Stalling speed related to load factor

12 Answers

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   Brian on Jul 10, 2013

   Load factor is mathematically equal to lift divided by weight. When lift is equal to weight, load factor is 1. A sharp pull back increases lift, weight remains the same, and the result is an increase in load factor.

   Stall speeds change with load factor is indicated by Stall speed corrected for load factor = Sqrt (load factor) * stall speed.

   Think of it this way, how do you determine stall speed? Simple, rewrite the lift formula from Lift = 1/2 (pressure) * (velocity squared) * (wing area) * (lift coefficient) to:

   Velocity stall = Sqrt [ 1/2 (lift) / (pressure) * (wing area) * (lift coefficient) ]

   Since lift is on top of this equation, if lift must be increased, either by carrying more weight or by pulling higher g’s, then so does the velocity of stall.

   I’ll let someone else explain it in words if following the math is not your style. 🙂

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   Ramkumar_Sp on Jul 12, 2013

   Stalling speed and load factor……

   stalling speed is the minimum speed at which the flight can flew.
   As we know that this speed will occur when coefficient of lift is max.from lift equation we can see that speed which is inversely proportional to the lift.so definitely speed is minimum.at that time lift is equal to weight then our load factor became 1
   so if the speed become stalling speed, load factor will be 1

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3. 
   

   
   

   Ramkumar_Sp on Jul 12, 2013

   Stalling speed and load factor……

   stalling speed is the minimum speed at which the flight can flew.
   As we know that, this speed will occur when coefficient of lift is maximum.From lift equation we can know that, speed which is inversely proportional to the lift.so speed is minimum.when CL is max .At that time lift is equal to weight (aircraft gets aloft from the round )then our load factor became 1.
   speed become stalling speed,then load factor wiil be 1.

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4. 
   

   
   

   Randy Lewis on Jul 12, 2013

   To answer your question about stall speed and load factor:

   Load factor, in logical terms, is how much “load” (weight) an airplanes lifting surfaces (wings and horizontal stabilizer/stabilator) can support. If I hand you a suitcase that weighs 40 pounds, I’m sure you’d have no problems – I then hand you a 400 pound suitcase, and your “lifting surfaces” may not be able to support that. A 2500 pound airplane must produce 2500 pounds of vertical lift to maintain altitude, and may be capable of producing up to 10,000 pounds of lift (if the maximum positive load factor of the airplane is +4.0 G’s. 2500 * 4 = 10,000).

   Let’s now consider two things you may already know – the law of conservation, which states that energy cannot be destroyed, it only changes form, and the simple fact that an airfoil stalls at a critical angle of attack. Also recall that, to turn an airplane, you must convert vertical lift to horizontal lift (Note: this is the “lift vectors” reference). As we increase our bank angle (assuming constant speed), we pull further back on the flight controls to maintain altitude, increasing the wings angle of attack to produce more lift. Why? Because we traded some energy of vertical lift, and converted it into horizontal lift, we then add backpressure to produce more lift to compensate. Increasing our angle of attack then gets us closer and closer to our critical angle of attack.

   Two things to consider: exceeding the critical angle of attack, which will always result in a stalled condition, and exceeding the load factor of the airplane (which can be found in Section 2: Limitations of your AFM/POH). Two totally different things!

   Randy

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5. 
   

   
   

   Brian on Jul 12, 2013

   Randy, your definition of load factor, while common amongst us pilots, is quite inaccurate. Load factor effects all portions of an airplane, not just the lifting surfaces. In fact, the primary lifting surface, to use your example, may be able to hold 10,000 pounds. It can still hold 10,000 pounds if you reduce the weight to 2,000, but now you’re pulling 5 g’s and the 200 pounds in your baggage compartment might travel through the floor. Fear not though, the wings will still be on. 🙂

   I hope my sarcasm is taken lightly, I mean no disrespect and just recently came to this realization myself. Just remember load factor is the increase in load due to centripetal force experienced by any (airplane, car, roller coaster, you in one of those spinning things at the amusement park) moving body.

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6. 
   

   
   

   Sam Dawson on Jul 12, 2013

   A good example of the above discussion can happen in an aerobatic airplane with a stall horn during a loop.
   At the beginning of the loop the stall horn will be screaming. Makes sense. You yank back into a 5G turn, or pitch up.
   At the top of the loop something funny happens to the uninitiated. You are going about 30 MPH. Well below the 1G stall speed. But no stall horn (if you are doing it right). Because you are also at about 0 Gs. If you are at 0 Gs the airplane weights… zero.
   The last 3/4 of a loop the airplane is pointed to the ground and speed is about 120 MPH (depending on the airplane), yet the stall horn is blaring as you ride the edge of a stall.

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7. 
   

   
   

   RandyLewis on Jul 13, 2013

   Brian – no hard feelings, it’s all in good fun, and I welcome criticism – aerodynamics is not simple. I value your opinion as well, however I still stand behind my answer. Let me explain how I derived my answer:

   By definition, load factor is the lift the aircraft produces divided by aircraft weight. Therefore, we can use the words “load factor” and “G’s” interchangeably (reference Aerodynamics for Naval Aviators). Yes, load factor does affect more than just the aircrafts lift devices – it puts stress on the entire aircraft. However the designed structural limits (maximum load factor) is pertinent to “the wing, wing carrythrough, and attaching structure whose failure would be catastrophic…” (Part 23, “Fatigue Evaluation”) The FAA is more concerned with the aircraft than lost luggage.

   Load factor is a byproduct of the aircrafts weight and centrifugal force (“In a constant altitude, coordinated turn in any aircraft, the load factor is the result of two forces: centrifugal force and gravity.” 4-29 PHAK). The PHAK also states that “study…has revealed that the aircraft’s stalling speed increases in proportion to the square root of the load factor. This means that an aircraft with a normal unaccelerated stalling speed of 50 knots can be stalled at 100 knots by inducing a load factor of 4 Gs. If it were possible for this aircraft to withstand a load factor of nine, it could be stalled at a speed of 150 knots.”

   I am open to discussion and criticism of my findings, and to all viewers, please feel free to contact me directly with any questions or comments.

   Randy

   PS – For an applied use of load factor and stall speed, reference Rod Machado’s discussion about maneuvering speed, found here: http://flighttraining.aopa.org/magazine/1999/March/199903_Flying_Smart_A_New_Look_at_Maneuvering_Speed.html

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   Brian on Jul 16, 2013

   23.787 (1) Be designed for its placarded maximum weight of contents and for the critical load distributions at the appropriate maximum load factors corresponding to the flight and ground load conditions of this part.

   and

   A23.9 Flight Conditions: (d) (2) Each engine mount and its supporting structures must be designed for the maximum limit torque corresponding to METO power and propeller speed acting simultaneously with the limit loads resulting from the maximum positive maneuvering flight load factor n 1.

   Part 23 has over 100 sections pertaining to aircraft loads on the various sections of the airframe from the propeller through tothe hinge on the elevator trim tab and anything and everything in between. Most of this can be found in sub part C on structure or D on design and construction.

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9. 
   

   
   

   RLewis on Jul 16, 2013

   Brian,

   23.787(1) (Baggage and Cargo Compartments) – this agrees with my argument. It states that the baggage/cargo compartment must be constructed to, with the maximum weight of luggage/cargo in the compartment, maintain structural integrity under the aircrafts certification (Utility, Normal, etc.) If the maximum loading weight of a baggage compartment is 100 pounds, that is the maximum weight the structure can support under the maximum load factor.

   A23.9(d)(2) – this too proves that the aircrafts components are designed at or exceeding the maximum load factor of the airplane. I read this paragraph as stating that the engine mount must be able hold the powerplant in place while being subjected to maximum takeoff power setting and the maximum load factor of the airplane (n 1, which listed in Table 1 – Limit Flight Load Factors, is the maximum flaps up load factors for each aircraft category). This means that a Cessna 172 at 2700RPM can pull +3.8 G’s (assuming normal category) without overstressing the engine mount. If you read the beginning of A23.9, it states that the structural design s in the section must fall within the Vg diagram (listed as V-n in Part 23) – the Vg diagram is a mapping of the positive and negative load factors of the airplane.

   You referenced Subparts C and D – the first sentence of Supbart C states that “Strength requirements are specified in terms of limit loads (the maximum loads to be expected in service) and ultimate loads (limit loads multiplied by prescribed factors of safety).” When looking into Subpart D, I did not see any discussion about load factors in the sense of aerodynamics, but I do see that the regulations require equipment to be held to high standard. Reference 23.627 – Fatigue strength: “The structure must be designed, as far as practicable, to avoid points of stress concentration where variable stresses above the fatigue limit are likely to occur in normal service.”

   The bottom line here is that the FAA has set a maximum load factor per category – those parameters are the envelope in which the pilot can safely operate the airplane without causing structural damage. I say damage because the safety factor the regulations require (about 150% safety margin) is where components may begin to fail.

   Kent, to summarize the answer to your question, the aircraft stalls at a higher airspeed in a banked turn due to an increase in angle of attack. This increased angle of attack derives from the need to produce more lift (transfer of energy from vertical to horizontal lift), and hence an increase in load factor. As you increase your angle of attack, you get closer to your critical angle of attack. This can be proven by the following equation: Stall Speed at Bank Angle X = Wing Level Stall Speed * Square root of Load Factor. Reference page 37 of Aerodynamics for Naval Aviators for more information.

   Randy

   PS – I apologize for the constant name change, the website keeps locking me out of accounts.

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10. 
    

    
    

    Brian on Jul 17, 2013

    “However the designed structural limits (maximum load factor) is pertinent to the wing…”

    I merely point out that it is inaccurate to claim load factor as pertaining solely to the wing. Or even to say the wing is the most important. The engine mount or aircraft tail (both fixed weight items) tearing off the airplane can be equally catastrophic.

    —

    Consider this: Aircraft gross weight 2500 pounds. Maximum load 4g.

    Maximum sustainable wing load can be calculated to 10,000 pounds (4*2500).

    Fly that same airplane at 2000 pounds, a 4g pull only induces 8,000 pounds on the wing. The wing hasn’t changed, it can still hold 10,000 pounds. By your definition of load factor and ensuing argument we should now be able to pull 5g. We cannot because other fixed weight items within the aircraft, whose strength is limited by the 4g load factor, prevent us from doing so.

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11. 
    

    
    

    RLewis on Jul 17, 2013

    Brian, you’re correct in saying that load factor affects all portions of the aircraft, from engine mounts to empennage. In the future I will expand my definition to include these components, I’m glad you brought those things to mind.

    Your scenario of the 2500 pound aircraft reduced to 2000 pounds is a perfect example of the importance of maneuvering speed. The two parts missing are angle of attack and airspeed. If you click on the previous link I posted, you’ll see the explanation to that exact issue you bring up (it’s under Weight Change and Va).
    http://flighttraining.aopa.org/magazine/1999/March/199903_Flying_Smart_A_New_Look_at_Maneuvering_Speed.html

    Randy

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    JTX on Aug 01, 2013

    I think about it this way: weight [W] is constant, in way it always acts in the same direction (toward the earth centre) and assuming irrelevant variations of magnitude in flight (at least for the sake of the explanation).

    The aircraft wings (mainly) produces lift [L] to balance W, that always acts perpendicular to the wings.

    You will have load factor equal to 1 whenever the L=W, meaning both forces in balance.

    Why would you have LF>1? Because in some ocasion L>W. When? Basically whenever the L vector isn’t in the same line of the W vector. Can be in a climb, in a turn, even in S&L flight. If the L vector isn’t aligned with the W vector it will act as an hypotenuse of a triangle, and one of the sides of the triangle (smaller than the hypotenuse) will balance W.

    This basically means that the wings have to generate more L to sustain the same amount of W, just because the aircraft is in a different attitude.

    If you understand this, ,making some draws, it’s easy to explain the Stall part:

    Stall happens when you reach the critical AoA.

    Stall speed is the airspeed at which you reach the critical AoA for a certain L. The Vs used as reference are related to S&L flight, when the L=W. In those other atitudes, L>W (LF>1), so the airspeed for the same critical AoA (ALWAYS the same) will be higher, meaning higher Vs.

    Hope the explanation works…

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