Calculating Stall Speed of an aircraft

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Laurelix

Airman 1st Class
290
185
Jun 13, 2016
So why is stall speed so significant?
Firstly the obvious one is that planes with lower stall speeds have smaller turn radius and if they have good power to weight ratio they can do a sustainable low radius turns such as the A6M Zeros.

If you ever seen any of my performance posts for planes, i usually state their stall speed, this is how i was able to get those figures for different planes.

Guide to using this calculator:
Airplane Aircraft Wing Lift Design Equations Formulas Calculator - Velocity

Let's do BF-109E as an example.
Kurfürst - R.A.E. - Messerschmitt Me.109 Handling and Manoeuvrability Tests


• It says that BF-109E has CL_Max of 1.4 without its flaps deployed and that its stall speed is 95.5mph (154km/h) at 5580lb (2530kg) loaded weight.
- First the calculator requires Lift Force value. This is achieved by multiplying the weight (kg) by gravitational pull (x9.81). 2530 x 9.81 = 24819 Newtons

- Wing Lift Coefficient is already stated for us being 1.40
(Infact all BF-109A/B/C/D/E/F/G/K wings have 1.4 CL Max)

- Air Density at Sea Level is 1.225kg/m3
If you want to find the stall speed for a different altitude, you will use a value representing different altitude.
U.S. Standard Atmosphere
Here under ''U.S. Standard Atmosphere Air Properties - SI Units'' are the air density values in kg/m3 for different altitudes.

- Wing Area, well the BF-109E has 16.2m2
(If you want to find stall speed with flaps down you have to add flap area on top of wing area and set the correct CL_Max value, which in this case for BF-109E would be 1.9 as stated with flaps down)





All we need to do now is press "calculate"





We got 152km/h stall speed for BF-109E whilst the British have 154km/h (probably cuz the stall was performed few hundred metres above sea level)

================================

There are few other fun things you can do with this... like 'Why cant SR-71 Blackbird reach altitude of 25,000m?' (has 24,000m service ceiling)
At 25,000m the air density is 0.04008kg/m3

SR-71 has like 250km/h Stall Speed at Sea Level. At 25,000m altitude tho the stall speed is 1381km/h, and 1115km/h is Mach 1.0 at 25,000m...

'The Karman line is named after Theodore von Kármán (1881–1963), a Hungarian American engineer and physicist, who was active primarily in aeronautics and astronautics. He was the first person to calculate the altitude at which the atmosphere becomes too thin to support aeronautical flight and arrived at 83.6 km (51.9 miles) himself. The reason is that a vehicle at this altitude would have to travel faster than orbital velocity to derive sufficient aerodynamic lift to support itself. The line is approximately at the turbopause, above which atmospheric gases are not well-mixed. The mesopause atmospheric temperature minimum has been measured to vary from 85 to 100 km, which places the line at or near the bottom of the thermosphere.

The SR.71 stall speed would be 64,353km/h if it ever reached the altitude of 80,000m. It would have to fly over Mach 66.3 just to avoid stalling
 
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Remember that service ceiling is a number set by climb performance, while max altitude is set by maintenance of level flight only

FAI official altitude record for the SR-71 is 25,929 meters and has unofficially been much higher. The big problem for the-71 above the published service ceiling of 26,000 meters is compressor inlet temps and flow stability. The official record flight was on 28 July 1976.


Been around 35 years since I did transonic wind tunnel model design and testing, but from what I remember, the calculations get a bit more complex in the transonic region and then smooth out in the Mach region, until you start having multiple shock waves on the structure. The theory side of things was not my strong point.
 
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I'm not so sure all Bf 109 have CL Max at 1.4. They have leading edge slats that basically cover the aileron area and serve to keep the airflow attached to the wing going over the ailerons during stall, but they ALSO increase the CL Max of the area they cover. It amount to about 1/3 of the wing span, and SHOULD raise the average CL Max for the entire wing when they are deployed.

I mention the slats only because this thread mentions stall speed, and the slats will be deployed before the stall happens, sometimes even asymmetrically.
 
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Calculating the stall speed with a notional CL doesn't really work. Usually the CL you find in your reference is calculated from the stall speed, which itself is found by flight testing. You also need to be sure the stall speed is true air speed in the flight test. If you take the speed in the pilot's manual it will be the indicated air speed. That is what the pilot needs to know, what number will be on the ASI when the bottom drops out. He is not interested in the TAS except for navigation. For comparison between different aircraft use the stall speed in the manual with the ASI correction applied. That should be in the manual too.

The stall starts at the wing root (usually) where fuselage interference, prop wash and asymmetrical flow all act to make the speed differ from what it might be using the reference book CL for the wing aerofoil section.
 
Laurelix said:
So why is stall speed so significant?
Firstly the obvious one is that planes with lower stall speeds have smaller turn radius and if they have good power to weight ratio they can do a sustainable low radius turns such as the A6M Zeros.
Click to expand...
The Zero was a carrier based plane, like all such planes it needs a low stall speed and control near stall speeds to land on a carrier.
 
K5083 said:
Calculating the stall speed with a notional CL doesn't really work.
Click to expand...
Wait, how do you calculate this this then? As a fast and loose estimate I often take power-off stall x square root of the rated g-load for turns, and power-on for loops. The TAS figures require you to know the airspeed correction figures (at least that can usually be found in flight-manuals).
 
My intended meaning was you can calculate it, but you only get a ballpark figure. You will need real flight data. Your Cl is an ideal. Flows over the wing, affected by propwash, wing twist, whatever rudder you need to input and any number of other factors, mean you are going to do worse in practice. Or sometimes better because the effective airspeed over the wing downstream of the prop under power will work in your favor. So does any downward component of thrust due to angle of attack. Anyhow, the result is that you need flight test data for the applicable speed, configuration and power setting.
 
Would it be redundant to create a thread that includes all the following data so we have reliable data at our disposal
  1. Coefficient of Lift
    • Flaps up
    • Flaps either down or at combat settings used in flight
  2. Wing Area
    • Flaps up
    • Flaps down depending on flap type
  3. Stall Speed
    • Power on
    • Power off
The power on/off stall speed probably seems to be the hardest one to come across since the British don't even seem to bother to include both, and the figures are sometimes based on power-settings that are either low power-settings or settings that don't correspond to various combat settings (i.e. military or WEP settings).
 
There is little point in high power-on stall speeds. At the speeds you'll typically be doing with these power settings, you'll likely be getting high-speed stall, which can happen at any speed.
Low power stall settings are typically at approach and landing power settings, as this is where you'll most likely experience a power-on stall. They also give a good indication of approach speeds. Modern GA typically use 1.3 Vs as a guideline for approach.
 
gumbyk said:
There is little point in high power-on stall speeds.
Click to expand...
Actually it could be used for loops since that's symmetrical flight. The complexity of turns tend to make using power-off stall or using the weight/coefficient of lift as the means of calculating turn-rates. There's probably other uses for this as well.
Low power stall settings are typically at approach and landing power settings, as this is where you'll most likely experience a power-on stall.
Click to expand...
Go-arounds and wave-offs do hinge upon large applications of power...
 
Stall speed is only valid for 1G applications. You don't fly a loop at a constant G loading, so your stall speed will vary all te way around.

In a high-power WW2 fighter, stall speed is the least of your worries on a go-around. Not rolling inverted by putting on too much power is a far more pressing concern. And, if you've been approaching at the correct speed, you'll have a buffer over stalling. All go-around accidents I've seen and heard of have been due to not following correct order of things.
 
gumbyk said:
Stall speed is only valid for 1G applications. You don't fly a loop at a constant G loading, so your stall speed will vary all te way around.
Click to expand...
I just figured you could calculate stall speed times the square root of the g-load. So if you were flying level but looping, you could use power-on, and for turns, power-off.
 
Zipper730 said:
I just figured you could calculate stall speed times the square root of the g-load. So if you were flying level but looping, you could use power-on, and for turns, power-off.
Click to expand...
Sorry, I forgot to add that published figures are for straight and level, 1G flight. Climbing, descending or turning will change the figures.

The problem is, that you stall at an angle of attack of the wing, not at a speed, so you can stall at pretty much any speed below Maneuvring Speed (Va, where it will break before it stalls). Any control inputs will change stall onset, and speed. An aircraft in flight is a dynamic system, and doesn't lend itself easily to simple calculations.
If you've ever seen an aerobatic aircraft do a snap roll, that's an accelerated spin with rudder input.
 

The Bf 109 has slats for about 1/3 of it's span. Basically, they cover the aileron span. When the slats are out, the CL changes for the better, but only for the slatted area, not the rest of the wing. This is not a straightforward calculation. You very certainly will NOT get CL = 1.4 for the entire wing area. If you HAVE a Bf 109, you could measure and calculate the slatted area. If you don't have a Bf 109 handy, it isn't quite so easy.
 
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