than reverting so 76.247.112.48 doesn't have to write everything twice? -- Another Stickler (talk) 19:41, 12 January 2009 (UTC)


 * Hi Another Stickler. My motivation for reverting the changes was not primarily because they were without citation.  My primary motivation was that they were technically unsound.  I explained my reasoning at the commencement of this Section.  See above.  WP:BURDEN shows that there are various responses available when material that appears to be unsound is added to an article - varying from a "fact" tag right through to reversion.  The material in question appears to me to be technically unsound and I explained that it in detail in this Section.  76.247.112.48 defended his (or her) changes, but I was not persuaded by any of the defences.  After a week no attempt had been made to correct things so reversion was the best course of action.  (Many editors would have reverted immediately, and without ever leaving a detailed explanation on the Talk page.)


 * If 76.247.112.48 wishes to re-use some of his/her text he/she doesn't have to write it again. By using the History tab at the top of the article he (or she) can get access to all previous versions of the article, right back to its creation.  On Wikipedia, nothing is lost except when an article is deleted and I am confident Drag (physics) will never be deleted.  Dolphin51 (talk) 21:42, 12 January 2009 (UTC)


 * OK on the reversion for unsoundness. Yes copy-and-paste from history is possible, I repaired inertia from 3 months of vandalism that way, but it is still a bigger hassle than just adding citations to existing text. I personally am satisfied with the soundness of the explanation above for how kinetic energy is lost from a body to the fluid it is moving through, for example in terminal velocity. The only other way to say it is that the force of gravity is directly affecting the kinetic motion of the fluid particles, but that seems to skip a step, don't you think? I mean the body is the carrier of the kinetic energy that is derived from gravitational potential energy and imparted to the fluid particles by collision. Even if the body's speed is grossly constant, if you look closely enough, each collision slows down the body slightly, and during the interims between collisions the body speeds up again. -- Another Stickler (talk) 07:32, 13 January 2009 (UTC)


 * Hi AS. I am aware of a movement among physics enthusiasts to explain just about everything in gas dynamics in terms of the kinetic theory.  They avoid the notion of pressure, and even the word pressure.  76.247.112.48 may be part of this movement, and hence his desire to relate drag to the kinetic theory of gases.


 * Drag can be divided into two components - pressure drag and surface-friction drag. Pressure drag can be considered the integral, over the entire surface of the body, of forces acting normal to the surface of the body; whereas surface-friction drag can be considered the integral, over the entire surface of the body, of forces acting parallel to the surface of the body. Pressure drag comprises induced drag plus form drag. Surface-friction drag is the retarding force exerted by the boundary layer and hence is related to the viscosity of the fluid, and unrelated to exchange of momentum at the molecular level.


 * When 76.247.112.48 uses the kinetic theory of gases to describe drag it appears to me that he (or she) is omitting surface-friction drag. Dolphin51 (talk) 11:27, 13 January 2009 (UTC)


 * Hi Dolphin51. I'm using editing wikipedia as a learning process. I figure if I can explain something in my own words well enough for it to stick in an article, and can cite sources, that means I understand it the way the sources would want me to understand it. I consider myself a "physics enthusiast", but champion no pet theories such as the kinetic theory of gases. I just want to examine all the ideas. You must know more than I yet do on mechanics, but I found a quote that seems to contradict your "surface-friction drag is the retarding force exerted by the boundary layer and hence is related to the viscosity of the fluid, and unrelated to exchange of momentum at the molecular level", and I was wondering if there is something I'm not understanding. It's from the McGraw-Hill Encyclopedia of Science & Technology, 9th edition, Viscosity article, by Frank M. White (copied by pencil from the local library reference shelves), "...a fluid...subject to shear stress,...flows and resists the shear through molecular momentum transfer." -- Another Stickler (talk) 06:22, 20 January 2009 (UTC)

Hi again AS. I compliment you on going to the local library to gather information. Wikipedia can have such a beneficial effect on the lives of those of us who contribute to it!

I don't challenge the notion that viscous forces can be traced to a molecular origin as momentum migrates across the boundary layer, so I have no dispute with Frank M. White on this point.

One of my original challenges to 76.247.112.48 was his (or her) statement When an object experiences drag forces, then some of its kinetic energy will be converted ("dissipated") to heat. He defended this statement by invoking the kinetic theory of gases. In particular, he wrote The plane is continuously colliding with air molecules, and in every collision, some momentum is transferred from the plane to the air. This appears to me to be a reference to the kinetic theory's explanation of pressure. I don't believe he had viscous forces in mind when that statement was written, so I have been working on the assumption that the above sentence might somehow cover pressure drag, but not surface-friction drag. However, if he wants to assert that his reference to continuously colliding with air molecules covers both surface-friction drag and pressure drag I will accept that, but it would be a giant leap to say molecules continuously colliding with a surface is a reasonable explanation of viscous shear forces that exist only when the surface is moving relative to a fluid.

It will be worthwhile re-visiting the statement The plane is continuously colliding with air molecules, and in every collision, some momentum is transferred from the plane to the air. The words about the plane continuously colliding with air molecules is just as true for a plane that is stationary on the ground as it is for a plane in flight. The momentum of a stationary airplane is zero, so where 76.247.112.48 writes that molecular collisions cause transfer of momentum to the air it clearly isn't true, at least not as a general principle (which is the way it is written.)

The aerodynamic forces on an aircraft can be simply and accurately explained without resorting to kinetic theory or the notion of molecular motion. I think anyone would have a difficult task trying to provide a simple and accurate explanation of drag, suitable for Wikipedia, based on kinetic theory and molecular motion. I also doubt a suitable reference can be found among the mainstream sources in the field of aerodynamics. Dolphin51 (talk) 11:57, 20 January 2009 (UTC)


 * On 1 January I suggested IP address 76.247.112.48 become a registered user. He (or she) agreed to do so.  It appears that this user is now Kaybet (talk).  Welcome Kaybet!


 * A month ago, 12 January, you restored the comment about drag causing heating, necessitating that some airplanes and ballistic missiles be designed to withstand significant thermal stresses. You quoted Allen's book about aerodynamic heating of ballistic missiles entering the earth's atmosphere at high supersonic speeds.  While your comment, and this reference, have relevance to supersonic speeds and stagnation temperatures, they are out of place in a general article on drag.  Supersonic re-entry to the earth's atmosphere is a very, very specialised case of motion in a compressible fluid, and aerodynamic drag.  Your comment would be appropriate in Stagnation temperature or Supersonic.  I will delete the comment from Drag (physics) but you should feel free to re-insert it in a more appropriate place.  Dolphin51 (talk) 02:31, 12 February 2009 (UTC)

Revisions to Aerodynamic Drag
I've included a number of revisions to the section on aerodynamic drag, including the addition of a more thorough description of the types and sources of wave drag. I'm pretty new at editing pages, so I hope I didn't step too badly on anyone's toes, but the definitions as they existed were incomplete and in many cases misleading (if not simply incorrect). I'm at a loss as to what to do with the paragraph begining "In aviation, induced drag tends to be greater at lower speeds ...", except to say that some of the information is correct, but I don't believe that this information should go under parasite drag. Would it maybe be better to move most of this under another heading regarding the balance of drag in different phases of flight? Also, it should also be noted that some of the content in this paragraph, specifically that relating to transonic wave drag, is only applicable to aircraft which fly transonically, and that's not really clear.

Being that I'm fairly new to this, I'll ask a dumb question. A lot of the descriptions of aerodynamic drag are really a subset of fluid mechanics, and it seems as though little is done to tie this in. Specifically, Reynolds number has a significant effect on aerodynamic drag, but the only mention of Reynold's number on this page is in reference to very low Re flows (Stoke's flows). Additionally, the presence of the discussion of Quadratic drag is really just a definition of the drag coefficient; "quadratic drag" is no more a real force than "stoke's drag" is, whereas lift-induced and zero-lift drag in incompressible flow encompass both of these definitions when you account for Reynold's number effects. Would it not be better than to separate the page in terms of canonical drag types - zero-lift, lift-dependent, and compressibility drag, and then maybe discuss historical contexts of the types of drag separately, or perhaps place each of these definitions under whichever type of drag they exist? It's late, so I'm not sure if that makes sense, but I'm certainly interested in your opinions.

Airplanenerd (talk) 07:35, 6 April 2009 (UTC)


 * Hi Airplanenerd. Welcome to Drag (physics).  Your suggestions look sound.  This article is not a first-quality article, and it looks like it has been written by a lot of different editors, all working independently. (Which is true, but the objective is to have articles which look like they were written uniformly and with a clear plan.)  It would benefit from some extra work and extra in-line citations.


 * I will leave you some advice on your User page. Dolphin51 (talk) 08:00, 6 April 2009 (UTC)

Lift-induced drag
On 28 December 2009 Aerokiwi added the following comment at the end of the paragraph headed Drag (physics). This comment is more appropriate here on the Talk page. I will delete it from the article. Dolphin51 (talk) 11:09, 28 December 2009 (UTC)

(This paragraph is misleading. While it's true that induced-drag increases with angle of attack, it argues that the reason this happens is because lift increases. This is true but not very useful observation since generally speaking keeping 'other parameters the same' means planform and weight of the aircraft, in which case assuming that the lift increases doesn't make sense (lift=weight assumption in steady flight, the main exception to this is maneuvers with a load-factor greater than 1 such as turns ). It's more usual to talk about increased induced drag as a function of airspeed since as the aircraft slows down, it needs a higher angle of attack in order to have a higher lift-coefficient to maintain the same lift. The higher lift coefficient is associated with a higher induced-drag coefficient, which in turns leads to a higher induced drag. From the induced-drag article: $$D_i = \frac{k L^2}{\frac{1}{2} \rho_0 V_e^2 S \pi AR} $$. So if all parameters are held constant, lower speed implies higher induced-drag.)

Table
The numbers attached to the illustrations on the top-right are wrong. Skin friction would be more than 0% of the drag on the last entry, and the rest of the numbers seem to be arbitrarily made up. —Preceding unsigned comment added by 76.85.196.138 (talk) 05:48, 21 April 2010 (UTC)


 * The table appears to be a simple diagrammatic illustration of the difference between form drag and skin-friction drag. The diagrams are of simple, readily-recognizable shapes.  No dimensions are attached to them.  It is intended as an introduction to the subject, not a reference source.  Dolphin  ( t ) 08:06, 21 April 2010 (UTC)


 * The table is ridiculous at this point. It appears that someone has changed the skin friction to 8% on the last entry.  I doubt that I have to point out the exact flaw in that.  Also, I would like to rebuttle to the first comment.  Usually, in examples such as this, the lines are viewed as arbitrarily thin and perfectly oriented to the direction of motion (or relative motion).  In such a case the skin friction would be negligible to the point of stating that 0% of the friction is due to skin friction.  The two center cases, however, seem uncalled for without some sort of sourcing provided 168.28.180.30 (talk) 19:20, 19 March 2012 (UTC)

Wind and Cars
I think there needs to be a section or entry describing the physics of wind power. In particular, the use of the power equation:

http://en.wikipedia.org/wiki/Air_resistance#Power

for a wind turbine. I checked:

http://en.wikipedia.org/wiki/Wind_power http://en.wikipedia.org/wiki/Wind

Maybe, call it Wind Performance equation. When done cross links need to be built between the above three pages.

Also, how does the equation relate to drag with a car? I know that the solar car page:

http://en.wikipedia.org/wiki/Solar_car_racing#Performance_equation

Has a term in the Performance Equation which is drag. But, there is not a section for all cars.

The solar car performance equation looks good, but I wonder about the source.

Reddwarf2956 (talk) 02:26, 13 September 2010 (UTC)

Newtonian drag?
The animated graph showing the trajectory of objects undergoing pure ballistic motion and two types of drag refers to "Newton drag" without defining it. I don't see any other mention of Newton in the article. Karn (talk) 19:09, 16 March 2011 (UTC)
 * You are right, there is no adequate explanation of the expression Newton drag. I'm sure what is intended is drag associated with a constant coefficient of viscosity, which is the defining feature of Newtonian fluids.  I have added some clarification in the animated graph by turning Stokes' drag and Newton drag into Wikilinks leading to relevant articles.  For an understanding of Newtonian fluids it will also be helpful to understand the opposite - Non-newtonian fluids.
 * However, I can't explain why drag in Stokes flow would be less than Newton drag. Stokes flow is creeping flow so I would expect very high viscous forces and very high drag. Dolphin  ( t ) 21:51, 16 March 2011 (UTC)

Interpretation of equation
$$\mathbf{F}_D\, =\, -\tfrac12\, \rho\,A\, C_d\, (\mathbf{v}\cdot\mathbf{v})\, \frac{\mathbf{v}}{||\mathbf{v}||},$$

I am struggling a bit with this. Is $$(\mathbf{v}\cdot\mathbf{v})\, \frac{\mathbf{v}}{||\mathbf{v}||}$$ just a cryptic way of getting v^2, but in the same direction as v?? 86.176.209.74 (talk) 22:10, 5 July 2011 (UTC)
 * Yes, the most common presentation of the drag equation gives only the scalar magnitude of the drag force. The direction of the drag force is simply stated to be the component of aerodynamic force that is parallel to the vector representing the relative velocity of the body and the freestream.  The equation above is a vector equation, giving both magnitude and direction.  I greatly prefer the common presentation of the drag equation accompanied by a narrative description of the direction of the drag force.  I guess the above equation serves only to show that it can be done!  Dolphin  ( t ) 22:44, 5 July 2011 (UTC)
 * Thanks. I have clarified this in the article. If there's a better way of doing it then please go ahead. 86.176.209.74 (talk) 00:40, 6 July 2011 (UTC)


 * Thanks for alerting us to this problem! Up until 11 November 2010 this equation was presented in its scalar form - simple and easy to comprehend.  On 11 November 2010 it was changed to the vector form by IP address 198.37.20.78.  The complexity of the vector form is not warranted in this article - WP:Make technical articles understandable!  I have reverted the paragraph back to the presentation used before the change.  Dolphin  ( t ) 02:30, 6 July 2011 (UTC)

I know I'm late to this party, but I'd suggest $$\mathbf{v}\cdot|\mathbf{v}|$$ if you absolutely need technical accuracy. I still recommend v^2 (as it currently stands) though. Mechanical Rose (talk) 08:17, 5 March 2012 (UTC)
 * Thanks. I don't believe we need that level of technical accuracy.  I agree that v^2 says it all, and says it well.  Dolphin  ( t ) 22:14, 5 March 2012 (UTC)

Wave drag
"In transonic flight (Mach numbers greater than about 0.8 and less than about 1.4), wave drag is the result of the formation of shockwaves on the body, formed when areas of local supersonic (Mach number greater than 1.0) flow are created. In pra..."

Whats right? Just stumbled over this.

Transsonic flight = >0.8 & <1.4 Supersonic flight = >1.0

somethings wrong here

greets, dennis --46.182.136.60 (talk) 15:34, 30 August 2011 (UTC)

Direction of action of drag
On 16 October User:Bcebul added some new material to the lede section. (See Bcebul’s diff.) This new material included the following paragraph: Depending on the direction of the velocity of the solid relative to the fluid (a liquid or gas), the drag may be the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of the movement such as in a car or aeroplane, or it may act in the same direction of motion as the solid, such as in a boat sailing down wind.  The paragraph was unsourced. I objected to it technically because it suggests that the drag on a boat sailing downwind experiences drag in the direction of motion. It is true that any body moving through a fluid can experience drag in the direction of motion relative to the Earth’s surface, but this is misleading because the direction and magnitude of drag is a function of motion relative to the fluid, not to the motion relative to the Earth’s surface.

I deleted the paragraph. (See my diff.) Bcebul has now restored the paragraph. (See Bcebul’s diff.) He has also cited four sources. The third of these citations is not an independent source – it is a polar diagram in a Wikipedia article.

The opening sentence in our article states: In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers to forces which act on a solid object in the direction of the relative fluid flow velocity. This clearly states that drag forces act in the direction of the relative fluid flow velocity, therefore I consider it  inappropriate for the second paragraph to be alluding to the direction relative to the Earth’s surface. This material may have some application in an article on sailboats, but it has no application in our article on Drag (physics) (which begins In fluid dynamics, ...)

What do other’s think? Dolphin ( t ) 11:39, 16 October 2011 (UTC)

I agree with Dolphin. Bcebul (talk) 10:50, 18 October 2011 (UTC)

Flow visualisation images at the top of the page
The images at the top of the page show flow around various objects. The streamlines drawn are incorrectly. Streamlines do not split up and they should be drawn to go straight into the body at the stagnation point. These images should either be removed or corrected. — Preceding unsigned comment added by 78.86.13.119 (talk) 16:25, 19 November 2011 (UTC)

Ok, the changes aren't happening so i'm going to do it myself. — Preceding unsigned comment added by 78.86.13.119 (talk) 12:28, 21 November 2011 (UTC)
 * The diagrams show simple illustrations of the flow around four elementary bodies. Nowhere does it state or suggest that these lines are streamlines or streaklines or pathlines.  For a layman, these simple illustrations are likely to be more meaningful than a diagram showing the streamlines in steady flow.  A young person, or someone new to the field of fluid dynamics, is likely to be confused by the significance of a stagnation streamline terminating on the surface of the body.  My view is that if this image stated that these lines were streamlines, the statement would be incorrect and should be corrected or removed.  However, no such statement is made.
 * For technical articles to be understandable to the greatest number of readers they should begin with the simplest presentation of the subject and progress to more comprehensive aspects of the subject. WP:Make technical articles understandable is relevant.
 * You are entirely correct in saying that streamlines do not split. You are also correct in expecting the stagnation streamlines to terminate on the surface of the body.  However, these are not diagrams of streamlines.  The diagram has a role to play in this article, explaining the nature of fluid drag.  I think the diagram should be restored.  Dolphin  ( t ) 06:01, 26 November 2011 (UTC)

Satellite drag
Information is missing from this article: there is another type of aerodynamic drag that does not fit into the existing categories: the drag caused by the rarified atmosphere on a satellite, space station, or spacecraft in low Earth orbit. This is neither lift-induced, parasitic, nor wave drag, and is driven by plasma physics (individual molecules striking the craft). It is strongly driven by the amount of solar energy variation, and cannot follow the usual rules of aerodynamic drag, driven by dynamic pressure (1/2 rho v squared), because the density rho is so low. JustinTime55 (talk) 17:39, 21 February 2014 (UTC)
 * Surely satellite drag does follow the normal/hypersonic rules - density might be low but velocity is very high. - Rod57 (talk) 19:47, 7 May 2017 (UTC)

Poor structure
There is a lot of redundancy in this article's structure; this is obviously left over from the merge of the two articles and needs to be fixed (serious cleanup). There is also an important subtopic missing: the drag on an orbiting spacecraft which still exists "above the atmosphere". JustinTime55 (talk) 20:56, 25 February 2014 (UTC)

I would like add in that the whole article could be written in clearer, simpler language, without making it superficial. As it stands there is not a lot that can be readily followed by someone without particular expert knowledge of this field, and it doesn't need to be this way surely. — Preceding unsigned comment added by David17606 (talk • contribs) 07:51, 29 November 2021 (UTC)

Equation as text
How come we don't just use FD = ½pv²CDA so that people can copy the equation? Using the math function presents an image and some people want to copy text so they can paste it on IRC or in a forum that doesn't allow image embedding. Ranze (talk) 04:54, 27 July 2014 (UTC)


 * Part of the problem is that the "p" isn't a p, but rather the Greek letter rho (equivalent to lowercase r). Is the alternate character "ρ" portable? JustinTime55 (talk) 16:32, 29 July 2014 (UTC)

Reference 15
Reference 15 is a bad link. Is it a typo or do we need to find another source? 161.31.231.168 (talk) 17:31, 31 August 2014 (UTC)
 * Reference 15 is currently Drag Force. (The address is www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Dynamics/Forces/DragForce.html .) Dolphin  ( t ) 06:59, 1 September 2014 (UTC)

Proposed merge with Aerodynamic drag
WP:MERGEREASON overlap of the technical details which are the same regardless on if the fluid is a gas, liquid, or solid. If the physics and underlying math for describing drag are different for gas, liquids, and solids then I could see doing the merge in the other direction with separate articles for aerodynamic drag for drag in gas versus whatever fluid drag and solid drag are called. --Marc Kupper&#124;talk 18:40, 12 February 2016 (UTC)
 * Support (same subject) --Marc Lacoste (talk) 06:04, 7 April 2017 (UTC)
 * Support (same subject) --Mano Math (talk) 22:50, 25 October 2017 (PT)
 * Agreed and ✅ Klbrain (talk) 16:05, 3 January 2018 (UTC)

Assessment comment
Substituted at 13:47, 29 April 2016 (UTC)

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Types of drag
The 'Types of drag section lists a few types - Could we say form drag is that part of the drag dependent on the fluid density, and "skin friction" is that part of the drag dependent on the fluid viscosity ? or what can we say to clarify ? - Rod57 (talk) 19:41, 7 May 2017 (UTC)


 * No, we can’t summarise drag in the way you have suggested. However, it may be reasonable to say form drag is the sum of all force components perpendicular to the surface of the object; and skin friction drag is the sum of all force components parallel to the surface. Dolphin  ( t ) 12:55, 5 April 2018 (UTC)

Air friction
Air friction redirects to this article. Although closely associated, the terms are not synonymous. For example, the heating due to air friction on the leading edge of a supersonic plane's wing is not drag. 2606:A000:4C0C:E200:29AF:8B75:2D37:5BB4 (talk) 22:47, 9 October 2017 (UTC)
 * Drag is a force, the sub-mechanisms of which include friction, which results in heat transfer, whichever the fluid or the regime. I don’t see the distinction you are trying to make. Ariadacapo (talk) 06:47, 10 October 2017 (UTC)
 * Redirection to this article doesn’t mean the two terms are synonymous. It simply indicates Wikipedia doesn’t have an article on air friction but someone thought this article was the closest we have and created the redirect. Everyone is at liberty to amend the redirect and expand it into a stub article. However, our standards for verifiability and notability require that the new article be based on one or more reliable published sources, and the content be able to withstand any action to delete the article or merge it with this article. Dolphin  ( t ) 21:17, 10 October 2017 (UTC)

≠≤≥≥≥≥≥≥≥≥x — Preceding unsigned comment added by 188.50.249.192 (talk) 19:23, 28 December 2018 (UTC)