Wing Loading & Stall Speed Question

[Zipper730]

For some reason my mind doesn't seem to be working as well as it should be: I understand that if a plane's weight doubles the plane's stall speed increases by the square root of 2 and when calculating for g-load on stall-speed you generally multiply the square of the load-factor against stall-speed to determine what speed the aircraft can pull that load-factor at a bare minimum.

What I'm curious about is the matter of increasing wing area: If the wing area increases two-fold (weird if, but...), does the stall speed decrease by the square root of two or the square of two (four)? I'm curious because there was an aircraft design which had a wing-area of 450 square feet and a proposed derivative with a wing area of 467 square feet (IIRC), I'm curious if it would be (467/450)^2 or sqrt(467/450) to calculate the effect on stall speed?

drgondog , M MIflyer , MiTasol , P pbehn , X XBe02Drvr

 

[pbehn]

For some reason my mind doesn't seem to be working as well as it should be: I understand that if a plane's weight doubles the plane's stall speed increases by the square root of 2 and when calculating for g-load on stall-speed you generally multiply the square of the load-factor against stall-speed to determine what speed the aircraft can pull that load-factor at a bare minimum.

What I'm curious about is the matter of increasing wing area: If the wing area increases two-fold (weird if, but...), does the stall speed decrease by the square root of two or the square of two (four)? I'm curious because there was an aircraft design which had a wing-area of 450 square feet and a proposed derivative with a wing area of 467 square feet (IIRC), I'm curious if it would be (467/450)^2 or sqrt(467/450) to calculate the effect on stall speed?

drgondog , M MIflyer , MiTasol , P pbehn , X XBe02Drvr

Are you planning on taking passengers in this aircraft?

 

[MiTasol]

Good question but it is too many years since I did that theory so I cannot give an answer that I would trust but I will comment that a multitude of other factors like wing washout will affect the answer.

 

[Simon Thomas]

 

[drgondog]

Simon presented the fundamental relationship for your question. That said, for CL vs alpha, the stall point varies also by aspect ratio of three dimensioal airfoil sections. All Cl vs Alpha presented for airfoils in say, Abbott and Doenhoff, are for infinite span two dimensional wings with no tip effects. The two dimensional data must be modified to account for Aspect Ratio where low AR achieves lowest angle of attack before stall 'break occurs'

For your question to have a neutral answer with respect to increase in span area (S), you must also increase the span (b) and chord MAC.

AR = same = S1/b1^2 = S2/b2^2
S2/S1 = 2 for double area; 2 = b2^2/b1^2; 2(b1^2) =b2^2
For Aspect ratio to remain same, b2= sqrt(2*b1^2).

For this stall condition velocity to remain the same, b2= sqrt(2) x b1.

For lower stall speed, increase the span/hold Wing Area (S1) same ---------> AR higher, CL vs alpha break point higher.

If you increase b by factor of 2 but hold Area S1 constant: AR1 = S1/b1^2; AR2 = S1/(2*b1^2); AR2/AR1 = S1/(2*b1^2)/[S1/b1^2]; AR2 = AR1*Sqrt 2) = 1.414 AR1

This condition will yield a higher break point and angle of attack (Higher CL) before stall and makes possible lower airspeed for same gross weight condition.

BTW - this discussion, that of section lift co-efficients, is why one May Not assume lower wing loading means better turn performance. Equally important for best constant altitude turn performance are 1.) Maximum CL vs angle of attack, 2.) Power Available vs Power Reqired, 3.) N load

 

[Snautzer01]

Thats dirty talk right there.

 

[Simon Thomas]

Often questions like this are framed in terms of the desired solution.
No designer ever looks at a plane and says "I want it to have 50% more wing area".
The questions should be framed around the desired mission improvement. "I want 20% more range/speed/payload/mpg/whatever".
As shown by drgondog, there are way too many variables to optimise than a simple increase in wing area.
Have you got more details on what you are trying to achieve?

 

[Shortround6]

The questions should be framed around the desired mission improvement. "I want 20% more range/speed/payload/mpg/whatever".

And many times the whatever is the take-off and landing speed,

Or 20% more range/payload at the same take-off or landing speed.

 

[Zipper730]

View attachment 732084

While this should be something easily understood, I had to plug in numbers to make sense of this (jeez): As I calculate this, the speed decreases by the square of the relationship of the wing area, so if wing area goes up by 2, speed decreases by the square root of 2.

Am I correct?

Simon presented the fundamental relationship for your question. That said, for CL vs alpha, the stall point varies also by aspect ratio of three dimensioal airfoil sections. All Cl vs Alpha presented for airfoils in say, Abbott and Doenhoff, are for infinite span two dimensional wings with no tip effects. The two dimensional data must be modified to account for Aspect Ratio where low AR achieves lowest angle of attack before stall 'break occurs'

Both wings had the same aspect ratio (that was actually something of interest in my case). It was effectively an advanced F8U-3 derivative and I asked him if the enlarged wing (which the book listed as having a lengthened leading edge that helped deal with the CG drifting excessively far forward) had the same aspect ratio and if the aircraft was also longer. He said the plane was longer and I was able to determine the length of the aircraft and the wing-span by using the position of the fold-line (which would be unlikely to change). While I don't remember how I calculated the wing-area based on what I had, I apparently got the numbers from that and it was either 467 or 469 square feet with the aircraft being around the same as the RF-4B (which struck me as a bit long for a carrier plane, but it wasn't unheard of with RF-4B's being carrier suitable).

In an ironic twist, the CG was somewhat rectified by the fact that the AIM-9 pylons added (which featured one pylon per missile instead of the F8U-2/F-8C's Y-pylon) actually produced a small amount of lift up front which helped balance things out to some extent.

 

[pbehn]

The Spitfire could easily have its wing area increased or decreased. Taking the wing tip off increased rate of roll and decreased rate of climb, extending the wing tips increased maximum service ceiling on an aircraft that was a bit of a dog at almost all altitudes.

 

[Simon Thomas]

I suggest the Roncz spreadsheet for doing rough design calcs. I am not familiar with turbine, so I don't know how to implement thrust in place of hp in his calc.

Downloads

The following files are available for free download. This spreadsheet will allow you to get all the major measurements right. You will need to make some basic choices (eg: desired stall speed, e…

rtfmaero.wordpress.com

John Roncz is a legend of airfoil design. He worked on many Rutan designs including Voyager, the Pond Racer and numerous others. He also wins the prize for the most creative names for airfoils.

 

[Greg Boeser]

Simon presented the fundamental relationship for your question. That said, for CL vs alpha, the stall point varies also by aspect ratio of three dimensioal airfoil sections. All Cl vs Alpha presented for airfoils in say, Abbott and Doenhoff, are for infinite span two dimensional wings with no tip effects. The two dimensional data must be modified to account for Aspect Ratio where low AR achieves lowest angle of attack before stall 'break occurs'

For your question to have a neutral answer with respect to increase in span area (S), you must also increase the span (b) and chord MAC.

AR = same = S1/b1^2 = S2/b2^2
S2/S1 = 2 for double area; 2 = b2^2/b1^2; 2(b1^2) =b2^2
For Aspect ratio to remain same, b2= sqrt(2*b1^2).

For this stall condition velocity to remain the same, b2= sqrt(2) x b1.

For lower stall speed, increase the span/hold Wing Area (S1) same ---------> AR higher, CL vs alpha break point higher.

If you increase b by factor of 2 but hold Area S1 constant: AR1 = S1/b1^2; AR2 = S1/(2*b1^2); AR2/AR1 = S1/(2*b1^2)/[S1/b1^2]; AR2 = AR1*Sqrt 2) = 1.414 AR1

This condition will yield a higher break point and angle of attack (Higher CL) before stall and makes possible lower airspeed for same gross weight condition.

BTW - this discussion, that of section lift co-efficients, is why one May Not assume lower wing loading means better turn performance. Equally important for best constant altitude turn performance are 1.) Maximum CL vs angle of attack, 2.) Power Available vs Power Reqired, 3.) N load

I wonder how many flight sim games fail to recognize that last part?

 

[Zipper730]

Message Deleted

 

[drgondog]

And many times the whatever is the take-off and landing speed,

Or 20% more range/payload at the same take-off or landing speed.

for combat aircraft, such speeds are important - but even more important are the take off and landing roll distance to clear a 50 foot obtacle at either max gross weight or soe other designed load out - usually GWmax.

 

[drgondog]

I wonder how many flight sim games fail to recognize that last part?

A game type flight Sim is a classic example of KISS and having the same rules based on CLmax, Vmax for a turn at some defined N when THp avail=Thp required where simple assumptions like incompressible flow, parasite drag is supplied from available wind tunnel hisory, all dimenions 'validated' by Wiki lead to to calculations that can be extraced from a 1st year aero book or, say Aerodynamics for Naval Aviators'.

BUT, to your sneaky question and a good one - to get to intermediate sophistication of predictable model of something like a Mustang?

Power Available:

1. a subroutine to calculate Ram air and apply to all altitudes and supercharger stages
2. a subroutine and table set to calculate mass flow rate of engine exhaust as a f(ambient static pressuer, engine charge consumption, MP, engine discharge consumption (Me), total stack area. (NACA derivative charts), tota exhaust stack area, angle of stacks to free flow ----> jet thrust and Me
3. a subroutine of Hamilton Standard prop parameters as function of tip speed, advance ratio, blade angle, etc. (NACA testing and reports for thrust efficiency, power coefficient and advance ratio).
4. a subroutine to adjust propeller efficiency based on altitude, flight speed as a function of Ham Std data and calculations. (3. and 4. to yield prop efficiency and Thrust coeffient Tc))

Calculate THP avail = (prop efficiency)*THP(altitude and ram ajusted)*V/375
THPjet = Tjet(calculated in 2. above)*V (exhaust)* Me (mass flow rate, slugs/sec)/375
THPavail = THPprop + THPjet


Power Required

1. CDp-basis minimm values for the airframe, usually derived from low speed, low RN (~ 2x 10^6) scale model wind tunnel tsting
2. delta CDp1 values for misc. items such as gun ports, exhaust stack, radio masts, leaks, friction, etc. Data origin usually derived from estimeated or full scale actual values.
3. a subroutine to calculate new airframe CDp as function of change to RN. RN changes with Velocity and altitude and viscosity.
4. a subroutine to access table CD vs CL for delta CDcl values for increase in parasite drag due to angle of attack (climb, low speed, cruise at high altitude) - also derived from wind tunnel.
5. a suboutine to apply Cdp values due to CL changes to external rack/bomb/fuel tank which are pressure/profile drag items - considered independent of Reynolds number.
6. a subroutine to calculate incremental pressure drag losses over that portion of the airframe immersed in prop vortex. CDvortex = CDpa*(1+8Tc/pi) over enclosed airframe surfaces. CDps=CDpa(Vs*2/Va)^2. Va= freestream velocity; Vs = slipstream vortex velocity. DelCDps=CDpa(8Tc/pi)
7. a subroutine to calculate the delta THP loss due to slipstream. DelTHPreq=DelCDps*S*V^3*c/146000 ---S = wing area, c = mach no. Tc= Prop thrust coefficient.
8. a subroutine to calculate incremental pressure drag of cooling system varying with speed and CL ( wind tunnel). From NAA, Assume CDc=0 for cruise, CDc=0.0064 for climb. Note that this value is close to total wing contribution.
9. a subroutine to calculate CD vs M multiplier
10. Calculate Base CDp for combined pressure/profile drag and parasite drag -
11. Calculate new flight condition CDp based on CD vs RN subroutine.
12. Add Delta CDp for Angle of attack increases to CL.
13. Calculate air momentum loss due to carb. -----> for P-51, THPcarb =39.1*Mcarb*(V/100)^2
14. Calculate CL for specific GW, V, Wing area and altitude air density.

Calculate Induced Drag = Cdi =(CL)^2/AR*pi
A. Calculate the total drag for specific flight condiion; CDtotal = (CDp + del CDp1 +del CDcl) CDm/CD-base + CDi.

To calculate the THPreq for a desired airspeed V:
For an 8600 pound P-51B-1, at 61"MP, at 29000 feet, S=233

B. From basic aero texts the THPreq = W*CD/CL*V/375. For the above conditions, THPreq = 22.95*(CD/CL)*V where V in mph. for 475mph, THPreq= 1547. for 442mph, THPreq =1260

Another approach, using the above process:
THPavail = THPprop + THPjt - THPcarb - THPvortex (from A and B above).

NOTE !! Step 1 in Drag discussion above is often and incorrectly named 'CDo' and as such plugged into all drag calculations - when it is Only valid for very low speed 'zero lift drag' at SL for the RN specifid. It changes (rapidly) as function of RN as airspeeds increase from the wind tunnel origin to different altiudes.

Note 2: You now have Thrust HP required for level flight to achieve a Desired airspeed.

Note 3: ALL the above analytics apply to steady symmetrical, constant altitude/speed performance analysis. What happens when you are in high G asymmetrical and rapidly losing airspeed as well as altitude and energy? First prop effiiency greatly suffers at large blade angle/max power/low(er) airspeeds, exhaust jet values may change - adversely affecting THPavail for same airspeed. Second, the asymmetric lift conditions on each wing (high CL and drag on high wing which will stall sooner on that wing), large rudder and elevator inputs for trying to maintain hard turns at constant altitude ---> leads to rudder/elevator trim drag additions to base drag calcs for a pilot stuggling for a carved turn. This further increases THPreq to maintain high G - same altitude. In addition, this is yet another pending snap roll opportunity.

For a Mustang specifically, there will be high cooling drag compared to cruise and as airspeed deteriorates such will probably approach climb cooling drag values. For an FW 190 with no washout outer 20% of wing span, this is a bad place to be when the abrupt stall breaks in an over aggressive turn.

I suspect a rare gamer programmer that considers all the above, MUCH Less - have access to Bf 109, FW 190, Spitfire, etc details and wind tunnel data that I have relative to only the P-51.

I doubt seriously that I will ever approach this in detail again. Take what you want and leave the rest.

BTW - I haven't checked the steps abover - if mistakes, then KMACYOYO as we said in the consulting biz. 'kiss my ass kid, you're on your own".

Note: I devoted some time on this to explain why I roll my eyes when a gamer sez in no particular order:
"I used CDo for the parasite drag calcs" (but no reference to context of RN, or whether CDp1 or CDp2 relative to CL related pressure/profile is a known factor.
"The Flat plate drag is X compared to other guy's Y" without explaining the drag calcs, the prop effciency, or even if they compared FP drag at same airspeed and altitude for comparisons.
"Higher CLmax or Lower Lift loading'' will achieve bettter turn rate and radius" - True, all else equal, But..

 

[Barrett]

Simon presented the fundamental relationship for your question. That said, for CL vs alpha, the stall point varies also by aspect ratio of three dimensioal airfoil sections. All Cl vs Alpha presented for airfoils in say, Abbott and Doenhoff, are for infinite span two dimensional wings with no tip effects. The two dimensional data must be modified to account for Aspect Ratio where low AR achieves lowest angle of attack before stall 'break occurs'

For your question to have a neutral answer with respect to increase in span area (S), you must also increase the span (b) and chord MAC.

AR = same = S1/b1^2 = S2/b2^2
S2/S1 = 2 for double area; 2 = b2^2/b1^2; 2(b1^2) =b2^2
For Aspect ratio to remain same, b2= sqrt(2*b1^2).

For this stall condition velocity to remain the same, b2= sqrt(2) x b1.

For lower stall speed, increase the span/hold Wing Area (S1) same ---------> AR higher, CL vs alpha break point higher.

If you increase b by factor of 2 but hold Area S1 constant: AR1 = S1/b1^2; AR2 = S1/(2*b1^2); AR2/AR1 = S1/(2*b1^2)/[S1/b1^2]; AR2 = AR1*Sqrt 2) = 1.414 AR1

This condition will yield a higher break point and angle of attack (Higher CL) before stall and makes possible lower airspeed for same gross weight condition.

BTW - this discussion, that of section lift co-efficients, is why one May Not assume lower wing loading means better turn performance. Equally important for best constant altitude turn performance are 1.) Maximum CL vs angle of attack, 2.) Power Available vs Power Reqired, 3.) N load

I was lost at "square root of 2" but surely admire Bill's knowledge!
My method of testing stall speeds: play with the throttle and pitch angle, then try to remember what happens in each combination...

 

[SaparotRob]

I was lost at "square root of 2" but surely admire Bill's knowledge!
My method of testing stall speeds: play with the throttle and pitch angle, then try to remember what happens in each combination...

That's the kind of aeronauviating I can understand.

 

[MIflyer]

Download your own copy: Aerodynamics for Naval Aviators : Free Download, Borrow, and Streaming : Internet Archive

 

[thunderbird]

Course, one can't double the size of a wing without also considering that the wing will now weigh more. And the landing gear, fuselage, will have to be beefed up which will also increase the vehicle weight, and now maybe you need more fuel to achieve the required payload and range, which adds more weight and you'll need a bigger tail for trim, which adds a little more weight... So the ratio of stall speed to wing area increases by more than the square root of the area.

 

[MIflyer]

Course, one can't double the size of a wing without also considering that the wing will now weigh more.

A friend of mine said he knew a guy who decided to convert a J-3 Cub into a biplane. The result was that the aircraft had lower performance in every parameter.