# Aircraft Design - Reynold's Number & Stalling Speed

• mengshuen
In summary: At high speeds, the plane needs more lift to stay in the air. But as airspeed decreases, the plane requires less lift to maintain altitude. This is why you can stall at a high speed and still have a safe landing.
mengshuen
hello all,

i was reading up on aircraft design one fine day when they talked about landing speed; they have to be higher than one critical speed, the stalling speed.

if i remember correctly, is there another stalling speed, the upper limit? reynold's number increases at increasing speed of airflow, and the air would detach easily, lowering lift and causing turbulent airflow behind the trailing edge. am i correct?

I'm not sure about that aspect of it; aircraft are designed such that their power plants can't take them faster than their airframes are able to handle (in any normal situation).
Remember that a stall is based more upon the angle of attack than the speed, although both are important. And some landings are essentially controlled stalls.
I'll leave this in the hands of the experts now.

at each Rn, there is a different (perhaps unique) AoAcritical for stalling right?

Perhaps you are reffering to the "highspeed stall"? This is a stall that can take place at any speed when a climb or turn (which is a sideways climb) is too sharp. Exceeding a certain angle of attack on the wing will cause a stall, even at high airspeed.

Cool! Simulposting!

Yeah, that's pretty much it. As speed (inertiall forces) increases, assuming viscous forces remain constant, the critical angle gets higher, but it's never infinite. Also, as viscous force decreases (higher altitudes), a stall can occur at a speed and AoA that would have been safe in thicker air.

Here's a graph for a Piper Warior II that shows how to find stall speed for varying conditions. (sorry about the quality, it is a digital photo of a page from a book, compressed to fit the allowed attachment size.)

The Warrior has a "dirty" stall speed of 44 kts

Note that the actual stall speed can vary from about 35 kts (empty plane, minimum fuel, straight flight, full flaps.) to about 70 kts (maximum take off weight, 60 degree bank turn, no flaps).

Landing approach speed is 63 kts.

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Note that stall speed is a way of relating speed and angle of attack for the benefit of the pilot. The stall speed is the speed at which the plane stalls in level flight (or in a level turn) based on the angle of attack increasing in an attempt to stay level (which is why it depends on weight). It's still the angle of attack that causes the stall.

thanks LURCH and janus.

russ_watters: i understand what you are trying to put across, but if the speed is changed, the AoAcritical would change too, no? anyway i don't think any aircraft would hit the "highspeed stall" scenario, unless they are like supersonic? but that's a different story, isn't it?

mengshuen said:
thanks LURCH and janus.

russ_watters: i understand what you are trying to put across, but if the speed is changed, the AoAcritical would change too, no?
A little, but nowhere near as much as the weight affects how much lift is required to keep the plane aloft.

from a few sources on the net and in books, there is only one stalling speed, that is the lower speed that insufficient lift is generated to keep the aircraft in a level flight.

assume the the AoA is 14 degrees, Rn 183 000, and the stall speed is at 24mph, for an airfoil. keeping the AoA at 14 degrees, air density the same, any speed above 24mph will not cause the airfoil to stall?

an airfoil at 14 degrees, with an increasing speed of airflow will cause increased lift. so my question is, it there a limit to this lift? and if so, there exist a upper stalling speed isn't it?

i am quite confused now about the lack of knowledge of my brain :(

For a constant AoA and air density there is only one stall speed.

The limit to lift is the speed at which the structure can no longer support the stresses and breaks apart.

A confounding factor is that the increased lift with speed means that you will go up. Eventually running out of air.

i see. lift is proportional to the square of the airspeed.

p.s. what about in a wind tunnel? a supersonic wind tunnel? with a constant AoA?

NoTime and mengshuen, you really do have it backwards. When airplanes try to maintain level flight, they do not keep a constant AoA. If you lower the speed without raising the AoA, the plane does not stall, it simply starts to decend. In landing, pilots try to maintain a constant AoA and use their throttles to control their sink rate. If you use the stick to control your sink rate, you'll find yourself in an unstable situation - needing more and more AoA to keep level as your speed drops due to the increase in drag.

The reason the stall speed changes is that if you add weight to a plane, you need to raise the AoA to keep level flight for a given speed - hence you will reach the stall AoA at higher speed.

In the graph in http://selair.selkirk.bc.ca/aerodynamics1/Lift/Page9.html" link, you can see that there are 4 curves corresponding to 4 different angles of attack. CLmax occurs at the maximum angle of attack and because of that, the stall speed will be on that curve. Where the stall speed (x-axis) is on that curve is determined by the weight of the aircraft (y-axis).

Using the same curve and some trig, you can figure out how much lift you need at any given bank angle to stay aloft. Ie, at a 60 degree bank angle, your lift vector creates a 30/60/90 triangle with its horizontal and vertical components, with half of the lift acting vertically. As a result, you need double the lift to actually keep the plane aloft.

...And using the other side of the triangle, you can calculate the radius of the turn.

[warren, aren't you a pilot...?]

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mengshuen said:
p.s. what about in a wind tunnel? a supersonic wind tunnel? with a constant AoA?
In a wind tunnel, as long as the wing is below the critical angle of attack, it won't stall in a very wide range of speeds.

Everything changes when you get to supersonic flight, though.
an airfoil at 14 degrees, with an increasing speed of airflow will cause increased lift. so my question is, it there a limit to this lift? and if so, there exist a upper stalling speed isn't it?
In general, no. At 14 degrees AoA, the upper limit of lift is probably the speed at which you rip the wings off the airplane.

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russ_watters said:
NoTime and mengshuen, you really do have it backwards. When airplanes try to maintain level flight, they do not keep a constant AoA. If you lower the speed without raising the AoA, the plane does not stall, it simply starts to decend.
I'm somewhat confused about where you are going here.
What does this have to do with the stall speed of an airfoil at constant AoA and air density?

In flying a plane you do maintain a more or less constant AoA.
More power = up, less power = down.
Changeing the AoA trades speed for height.
If you do this too greatly you stall or exceed Vne.
If you want to go faster at the same altitude then you have to increase power and reduce AOA or vice versa.

russ_watters said:
In landing, pilots try to maintain a constant AoA and use their throttles to control their sink rate. If you use the stick to control your sink rate, you'll find yourself in an unstable situation - needing more and more AoA to keep level as your speed drops due to the increase in drag.
In landing, while you can maintain a constant AoA and get the job done, it tends to result in excessive float time in ground effect.
Not to mention it really annoys your instructor.

Generally you want to slowly increase your AoA to increase drag reducing speed for the final landing stage and use power to control your sink rate if necessary.
Increasing the AoA too quickly results in pop up.
The point being the transition to ground effect and to stall out as you touch the ground.
If you use the stick to lower the AOA and push the plane to the ground you tend to end up with multiple landings and an extremely high taxi speed.
Neither of which is a good thing.

Yes this is somewhat unstable and tremendously difficult to learn to do correctly and there are corection factors for gusty winds.

I think that perhaps the way that I was taught to fly might help explain it to the OP. NoTime already alluded to this. Throttle controls altitude; yoke controls speed. That's intuitively backwards, but essentially the way it works. Of course, both have to be used in concert. As for landing, I was taught to pick a spot on the runway and keep it pinned in exactly the same 'pixel' of the windscreen. Sideslipping and whatnot are just variations on the theme.

Danger said:
I think that perhaps the way that I was taught to fly might help explain it to the OP. NoTime already alluded to this. Throttle controls altitude; yoke controls speed. That's intuitively backwards, but essentially the way it works. Of course, both have to be used in concert. As for landing, I was taught to pick a spot on the runway and keep it pinned in exactly the same 'pixel' of the windscreen. Sideslipping and whatnot are just variations on the theme.
True, and they make some effort to point this out.

For the landing that's also true up to the point where you reach threshold.
Lots of airports have VASI to help with final approach glidepath, much the same as the pixle thing.
Or the electronic version for IFR.

Last little bit is different though
You want to get the nose up and the tail down.

Ah yes, the flare. Very familiar with it. Nothing quite like coming out of a crab on the end of the flare in a 40 knot crosswind. Anyhow, I didn't mention it before because I figured that it would just further confuse the OP.

Danger said:
Ah yes, the flare. Very familiar with it. Nothing quite like coming out of a crab on the end of the flare in a 40 knot crosswind. Anyhow, I didn't mention it before because I figured that it would just further confuse the OP.
40 knots
That's one heck of a sidesliping crab flare.
Another knot or two you could have gone VTOL and landed perpendicular to the runway

What can I say? Canadian weather. You get used to it.
Mind you, we didn't go if it was more than 30 knots or so unless, as in the 40k example, the angle was less than 10 degrees from head-on.

Err, that 10 degree is only about 7 knot crosswind.
But still, things can get funky real quick with that kind of breeze.

Ooos! Sorry. Yes, I expressed that badly.
Good catch.
The nasty part was that it would switch direction in a matter of a couple of seconds.

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## 1. What is Reynold's Number and how does it relate to aircraft design?

Reynold's Number is a dimensionless number that is used to predict the behavior of fluids, such as air, around objects. In aircraft design, it is used to determine the flow conditions around the wings and other components, which is crucial for determining their performance and efficiency.

## 2. How does Reynold's Number affect the stalling speed of an aircraft?

Reynold's Number plays a significant role in determining the stalling speed of an aircraft. As the Reynold's Number increases, the flow around the wings becomes more turbulent, resulting in a higher stalling speed. This is why larger aircraft, which have higher Reynold's Numbers, tend to have higher stalling speeds compared to smaller aircraft.

## 3. Can Reynold's Number be used to compare the performance of different aircraft designs?

Yes, Reynold's Number can be used to compare the performance of different aircraft designs. It is commonly used in wind tunnel testing to evaluate the aerodynamic characteristics of different designs and make comparisons between them. However, it should be noted that Reynold's Number is not the only factor that affects the performance of an aircraft.

## 4. How can Reynold's Number be calculated for an aircraft?

Reynold's Number can be calculated using the formula Re = (ρ * V * L) / μ, where ρ is the density of the fluid, V is the velocity of the aircraft, L is the characteristic length (such as the wingspan), and μ is the dynamic viscosity of the fluid. This formula can also be simplified to Re = (V * L) / ν, where ν is the kinematic viscosity of the fluid.

## 5. Are there any limitations to using Reynold's Number in aircraft design?

While Reynold's Number is an important factor in aircraft design, it is not the only factor that affects the performance of an aircraft. Other factors such as airfoil shape, angle of attack, and surface roughness can also play a significant role. Additionally, Reynold's Number is only a predictive tool and may not always accurately reflect the actual performance of an aircraft in real-world conditions.

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