Article #2 is finally here! Thank you to everyone who provided feedback from last month's article, and inspiration to write this one!
Last month we reviewed inoperative equipment, and I was so pleased to see that since its publication, applicants have had such a better grasp of this area.
This month, I would like to review the factors that affect stall speed. This topic is not as simple or black and white as the article on inoperative equipment. As with any technical subject, expect to need to re-read portions. Obviously, a book could be written about this topic, and it can get way too complicated. I’ll try to limit the article to what I feel like would be helpful in understanding the topic of stall speeds. My goal is not for applicants to memorize formulas, but to have a base of knowledge which would allow a student to understand the concepts of stall speeds, and why they change.
What is a stall?
This is basic, but we should review it before moving on. As an airfoil increases its angle of attack, the coefficient of lift is increased, resulting in greater lift being produced. The point at which a reduction in lift occurs as a result of the reduction of smooth airflow over the wing is called the critical angle of attack. Exceeding the critical angle of attack is what causes an airfoil to stall. An airfoil will stall at the same angle of attack, but the speed at which this occurs varies, and is dependent on many factors. We will discuss SOME of those factors here.
Weight
If you had two identical Cessna 172’s, but you loaded one with a single pilot, and the other with a pilot and 500 additional pounds of passengers and cargo, which aircraft would have a higher stall speed, and why?
Both aircraft would stall at the wing’s critical angle of attack, and that angle of attack would be the same for both aircraft. But the heavier aircraft would reach that critical angle of attack at a higher speed.
During level flight, the amount of lift must equal the amount of weight. So if both aircraft in the above example are flying straight and level at 100 knots, the heavier aircraft is creating more lift (it weighs more!). So if the heavier aircraft is flying at the same speed, and creating more lift, it must be doing so having a higher angle of attack. So both aircraft are flying at 100 knots, but the heavier one has a higher angle of attack, thus being closer to its critical angle of attack than its lighter counterpart.
If both aircraft continued to decelerate in straight and level flight, the heavier aircraft would stall first (at a higher airspeed), due to its wing constantly flying at a higher angle of attack relative to the lighter aircraft.
Is there a formula to determine the changes in stall speed as weight changes? Of course!
Vsnew = Vsold x √ (new weight /old weight)
Let’s apply some real data here.
Vsnew = 45 x √ (2,200 /1,800)
Vsnew = 45 x √ (1.22)
Vsnew = 45 x 1.104
Vsnew = 49.68
Assuming a 45 knot stall speed at 1,800 pounds, the aircraft at 2,200 pounds will stall at 50 knots!
Bank Angle
Why would increasing angle of bank change your stall speed? Since you now understand why weight increases stall speed, this should be fairly straightforward. Assuming you maintain level flight, when you increase your bank angle, you increase your load factor. Load factor and weight are similar. Load on an aircraft is stress, and load factor is the ratio of lift to weight.
Load factor (G’s) = Lift / Weight
Hence in level flight, where a 2,000 pound aircraft is creating 2,000 pounds of lift, the aircraft is experiencing 1 G. But in a bank, we are increasing lift to remain in level flight… so we are increasing our load factor. Remember your instructor telling you that you experience 2 G’s at 60 degrees of bank? Why is this, and how can we determine its affect on stall speed?
Another formula, of course! The above equation is a great way to understand the relationship between lift, weight and load factor. But to determine the load factor in a bank, we use the following:
Load Factor (G) = 1/cos (bank angle).
Run the math with using 60 for bank angle, and you get 2! So a 60 degree angle of bank will result in a load factor of 2. Or 2 G’s of stress.
So how do we use the increased load factor to determine our increase in stall speed? Simply take the square root of the load factor to get the increase in stall speed. √2 is 1.414. So the stall speed at 60 degrees of bank is 41.4% higher! A stall speed of 48 knots would now be 68 knots at 60 degrees of bank. Take a look at the angle of bank/stall chart below for a Cessna. They did the math for you at 30, 40, and 60 degree bank angles. But now you know how they got those figures, and how to figure it out yourself!
Flaps
Flaps increase lift. Increasing lift without increasing angle of attack means you can create more lift while preserving the margin between your speed and stall speed. So you can safely fly a slower approach speed.
Is there a formula for this? Silly question. But it’s just the lift formula. L = 1/2 p V2 S CL
L= Lift
CL = Coefficient of lift
1/2 p = 1/2 rho (refers to air density)
V2 = Velocity squared
S = Wing surface area
Certain types of flaps increase the surface area of the wing. If the surface area of the wing is increased, the formula shows that for lift to remain constant, airspeed and angle of attack must be reduced.
Other types of flaps increase a wing’s camber (curvature) without increasing surface area. These types of flaps may not affect the surface area portion of the lift equation, but they simply have a higher coefficient of lift with flaps extended. The coefficient of lift (CL) is a representation of the lift an airfoil can produce. Increasing flaps can increase CL, increase surface area… or both!
So with flaps, we can increase lift and decelerate all while decreasing (or at least not increasing) our angle of attack. This will obviously reduce our stall speed since decreasing our angle of attack means we are farther from our critical angle of attack. Take a look at the graph below to see the relationship between CL and angle of attack with flap extension.
Center of Gravity (C.G)
Lucky you… I won’t be throwing a formula at you this time.
A critical feature of a stable aircraft is the relationship between its center of lift and its center of gravity. The center of gravity is forward of the center of lift. Generally, just aft of the center of gravity is what is called a neutral point. The relationship of the center of lift to the neutral point is called ‘static margin’. The response of an aircraft to a pitch disturbance is due to its static margin. It is static margin that has a direct correlation to stability along the longitudinal axis of an aircraft. Note: not all of the above is true in some fighter aircraft, or aircraft with canards.
All that may be interesting, but the crux of the C.G and stall speed issue is that if the center of gravity is moved forward (within limits, of course), you increase the arms between the C.G. and the center of lift, and the C.G. and the tail (which produces a down force). So, the center of lift remains the same, but the C.G. moved forward. If an aircraft rotates around it’s C.G. and that point is now even more forward of the center of lift, this would result in a lift-weight couple (nose down pitch). The result is an increased down force on the tail. The down force on the tail is in the same direction as weight. The aircraft weight remains the same, but the load has increased due to the tail down force, so we need to generate more lift to counteract the extra load (‘weight’) of the aircraft.
As mentioned earlier, a heavy airplane has a higher stall speed. And so does an aircraft with a forward C.G., because the extra tail down force is acting similarly to additional weight.
Power
This one seems simple, but the vast majority of applicants get this wrong.
When an aircraft has power applied in a climb, the resultant thrust vector offsets weight. With power applied, thrust will offset weight, thus reducing the requirement to increase lift via increasing the angle of attack. Additionally, the increased slipstream over the wings resulting from power application will delay air flow separation. As such, with power applied, we can fly at slower speeds without increasing our angle of attack as much as we would have to without power application. Our relatively lower angle of attack with power allows for a higher stall margin/distance from the critical angle of attack.
So why do applicants state that power increases stall speed? Because we practice power on stalls in the clean configuration, and power off stalls in the landing configuration. It is the configuration which has the most pronounced effect on stall speed in these scenarios, thus muddying the waters for students.
Altitude
This one might be the trickiest concept.
Let’s look at the lift equation again and see if we can break this down. L = 1/2 p V2 S CL
We know that CL is the coefficient of lift, and is determined by the wing design. V2 is velocity, and S is surface area. None of these are effected by altitude. But 1/2 p relates to air density. As we increase altitude, air density decreases. As the density of air decreases, our TRUE airspeed increases. If air density decreases, for lift to remain the same, true airspeed must increase to maintain the same indicated airspeed. As we climb, indicated airspeed is unaffected, but true airspeed increases. Therefore, indicated stall speeds remain the same, however the true airspeed at which the critical angle of attack is reached will be higher.
Confused yet? Let’s try this.
Your airspeed indicator will tell you true airspeed… at sea level on a standard day. The airspeed indicator simply reports dynamic pressure. Which is the difference between total pressure (from the pitot tube) and static pressure (from the static port). As you climb, the airspeed indicator no longer tells you true airspeed, because air density is decreasing. As a rule of thumb, true airspeed increases 2% per 1,000 feet. So if you are flying at 100 knots indicated at 15,000 feet, your true airspeed is closer to 130 knots.
In conclusion, an aircraft’s wing is exposed to a particular dynamic pressure. The airspeed indicator happens to also indicate dynamic pressure. We usually care to simply see how fast we are moving through the air when we look at an airspeed indicator… but at higher altitudes, this just isn’t feasible. However, since the airspeed indicator is reporting the same dynamic pressure that the wing is experiencing, the indicated stall speeds will not change! So when you stall at altitude, at the same indicated airspeed, your true airspeed will be faster.
In Summary
This can be an immensely complicated subject… but it is kind if fun, isn’t it! The above factors are what I believe to be the most important for applicants to understand with regards to stall speed conditions and changes. At the private pilot level, simply understanding when stall speeds go up or down is enough. At the commercial level and beyond, the ability to converse more about the subject is desirable.
The items we reviewed are not by any chance a complete list of factors that affect stall speed! Various aircraft designs, additional types of high lift devices or devices that delay boundary layer separation obviously would take additional discussion. But for the average general aviation applicant, this should suffice… for now!