Is my Kasamba.com expert on crack?

[Diresu]

Is my Kasamba.com "expert" on crack?

This question is not for school, it's something I'm doing on my own.

About a year ago I was told on this board that in theory Mass has no effect on the top speed of an aircraft. Drag opposes thrust, Mass (weight) opposes Lift. Mass may slow down the acceleration of a plane but it has no effect on top speed. Top speed is limited by drag.

Ok, so fast forward to 24 hours ago. I'm getting ready to do some testing of some variables and I break down and pay an "expert" on Kasamba.com $40 so that I'm absolutely sure I'm doing it right. Here is what I got...

Max Velocity = Sqrt[(Thrust - Weight)/(.5*Fluid Density*Reference Area*Drag Coefficient) ]

It's basically the drag equation with Weight added in.
http://en.wikipedia.org/wiki/Drag_equation

Weight limits the top speed of a theoretical aircraft? Is this guy right?

 

[vanesch]

About a year ago I was told on this board that in theory Mass has no effect on the top speed of an aircraft. Drag opposes thrust, Mass (weight) opposes Lift. Mass may slow down the acceleration of a plane but it has no effect on top speed. Top speed is limited by drag.

It is not true that mass has no effect on the top speed of an aircraft, although it is true of course that the topspeed is found when drag opposes thrust.

The reason is that the heavier the airplane, the more LIFT you require to counter the force of gravity. Now, the more lift you require, the more drag you will generate at equal horizontal velocity. The relationship between lift and drag, however, is not simple, and depends on the design of the wings and all that. But usually, the more lift you generate, the more turbulence you generate (and hence the more drag).

 

[J77]

You paid some guy on the net $40 to get the answer to a question - shocking!

< resists urge to launch into rant about internet, dilution of information and why books will always be better >

Having said that - NASA sum it up quite nicely (though not to an advanced level), and it's free: http://www.lerc.nasa.gov/WWW/K-12/airplane/forces.html

 

[Diresu]

Vanesch,

But what you are essentially saying is that the drag created by the increased wing size is slowing down the aircraft, not the weight of the aircraft. If there was a way to increase the lift created by the wings and NOT increase the drag top speed would not be affected. Short story... it still comes back to drag slowing down the plane, not weight.

 

[Diresu]

Hey J77,

Thanks for the link I will definitely scour it thoroughly. One thing all of these websites/books seem to have in common is no simple equations! I would have thought that a simple top speed equation on the web would be as common as blades of grass at a golf course. DOH! It isn't that I can't get halfway to my solution it's just that I can't find someone to check my work or a site to check my work against. DAG! I don't completely trust myself when it comes to physics.

 

[Q_Goest]

Hi Diresu. You're correct. The equation you gave is the one commonly used for drag. Weight doesn't enter into it since in level flight the weight is perpendicular to the drag vector and thus has no horizontal component.

Here's the link you need to prove everything:
http://www.grc.nasa.gov/WWW/K-12/airplane/drageq.html

 

[Diresu]

Q Goest,

YOU ROCK! Thanks for giving me the definitive call on that one. I was pretty sure that was true but I didn't trust myself enough to question an expert. I guess I better get my $40 back from Kasamba.com, hehehe.

THANKS!

 

[vanesch]

Vanesch,

But what you are essentially saying is that the drag created by the increased wing size is slowing down the aircraft, not the weight of the aircraft. If there was a way to increase the lift created by the wings and NOT increase the drag top speed would not be affected.

Imagine a given airplane, and have it fly horizontally at, say, 200 km/hr.
Now, load that given airplane with 500 kg of lead blocks, and have it again fly horizontally at 200 km/hr. Normally, the angle of incidence on the wings will be slightly higher, to create more lift (to compensate for the 5000 N of weight extra). The pilot will have to pull a bit more on the stick to have the plane fly horizontally this time. With this higher angle of incidence, the drag created will be higher.

This will be the case generally, because the lift is produced by the circulation of the airflow around the wing. If you need more lift, you need more circulation (integral of velocity vector along contour around the wing). This circulation is also the origin of turbulence (unless you're flying in sirup). The more turbulence you produce, the more drag you have, in general.

 

[vanesch]

Hi Diresu. You're correct. The equation you gave is the one commonly used for drag. Weight doesn't enter into it since in level flight the weight is perpendicular to the drag vector and thus has no horizontal component.

Here's the link you need to prove everything:
http://www.grc.nasa.gov/WWW/K-12/airplane/drageq.html

Yes, but the devil is in Cd. Cd depends on the angle of incidence (which, in turn, is determined by the required lift, and which, in turn, is in relationship to the weight of the plane).

http://www.grc.nasa.gov/WWW/K-12/airplane/inclind.html

Read the last paragraph.

 

[Diresu]

Vanesch,

Thanks for the insight, but what you are still saying is that increased weight is causing the plane to operate in a manner that increases drag. And the drag is what's actually slowing down the aircraft. If the weight could be compensated for in some other manner the drag would not increase and the plane would still reach the same top speed.

Thanks for the help though, I apreciate it!

 

[Danger]

Diresu, I don't have time now to check out the links mentioned, so this might be a duplication of something in them. There is a way to compensate for the weight to some extent without changing the angle of attack. As Vanesch mentioned, the shape of the wings is a major factor. There's a (device? system? whatever) called 'Whitcomb winglets'. You see them most often on small private jets such as the Lear. They're very much like the vertical stabilizer (tail fin) on a plane, but they're built onto the tips of the wings. In some manner that I'm not sure of, since I'm not that versed in the field, they 'trick' the wings into thinking that they're longer than they really are. Lift goes way up, without introducing much in the way of additional drag.

 

[Q_Goest]

Hi Vanesch,

Yes, but the devil is in Cd. Cd depends on the angle of incidence (which, in turn, is determined by the required lift, and which, in turn, is in relationship to the weight of the plane).

True, I wouldn't argue that. But it's a bit more complex than that. Also, this responce doesn't directly answer the OP.

The reference you gave (last paragraph) also points out:

Since the amount of drag generated at zero angle and the location of the stall point must usually be determined experimentally, aerodynamicists include the effects of inclination in the drag coefficient.

Drag coefficient is determined experimentally (or using CFD). But there are other considerations.
1. The angle of attack also changes the area, another variable in the equation.
2. Velocity also must be considered, since the slower the aircraft goes, the higher the angle of attack.
3. And even if there is no change in angle of attack, or weight, the Cd STILL changes with a change in velocity (for example, a sphere falling straight down will experience a continuously varying Cd as velocity changes).

So the Cd will change depending on these other variables also, not just weight. The point is that the drag on an object is normally calculated per the equation given by the first post, except without the weight term, and drag coefficient varies according to a wide variety of variables.

To put the weight term into the equation as shown by Kasamba.com is incorrect. The weight term should not be part of the equation.

 

[russ_watters]

In reference to the equation in the OP: if the weight is less than or equal to the thrust, the aircraft will go down or backwards. So that equation can only be for vertical flight.

Anyway, as others mentioned, weight does affect the top speed of an aircraft, but that is covered by Cd, and it generally doesn't affect things much.

Incidentally, if you are a sailplane (glider) in a race, higher weight means higher speed, as long as you have enough updraft available. IIRC, though, there is a maximum weight for pilots.

 

[Gokul43201]

In reference to the equation in the OP: if the weight is less than or equal to the thrust, the aircraft will go down or backwards. So that equation can only be for vertical flight.

If weight < thrust, then thrust - weight > 0 and top speed > 0.

When weight = thrust, top speed = 0.

When weight > thrust, there are no real solutions => flight is not possible.

I don't see a problem.

But whether that weight term should be there at all... ?

 

[russ_watters]

If weight < thrust, then thrust - weight > 0 and top speed > 0.

When weight = thrust, top speed = 0.

When weight > thrust, there are no real solutions => flight is not possible.

I don't see a problem.

How many aircraft besides military fighter jets have a thrust to weight ratio (your first expression) greater than 1...? According to the equation in the OP, most aircraft should not fly.

 

[FredGarvin]

I think there is a misunderstanding between the term "thrust" and "lift". The Cd wraps up all of the essentials when it comes to the airfoil producing lift. There is no necessity for aircraft weight in there since the particular airfoil will generate the same amount of lift whether attached to a glider or a sherman tank. The use of the term "max velocity" is also an inappropriate usage.

The area in question usually does not change in that it is the planform area of the airfoil. It is a characteristic dimension akin to x or d in calculating Reynolds number.

The OPs original statement that weight has no effect on top speed is also incorrect. The more mass, the more power required due to increased lift required and thus more induced drag.

 

[Diresu]

Hey Fred,

But the mass itself isn't slowing down the top speed of the aircraft. The drag created by the increased lift requirements is slowing down the aircraft. I'm not saying in reality you aren't right 99% of the time. I'm saying that when accounting for this theoretically mass does not effect top speed.

 

[vanesch]

How many aircraft besides military fighter jets have a thrust to weight ratio (your first expression) greater than 1...? According to the equation in the OP, most aircraft should not fly.

Uh, yes, I think that this is a confusion between horizontal flight (what we are discussing, I thought) and vertical flight, which, as you say, is only accessible in stationary mode for acrobatic and military airplanes (and rockets :-).

 

[vanesch]

Hi Vanesch,

True, I wouldn't argue that. But it's a bit more complex than that. Also, this responce doesn't directly answer the OP.

Well, I thought that the question was, all else equal (altitude, velocity, horizontal flight, same airplane), does the total drag depend, or not, on the weight of the airplane ? And my answer to this, is, in general: yes, it does depend on it. As to the specific *formula* I don't know, I would think it is a complex relationship, which, as you say, only comes about from experimental measurements or CFD calculations. I would think it highly improbable that the effect of the weight would not show up in the drag (unless specifically designed so on purpose).

The handwaving argument I used was that lift (equal to weight for stationary horizontal flight) is essentially caused by the circulation of the fluid flow around the wing (in a perfect, rotationless, fluid, there is no lift). Now this circulation (by conservation of angular momentum: there was no circulation before the airplane passed, so this circulation around the wing must be compensated somewhere else by an opposite circulation) is usually totally "dissipated" by turbulence behind/below the airplane.
So it seems to be an indication that the more lift you need (and hence the bigger the circulation needed around the wing), the more turbulence you're going to create, and hence the more overall drag.
But of course you could start by a "bad" design that creates more turbulence than strictly necessary to generate lift, and have this extra loss diminish exactly to compensate the increasing turbulence which is necessary to create lift. You could as such keep drag constant or even lower it. You could also introduce a feedback system which measures lift, and actuates the air brakes or not in order to keep drag constant

Drag coefficient is determined experimentally (or using CFD). But there are other considerations.
1. The angle of attack also changes the area, another variable in the equation.
2. Velocity also must be considered, since the slower the aircraft goes, the higher the angle of attack.
3. And even if there is no change in angle of attack, or weight, the Cd STILL changes with a change in velocity (for example, a sphere falling straight down will experience a continuously varying Cd as velocity changes).

So the Cd will change depending on these other variables also, not just weight. The point is that the drag on an object is normally calculated per the equation given by the first post, except without the weight term, and drag coefficient varies according to a wide variety of variables.

To put the weight term into the equation as shown by Kasamba.com is incorrect. The weight term should not be part of the equation.

That's correct, it must be in general a quite involved relationship (which I would think - see my handwaving argument - that for a well-designed airplane, the effective Cd as a function of weight (all else equal, angle of attack determined by the condition of horizontal flight) will increase.

Which is, honestly, just common sense: you will have to throttle the engines harder when the plane is heavily loaded than when it is empty, for exactly the same flight !

 

[russ_watters]

Well, I thought that the question was, all else equal (altitude, velocity, horizontal flight, same airplane), does the total drag depend, or not, on the weight of the airplane ? And my answer to this, is, in general: yes, it does depend on it. As to the specific *formula* I don't know, I would think it is a complex relationship, which, as you say, only comes about from experimental measurements or CFD calculations. I would think it highly improbable that the effect of the weight would not show up in the drag (unless specifically designed so on purpose).

I didn't get much into the CFD, so the way I would do it is use the lift equation to calculate the required Cl for a plane at a certain weight, then look at the l/d graph to see what Cd corresponds to that Cl, and plug it into the drag equation, solving for speed. Of course, lift and drag both depend on speed, so you'd need to do several iterations of that to pin it down (pug the new speed back into the lift equation and find the new AoA...).

I think you'd find, though, that weight has some, but very little effect on max level speed, since at those high speeds, the angle of attack is near zero (it may even be zero if it is an asymetric airfoil) and so drag coefficient is near its minimum anyway. Increasing the weight increases the required aoa by small fractions of a degree, having a very small effect on the drag coefficient.

Where it matters more is takeoff: since your speed is relatively low, more weight would mean a lot more angle of attack to get the same increase in lift...which, of course, is impossible, since it would cause the wing to stall. So the takeoff speed would need to be much higher, while the angle of attack would stay the same.

 

[FredGarvin]

Hey Fred,

But the mass itself isn't slowing down the top speed of the aircraft. The drag created by the increased lift requirements is slowing down the aircraft. I'm not saying in reality you aren't right 99% of the time. I'm saying that when accounting for this theoretically mass does not effect top speed.

I see where you're coming from. I must be more precise with what system I am considering. I had to reread your post a couple of times to come to the same conclusion.

 

[Gokul43201]

How many aircraft besides military fighter jets have a thrust to weight ratio (your first expression) greater than 1...? According to the equation in the OP, most aircraft should not fly.

Yeah, that's right. The equation posted in the OP is wrong.

Now that I've spent a minute thinking about this, the equation of motion of a horizontally flying plane should exactly match that of a free falling object (with the weight of the object replaced by the thrust of the plane) - the two situtations are physically identical. A small correction to the equivalence will come from the loss of mass of the airplane due to combustion+ejection of fuel.

For a free falling body :

$$V_t = \sqrt{\frac{2mg}{C_d \rho A}$$

So, for a plane, it should be :

$$V_{max} = \sqrt{\frac{2*F_{thrust}}{C_d \rho A}$$

The mass (enters into Cd and A, but) does not appear explicitly in the above equation.

Kasamba had better cough up that cash.

 

[vanesch]

I have to appologize here, because I badly read the OP. In fact, I latched on "drag is independent on weight", but didn't read carefully the formula presented by the kasamba expert. In horizontal flight it is wrong of course, because whatever drag change would occur indirectly as a function of weight, would be included in the Cd and so the formula is valid WITHOUT the weight in the case of horizontal flight.

However, the formula is right in the case of stationary vertical flight (only accessible to a few airplanes, like acrobatics and some fighter jets).
So the formula gives you the maximum vertical speed.

 

[NoTime]

I don't know where the OP is going with their question, but asking how weight effects top airspeed raises a red flag for me.

The maximum indicated airspeed of any aircraft is limited by airframe design.
Unlike highway speed limits the risk of exceeding the limit is breaking something and making a hole in the ground.
I never piloted any aircraft where you couldn't exceed that number.

The indicated airspeed is different from the ground speed.
Ground speed goes up significantly with an increase of altitude, even while indicated airspeed remains a constant, assuming no confounding factors like wind.

Perhaps the question you really want to ask is does weight effect fuel consumption.
This question never occurred to me so I don't know the answer.
If there is an effect, it would be very minor compared to other factors.

 

[Gokul43201]

So the formula gives you the maximum vertical speed.

I concur with this. It is the top speed for purely upward vertical flight. For downward vertical flight, there is a greater top speed given by adding the thrust and weight (instead of subtracting).

I think this equation applies to that F15 in one of Clancy's novels (can't recall which one...and I think it's Clancy) that flies straight up to shoot out a Russian Recon-sat.

 

[russ_watters]

I think this equation applies to that F15 in one of Clancy's novels (can't recall which one...and I think it's Clancy) that flies straight up to shoot out a Russian Recon-sat.

Well, a lot of military fighters can do that, but you're thinking of http://www.wpafb.af.mil/museum/space_flight/sf14.htm". It does actually exist (as do most technologies Clancy utilizes in his books), it just wasn't ever deployed (that we know of :uhh: ).

And yeah, that equation could be used along with the fact that at that attitude, Cd is constant because AoA is zero and engine performance varies with altitude, to calculate how high that F-15 could fly before its speed gets too low for control.

I think, though, that the F-15 did a "zoom climb" - started at like mach 2 and then pulled up, decelerating all the way, and never reaching an equilibrium between its engines and drag - exceeding the altitude it could have reached on vertical flight alone.